Механобиологические аспекты роста клеток растений тема диссертации и автореферата по ВАК РФ 03.01.05, кандидат наук Липчинский Андрей Анатольевич

• Липчинский Андрей Анатольевич
• кандидат наук
• 2019

Оглавление диссертации кандидат наук Липчинский Андрей Анатольевич

Введение

Глава 1. Эластические свойства первичных клеточных стенок

1.1. Введение

1.2. Материалы и методы

1.3. Результаты и обсуждение

Глава 2. Пластические свойства первичных клеточных стенок

2.1. Введение

2.2. Кислый рост

2.3. Модель дефект-опосредованной вязкопластичности

Глава 3. Механобиология поляризованного клеточного роста

3.1. Введение

3.2. Транспортные явления в пыльцевых трубках

Заключение

Список литературы

Введение диссертации (часть автореферата) на тему «Механобиологические аспекты роста клеток растений»

Введение

И.В. Гёте, подвижник научной и творческой мысли, основоположник общей морфологии и биологии развития растений, провозгласил одной из наиболее важных задач науки познание законов и сил, управляющих преобразованием формы живых организмов в процессе их развития (Goethe, 1790, 1796/1820). Спустя столетие после основополагающих исследований Гёте в области онтогенетических трансформаций и морфоэволюционных гомологий, Д'Арси Томпсон сформулировал подкупающую своей элегантностью и обескураживающую своей кажущейся простотой максиму биологического морфогенеза: "Форма - это диаграмма сил" (Thompson, 1917). Подход Томпсона подвел черту под восходящей к Аристотелю традицией объяснения (causa efficiens sensu) биологических процессов с помощью понятий и принципов механики и породил задачи непреложной важности по выявлению динамических паттернов механических напряжений в живых организмах и законов, управляющих их эволюцией.

Прогресс структурно-динамической биологии на рубеже 19 и 20 веков, связанный с работами великих физиологов и морфологов - Гофмайстера (Hofmeister, 1860/1863; 1868), Сакса (Sachs, 1874), Швенденера (Schwendener, 1874), Гиса (His, 1888), Пфеффера (Pfeffer, 1904), Ру (Roux, 1895) и де Фриза (de Vries, 1919) - совпал по времени с активным развитием биологической химии (Buchner, 1897; Haldane, 1921; Sumner, 1926). Быстрое развитие биохимии в начале 20 века и всколыхнувшее середину 20 века рождение молекулярной биологии (Franklin and Gosling, 1953; Watson and Crick, 1953; Astbury, 1961; Hess, 1970) на время оттеснили биомеханическую императиву на второй план. Сложность и своеобразие обнаруженных молекулярно-биологических процессов на фоне кажущейся заурядности действующих в живом организме механических сил привели к доминированию в 20 веке представления о том, что механические силы играют в биологических явлениях второстепенную роль, лишь обеспечивают условия, необходимые для протекания биохимических и геноцентрических процессов, которые стали рассматриваться как квинтэссенция жизни (Schrödinger, 1944; Wolpert, 1969; Dawkins, 1976; Koch and Meinhardt, 1994). Одним из результатов такого парадигмального сдвига стал тот факт, что биомеханика стала восприниматься как своего рода прикладная инженерия, то есть произошел перенос семантического ударения в термине биомеханика с первого корня на второй ((Benedikt, 1912; Thompson, 1917) vs. (Раздорский, 1955; Herbert, 1974)).

Начало нынешнего века ознаменовалось ренессансом биоцентрически рационализированных биомеханических парадигм. Открытие фундаментальной роли механических сил в регуляции генной экспрессии (Brouzes and Farge, 2004; Braam, 2005; Shivashankar, 2011), в модуляции биохимических реакций (Chowdhury, 2013; Brinkmann et al.,

2018), в векторизации транспорта сигнальных молекул (Nakayama et al., 2012), в формировании и поддержании архитектуры клеток и тканей (Ingber, 2003; Traas, 2019), в контроле клеточной дифференцировки (Engler et al., 2006; Malivert et al., 2018; Messal et al.,

2019) и - что особенно важно - в непосредственной регуляции онтогенетических и морфогенетических трансформаций (Nelson et al., 2005; Hamant et al., 2008; Mammoto and Ingber, 2010; Pien et al., 2001; Beloussov, 2015; Bredov and Volodyaev, 2018) - все это привело к тому, что в начале 21 века биомеханика вновь стала неотъемлемой частью современной биологии, переродилась в механобиологию - науку, в пролегоменах которой лежит признание фундаментальной роли и специфики биомеханических процессов и сил.

Наиболее ярко и многогранно физиологическая роль эндогенно генерируемых механических сил проявляется в процессах роста и развития растений. Одна из причин этого заключается в том, что рост растений сопряжен с поддержанием и перераспределением огромных механических напряжений. Гидростатическое давление внутри типичной растительной клетки соответствует нескольким атмосферам, при этом механическое натяжение в клеточных стенках оказывается в десятки и сотни раз больше (> 1 МНм ). Одним из главных источников механических напряжений в растениях являются трансмембранные градиенты осмотического потенциала. Осмотические градиенты наряду с механо-геометрическими характеристиками клеток и тканей (форма, размер и расположение клеток; толщина, жесткость и структурно-механическая анизотропия клеточных стенок) и кинетическими параметрами, отражающими проницаемость биологических мембран для ионов и молекул, задают общий паттерн механических напряжений в растениях (Nobel, 2009; Niklas and Spatz, 2012; Bidhendi et al., 2019). Дополнительную роль в субклеточном распределении механических напряжений могут играть силы, генерируемые в процессах перестройки цитоскелета и работы моторных белков (Steinberg, 2007).

В соответствии с развиваемыми в последние годы модельными концепциями (Boudon et al., 2015; Abad et al., 2017; Bidhendi and Geitmann, 2018; Dumond and Boudaoud, 2018), учет указанных выше осмотико-кинетических и механо-геометрических факторов может быть использован для анализа напряженно-деформационного состояния растущих растительных тканей и объяснения динамики механозависимых морфогенетических процессов в

растительных организмах. Однако на практике предсказательная сила таких моделей оказывается ограниченной по целому ряду причин. Во-первых, рассматриваемые в моделях факторы часто являются трудно формализуемыми (например, жесткость клеточных стенок включает в себя огромное множество разноплановых компонент, феноменологическое описание и физическая интерпретация которых крайне сложны). Во-вторых, механические и осмотико-кинетические параметры способны быстро и существенно изменяться в ответ на слабые физиологически значимые сигналы, причем непосредственные триггеры и базовые механизмы, лежащие в основе этих изменений, по большей части неясны. До недавнего времени морфогенетические эффекты механо-геометрических, осмотико-кинетических, электрофизиологических и молекулярно-биологических факторов исследовались по большей части изолированно, но в последние годы становится все более очевидным, что лишь их интегральный анализ способен раскрыть многоплановую картину системных взаимодействий, лежащих в основе биологического морфогенеза.

Целью настоящей работы являлось экспериментальное и теоретическое исследование морфогенетически значимых механобиологических процессов на молекулярном, клеточном и тканевом уровнях организации растительного организма.

Задачи работы включали:

1. Исследование зависимости модуля упругости клеточных стенок, изолированных из колеоптилей проростков кукурузы в возрасте 4-х и 6-ти суток (стадии ауксентичного роста и старения колеоптилей, соответственно), от механического напряжения, рН и температуры.

2. Исследование молекулярных механизмов вязкопластической деформации клеточных стенок, лимитирующей скорость роста клеток растяжением.

3. Исследование внутриклеточных транспортных процессов, возникающих вследствие сопряжения осмотических, механических и электрических градиентов в поляризовано растущих клетках.

4. Анализ применимости концепции гипервосстановления механических напряжений к морфогенетическим процессам в растительных организмах.

Использованные для решения поставленных задач методы включали математическое моделирование и экспериментальное исследование механических свойств биологических материалов с использованием датчика линейных смещений.

Основным объектом экспериментального исследования служили клеточные стенки колеоптилей проростков кукурузы в возрасте 4-х и 6-ти суток. Выбор колеоптилей в качестве экспериментальных объектов был обусловлен следующими причинами. Во-первых, колеоптили являются ювенильным органами, характеризующимися быстрым, но строго детерминированным ростом: в 4-х суточных проростках кукурузы скорость роста колеоптилей достигает максимальных значений, в то время как в проростках возрастом 6 - 7 суток рост колеоптилей прекращается. При этом в проростках в возрасте 4-х суток колеоптиль растет ауксентично, то есть за счет увеличения размера уже существующих клеток (клеточные деления отсутствуют). Поскольку ауксентичный рост связан с физиологически контролируемым растяжением клеточных стенок, исследуемое деформационное поведение изолированных клеточных стенок должно в полной мере отражать их морфогенетически значимые компетенции. Другая важная особенность роста колеоптилей как экспериментальных объектов заключается в том, что эпидермальные клетки, на клеточных стенках которых проводилось большинство экспериментов, у колеоптилей сильно анизодиаметричны: их длина в аксиальном направлении на порядок превышает их ширину. Это свойство позволяет осуществлять одноосевое растяжение клеточных стенок колеоптилей без значительного изменения их архитектуры и связать наблюдаемое деформационное поведение стенок in vitro с их физиологической растяжимостью в процессе роста клеток in vivo.

Главные полученные в работе результаты:

1. Показана зависимость модуля упругости клеточных стенок колеоптилей кукурузы от механического напряжения. Предложена модель, объясняющая обнаруженную зависимость неоднородным распределением напряжения в клеточных стенках.

2. Описано обратимое удлинение клеточных стенок при уменьшении температуры.

3. Предложена и обоснована модель действия регулирующих растяжимость клеточных стенок белков экспансинов, предполагающая участие этих белков в образовании на поверхности микрофибрилл целлюлозы подвижных конформационных дефектов.

4. Предложены и обоснованы новые механизмы везикулярного транспорта и возникновения градиентов давления в поляризовано растущих клетках.

5. Показано, что по крайней мере некоторые ключевые события в морфогенезе растений могут быть интерпретированы в рамках концепции гипервосстановления механических напряжений.

