Текст книги "Логика случая. О природе и происхождении биологической эволюции"

Вероятность случайного возникновения различных революционных систем в Н-области: грубая прикидка верхних пределов

Общие предположения: в Н-области содержится 10²² звезд, у каждой десятой есть пригодная для жизни планета; то есть имеется 10²¹ таких планет (несомненно, это сильное преувеличение; в действительности большинство звезд не имеет планет вовсе, не говоря о пригодных для жизни). Каждая планета размером с Землю, у каждой имеется пригодный для обитания слой толщиною 10 км (10⁶ см); отсюда объем этого слоя 4/3π[R³-(R-l)³] ≈ 5 × 10²⁴ см³, где R – радиус планеты, l – толщина обитаемого слоя. Синтез РНК происходит в 1 % объема обитаемого слоя – то есть в объеме 5 × 10²² см³ (опять сильное преувеличение – в действительности «фабрик РНК» будет очень мало). Положим концентрацию нуклеотидов в объеме V и скорость синтеза молекул РНК размера n (свободный параметр, зависящий от специфики модели революционной стадии, далее n-мер) за 1 молекулу/см³/сек (и снова сильное преувеличение для любой молекулы сколько-нибудь значительного размера; более того, не учтена обратная зависимость от n, которая должна быть достаточно сильной). Время после Большого взрыва в данной Н-области (как верхний предел) для всех планет 10¹⁰ лет ≈ 3 × 10¹⁷ секунд. Тогда количество уникальных n-меров, опробованных за время после Большого взрыва, будет:

S ≈ 5 × 10²² × 10²¹ × 3 × 10¹⁷ ≈ 1,5 × 10⁶¹

Предположим, что для начала биологической эволюции требуется уникальный n-мер. Количество возможных последовательностей, состоящих из n нуклеотидов, N = 4ⁿ ≈ 10^0,6n.

Можно ожидать, что уникальный n-мер возникнет в Н-области E раз:

E = S/N = 1,5 × 10⁶¹/10^0,6n

и

n = log (E × 1,5 × 10⁶¹)/0,6

Подставив E = 1, получаем n ≈ 102 (нуклеотида). Заметим, что, так как величина n прямо пропорциональна логарифму S, оценка будет мало зависеть от начальных предположений о величине переменных; например, изменение S на порядок величины приведет к увеличению или уменьшению n менее чем на 2 нуклеотида.

Можно представить себе рибозим-репликазу, состоящую из приблизительно ста нуклеотидов; таким образом, в принципе спонтанное появление таковой в конечной вселенной, состоящей из единственной Н-области, нельзя исключать в нашей «игрушечной» модели (и снова, скорость синтеза РНК, принятая здесь, намеренно сильно переоценена).

Для появления примитивной системы сопряженной репликации-трансляции, что в данном контексте рассматривается как революционная стадия, требования гораздо жестче. Как минимум, необходимо спонтанное появление следующего:

• Две рРНК, с общим размером не менее 1000 нуклеотидов.

• Примерно 10 примитивных адаптеров по 30 нуклеотидов каждый, в целом около 300 нуклеотидов.

• По меньшей мере одна РНК, кодирующая репликазу, размером примерно 500 нуклеотидов (оценка снизу). В принятой модели, n = 1800, и в результате E < 10^–1018.

Другими словами, даже в нашей игрушечной модели, которая предполагает сильно преувеличенную скорость синтеза РНК, вероятность случайного зарождения системы трансляция – репликация в единственной Н-области будет P < 10^–1018. Очевидно, эта версия революционной стадии может рассматриваться только в контексте вселенной с бесконечным (или, по меньшей мере, очень большим) количеством Н-областей.

Модель, рассмотренная здесь, ни в коем случае не предполагалась реалистичной. Она только иллюстрирует разницу в требованиях, накладываемых на вероятность возникновения разных версий революционных систем, и следовательно, связь этой версии с разными космологическими моделями вселенной.

Таблица II-1. Новые определения и новые интерпретации известных определений в модели МММ.

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