Математик Алан Тьюринг известен не только как взломщик знаменитого кода «энигма» во II мировую войну, но и как автор математических моделей эмбриональных процессов. В частности, т.н. модель реакции-диффузии вошла во все современные учебники эмбриологии. Эта модель хорошо описывает такие процессы, как пигментация кожи рыб или распределение волосяных фолликулов в эмбриогенезе. В замечательной статье в Science испанские исследователи применили модель реакции-диффузии к совсем другому эмбриональному процессу — формированию пальцев при развитии конечностей. Традиционно считалось, что разметкой конечности управляет в основном сигнальный каскад Shh (Sonic hedgehog). Однако со временем накопилось значительное количество фактов, свидетельствующих о том, что разметка пальцев контролируется не активностью Shh, а каким-то другим самоорганизующимся процессом.

Авторы рассматриваемой статьи обратили внимание на тот факт, что экспрессия в зачатках конечностей раннего скелетного маркера Sox9, в норме и при определенных экспериментальных воздействиях напоминает модель Тьюринга. Сам Sox9 является не только downstream-эффектором, но и активным участником сети Тьюринга — он влияет на активность сигнальных каскадов BMP, Wnt и FGF. При этом активность каскадов BMP и Wnt оказывается в пространственной противофазе с экспрессией Sox9. Исходя из экспериментальных данных, авторы разработали мат. модель, суть которой понятна из приводимого рисунка: BMP активирует экспрессию Sox9, Wnt ее подавляет, а сам Sox9 подавляет активность обоих каскадов, т.н. BSW, Bmp-Sox9-Wnt модель. Эта модель несколько сложнее, чем исходная модель реакции-диффузии (состоящая из двух компонентов - активатора и ингибитора). Модель BSW неплохо моделировала формирование полос Sox9 и Bmp/Wnt при искусственном культивировании клеточной массы, однако для большего приближения к реальному процессу эмбриогенеза авторам пришлось учесть модулирующее влияние гена Hoxd13 и каскада FGF. Итоговая компьютерная симуляция воспроизводила природный процесс с большой точностью. Кроме того, моделирование искусственных воздействий на систему было подтверждено экспериментально. Так, подавление Bmp приводило к исчезновению экспресии Sox9, подавление Wnt — к ее равномерному распределению, а подавление обоих каскадов — к увеличению «длины волны», т.е размеров пальцев, в точном соответствии с моделью.

Таким образом показано, что в разметке конечности участвуют два не зависимых друг от друга процесса (см. рис.). На более ранней стадии развития каскад Shh определяет передне-заднюю полярность конечности, а затем, в соответствии с вышеописанным механизмом, происходит разделение на отдельные пальцы. Zuniga and Zeller, к тому же, предполагают, что взаимодействие этих двух процессов (Shh регулирует экспрессию Hoxd13, а тот, вместе с FGF, влияет на BSW систему) привело к уменьшению числа пальцев в ходе эволюции тетрапод до 5.

Источники:
Сама статья в Science
Raspopovic et al. Modeling digits. Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients. Science. 2014 Aug 1;345(6196):566-70.

Science perspective
Zuniga and Zeller.In Turing's hands--the making of digits. Science. 2014 Aug 1;345(6196):516-7.

Картинка из Science perspective: Слева — ранний зачаток почки конечности; цветом показан градиент Shh, определяющий передне-заднюю ось формирующейся конечности. Внизу — трехузловая модель реакции-диффузии Тьюринга. Справа — пространственное распределение Bmp, Wnt и Sox9 в более позднем зачатке конечности. d1-d5 – пальцы с 1го по 5й, соответственно.
авторский текст

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Модель BSW неплохо моделировала формирование полос Sox9 и Bmp/Wnt при искусственном культивировании клеточной массы, однако для большего приближения к реальному процессу эмбриогенеза авторам пришлось учесть модулирующее влияние гена Hoxd13 и каскада FGF.
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