Все вышеперечисленные результаты являются оригинальными и получены диссертантом в ходе исследований, проводимых под руководством старших коллег (УрсЫ^ку et а1., 2013) или самостоятельно (УрсЫ^ку, 2013; Lipchinsky, 2015а; Lipchinsky, 2015Ь; Lipchinsky, 2018). Теоретическая значимость и новизна результатов отражены в вышеуказанных публикациях и в соответствующих разделах основного текста диссертации (1.3, 2.2, 2.3, 3.2). В части практической значимости работы можно отметить следующие моменты. Во-первых, в работе предложена и обоснована модель пластификации клеточных стенок в результате дефект-опосредованной дестабилизации несущих механическую нагрузку связей между микрофибриллами целлюлозы и связующими гликанами (глава 2). Дальнейшее исследование данного механизма может способствовать развитию технологий промышленного гидролизы целлюлозы, которая является самым распространенным, но крайне рекальцитрантным органическим веществом на Земле. Практическая значимость работы может быть также проиллюстрирована тем фактом, что в работе анализируются внутриклеточные транспортные процессы, обусловленные деполяризацией апикального участка клеточной мембраны (глава 3). Поскольку апикальная деполяризация свойственна как клеткам растений, так и нейронам животных (Nishiyama et а1., 2008), представленный в работе анализ внутриклеточных электрокинетических транспортных процессов может быть востребован как сельскохозяйственной, так и биомедицинской наукой. Результаты работы могут также быть использованы в курсах лекций по росту и развитию растений, механобиологии, цитологии и другим дисциплинам.

Глава 1. Эластические свойства первичных клеточных стенок

1.1. Введение

Реологическая модель роста клеток растений (Lockhart, 1965; Ortega, 1985) рассматривает рост растяжением как процесс необратимой деформации клеточных стенок под действием тургорного давления. В рамках этой модели механическое поведение клеточных стенок обычно описывается как разновидность вязкоупругопластического, в котором главную роль играют линейно-эластическая (гуковская) и вязкопластическая (бингамовская) составляющие (Ortega, 1990; Proseus et al., 1999; Geitmann and Ortega, 2009; Dumais and Forterre, 2012). Под линейной, или гуковской эластичностью понимается такое деформационное поведение материала, при котором наблюдается прямая пропорциональность между механическим напряжением в нагружаемом материале и обратимой компонентой его деформации. Под бингамовской, или вязкой пластичностью понимается такое деформационное поведение, в котором необратимая компонента деформации развивается лишь после превышения напряжением некой пороговой величины и при условии постоянного надпорогового напряжения является линейной функцией времени нагружения.

В данной главе, основанной на работе Lipchinsky et al. (2013), представлены результаты исследования деформационного поведения клеточных стенок колеоптилей кукурузы, которые свидетельствуют о том, что вопреки классическим представлениям связь между механическим напряжением и эластической деформацией стенок является нелинейной. Обнаруженная нелинейная зависимость рассматривается как следствие неоднородного распределения механического напряжения между разными компонентами клеточных стенок.

1.2. Материалы и методы

Объектом экспериментального исследования служили клеточные стенки колеоптилей этиолированных проростков кукурузы (Zea mays L. cv. Kamerad) в возрасте 4 и 6 суток. Для получения проростков зерновки кукурузы замачивали 2 часа в воде при температуре 55 °С и проращивали в термостате в темноте при температуре 27 °С и 100 % влажности. После достижения проростками возраста 4 или 6 суток с колеоптилей пинцетом снимали полоски

эпидермиса шириной около 1,8 мм. Полоски подрезали в длину до 13 мм, причем верхняя граница среза соответствовала линии, расположенной на расстоянии около 3 мм от верхушки колеоптиля. Полученные эпидермальные полоски размером ~ 13*1,8 мм (± 5%) промывали в цитратно-фосфатном буфере рН 7,0 (10 тМ лимонной к-ты, 80 тМ №2НР04) и замораживали при - 40 °С. В замороженном виде материал хранился от нескольких часов до двух суток, оттаивание производилось в том же цитратно-фосфатном буфере непосредственно перед опытом. После замораживания и оттаивания растительный материал терял тургор, и его механическое поведение определялось непосредственно свойствами клеточных стенок.

Исследуемый материал фиксировался в измерительной установке (Рис. 1.1) между кварцевыми зажимами таким образом, чтобы длина растягиваемого участка ткани составляла 5 мм. Для обеспечения мягкого (не приводящего к механическому повреждению стенок), но прочного контакта с растительным материалом кварцевые зажимы были покрыты силиконовой пленкой (одна из двух створок зажима) и слоем тонкого наждака (вторая створка). Нижние зажимы были соединены с неподвижным основанием измерительной установки, а верхние зажимы были прикреплены к плечу рычага, соединенного с одним из анодов вакуумного триода, используемого в качестве датчика линейных смещений. Нагрузка подавалась на второе плечо рычажной конструкции путем подвешивания грузиков требуемой массы. Вся система располагалась в термостате при температуре 30 ± 1 °С.

Рис. 1.1. Схема системы для измерения растяжимости клеточных стенок. Исследуемый материал (1) фиксируется между кварцевыми зажимами (2, 3). Нижний зажим (2) неподвижно соединен с основанием измерительной системы, а верхний зажим (3) соединен с плечом рычажной конструкции (4), передающей на образец растягивающую нагрузку (М). Дополнительная нагрузка (В) служит противовесом для верхнего зажима (3). Изменение длины растягиваемого материала (1) фиксируется

вакуумным триодом (5). Триод включает в себя два анода, один из которых (6) находится в неизменном положении, а второй (7) соединен через подвижный штырь (8) с плечом рычажной конструкции (4). Изменение положения штыря вызывает изменение электрического тока в триоде, измеряемое с помощью амперметра (А). Во время опытов образец находится в буферной среде инкубации (9) в силиконовой камере (10).

В ходе опытов по исследованию эластических (первая серия опытов) и термоэластических (вторая серия опытов) свойств клеточных стенок растягиваемый растительный материал непрерывно находился в буферном растворе с рН 7,0 (10 тМ лимонной к-ты, 80 тМ №2НР04). Прикладываемая к материалу нагрузка постепенно увеличивалась с 2,2 сантиньютонов (сН) до 11,8 сН с шагом в 2,4 сН и временным интервалом между последовательными увеличениями нагрузки в 6 - 10 мин. Затем нагрузка уменьшалась в порядке, обратном нагружению.

В первой серии опытов проводилось определение модуля упругости клеточных стенок на основании данных о деформационном поведении стенок в процессе кратковременных (5 сек) циклов разгрузки-нагрузки на 1 сН после 6-10 мин изотонического растяжения. Модуль упругости рассчитывался в соответствии с уравнением:

Да X Ь

Е" = — (1)

где Аа - уменьшение напряжения в пятисекундном цикле разгрузки-нагрузки, L - исходная длина растягиваемого участка ткани (5 мм), АL - уменьшение длины растягиваемого участка в течение 2 сек после уменьшения напряжения на Аа.

Напряжение (а) рассчитывалось в соответствии с уравнением: тх а

(2)

где т - масса растягивающего стенки груза, g - гравитационное ускорение, А - площадь поперечного сечения клеточных стенок в исследуемом образце (на основании данных о толщине клеточных стенок, полученных методами электронной микроскопии, А принималось равным 0,003 мм для подвергаемых растяжению эпидермальных полосок шириной 1,8 мм).

Наряду с зависимостью модуля упругости от напряжения, в работе также исследовалось влияние на эластическую растяжимость клеточных стенок температуры (вторая серия опытов). Для этого в работе определялась деформация находящихся под

постоянной нагрузкой клеточных стенок, вызываемая их охлаждением. В рамках данной серии экспериментов в процессе описанного выше ступенчатого изменения нагрузки производилась периодическая замена среды инкубации клеточных стенок: цитратно-фосфатный буфер (рН 7,0) с температурой 30 ± 1 °С отбирался шприцом, и вместо него на 20 сек инкубационная ячейка заполнялась тем же буфером, но с температурой 4 ± 1 °С. Между удалением теплого буфера и добавлением холодного раствора, а также между обратными действиями клеточные стенки находились в термостатируемой (29 ± 2 °С) воздушной среде не более 6 сек. Изменение длины клеточных стенок, вызванное их охлаждением, рассчитывалось как относительное уменьшение длины клеточных стенок в течение 3 сек после добавления холодного буфера.

Третий этап исследований эластических свойств клеточных стенок колеоптилей кукурузы заключался в определении зависимости модуля упругости от рН. Для этого в третьей серии экспериментов в процессе увеличения прикладываемой к растительному материалу нагрузки по вышеуказанной схеме (от 2,2 сН до 11,8 сН с шагом в 2,4 сН) в стандартном буфере (цитратно-фосфатный буфер, рН 7,0) осуществлялись кратковременные (5 сек) циклы разгрузки-нагрузки на 1 сН (после 6 - 10 мин изотонического растяжения) в условиях инкубации стенок в буферных растворах с разным рН. Сначала цикл разгрузки-нагрузки проводился при инкубации стенок в цитратно-фосфатном буфере рН 7,0, а затем (через 20 сек) буфер менялся на ацетатный рН 4,8, и через 30 секунд после замены буфера цикл разгрузки-нагрузки повторялся. Затем инкубационная камера вновь заполнялась цитратно-фосфатным буфером рН 7,0, после чего данная процедура повторялась на каждом шаге инкрементального увеличения нагрузки (2,2 сН, 4,6 сН, 7 сН, 9,4 сН, 11,8 сН).

Клеточные стенки обычно моделируются как вязкоупругопластическое тело, необратимая (вязкопластическая) компонента деформации которого имеет характер течения Бингама, а обратимая (эластическая) компонента удовлетворяет закону Гука (Ortega, 1985; Proseus et al., 1999; Geitmann and Ortega, 2009; Dumais and Forterre, 2012). В этом случае деформация клеточных стенок при их одноосном растяжении должна удовлетворять уравнению:

1.3. Результаты и обсуждение

dL dLpl dLel

= - atr) +

da

EYn x dt'

(3)

где L - длина деформируемого участка клеточных стенок, о - действующее в стенках напряжение, dLpl - приращение длины клеточных стенок за счет их пластической деформации, dLel - приращение длины клеточных стенок за счет их эластического растяжения, ¥ - коэффициент пластической растяжимости, otr - пороговое напряжение, после которого начинается пластическое течение, Ё?п - модуль Юнга.

Уравнение (3) предполагает линейную связь между механическим напряжением в клеточных стенках и их эластической деформацией. В рамках данного предположения эластические свойства клеточных стенок можно охарактеризовать единственным параметром - модулем Юнга (Nilsson et al., 1958; Ortega, 1985; Wang et al., 2004; Dintwa et al., 2011), который по определению есть коэффициент пропорциональности между напряжением в стенках и их эластической деформацией (EYn = o!ALel = const).

