2014 exam Flashcards
Assume we have a system according to the following: A -> B + C C -> 2D + E E + B -> F F + 2D -> A
a) Write the stochiometric matrix.
b) Write the flux equation (rate eq.) for A B + 2C
c) For the equation above in b), give the equilibrium constant.
a) The system can be described as dS/dt = M*J, where
S=(A B C D E F)’ and J=(j1 j2 j3 j4)’ and
M=-1 0 0 1 1 0 -1 0 1 -1 0 0 0 2 0 -2 0 1 -1 0 0 0 1 -1
b)
j=(dA/dt = -dB/dt = -dC/2dt) = k1A-k2B*C^2
c)
j=0 gives K = k1/k2 = b*c^2 / a
Which of the gene model types Stochastic, Continious or Boolean, is most general (makes the
least number of assumptions)? Motivate your answer.
The stochastic is most general, it only assumes a well mixed solution.
(at least locally well mixed, that is the probability of finding a molecule is the same anywhere, that is the frequency/rate of molecular collissions is much larger than the rate of the reactions)
Which of the gene model types Stochastic, Continious or Boolean, is computationally least
expensive? Motivate your answer.
The binary model. From the truth table, new states are given from present states.
The intra and extra cellular concentrations of K+, Na+, Cl- and the anion A- of a neuron is given
by the following table:
I on species Inside (mM) Outside (mM)
Na+ 10 100
K+ 200 100
Cl- 100 200
A- 110 0
The plasma membrane is permeable for K+ och Cl- but not for Na+ och A-. The cell is in
electrochemical equilibrium, and space charge neutrality holds. Show this.
b) For the Giant squid axon, the intracellular concentration of chloride is 40 mM and the
extracellular concentration is 560 mM. The resting membrane potential is -60 mV. What is the
reversal potential for chloride at room temperature (20 degrees Centigrade) if chloride is the
only permeable ion? Is chloride a depolarizing or hyperpolarizing factor?
Donnan equilibrium holds:
[K_out/K_in]^1 = [Cl_out/Cl_in]^-1 e.g. 100/200 = 100/200
Charges inside: 10+200-100-110 = 0
Charges outside: 100+100-200-0 = 0
b)
Vm=-58 log (560 / 40) = -66.48 mV
-66 is more negative than -60, so chloride is hyperpolarizing.
a) Describe shortly the Hodgkin and Huxley model of an ion channel. (2p)
b) With the formalism of above, describe the current through a sodium channel. Write out what
the symbols stand for. (1p)
c) The action potential is essentially an All-or-none phenomena (there is a ”threshold” for
initiation of the action potential). Explain briefly why this is so, i.e. how is the action potential
initiated?
alpha
a) closed open
beta
The model consists of gates, each of which can be open or closed. For the channel to be open, all gates must be open.
open m, closed 1-m
rate constant alpha opens ->, beta closes
Potential spread along a cable depends on a number of factors/parameters that enter the cable
equation/wave equation. Give two of these, including the symbol, name, and how it affects the
potential spread in space and/or time.
space constant lambda, lambda=sqrt(r_m/r_i)=sqrt[(aR_m)/(2R_i)], longer space constant means longerspread of a potential
membrane time constant tau, tau=Rm*Cm, longer time constant produces longer integration and thus more averaging over time
frequency f, higher frequency gives larger attenuation/smaller space constant
Discuss modeling of diffusion of calcium either from a spatial point of view, or from a
biochemical reaction perspective. Do not pick an example describing the electrical aspects of
this.
Diffusion of calcium in concentrical (spherical or cylindrdical) shells. The problem thus becomes a 1D-diffusion problem. Each shell is a iso-concentration compartment. Shells exchange calcium. The amount of Ca-flux depends on the diffusion constant and the difference in concentration between the shells. The outermost shell acts like a source (Ca-channels) and a sink (Ca-pumps).
Alternative, for a calcium buffer,
J
-> Ca + B CaB
Ca calcium, B buffer, CaB calcium bound to buffer
d[Ca]/dt = k1[Ca][B] + k1[CaB] + J
total concentration [Bt] = [B] + [CaB]
diffusion constant Db
steady-state K_D = [Ca][B] / [CaB] = k2/k1
dissociation constant kappa = d[CaB]/d[Ca]=K_D*[Bt] / (K_D+[Ca])^2 = [Bt]/K_D
buffering factor beta = d[Ca]/d[Ca]tot = 1 / 1 + kappa
