Get Equations of Membrane Biophysics PDF

By N. Lakshminarayanaiah

ISBN-10: 0124342604

ISBN-13: 9780124342606

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The diffusion flux of species i is caused by the chemical potential gradient (dnJdx) (see Fig. 12). distance x Fig. 1 2 . Schematic illustration of the distance variation of concentration of a species and relative directions of the diffusion flux, etc. III. Physical and Electrochemical Principles 39 In the steady state, both the driving force and the flux J reach values that remain constant with time. The relation between the two can be expressed by a power series r r J = A + Bffi d + C& l + - - .

A) a n d (b) are complex networks of resistors a n d sources of emf. 2. Basic Principles 36 N. Kirchhoff's Laws A branch point in a network is a point where three or more conductors are joined. In Fig. 10a, a,/, c, and e are branch points, but b and d are not. In Fig. 10b, there are only two points a and b. A loop or mesh is any closed conducting path. Possible loops in Fig. 10a are abcfa, fcdef, hafegh, and hafcdegh. L A W 1: The algebraic sum of all currents meeting at a junction is zero. L A W 2: The algebraic sum of the Ri terms around any closed path is equal to the algebraic sum of the applied emfs in the given path.

Thus the net flux across the transit plane is given by 1 2 2 (138) J = 2(CL-CRKx y /t. transit plane unit area unit area y Fig. 14. Schematic diagram for the derivation of E i n s t e i n - S m o l u c h o w s k i equation showing the transit plane in between two imaginary c o m p a r t m e n t s . 2. Basic Principles 42 2 But the concentration gradient is ( C R - C L) / < x > rewritten 1 / 2 . Thus Eq. (138) may be (139) Equating Eqs. (139) and (129) gives 2 (140) D = (x >/2t. Equation (140) is the Einstein-Smoluchowski equation.

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Equations of Membrane Biophysics by N. Lakshminarayanaiah


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