Полученные нами при исследовании эластических свойств клеточных стенок колеоптилей кукурузы результаты (рис. 1.2) свидетельствуют о том, что отношение приращения длины клеточных стенок к приращению действующего в них механического напряжения является функцией напряжения (doldLel = f(o) Ф const), и, следовательно, понятие модуля Юнга как константы, характеризующей отношение напряжения к эластической деформации, не является применимым к исследуемому материалу. Поэтому для описания эластических свойств клеточных стенок в настоящей работе используется понятие тангенциального модуля упругости, определяемого в механике как предел отношения приращения напряжения к приращению деформации при приращении напряжения, стремящемся к нулю: Etg = lim¿0^o do/dLel. В представленных в настоящей работе практических расчетах тангенциальный модуль упругости рассчитывался в соответствии с уравнением (1) по данным об изменении длины клеточных стенок при уменьшении напряжения на 1 сН.

Полученные результаты свидетельствуют о том, что тангенциальный модуль упругости клеточных стенок колеоптилей кукурузы увеличивался с ростом напряжения (рис. 1.2). При этом величина тангенциального модуля упругости не зависит от направления деформационного цикла, то есть от того, были ли подвергнуты стенки предварительной вытяжке при максимальном напряжении в 38 МПа (табл. 1).

Рис. 1.2. Зависимость тангенциального модуля упругости эпидермальных клеточных стенок колеоптилей 4-х суточных (кружки) и 6-ти суточных (квадраты) проростков кукурузы от напряжения. Каждая точка представляет среднее из шести биологических испытаний на этапе пошагового увеличения нагрузки от 5.7 до 38 МПа. Бары соответствуют стандартной ошибке среднего.

а (МРа) Е8рЕ81 (%)

4-х суточные проростки 6-ти суточные проростки

5,7 97,4 ± 1,3 97,2 ± 1,5

14 103 ± 0,9 102,0 ± 1,1

22 101,9 ± 0,6 101,0 ± 0,5

30 97,7 ± 1,0 97,9 ± 0,6

Табл. 1. Модуль упругости клеточных стенок, рассчитанный по данным, полученным в ходе инкрементального увеличения напряжения (от 5,7 до 38 МПа), в процентном отношении к модулю упругости, измеренному в процессе инкрементального уменьшения напряжения (от 38 до 5,7 МПа), для клеточных стенок, изолированных из 4-х суточных и 6-ти суточных проростков (средние значения ± стандартные ошибки).

Обнаруженная зависимость тангенциального модуля упругости от напряжения может быть аппроксимирована линейным уравнением:

Е^ =Е0 +БХ а, (4)

где Е это кажущийся модуль упругости при нулевом напряжении, ^ - нормирующий параметр, соответствующий тангенсу угла наклона аппроксимирующей кривой (рис. 1.2).

Механическое поведение материала, при котором модуль упругости зависит от напряжения принято называть нелинейным эластическим поведением, поскольку в данном случае не соблюдается пропорциональность между напряжением и обратимой деформацией. Нелинейный характер эластического поведения клеточных стенок проявляется в экспоненциальной зависимости напряжения (с) от эластической деформации (е), которая может быть получена путем интегрирования уравнения (4):

а = (а* + х е5(£-£*) - у, (5)

где а* и е* - константы интегрирования (напряжение а* при заданной эластической деформации е*). Численные значения параметров уравнений (4) и (5) приведены в таблице 2.

Возраст проростков (дни) s Е0 (МПа) а* (МПа) е* (%)

4 60,4 ± 4,2 140 ± 45 5,7 5,3 ± 0,3

6 79 ± 5,3 361 ± 70 5,7 4,1 ± 0,3

Табл. 2. Параметры уравнений (4) и (5), описывающих эластические свойства клеточных стенок 4-х и 6-ти суточных проростков кукурузы (средние значения ± стандартные ошибки).

Из графика, построенного на основании уравнения (5), видно, что с увеличением напряжения клеточные стенки становиться более упруго-жесткими, то есть на стандартное приращение напряжения отвечают более слабым приращением эластической деформации (рис. 1.3).

10 20 30 40

Напряжение, МПа

Рис. 1.3. Зависимость эластической деформации клеточных стенок от напряжения. Представлены характерные результаты опытов по растяжению эпидермальных клеточных стенок колеоптилей 4-х суточных (кружки) и 6-ти суточных (квадраты) проростков кукурузы. Аппроксимирующие кривые построены по уравнению (5) с параметрами а* = 5,7 МПа, E =109 МПа, s = 62,5 и 8* = 5.3 % (кривая 1), и а* = 5,7 МПа, E =340 МПа, s = 83 и 8* = 4.1 % (кривая 2).

По-видимому, впервые нелинейные эластические свойства клеточных стенок были описаны в работе Лепешкина (1907), выполненной в лаборатории Фаминцына более века назад. Автор методами микроскопии исследовал зависимость объема клеток от осмотического потенциала окружающего клетки раствора и пришел к выводу о положительной связи между упругой жесткостью клеточных стенок и тургорным давлением. Несмотря на последовавшее вскоре признание работ Лепешкина в области общей физико-химической биологии (Lepeschkin, 1924), его исследования эластичности клеточных стенок прошли для современников незамеченными и лишь полвека спустя были частично переоткрыты Kamiya et al. (1963).

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St. Petersburg State University

Manuscript Copyright

Andrei A. Lipchinsky Mechanobiological aspects of plant cell growth

03.01.05 - plant physiology and biochemistry

Dissertation submitted for the degree of Candidate of Biological Sciences

Academic supervisor: Doctor of Biological Sciences, Professor Sergei S. Medvedev

St. Petersburg 2019

Contents

Introduction.....................................................................................................................................66

Chapter 1. Elastic properties of primary cell walls...............................................................70

1.1. Introduction.......................................................................................................70

1.2. Materials and methods......................................................................................70

1.3. Results and discussion......................................................................................73

Chapter 2. Plastic properties of primary cell walls...............................................................84

2.1. Introduction.......................................................................................................84

2.2. Acid growth.......................................................................................................84

2.3. A model of defect-mediated wall loosening.....................................................87

Chapter 3. Mechanobiology of polarized cell growth..........................................................95

3.1. Introduction.......................................................................................................95

3.2. Transport phenomena in pollen tubes...............................................................96

Conclusion.....................................................................................................................................106

References.....................................................................................................................................108

Introduction

J.W. von Goethe, a child and apostle of the Enlightenment, a founding figure in general morphology and plant developmental biology, hailed the challenge of unraveling the laws and forces underlying the development of living beings as one of the most fundamental research priorities (Goethe, 1790, 1796/1820). A century after the seminal studies of Goethe in the fields of ontogenetic transformations and morphoevolutionary homologies, D'Arcy Thompson coined his celebrated apophthegm of biological morphogenesis, the maxim bribing with its elegance and perplexing with its semblable simplicity: "the form [...] is a diagram of forces" (Thompson, 1917). Thompson's approach can be seen as the culmination of the modern creative reconstruction of the Aristotelian tradition to explain (causa efficiens sensu) biological processes using concepts and principles from the field of mechanics. This approach spawned new imperative directions and questions in the studies of dynamic patterns of mechanical forces in living organisms and in examination of laws governing their evolution.

At the cusp between the 19th and 20th centuries, the progress in dynamic structural biology marked by works of great physiologists and morphologists - Hofmeister (1860/1863; 1868), Sachs (1874), Schwendener (1874), His (1888), Pfeffer (1904), Roux (1895) and de Vries (1919) -coincided in time with a profound advancement in biological chemistry (Buchner, 1897; Haldane, 1921; Sumner, 1926). The development of biochemistry at the beginning of the 20th century and the birth of molecular biology roiled the mid-20th century (Franklin and Gosling, 1953; Watson and Crick, 1953; Astbury, 1961; Hess, 1970) pushed the biomechanical paradigm aside. The complexity and specificity of the molecular biological processes revealed in the that period against the backdrop of the seemingly ordinariness of mechanical forces operating in living organisms led to the dominance in the 20th century of the idea that mechanical forces do not play in biological phenomena an essential role, but just provide conditions necessary for the operation of biochemical and genocentric processes, which had begun to be looked upon as the quintessence of life (Schrodinger, 1944; Wolpert, 1969; Dawkins, 1976; Koch and Meinhardt, 1994). One of the repercussion of such a paradigm shift was the fact that biomechanics had begun to be perceived as a kind of applied engineering, that is, there had been a swing in semantic emphasis in the word biomechanics from its first to the second root ((Benedikt, 1912; Thompson, 1917) vs. (Razdorsky, 1955; Herbert, 1974)).

The beginning of the present century brought a renaissance of biocentrically rationalized biomechanical paradigms. Revealing of the role of mechanical forces in the regulation of

biochemical reactions (Chowdhury, 2013; Brinkmann et al., 2018) and gene expression (Brouzes and Farge, 2004; Braam, 2005; Shivashankar, 2011), in the vectorial transport of signal molecules (Nakayama et al., 2012), in the maintainance of cell and tissue architecture (Ingber, 2003; Traas, 2019), in the control of cell differentiation (Engler et al., 2006; Malivert et al., 2018; Messal et al., 2019) and - most significantly - in the immediate regulation of ontogenetic and morphogenetic transformations (Nelson et al., 2005; Hamant et al., 2008; Mammoto and Ingber, 2010; Pien et al., 2001; Beloussov, 2015; Bredov and Volodyaev, 2018) - all that have led to the striking transformation of biomechanics, and at the beginning of the 21th century it again became an integral part of modern biology, morphed into mechanobiology - the science founded on the prolegomena of the high specificity and fundamental role of biomechanical processes and forces.

The physiological role of endogenously generated mechanical forces is most pronounced and manifold in the processes of growth and development of plants. One of the reasons for this is that plant growth is associated with the maintenance and redistribution of enormous mechanical stresses. Hydrostatic pressure inside a typical plant cell equals several atmospheres, while the mechanical tension in the cell walls is tens to hundreds of times higher (> 1 MNm ). Mechanical stresses in plants arise primarily from transmembrane osmotic gradients. Osmotic gradients along with the mechanical and geometric parameters of cells and tissues (shape, size and mutual bracing of cells; thickness, rigidity and mechanical anisotropy of cell walls) and kinetic parameters reflecting the permeability of biological membranes for ions and molecules define a general pattern of mechanical stresses in plants (Nobel, 2009; Niklas and Spatz, 2012; Bidhendi et al., 2019). An additional role in the intracellular distribution of mechanical stresses can be played by the forces generated by cytoskeleton treadmilling and the work of motor proteins (Steinberg, 2007).

