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Здравствуйте! Прошу помощи в следующем вопросе: Стенка нейрона состоит из эластичной двуслойной липидной мембраны, которая сопротивляется сжатию так же, как пружина. Она имеет эффективную жесткость k и равновесную толщину d0. Локально рассмотрим участок мембраны, имеющий незначительную кривизну, у которого площадь поверхности каждого из двух слоев равна S. В стенках клетки находятся специальные белковые ионные помпы, которые могут перемещать различные ионы через мембрану. В результирующем заряженном состоянии в межклеточной среде положительный и отрицательный ионный заряд равномерно распределяется вдоль внешней и внутренней поверхностей мембраны соответственно. После того как ионные насосы проделали некоторую работу, на внешней и внутренней поверхностях наводится заряд, поэтому толщина мембраны изменяется до некоторого нового значения. Предположим, что ионные помпы включаются, когда мембрана незаряжена, а мембрана заряжается достаточно медленно (квазистатически). Помпы прекращают работу в случае, если разность напряжений на мембране станет больше определенного порогового значения Vn. Насколько должна быть велика жесткость пружины k, чтобы ионные помпы отключились до того, как мембрана разрушится? Диэлектрическая проницаемость мембраны є.
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