Математическое и компьютерное моделирование биологических систем на разных иерархических уровнях организации

Современная биология все в большей степени опирается на математическое и компьютерное моделирование для описания сложных иерархически организованных биосистем. В данном обзоре рассматриваются математические модели, охватывающие основные уровни биологической организации – от молекулярногенетического и клеточного до тканевого/органного, организменного, популяционного и экологического. Цель работы состоит в систематизации ключевых подходов к моделированию на каждом из этих уровней, анализе их возможностей и ограничений, а также в обсуждении стратегий построения многомасштабных и гибридных моделей, связывающих воедино процессы разных пространственно-временных масштабов. Рассматриваются классические детерминированные и стохастические модели на основе дифференциальных уравнений в частных производных, логические и графовые модели регуляторных сетей, клеточные автоматы, агентно-ориентированные и индивидуально-ориентированные модели и подходы, базирующиеся на балансе потоков. Приводятся типичные примеры моделирования молекулярно-генетических сетей, метаболизма и хемотаксиса, роста тканей и органов, динамики популяций и генетической структуры, а также функционирования экосистем. Особое внимание уделяется сопоставлению подходов по критериям масштабов описания, сложности моделируемых процессов, доступности исходных данных, вычислительной трудоемкости и интерпретируемости результатов. Обзор обобщает отечественный и зарубежный опыт, подчеркивая вклад российских и, в частности, новосибирских коллективов в развитие гибридных методов моделирования, построения многомасштабных моделей и реализации программных платформ для системной биологии. В результате проведенного анализа показано, что гибридные и многомасштабные модели позволяют наиболее полно учесть нелинейность, стохастичность и структурную неоднородность биологических систем, но требуют значительных вычислительных ресурсов и тщательной калибровки по данным. Отмечаются методические и программно-технологические тенденции, включая развитие специализированных платформ и репозиториев моделей, средств стандартизации описания и повторного использования модельных компонентов.

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