In accordance with the concepts of modelling developed in recent years (Boudon et al., 2015; Abad et al., 2017; Bidhendi and Geitmann, 2018; Dumond and Boudaoud, 2018), the above osmotic and mechanical factors can be used to comprehensively analyze the stress-strain status of growing plant tissues and to explain the dynamics of mechano-dependent morphogenetic processes in plants. However, in practice, the predictive power of such models is limited for a number of reasons. First, the factors considered in the models are often difficult to formalize (for example, the rigidity of cell walls includes diverse components, the phenomenological description and physical interpretation of which are extremely complex). Secondly, the mechanical and osmotic parameters can quickly and significantly change in response to weak physiologically significant signals, and immediate triggers and underlying mechanisms for these changes are largely unclear. Until recently, the morphogenetic effects of mechanical, osmotic, electrophysiological, and molecular factors were

studied largely in isolation, but in recent years it has become increasingly clear that only their integral analysis can reveal the multi-dimensional pattern of systemic interactions underlying biological morphogenesis.

This work is aimed to explore experimentally and theoretically the morphogenetically significant mechanobiological processes that take place in plants at the molecular, cellular and tissue levels. Primary research objectives are the following:

1. Investigation of the dependence of the elastic modulus of the cell walls isolated from coleoptiles of maize seedlings at the age of 4 and 6 days (stages of auxetic growth and coleoptile aging, respectively) on mechanical stress, pH and temperature.

2. Analysis of molecular mechanisms underlying viscoplastic cell wall yielding that is the rate-limiting factor for plant cell growth.

3. Analysis of intracellular transport processes arising from the conjugation of osmotic, mechanical and electrical gradients in polarized cells.

4. Exploration of the applicability of the concept of stress hyper-restoration to morphogenetic processes in plants.

The methods used to achieve the above objectives included mathematical modeling and experimental measuring of mechanical properties of plant materials using a linear displacement transducer.

The primary objects of our experimental investigation were the epidermal cell walls of maize coleoptiles that were isolated from 4 and 6 days old seedlings. The choice of coleoptiles as experimental objects was due to the following reasons. First, coleoptiles are juvenile organs characterized by fast but deterministic growth: in 4-day-old seedlings, the rate of coleoptile growth is about maximum, while in seedlings of 6-7 days, the growth of coleoptiles stops. At the same time, in 4-day-old seedlings, the coleoptile grows in auxetic mode, that is, due to an increase in the size of existing cells (cell divisions are absent). Since the auxetic growth is associated with physiologically controlled cell wall extension, the stress-strain behavior of isolated cell walls should reflect their morphogenetically significant competences. Another important aspect of coleoptiles as experimental objects is that the epidermal coleoptile cells are strongly anisodiametric: their length in the axial direction exceeds their width by an order of magnitude. This enables uniaxial stretching of coleoptile epidermal cell walls without significant altering their architecture and allows linking the observed deformation of the walls in vitro with their physiological extensibility during cell growth in vivo.

The main results of the work:

1. The dependence of cell wall elastic modulus on mechanical stress has been shown. A mechanical model is proposed to explain the observed effect by a non-uniform stress distribution in the cell walls.

2. A reversible elongation of cell walls induced by a temperature decrease has been revealed.

3. A model for expansin-mediated wall loosening has been proposed and substantiated that suggests that proteins of the expansin superfamily generate mobile conformational defects at the surface of cellulose microfibrils.

4. Unconventional mechanisms of intracellular vesicular transport and of apical pressure gradient emergence in tip-growing cells have been proposed.

5. Some key events in plant morphogenesis have been interpreted within the concept of stress hyper-restoration.

The above results are original and obtained under the supervision of senior colleagues (Lipchinsky et al., 2013) or unassisted (Lipchinsky, 2013; Lipchinsky, 2015a; Lipchinsky, 2015b; Lipchinsky, 2018). The theoretical significance and novelty of the results are reflected in the above publications and in the relevant sections of the dissertation (1.3, 2.2, 2.3 and 3.2). As concerns potential practical implications, the following points can be noted. First, the work proposes and substantiates a model of defect-mediated destabilization of interactions between cellulose microfibrils and cross-linking glycans (chapter 2). An investigation of this mechanism may contribute to the development of technologies for industrial hydrolysis of cellulose, which is the most commonly occurring but extremely recalcitrant organic substance on Earth. The potential practical implications of the work can also be illustrated by the fact that the work deals with intracellular transport processes mediated by cell apical membrane depolarization (chapter 3). Since the apical depolarization is characteristic of both plant and animal tip-growing cells (Lipchinsky, 2018), the analysis of intracellular electrokinetic transport processes addressed in this work can be used in both agricultural and biomedical sciences. The results of the work can also be used in academic studies on plant growth and development, mechanobiology, cell biology and in some other research fields.

Chapter 1. Elastic properties of primary cell walls

1.1. Introduction

The rheological model of plant cell growth (Lockhart, 1965; Ortega, 1985) considers the cell extension growth as a process of irreversible cell wall deformation driven by turgor pressure. In this model, the mechanical behavior of cell walls is usually described as a type of viscoelastoplastic, in which linear elastic (Hookean) and viscoplastic (Bingham) components play a major role (Ortega, 1990; Proseus et al., 1999; Geitmann and Ortega, 2009; Dumais and Forterre, 2012). Linear, or Hookean elasticity refers to a deformation behavior characterized by a direct proportionality between the mechanical stress in the loaded material and the reversible component of the material's deformation. Bingham, or viscous plasticity can be understood as a deformation behavior in which the irreversible component of the deformation occurs only after the stress exceeds a certain threshold value and, under constant above-threshold stress, is a linear function of time.

This chapter is based on the paper of Lipchinsky et al. (2013) and considers the results of the experimental investigation of deformation behavior of cell walls of maize coleoptiles. The results suggest that, contrary to paradigmatic views, the relationship between mechanical stress and elastic strain of the walls is nonlinear. The observed nonlinear dependence is considered as a consequence of the non-uniform distribution of mechanical stress between different components of the cell wall.

1.2. Materials and methods

Seedlings of Zea mays L. cv. Kamerad were grown in darkness at 27 °C and 100 % humidity. Epidermal strips were obtained by making a slight 1.8-mm-wide longitudinal incision in the basal end of coleoptile sections cut off 4 mm above the coleoptilar node followed by grasping the incision margin with a forceps, bending it sharply outwards and slowly pulling in an apical direction. The peeled strips were trimmed to 13 mm in length with the upper cut being made about 3 mm below the coleoptile tip, and frozen at -40 °C in a small quantity of citrate-phosphate buffer (10 mM citric acid, 80 mM Na2HPO4, pH 7.0). The frozen material was stored up to 48 h and thawed immediately before the experiment in the above buffer. The thawed segment was settled in quartz clamps with 5 mm of tissue exposed between the clamps. To provide a gentle yet solid contact with the plant material the quartz clamps were covered with a silicon film (one jaw of the clamp) and a layer of emery (its counterpart). The lower clamp was firmly secured to the base,

while the upper clamp was attached to one arm of the centrally pivoted lever connected to a vacuum tube diode used as a displacement transducer (Fig. 1.1). The diode has two anodes, one of which was fixed, and the second was engaged through a sealed membrane to a movable rod the impact on which caused the respective anode to be repositioned with a concomitant change in the electrical current. The dual transducer design allowed balance power supply fluctuations and electron tube noise because the current through the stationary anode was used as a reference signal. This yielded a registration accuracy of about 0.2 |im.

During the experimental examination of the elastic (first series of experiments) and thermoelastic (second series of experiments) properties of the cell walls, the sample chamber was filled with the buffer described above and maintained at 30 ± 1 °C unless otherwise mentioned. The applied load was increased from 2.2 to 11.8 cN in steps of 2.4 cN with the time interval of 6-10 min. After that the load was incrementally decreased in the reverse order of loading.

Fig. 1.1. Apparatus for measuring elasticity of isolated tissues. The sample (1) was inserted between a lower clamp (2) secured to the base and an upper clamp (3) attached to one arm of the centrally pivoted lever (4). A tensile load was provided by the weight (M) attached to the opposite lever arm. An additional counterbalance load (B) was designed to offset the weight of the sample upper clamp (3). The sample strain was detected by a vacuum tube diode (5). The diode has two anodes, one of which (6) was fixed, and the second (7) was connected through a movable rod (8) to the lever arm engaged to the sample upper clump. The impact on the movable rod caused the respective anode to be repositioned with a concomitant change in the electrical current measured by an ammeter (A). The sample was immersed in the incubation medium (9) inside the silicone chamber (10).

To determine the elastic modulus, a number of short term (5 s) cycles of unloading-reloading at 1 cN were performed after 6-10 min of isotonic cell wall deformation. The elastic modulus (Etg) was calculated according to the following equation:

Aa XL

E's = -AT-- (1)

where Aa is the stress reduction, L is the initial segment length (5 mm), and AL is the segment shortening during the first two second after the stress had been reduced by Aa.

The tensile stress (a) was calculated as follows: F

a = A' (2)

2

where F is the load and A is the sample cross-sectional area, 0.003 mm , as measured from microscopic examination.

To determine the thermally induced wall strain (second series of experiments), the standard bath solution at temperature 30 °C was periodically replaced for about 20 s by the same buffer but at 4 ± 1 °C. Between the removal of the warm buffer and the addition of the cold solution and between the reverse operations the segment was surrounded by humid air at 28 ± 2 °C not more than 6 s. The thermally induced wall strain was calculated according to the data on segment length change within the first 3 s after the addition of cold buffer.

The third series of experiments in the study of elastic properties of the cell walls of maize coleoptiles was carried out to determine the dependence of the elastic modulus on pH. In these experiments, during the process of increasing the load applied to the plant material according to the above scheme (from 2.2 cN to 11.8 cN with a step of 2.4 cN) in the standard buffer (citrate-phosphate buffer, pH 7.0), the short-term (5 sec) unloading-reloading cycles per 1 cN (after 6-10 min of isotonic stretching) were carried out provided wall incubation in buffer solutions with different pH. First, the unloading-loading cycle was carried out during the incubation of the walls in citrate-phosphate buffer pH 7.0, and then (after 20 seconds) the buffer was changed to acetate pH 4.8, and 30 seconds later, the unloadin-reloading cycle was repeated. Then the incubation chamber was again filled with citrate-phosphate buffer pH 7.0, and after that the original procedure was repeated at each step of the incremental increase in load (2.2 cN, 4.6 cN, 7 cN, 9.4 cN, 11.8 cN).

