429-2009-HW10key

# 429-2009-HW10key - HW10 by An-Chi Wei 1(Q8.6 M 2M M M = D 2...

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HW10 by An-Chi Wei Dec 07, 2009 2 2 0 2 2 1. (Q8.6) , boundary condition: at x=0, J=D constant , assume M(x= )=0 (assume zero boundary conditions far into the field, as in p.161) at steady state, x MM M M J DM tx x x D Also D tt α = ∂∂ =− = ⇒= / / 2 / 22 2 // / 2 2 / 00 / 0 Let trial function be M(x)= Ae M(x) = e M(x) = e eA e( ) e 0 plug in B.C., at x=0, e M(x)= Ae x x x xx x x x M A x A x MA D D A t DD MJ A A J A xD D λ λλ αα −− == = ∂− −= = = ⇒=⇒ = = = / 0 J e e ( assume J<0) D Compared to B.C. as M(x=0)=M (the solution is M(x)= e ), they have similar shape, only here M(x) depends on J, and D. D o J D M λα

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2.(Q9.2) assume v<<all other rate constants (a) Detailed balance: the flux of each reaction is exactly equal to the flux of the reverse reaction, and zero net flux along any cycle ' '* ' ' * '' ' [ ][ ] [ ]...(1) [ ] [ ]...(2) [ ] [ ][ ]. ...(3) multiply all these three equations, (1) (2) (3): [] [ ] [ ] [ ] ..... (4) similarly for d cc c c c c kcC kc C mcC mcC lcC lcC km lcCc CcC km CcC kml = = = ×× = = ' ' * ' , [ ] [ ] [ ] [ ] dd d d d d ldCd CdC km CdC = = ' ' Or if you assign and the other way, you will get . c c c c c c ll k m l k m l =
* correct (2) correct ' (1) correct '' ' (4) * correct c ' wrong ' () [] [ ] [ ][ ] (let K = = dissociation constant for c C) ,[ from c c from cc from c d d b Rv c C m c C m mk c C ll vc C c C lK l l similarly R v d l = ⎯⎯⎯→ = ⎯⎯⎯→ = ⎯⎯⎯→ = = = ' * d ' wrong c ' correct d ** ][ ] (let K = = dissociation constant for d C) K (assume tRNA concentrations are about the same, [c] [d]) [ ] K If the on-rates for both d and c are d dd dc l vd C C Kl R ll dC F Rl l c C = == ' wrong 00 ' correct

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429-2009-HW10key - HW10 by An-Chi Wei 1(Q8.6 M 2M M M = D 2...

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