580.439/639 Homework #2 Solutions
Problem 1
Part a) Using the principle of conservation of mass, the time rate of change of
concentration in the ith well is given by the difference between the flux into the well and the flux
out of the well. Let Ci be the
580.439/639 Solutions to Homework #1
Problem 1
Part a) At equilibrium, the electrochemical potentials of molecules in the A and B states
will be equal, so
A = B
al
al
or
0A + RT lnCA + FVA = 0B + RT lnCB + FVB
al
al
al
al
Note that zal = +1 and that it ha
580.439/639 Final Exam Solutions, 2011
Problem 1
Part a) In steady state, the net flux of sodium will be zero so that 3a = p. Here a and p have
units of moles/(s cell), so that a is the rate of consumption of ATP, but any reasonable flux measure
would be
580.439/639, Solutions to Final Exam 2010
Problem 1
The figure at right shows definitions of the rate
constants for use in this problem.
Part a) Steady state means the fraction of
channel in each state is fixed in time. As argued in
class, that means the
580.439/639 Final Solutions, 2009
Problem 1
Part a) The operating principle is that the Nernst equation holds simultaneously for all
permeant ions:
V = EA =
RT Aout
RT Bout
RT N out
ln
= EB =
ln
= ! EN =
ln
zA F Ain
zB F Bin
zN F N in
meaning that concent
580.439/639 Final Exam 2008, Solutions
Problem 1
Part a) Ionotropic receptors contain a channel that is directly gated open by activating the
receptor. Metabotropic receptors are coupled to a second-messenger system, like a G-protein, that
indirectly affe
580.439/639 Final Exam Solutions, 2007
Problem 1
Part a) Larger conductance in the postsynaptic receptor array; action potentials
(usually Ca+) propagating in the forward direction in the dendrites; amplification by
subthreshold conductances (Na+ or Ca+).
580.439/639 Final Exam, 2011
3 hours, closed book except 2 sheets of paper
Do all problems.
Problem 1
Short answer questions:
Part a) Consider the cell drawn at right,
which is a component of a transport epithelium in
the inner ear. In the right-hand memb
580.439/639 Midterm Exam Solutions, 2012
Problem 1
Part a) i) The w = 0 nullcline is just w(V),
so it will shift to the right by V0. The V = 0 nullcline
is unaffected by the w function and is not changed.
Thus the nullclines will look like the gray lines
580.439/639 Midterm Solutions, 2011
Problem 1
Part a) The flux equations assuming that all fluxes are equal. Note that the unknowns in this
system are J, X1, SX1, SX2, and X2, so five equations are needed.
J = k1S1 X1 k1 SX1
J=
k2 SX1 k2 SX 2
J=
k3 SX 2 k
580.439/639 Midterm Solutions, 2010
Problem 1
The data in the figure are from AL Hodgkin and RD Keynes, J. Physiol. 128:61-88 (1955). A
nice discussion of these data with an early interpretation of the result is in B Hille and W Schwarz, J.
Gen. Physiol.
580.439/639 Midterm Solutions, 2009
Problem 1
Part a) The change in free energy when the transporter goes forward by 1 mole (KCl out) is
as follows:
! = outK " inK + outCl " inCl
= RT ln K out + FVout " RT ln K in " FVin + RT ln Clout " FVout " RT ln Clin
Solutions for 580.439/639 Midterm Exam 2008
Problem 1
Part a)
1) Only the NaK ATPase is voltage sensitive, the others are neutral.
2) Only the ATPase depends on ATP in the short run. If ATP is removed, the
concentrations in the cells will begin to decline
580.439/639 Midterm solutions
Problem 1
Part a) No net transport of ions implies that
a
p
IK + IK = 0
a
p
I Na + I Na = 0
p
I Cl = 0 ,
where a means active transport and p is passive transport. There is no active transport of
chloride, so passive transpor
580.439/639 Midterm Exam, 2012
1.25 hour, closed book except for 1-page cheat sheet, do all problems.
Problem 1 (short answers)
Part a) Consider the MLE model as discussed
in class. For one parameter set, the model has nullclines
like those drawn at right
580.439/639 Midterm 2011
1 hour, closed book except for one sheet of paper. Do all problems, 12 points/problem plus 4 points
for your name.
Problem 1
The figure below shows a transporter model similar to the lactose transporter discussed in
class. Transpo
580.439/639 Midterm Exam, 2010
Do all problems. Closed book except for one page.
Problem 1
Part a) What does independence mean in ion flux models?
Part b) The Ussing flux ratio is a condition for independence of ion fluxes. It is usually
written as follow
-1-
580.439/639 Midterm Exam, 2009
One hour, closed book except for one sheet of paper, do all problems.
Problem 1
This problem is about steady-state conditions
for membranes. Consider the cell sketched at right.
This cell contains a KCl transporter which
580.439/639 Midterm Exam, 10/27/08
1 hour, closed book except for one sheet of paper. Answer all questions.
10 points per part plus 10 points for writing your name on the answer sheet.
Problem 1
Short answers:
Part a) It is not clear which active transpor
580.439/639 Solutions to Homework #5
Problem 1
Part a) The isoclines for this system are the equations:
dx
=0
dt
y = x 3 + 3x
dy
=0
dt
y = 3x + 4.5
The isoclines are plotted below (lines marked d()/dt=0).
The arrows show the directions of flow in the phas
580.439/639 Solutions to Homework #4
Problem 1
Part a) During the steady portions of a voltage clamp beginning at time 0, the HH
parameter h satisfies the following equations:
dh
H (V2 )
= h (V2 ) h
a nd
h(0) = h (V1 )
dt
where V1 is the potential to whi
580.439/639 Homework #3 Solutions
Problem 1
Part a) If the membrane is depolarized, the number of open gates increases in the HH
K+ channel; in the model, this means that the gating charges move to the outer membrane
surface. With this definition of gatin