1.3. Results and discussion

Cell walls are usually modeled as a viscoelastoplastic body, the irreversible (viscoplastic) deformation component of which has the characteristics of the Bingham flow, and the reversible (elastic) component satisfies Hooke's law (Ortega, 1985; Proseus et al., 1999; Geitmann and Ortega, 2009; Dumais and Forterre , 2012). In such a case, the deformation of the cell walls under uniaxial tension should satisfy the equation:

dL _ dL?1 dLel _ tr da

Lxdt = Lxdt + Lxdt = -a eYu x dt'

where L is the length of the stressed cell wall segment, o is the stress in the walls, dLpl is the wall strain differential due to plastic deformation, dLel is the wall strain differential due to elastic deformation, ¥ - plastic extensibility coefficient, atr - the threshold stress for plastic flow, EYn is Young's modulus.

As indicated above, equation (3) assumes a linear relationship between the mechanical stress in cell walls and their elastic strain. Under this assumption, the elastic properties of cell walls can be characterized by a single parameter, Young's modulus (Nilsson et al., 1958; Ortega, 1985; Wang et al. 2004; Dintwa et al., 2011), which, by definition, is the proportionality factor between wall stress and wall elastic strain (EYn ^ o/ALel = const).

The results obtained in the present study (Fig. 1.2) indicate that the ratio of the wall lenght increment to the wall stress increment is a function of stress (do/dLel = f(o) ^ const), and, consequently, the concept of Young's modulus as a constant characterizing the stress-strain ratio is not applicable to the material under investigation. Therefore, to describe the elastic properties of the cell walls, we use thereafter the concept of tangential elastic modulus, defined in mechanics as the limit of the ratio of the stress increment to the strain increment when the stress increment tends to zero: Etg = limd(T^0 do/dLel. In the calculations given in this work, the tangential modulus of elasticity was calculated from equation (1) according to the data on the wall length change induced by force reduction by 1 cN.

The results indicate that the tangential modulus of elasticity of the cell walls of maize coleoptiles increased with increasing stress (Fig. 1.2). At the same time, the tangential modulus of elasticity does not depend on the direction of the deformation cycle, that is, on whether the walls were prestressed at a maximum stress of 38 MPa (Table 1).

Fig. 1.2. Elastic modulus of coleoptile cell walls of 4-day-old (circle) and 6-day-old (square) maize seedlings as a function of tensile stress. Each point represents mean data from six biological samples assayed during the course of progressive (5.7 ^ 38 MPa) stepwise loading. Vertical bars denote the standard error of the mean.

a (MPa) EtgpEtgl (%)

4-day-old seedlings 6-day-old seedlings

5,7 97,4 ± 1,3 97,2 ± 1,5

14 103 ± 0,9 102,0 ± 1,1

22 101,9 ± 0,6 101,0 ± 0,5

30 97,7 ± 1,0 97,9 ± 0,6

Table 1. Elastic modulus as established during the course of stepwise loading (5.7 ^ 38 MPa, Etg|) in percentage of the modulus during the course of stepwise unloading (38 ^ 5.7 MPa, Etg[) at a given stress value (a) for cell walls of 4- and 6-day-old seedlings (mean ± SE, n = 6).

The change in tensile stress from 6 to 38 MPa caused the increase in cell wall elastic modulus from 0.4 to 3 GPa (Fig. 1.2). The relationship between the elastic modulus and the stress can be approximated by a linear equation:

Ets = E0 + s x a, (4)

where E is the apparent elastic modulus at zero stress, and s is a parameter that characterizes the nonlinearity of the stress-strain response (s is zero for materials that obey Hooke's law) (Fig. 1.2).

The mechanical behavior of a material when the elastic modulus depends on the stress is called nonlinear elastic behavior, since in this case there is no proportionality between stress and strain. The nonlinear pattern of the elastic behavior of the cell walls is manifested in the exponential relationship between tensile stress (a) and elastic strain (e), that can be derived by integration of equation (4):

a = (a* + y) x es(£-£t) - y, (5)

where a* and e* are integration constants, namely the strain (e*) at a particular stress (a*). The absolute values of the parameters of equations (4) and (5) are given in table 2.

Age of seedlings (days) s E0 (Mna) a* (Mna) e* (%)

4 60,4 ± 4,2 140 ± 45 5,7 5,3 ± 0,3

6 79 ± 5,3 361 ± 70 5,7 4,1 ± 0,3

Table 2. Parameters of Eqs. (4) and (5) describing cell wall elastic properties of 4 and 6 days old maize seedlings (mean ± SE, n = 6).

From the graph of equation (5) one can see that an increase in tensile stress causes the cell walls to become more elastically rigid, that is, to exhibit less strain response to a reference stress variation (Fig. 1.3).

The nonlinear elastic stress-strain behavior of plant cell walls apparently was first mentioned in the pioneering work of Lepeschkin (1907) more than a century ago. Lepeschkin, using light microscopy, investigated the dependence of the cell volume on the osmotic potential of the surrounding solution and found that there is a positive relationship between the elastic rigidity of the cell walls and the turgor pressure.

10 20 30 40 Tensile stress, MPa

Рис. 1.3. Cell wall instantaneous elastic strain as a function of tensile stress. The data shown are representative results obtained during the course of stepwise loading of coleoptile cell walls of 4 days old (circle) and 6 days old (square) maize seedlings. The approximating curves were plotted according to Eq. (5) with parameters o* = 5,7 MPa, E =109 MPa, s = 62,5 and s* = 5.3 % (curve 1), and o* = 5,7 MPa, E =340 MPa, s = 83 and s* = 4.1 % (curve 2).

The great advance in the studies of elastic properties of plant cell walls was due to the invention of capillary micromanometry technology, which allows measuring turgor pressure at the level of individual cells (Green and Stanton, 1967; Husken et al., 1978). Using this method, the dependence of the tangential volumetric elastic modulus of a cell on turgor pressure was investigated (Steudle et al., 1977; Husken et al., 1978; Pritchard et al., 1988; Murphy and Ortega, 1995; Franks et al., 2001). The cell volumetric elastic modulus by definition, is the limit of the ratio of the turgor pressure increment (dP) to the specific increment of the cell volume (dV/ V) with the pressure increment tending to zero:

dPxV

№ ^ lirn . (6)

r dp^o dV

The results showed that the cell tangential volumetric elastic modulus and cell turgor pressure are often related by a linear dependence, which in numerous cases is close to direct

proportionality (Steudle et al., 1977; Husken et al., 1978; Pritchard et al., 1988; Tyerman et al., 1989; Franks et al., 2001). Theoretical analysis yields the following relationships between the cell wall elastic tangential modulus (Eg) and the tangential volumetric elastic modulus ptg of an anisodiametric cell:

2 Et3t

Ptg =-, (7)

H 3r(1-v) v J

where t is the cell wall thickness, r is the cell radius, v is Poisson's ratio for cell wall (Saito et al., 2006). Since for a particular cell t, r and v during the pressure probe experiments could not change significantly, so, in accordance with the above equation, the proportionality between the cell tangential volumetric modulus and turgor pressure implies the proportionality between the elastic tangential modulus of cell walls and tensile stress.

Thus, the results presented here (Figs. 1.2, 1.3) are in good agreement with the literature data obtained by other methods and in other species (Kamiya et al., 1963; Steudle et al., 1977; Husken et al., 1978; Pritchard et al., 1988; Hejnowicz and Sievers, 1996; Franks et al., 2001). However, it should be noted that, along with these studies, there are studies indicating that in many cases the cell wall elastic modulus does not depend on the stress, and the elastic behavior of the cell walls can be approximated by the classical Hooke law (Nilsson et al., 1958; Probine and Preston, 1962; Tomos et al., 1981; Nonami and Boyer, 1990; Proseus et al., 1999; Wang et al. 2004; Dintwa et al. 2011). Consequently, the nonlinear wall elasticity cannot be considered as a general phenomenon.

The underlying cell wall structural particularities that give rise to the nonlinear stress-strain behavior are not known. In accordance with the hypothesis originally proposed by Wu et al. (1988) and further developed by Chaplain (1993), a significant dependence of the cell wall elastic modulus on tensile stress is mainly due to the fact that the increase in tensile stress causes the load to be redistributed from matrix polysaccharides to cellulose microfibrils. To test this hypothesis, we investigated the dependence of the elastic deformation of cell walls on temperature (Fig. 1.4). We proceeded from the fact that at about room temperature the crystalline cellulose has nearly zero thermal expansion coefficients (Wada, 2002). In the case of amorphous polymers the situation is more complicated (Wu and Sharpe 1979). Thermal response of amorphous polymers is not limited to an increase in the lengths of interatomic bonds, but also includes the intensification of bending and rotational motions. Thermal motions cause amorphous macromolecules to be randomly coiled and counteract the stretching of the molecules caused by an external tensile force. The result is a

negative coefficient of thermal expansion in the direction of tensile force. Its magnitude can be derived from the following relation:

JJtr jjrlx

where f is the tensile force, p is the material parameter, T is the Kelvin temperature, Lrlx and Lstr is the cell wall length at the temperature T in the stretched and unstretched (relaxed) states, respectively (Wu u Sharpe, 1979).

It follows from Eq. (8) that at small strains a decrease in temperature from Ti to T2 causes the elastic strain to increase proportionally to the change in temperature:

I Str _ I Str rp rp LTt LT2 ll — 12

J str _ jrlx f

LTi L,Ti 12

(9)

The numerator of the left-hand side of Eq. (9) represents the elastic strain caused by temperature change under constant mechanical stress (Fig. 1.4). The denominator of the left-hand side of Eq. (9) represents the elastic strain caused by mechanical stress at constant temperature (Fig. 1.2). The ratio of the cell wall strain caused by the decrease in temperature from 30 to 4 °C (Fig. 1.4) to its strain caused by mechanical stress (Fig. 1.2) is 0.5-1 %.

According to the Eq. (9), if the elastic elongation of an amorphous polymer material is due to the restriction of thermal motion, the temperature change from 30 to 4 °C (303 to 277 K) leads to the material elongation by (303 - 277)/277 = 9.4 % of the strain caused by mechanical stress. Comparing this value with the above experimentally derived data shows that less than 11 % of the cell wall elastic elongation could be attributed to the mechanism of restriction of polysaccharide thermal motions. Furthermore, the increase in tensile stress from 6 to 38 MPa caused only about 25 % reduction in the thermally induced strain (Fig. 1.4). Consequently, the sevenfold increase in the cell wall elastic modulus observed with increasing stress (Fig. 1.2) could not be due only to a decrease in the relative structural role of amorphous polysaccharides.

Fig. 1.4. Instantaneous elongation of coleoptile cell walls of 4-day-old (circle) and 6-day-old (square) maize seedlings caused by a decrease in temperature from 30 to 4 °C, depending on the tensile stress level. Each point represents mean data from six biological samples. Vertical bars denote the standard error of the mean.

Thus, contrary to the suggestion of Wu et al. (1988), the stress redistribution between amorphous and crystalline polysaccharides in the wall cannot explain the observed increase in the cell wall elastic modulus. Therefore, one can assume that non-Hookean cell wall behavior could be related to the wide strain spectrum within each type of cell wall polymers. Specifically, the nonlinear wall elasticity can be due to the transverse gradient of mechanical stresses between different layers of cell walls. Since the cell growth is associated with cell wall extension, the old components of the walls are in a mechanically stretched state. However, new components, recently embedded in the wall, are not stretched or even, on the contrary (due to turgor pressure and steric interaction with each other and with previously embedded components), are in a mechanically compressed state (Proseus and Boyer, 2006). The cell wall modulus corresponds to the sum of the stiffnesses of wall polymers under tension (kten) minus the sum of the stiffnesses of those under compression (kcomp):

E a Ikten - Zkcomp

(10)

A decrease in wall stress should lead to an inversion of the deformation state of some previously stretched cell wall components and thus should induce a decrease in the wall elastic modulus.

To evaluate changes in the cell wall elasticity caused by a decrease in tensile stress, consider the following situation. Suppose that all cell wall components were initially in tension. In this case, the initial cell wall modulus is:

where x is the total number of cell wall components and k is their mean stiffnesses. Suppose further that the reduction of stress caused Xx (X<1) components to be brought under compression and, consequently, (1-X)x components were left under tension. When this occurs, in accordance with the Eq. (10), the new modulus equals:

A comparison of Eqs. (11) and (12) shows that the new modulus 1-2X times larger than the initial one. It follows that to explain the sevenfold decrease in the modulus caused by the decrease in stress (Fig. 1.2) it is sufficient to assume that 43 % of initially stretched cell wall components passed into the compressed state.

As the wall stress decreases, an inversion of the deformation state of some previously stretched cell wall components should begin with the structural elements of the wall located in its newly formed (innermost) layers and spread to the periphery (to the outer layers). Therefore, this process should lead to a change in the pattern of mechanical stresses inside the cell walls. Remarkably, Hejnowicz u Borowska-Wykr^t (2005) observed the buckling of the inner wall layer of epidermal cells after the removal of tissue stresses and turgor pressure (peeling off the epidermis and bathing it in a plasmolysing solution). The authors propose the following explanation for this phenomenon. The cell wall constituents in their nascent state are not stressed but may experience a tensile stress further on, when due to cell growth they are stretched. The older components, the farther they are from the cell wall inner surface. Therefore, the elastic strain of a particular wall layer increases with distance of the layer from the wall inner surface. On elimination of turgor pressure all wall layers have to undergo equal length reduction, so the peripheral layers that initially were strained to a larger extent eventually exert a compressive force on the innermost wall layers.

Hejnowicz u Borowska-Wykr^t (2005) observed the characteristic pattern of transverse folds in the outer cell walls of maize coleoptile epidermis when the epidermal tissue layer was isolated and plasmolysed. Our results characterize the elastic properties of cell wall specimens

Einitial K xk,

(11)

Efinal k(1- X)xk -Xxk = (l- 2X)xk

(12)

comprising the same walls but with adjacent anticlinal and, sometimes, inner periclinal epidermal wall material. However, it should be stressed that the outer epidermal wall is much thicker than any other walls of the same and underlying cells and bear in situ more than 85 % of the total longitudinal expansive force produced in the coleoptile by turgor (Hohl and Schopfer, 1992). This implies that it is the outer epidermal walls that primarily determine the elastic behavior of the epidermal peels. It turns out that the essence of the present calculations should be applicable and relevant to the studied wall material. Our studies with Alexandra N. Ivanova (RRC MCT SPbSU) have confirmed the buckling of the innermost layers of maize coleoptile epidermal cell walls after their isolation and plasmolysis (Fig. 1.5).

1 MM

Fig. 1.5. Buckling of maize coleoptile epidermal cell walls after the removal of tissue stresses and turgor pressure (peeling off the epidermis and bathing it in a plasmolysing solution) visualized by transmission electron microscopy (top) and Nomarski interference contrast microscopy (bottom).

Thus, the results presented above suggest that the nonlinear dependence of wall elastic strain on wall stress (Fig. 1.3) may be due to a gradient of mechanical stresses between the inner and outer layers of the cell wall. In accordance with this suggestion, the wall tension is bearing mainly by

outermost wall elements. At moderate stresses, the resistance to extension of the outer wall layer is partially compensated by the opposite effect of the inner layer. Only at sufficiently large stresses the inner layer of the cell wall begins to make a positive contribution to counteracting extension. This may results in wall stiffening at large stresses.

Investigation of the dependence of wall elastic modulus on pH indicates that the acidification has no measurable effect on wall elasticity (Table 3). On the other hand, it is well known that the wall viscoplastic extensibility strongly depends on pH (Rayle and Cleland, 1992; McQueen-Mason et al., 1992; Cosgrove, 2000a). The differential effect of pH on the elastic and plastic extensibility of cell walls can be explained by the hypothesis of defect-mediated wall loosening discussed in Chapter 2.

a (MPa) Etg(pH 7,0)/Etg(pH 4,8) (%)

5,7 100,9 ± 1,0

14 100,8 ± 0,8

22 100,4 ± 0,6

30 100,3 ± 0,4

Table 3. The relative tangential elastic modulus of the epidermal cell walls of 4-day-old maize seedlings, calculated as the percentage ratio between the elastic tangential moduli of the walls at pH 7.0 and at pH 4.8 (mean values ± standard errors).

The nonlinear dependence of the wall elastic strain on the wall stress (Fig. 1.3) indicates a limited realism of the classic concept of cell wall deformation as a viscoelastoplastic process, the irreversible (viscoplastic) component of which has the character of Bingham flow, and the reversible (elastic) component satisfies Hooke's law (equation 3). The data presented in this work indicate that to adequately describe the mechanical properties of the cell walls, it is necessary to take into account the dependence of their elastic modulus on stress. In the case of linear relationships between the elastic modulus and stress (Fig. 1.2), the wall stress-strain behavior can be approximated by the equation:

dL dLpl dLel „ a* da

+ 7T7T77 = V(a - a») + ,pn (13)

Lxdt Lxdt Lxdt a*E°+aE*-aE° dt'

where E is the apparent tangential elastic modulus at a = 0, E* is the tangential elastic modulus at a

= a*.

A similar expression for volumetric cell deformation:

dV _ dVpl dVel _ tr P* dP

Vxli~Vx~dt + V^dt~v(P-P ^ + P*(30 + P(3* - P(3°X~dt'

where ft0 is the apparent volumetric elastic modulus at P = 0, ft* is the volumetric elastic modulus at P = P*.

Chapter 2. Plastic properties of primary cell walls

2.1. Introduction

Changes in the rate of plant growth are often accompanied by correlated changes in elasticity and plasticity of plant cell walls. More specifically, plant growth enhancement is usually associated with an increase in both elastic and plastic extensibility of cell walls, whereas plant growth retardation is usually associated with a decrease in both strain components. This general correlation is easily observed at prolonged time intervals, but in short terms the elasticity and plasticity of the cell walls can change independently. In particular, a cell wall acidification, which underlies one of the key physiological mechanisms of growth rate regulation (Rayle and Cleland, 1992), is usually accompanied by an instantaneous increase in plastic extensibility of the cell walls (McQueen-Mason et al., 2002; Cosgrove, 2000a), but may be not accompanied by a change in cell wall elasticity (Table 3). Since the wall elasticity is an integral parameter that characterizes the molecular connectivity of polymers in the wall load-bearing networks, the independent changes of wall elastic and plastic properties indicate that minor changes in the wall structure that do not affect the wall architectonics may be important for plastic extensibility. The present chapter is based on the work of Lipchinsky (2013) and addresses physiologically significant processes in the wall that in the short term do not affect the architecture, molecular organization and elasticity of the walls, but have a significant and rapid effect on the plastic cell wall extensibility.

2.2. Acid growth

Acid growth refers to the ability of young plant cells and isolated primary cell walls to increase the rate of their extension as pH in the walls decreases in the physiological range (from 6.0 to 4.7). Despite the almost century-long history of research (Bonner, 1934), the acid growth is still poorly understood at the molecular level. Cosgrove's (1989) discovery that the ability of cell walls to undergo acid-induced irreversible extension could be severely impaired by mild denaturation treatment entailed a series of the landmark experiments that led to the identification of several groups of wall-loosening proteins directly involved in the control of cell expansion. The major breakthrough came in the early 1990s when McQueen-Mason et al. (1992) showed that wall extensibility could be reconstituted by adding to denaturated walls a minor fraction of native wall protein, later named expansin (Li et al., 1993). Numerous subsequent studies extended this finding

and established the concept of expansins as essential endogenous catalysts of wall extension and restructuring widely implicated in the regulation of plant cell growth and differentiation.

Over the past quarter of a century, hundreds of studies on structure and function of expansins have been performed, the main results of which can be briefly summarized as follows:

I. The mature expansin protein comprises two compact domains. The amino-terminal domain (D1, ~110 a.a.) is characterized by the His-Phe-Asp motif and a number of conserved polar residues with sequence homology to the catalytic domain of glycosyl hydrolase family 45 (GH45). Members of GH45 family are found in a broad range of organisms including bacteria, fungi, plants and animals and act as endo-P-1,4-D-glucanases. The second expansin domain (D2, ~95 a.a.) contains a number of conserved aromatic amino acids suitable for polysaccharide binding and aligned on the surface of the immunoglobulin-like P-sandwich fold in a way similar to that observed for the type-A carbohydrate-binding modules of bacterial cellulases (Shcherban et al., 1995; Yennawar et al., 2006; Kerff et al., 2008; Georgelis et al., 2011).

II. Expansin preparations tested to date did not contain a detectable glycanase or transglycosylase activity (McQueen-Mason and Cosgrove 1994, 1995; Yennawar et al., 2006; Tabuchi et al., 2011, but: Cosgrove et al., 1998; Kerff et al., 2008).

III. The effects of expansins cannot be imitated by the action of glycosyl hydrolases, in particular, in the following aspects (Yuan et al., 2001; Kerff et al., 2008; Cosgrove, 2000b): (1) Expansins increase the wall extensibility transiently, only for the period of their activity. Glycanases, on the contrary, change the wall irreversibly and cause it to transit into in a new mechanical state with reduced breaking strength; (2) Expansins are able to enhance cell wall plastic extension in low amounts (< 0.02 % on a dry wall mass basis). Glycanases, on the contrary, do not affect wall extension in low concentrations, but at moderate concentrations induce wall breakage rather than wall extension.

The standard model for expansin action (Cosgrove, 1998, 2000a) proposes that expansin binds to the junctions between cellulose microfibril and matrix polymers and disrupt hydrogen bonds and van der Waals forces that hold these polysaccharides together (Fig. 2.1). The result is a transient release of the matrix polymer trapped in the cellulose microfibril and concomitant polymer slippage under the action of cell wall stress. As the polysaccharides shift their relative positions, non-covalent links that mediate glucan adhesion are immediately reformed in a new position. Such ready reversibility of hydrogen and van der Waals interactions could conceivably explain why the wall strength is maintained during expansin-mediated wall extension.

microfibril

Fig. 2.1. Schematic diagram of the classical model for expansin action (Cosgrove, 2000a). The putative catalytic expansin domain (D1) is hypothesized to interact with matrix polysaccharide, while the carbohydrate-binding domain (D2) could be able to attach to the surface of cellulose microfibril. The expansin motion (in the direction of dotted arrow) causes the unzipping of the non-covalent cross-links (dotted lines) between the microfibril and the matrix polysaccharide, resulting in a type of polymer creep, in which the short segment of matrix polysaccharide is released from the microfibril surface, moves, and then reassociates with the microfibril in a new place.

Providing a coherent conceptual framework for ongoing research in the field, the standard model leaves open a number of fundamental questions. One of them is related to the fact that expansin is a very minor component of the cell wall (Cosgrove, 2000b). In fast-growing cucumber seedlings expansin is found at roughly one part protein to 5,000 parts cell wall and can induce wall extension when added in amounts as low as 1:10,000. Taking into account the high density of hydrogen bonding between cell wall polysaccharides (Veytsman and Cosgrove, 1998), it is not clear how exactly expansins in such low concentration can significantly affect their adhesion. Another question that remains to be answered is why this protein, not exhibiting clear hydrolytic activity, possesses much of the conserved catalytic site of hydrolytic GH45 enzymes (Cosgrove, 2000a; Yennawar et al., 2006). Below, I make an attempt to address these and other issues pertaining to the function of these unusual proteins by reexamining the elementary processes that underlie plant cell wall extensibility.

2.3. A model of defect-mediated wall loosening

The model of defect-mediated wall loosening stems from the consideration of microfibril structural features, namely, spatial regularity, steric strain and geometrical anharmonicity that cooperatively would enhance the mobility of conformational defects present on the microfibril surface. Mobile defects, in turn, are considered as key players that promote the disruption of hydrogen bonds and van der Waals interactions at the microfibril-matrix interface in a high-stress environment. The proposed assumption is consistent with the fact that conformational defects are of fundamental importance for relaxation phenomena in oriented polymers. On the other hand, the cellulose chains within the microfibrils of primary cell walls have been shown to be well ordered (Smith et al., 1998; Davies et al., 2002; Ruel et al., 2012), yet chains located at the microfibril surface could undergo considerable segmental motion (Hardy and Sarko, 1996; Vietor et al., 2002). Taken together, these data hint that the rheological behavior of growing cell walls may have its molecular origin in the migration of conformational defects along the microfibril surface.

The model under consideration is illustrated in Fig. 2.2. The major difference between this diagram and the one depicted in Fig. 2.1 is that the present diagram suggests that expansin is needed only to initiate the release of the region of a polysaccharide chain from the microfibril surface, but the subsequent motion of this region along the microfibril is an expansin-independent process. Another important distinction is that the polymer chain that slides along the microfibril is a cellulose molecule in the case depicted in Fig. 2.2, whereas it is a matrix polysaccharide in the model shown in Fig. 2.1.

The proposed model is based further on three assumptions:

1. Microfibril-matrix interfaces cause steep stress gradients on the microfibril surface.

2. Stress gradients drive the movement of conformational defects along the microfibril surface toward the microfibril-matrix interfaces.

3. The approach of the defects to the microfibril-matrix interfaces facilitates the dissociation of matrix polysaccharides from cellulose microfibrils.

Рис. 2.2. Simplistic illustration of the recently proposed model for expansin action (Lipchinsky, 2013). (a) A region of the matrix polysaccharide (MP) is attached to the microfibril (MF). (b) Expansin interacts with the microfibril and catalyzes the hydrolysis of a glycosidic bond in a cellulose molecule laid at the microfibril surface; the newly-formed end of the cleaved cellulose chain undergoes reconfiguration with generation of mobile conformational defect (CD). (c) The motion of the defect results in the dissociation of the matrix polysaccharide from the microfibril surface. The microfibril is shown in the longitudinal section in Ia crystalline form, one straight-line segment corresponds to one glucose residue. D1 and D2 are the putative catalytic and carbohydrate-binding expansin domains, respectively.

To capture the stress gradients that are expected to exist on the microfibril surface, let us consider the following situation (Fig. 2.3a). Suppose that a region of cellulose microfibril is subjected to lateral adhesion of strained matrix polysaccharides and each of these polysaccharides tends to warp the microfibril in the direction nearly opposite to the forces exerting by the two neighbors. In such a case, the surface cellulose molecules are under mechanical stress whose magnitude and direction vary along and across the microfibril in such a way that tensile stresses nearby microfibril-matrix interfaces are balanced out by quantitatively equivalent compressive stresses on the contralateral microfibril portions (Fig. 2.3b).

Fig. 2.3. Schematic diagram of the bent region of cellulose microfibril (MF) subjected to lateral forces due to adhesion of three matrix polysaccharides (MP) (a) and the corresponding stress distribution as expected from Euler-Bernoulli beam theory (b) (Lipchinsky, 2013). The bending stress varies linearly from convex to concave microfibril surface and are tensile (diverging arrows) nearby microfibril-matrix interfaces and compressive (converging arrows) on the contralateral microfibril portions. Note that the stresses vary not only across the microfibril but also along any given cellulose chain.

If one of the surface cellulose chains interfaced with matrix polysaccharides forms a buckling-type conformational defect, these stresses could drive the movement of the conformational defect toward the region of the microfibril-matrix adhesion (Fig. 2.4a, b). Approach of the defect to this interface would allow tensioned matrix glucan to deviate from the microfibril at an additional distance S (Fig. 4c). This deviation results in the release of energy E in the amount equivalent to the product of S on the normal tension force f0 exerting by the matrix polysaccharides on the microfibril: E = S x f0.

In the case of simple topologically stable defects that could present on the microfibril surface, S is about the length of a glucose residue, that is about 0.5 nm. Assuming the tensile force f0 is 50 pN (Bergenstrahle et al., 2009) there is, according with above equation, the energy released: E ~ 0,5 x 10-9 x 50 x 1012 = 2,5 x 10-20 J (15 kJ/mol). This energy is approximately equal to the work required to desorb one glucose residue of the P-1,4-D-glucan chain from the crystalline cellulose surface to water environment (Bergenstrahle et al., 2009). It is noteworthy that this energy is calculated by taking into account only the changes in the polymer geometry and does not include the kinetic energy associated with the defect motion. Therefore, one would reasonably expect that the energy gain caused by the defect approaching to the microfibril-matrix interface is enough to induce desorption of at least one monosaccharide unit of the matrix polysaccharide from the

microfibril surface. Furthermore, given the initial assumption that matrix polysaccharides are under tension, desorption of one monosaccharide residue should lead to a new release of energy, which, following the above equation, appears to be sufficient to promote desorption of the next monosaccharide unit. Therefore, the movement of the conformational defect can trigger the critical process resulting in the complete unzipping of the microfibril-matrix interface.

Fig. 2.4. A mechanistic interpretation of the putative molecular mechanism by which the mobile conformational defect (CD) may destabilize microfibril-matrix interactions (Lipchinsky, 2013). (a) The buckling-type defect is located at the concave side of the bent cellulose microfibril (MF) and is subjected to compressive forces (f1, f2). These forces are out of balance, the predominant force (f1) is directed out of the concave. (b) The defect is located at the convex microfibril side and is subjected to tensile forces (f3, f4). These forces are also out of balance, and the predominant force (f4) is directed toward the microfibril-matrix interface. (c) The approach of the defect to the microfibril-matrix interface allows the tensioned matrix polysaccharide (MP) to deviate at an additional distance (5). Since the matrix polysaccharide is under tension (f0), this deviation results in the release of energy, which facilitates the interface dissociation.

Once the microfibril-matrix complex has pulled apart, the portion of the microfibril surface that previously interfaced with the polysaccharide that had been desorbed undergoes a transition from an extended to a compressed state. This stress inversion endows conformational defect with an

m

additional thermodynamic potential which forces the defect to leave the newly-formed area of compression and to move into the area of extension under the direct influence of the tensile field from the matrix polysaccharide interacting with the given cellulose chain. In the issue, the above scenario for defect-mediated polymer disengaging could be repeated with a new microfibril-matrix complex. Moreover, since the average stress produced in the wall by cell turgor is constant, the breakage of the previous polymer association should put extra load on the neighboring polysaccharide tethers thereby facilitating their subsequent detachment.

The above analysis implicitly assumes that the defect motion does not alter the type of cellulose packing. Otherwise, the difference in internal energy between initial and final cellulose packing can profoundly affect the dynamics of the conformational defect. A near 2-fold screw symmetry possessed by cellulose chains permits only three types of simple point defects whose movement displaces the polymer chain in such a way that the shifted region is able to incorporate into the microfibril with the same bonding pattern as it had prior to displacement. These defects are: (1) a 180° local chain rotation with longitudinal translation of the rotating region by the length of a glucose residue, (2) a translation of the chain region by the length of a cellobiose residue (without a rotation), (3) a 360° local rotation (without longitudinal translation). A point defect that is not one of the above mentioned and cannot be expressed as their combination should cause alteration of cellulose packing. If this is the case, a possible outcome is a reduction in cellulose crystallinity, although the prospect that the defect motion can lead to mutual transformations of native crystalline cellulose allomorphs or even to an improvement of microfibril crystallinity also could not be ruled out.

Two forms of native crystalline cellulose, Ia and Ip allomorphs (VanderHart u Atalla, 1984; Nishiyama et al., 2002, 2003), are known to occur in plant cell walls in close proximity, juxtaposed axially and, probably, laterally within the same microfibril (Sturcova et al., 2004; Horikawa and Sugiyama, 2009). In both forms glucan chains are arranged in sheets: within each sheet the chains are held together by hydrogen bonds and van der Waals forces, while each sheet adheres to the next primarily by van der Waals forces (Nishiyama et al., 2002, 2003; Sturcova et al., 2004). In Ia crystalline form all molecules possess the same conformations, but successively alternated (along a chain) glucose residues differ in conformation and hydrogen bonding. In Ip allomorph two non-identical molecular sheets regularly alternate, but within one molecular sheet all glucose residues are identical (except that they face alternately in opposite directions). Another distinction between cellulose Ia and Ip is in mutual arrangement of neighboring sheets. In the both forms the projections of two adjacent sheets on a plane parallel to them are related to each other by a translation by a

distance equals to half of the length of a glucose residue in the longitudinal (along chains) direction and by a distance slightly less than half of its length in the transverse direction. Because in a cellulose chain adjacent glucose residues are turned 180° relative to each other, the longitudinal translation by half of the length of a glucose residue can give rise to the formation of different structures. In the case of cellulose Ia form, all longitudinal translations are co-directional. In the case of cellulose Ip, each following sheet is translated in the longitudinal direction opposite to the previous one.

The above crystallographic relations imply that the principal operation needed to convert cellulose Ia to Ip (and vice versa) is either to slide some layers longitudinally by the length of a glucose residue or to rotate some chains by 180°. Molecular modeling (Hardy and Sarko, 1996) and solid state calculations (Jarvis, 2000) suggest that these transformations are feasible, especially for surface cellulose chains, which are known to have considerable conformational freedom (Vietor et al., 2002). Likewise, experimental evidence has shown that the balance between the two allomorphs is not finally determined at the stage of cellulose biosynthesis (Hackney et al., 1994; Tokoh et al., 2002). Jarvis (2000) first suggested that interconversions of the cellulose forms could be induced by microfibril bending that is accommodated by sliding of molecular sheets. He provided calculations showing that in the case of a 17 nm long microfibril segment the phase transition can be completed within a bending angle of about 40°. The author further pointed out that the original model for microfibril bending that assumes a regular sliding of cellulose molecular sheets may be advanced to account for more complex behavior of surface polymer chains. Therefore, although the above discussion have been focused on the behavior of surface cellulose chains, their movements could entail coherent sliding of inner cellulose molecules, in particular, since any local buckling-type defect at the convex microfibril side should enhance microfibril bending and therefore provide extra driving force for defect motion along neighboring cellulose chains. The detailed analysis of these cooperative effects and the dynamics of not only point but also linear and two-dimensional defects requires dedicated spectroscopic investigations and an in-depth molecular modeling, and is the intended subject of further research.

The relationship between expansin mode of action and the movement through the microfibril conformational defects appears to be supported by the following evidence.

1. The N-terminal expansin domain possesses much of the conserved catalytic site of hydrolytic GH45 enzymes but does not exhibit noticeable hydrolytic activity. The model under consideration suggests that the hydrolytic activity is necessary not for breaking the network of tethering matrix polysaccharides but for releasing an end of cellulose chain

being able to be reconfigured with formation of the defect. If this is the case, it is natural to expect a relatively low hydrolytic activity of expansin proteins compared with typical endoglucanases.

2. Expansin superfamily comprises two major protein families (ExpA u ExpB) with different biochemical and functional properties and very ancient evolutionary origin. Among flowering plants ExpA predominates in and preferentially loosens the cell walls of dicots while ExpB displays functional specificity on the cell walls of grasses. It has been proposed that the phylogenetic profile and peculiar properties of the two expansin families are due to differences in amorphous polysaccharides that cross-link microfibrils in the wall (Cosgrove et al., 1997; Tabuchi et al., 2011). However, observations of expansin influence on the rheological properties of pure cellulose (McQueen-Mason and Cosgrove, 1994; Georgelis et al., 2011) and findings that members of both expansin families are present in all groups of land plants from mosses to grasses notwithstanding the differences in their cell wall composition (Carey et al., 2013) cause difficulties in the specification of the natural substrate for expansin activity. Therefore, one could suppose that the existence of the two expansin families is related to the existence of the two crystalline forms of plant cellulose. The specificity of the action of ExpA and ExpB on grasses and dicots may be explained by observations (Hackney et al., 1994; Tokoh et al., 2002) demonstrating that the predominance of one or the other cellulose allomorph depends on the kind of noncellulosic polysaccharides surrounding the microfibrils. On the other hand, since the two cellulose allomorphs were found in all examined plants (Sturcova et al., 2004; Horikawa and Sugiyama, 2009), it is possible to explain why the two expansin families are also found in all plants (Cosgrove et al., 1997; Tabuchi et al., 2011).

3. The proposed model could also explain the fact that a very small amount of expansin is able to induce substantial wall extension (McQueen-Mason et al., 1992; Cosgrove, 2000b). The foregoing analysis implies that one mobile conformational defect can facilitate relaxation of numerous matrix polysaccharides. The effectiveness of such mechanism should be by orders greater than the effectiveness of what is traditionally proposed, when the direct participation of expansin is needed for disengaging each microfibril-matrix complex.

4. Indirect support for the model can be seen in the finding that the two expansin domains, D1 and D2, act strictly cooperatively, that is, no wall-loosening activity was detected for either domain tested alone as well as for a mixture of D1 and D2 assayed together

(Georgelis et al., 2011). Likewise, although D2 resembles carbohydrate-binding modules (CBM) of bacterial cellulases, it is not loosely linked to a catalytic domain by a flexible linker as it was found for classical CBMs, but it is tightly packed against D1. This close spatial configuration is consistent with the present model proposing that there is a need for tightly coordinated domain movement to distort cellulose chains on the microfibril surface and to generate mobile conformational defects.

Chapter 3. Mechanobiology of polarized cell growth

3.1. Introduction

Morphogenesis is a manifestation of anisotropy of the endogeneous mechanical force field (Thompson, 1917; Lintilhac, 2013; Beloussov, 2015). Proceeding from the biophysical model of plant growth (Lockhart, 1965; Ortega, 1985), the anisotropy of the force field can be due to local variations of cell turgor pressure, peculiarities of cell geometry and gradients of cell wall mechanical properties (Cosgrove, 1993; Niklas and Spatz, 2012; Tomos and Pritchard, 1994). Experimental data suggests that in many cases the principal direction of cell growth does correlate with gradients of biochemical and mechanical properties of cell walls and well as peculiarities of cell geometry and call bracing within the tissue (Wojtaszek et al., 2004; Zerzour et al., 2009; Chebli et al., 2012; Niklas and Spatz, 2012; Bidhendi et al., 2019). At the same time, the question concerning the relationship of morphogenetic patterns and local variations of cell turgor pressure remains open (Zonia and Munnik, 2009; Winship et al., 2010). This question was addressed in the work of Lipchinsky (2018), and some results obtained in that work are presented in this chapter. The second question posed in the same work and discussed shortly below deals with the mechanisms of conjunction between cell wall extension and incorporation of load-bearing components into the wall. Such conjunction is necessary to preserve cell wall integrity and nearly constant thickness during cell extension growth.

Cell wall macromolecules, depending on the place of their biosynthesis, can be divided into two large groups. The first group includes cell wall polymers that are synthesized in the endoplasmic reticulum and/or the Golgi apparatus and then transported to the walls by vesicular secretion. This group includes hemicelluloses, pectins and proteins. The second group is represented by polymers that are incorporated into cell walls simultaneously with their synthesis carried out by enzymatic complexes located in the plasma membrane. This group includes cellulose and callose. Although the synthesis of cellulose and callose is not immediately dependent on vesicular secretion, the enzymatic complexes synthesizing these polysaccharides are transported to the cell surface by vesicular mechanisms. This means that the logistics of vesicular transport, ensuring the delivery of hemicelluloses, pectins, proteins and enzymatic complexes that synthesize cellulose and callose into the wall, should depend on the rate of cell wall extension.

A steady conjunction between vesicular transport and cell wall extension is particularly important for cells exhibiting rapid polarized growth. The growth of these cells can also be strongly

dependent on local turgor pressure gradients within the cell apical cytoplasm (Zonia and Munnik, 2009; Winship et al., 2010). This chapter is based on the work of Lipchinsky (2018) and deals with both above tasks.

3.2. Transport phenomena in pollen tubes

Pollen tubes are apparently the fastest growing cells in nature: they are able to extend at unprecedented speeds up to 50 p,m sec-1 (Stone et al., 2004). Pollen tubes also are in a league of their own in their cytoarchitectural polarization, intracellular transport dynamics and ability to drive through themselves high-intensity ion fluxes (Fig. 3.1). Pollen tubes are essential for plant sexual reproduction; their emerge from germinating pollen grains as pathfinding vectors committed to deliver male gametes carried inside the tubes to the plant ovule for fertilization. To accomplish their vital mission, pollen tubes grow directionally, exclusively at the cell apex, and within a few hours after germination they attain millimeters to centimeters in length, while remaining typically less than 15 p,m in diameter.

To accommodate rapid and localized cell extension, the pollen tube growth requires an active supply of proximate constituents and high-energy intermediates from mature cell regions to the ever-expanding apex. Consistently, the vigorous intracellular traffic appears to be the most visually spectacular aspect of pollen tube growth (Lovy-Wheeler et al., 2007; Chebli et al., 2013). This traffic is bidirectional: vesicles and organelles rapidly cover large distances, moving along the tube forth and back in laterally arrayed oppositely directed lanes. In angiosperm pollen tubes, this bidirectional traffic is fashioned in the reverse fountain pattern: the cargoes move towards the cell tip along the edge of the tube, but in the apical and subapical domains of the cell they undergo a reversal in direction and stream rearwards through the central core of the tube (Fig. 3.1).

The reverse fountain streaming is common for both larger organelles and smaller vesicles, but their turnaround points depend on the moving particle identity. While organelles (amyloplasts, vacuoles, endoplasmic reticulum, mitochondria, Golgi bodies) reverse their direction not reaching the very apex of the tube, vesicles do enter the most apical region of the tube (Lovy-Wheeler et al., 2007; Bove et al., 2008; Chebli et al., 2013). In this apical region, vesicles slow down and wobble for a while, unless they get into the retrograde loop of the reverse fountain circuit and flow backwards with larger organelles through the center of the tube.

Fig. 3.1. Electrochemical and hydrodynamic fluxes in angiosperm pollen tubes (Lipchinsky, 2018).

2+ + — Cations, Ca and H , enter the cell at the apex and exit in the tube shank. Anions, most notably Cl ,

move in the opposite direction, entering the subapical region of the tube and leaving the cell at the

tip. Electrons are abstracted from cytosolic NADPH and funneled through the apical membrane to