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Most
of the MATLAB
computer codes were provided by Dr.
Carol Lucas in Biomedical
Engineering at the University
of North Carolina at Chapel Hill, and are available as
a single ZIP file, or by chapter.
The Goldbeter model codes in Chapter 9, however, were provided by
Maxime Dechesne at Montefiore Institute, University of Liège.
Chapter 1 - Dynamic Phenomena in Cell
| F1_10.m - Demonstrates different solutions of equation 1.13 as
demonstrated in Figure 1.10. The operator can pick parameters [tau
ninf noinitial
h time] or use defaults be just hitting return at prompt. In all
cases, plots are given for a simple euler simulation, the exact solution,
and a Matlab ODE call, provided through the subroutine “nofun”. |
| nofun.m -Called by F1_10. State Space function for Matlab ODE call:
ndot=(noinf-n)/tau; |
Chapter 2 - Voltage Gated Ionic Currents
| AppendixA_Dem.m - Demonstrates the idea of two equation linear
state-space equations of form: xdot=Ax+I. Systems with different
eigenvalues
are show and simulated. Phase plane with nullclines are plotted.
Needs “odenullcline” and “clode2” |
| odenullcline.m - The computing subroutine for AppendixA_Dem. Calls “clode2” for
Matlab ODE |
| clode2.m - Called by odenullcline to simulate system: |
| F2_6.m - Plots graphs shown in Figure 2.6. The operator can pick
parameters [Voa Soa Voi Soi phi].or use defaults by just hitting
return at prompt. |
| F2_7_VoltageClamp.m - Creates the voltage clamp studies shown in
Figure 2.7. Calls “vcfun” to do the simulation with Matlab
ODE. |
| vcfun.m - Called by F2_7 to simulate voltage clamp study. |
| GMorris_Lecar_Init.m - This model was run using globals for the
many parameters. The init file starts everything out with the values
shown
in Table 2.4, plus I=150, Vinit=-60 and Winit=.01. See problem 2.8.
The operator can change any variable in the command window. |
| GMorris_Lecar.m - This program can be used to generate pictures
as shown in Figure 2.9 A, B and C. Though designed for one set of
parameters,
by opting “not to erase”, the figures will be superimposed.
The program calls: “ Gmlfun” to simulate system, “GMorris_Lecar_Jac” to
plot the phase plane and nullclines, which will be shown in an individual
plot (Figure 3) with values for the intersections and eigenvalues,
and vector_field to draw little two second arrows at start of simulation. |
| GMorris_Lecar_Jac.m - Subroutine designed to plot nullclines of
system and find intersection points and eigenvalues. Solution is
done in
symbolic language – which can be slow. Calls “Intersect” to
find intersection points. |
| Intersect.m - Subroutine to find the intersection point of the
nullclines. . Solution is done in symbolic language – which at times has
difficulty with very complicated equations such as these tend to
be. Particularly has trouble between I=270 and 290 on this example. |
| GMorris_Lecar_Bif.m - Calculates bifurcation plot shown in Fig
2.9 D by brute force. Calls “Intersect” to get the steady
state solution if it were to exist. Calls “Gmlfun” to
find out what maximum and minimum values are. |
| Gmlfun.m - Called by programs listed above whenever the Matlab
ODE simulation is to be performed. |
| vector_field.m - plots initial 2 seconds for a simulation. |
| GMorris_Lecar_fW.m - Computes graph like that shown in Figure 2.10A.
The operator can enter a separate “fixed w value.” The
default is w=.35 as demonstrated in the figure. Other parameters
are set as above, e.g., set I=150 in the command window to get the
figure shown. Go back to GMorris_Lecar to get Figure 2.10B (by changing
phi from .04 to .004). |
| F2_9.m - Just a demo script to show how one might use the above
to get figures like 2.9 |
| F2_11.m - Just a demo script to show how one might use the above
to get figures like 2.11 |
| GHodgkin_Huxley_Init.m - Gets the parameters for the Hodgkin_Huxley
Model in the system |
| GHodgkin_Huxley.m - Runs the model based on the parameters in the
system. Operator has the option of erasing graphs or letting them
build up.
Calls “Ghhfun” to do simulation. |
| Ghhfun.m - Simulation program for Hodgkin_Huxley |
| F2_13.m - Just a demo script to show how one might use the above
to get figures like 2.13 |
| GFitz_Nag_Init.m - Gets starting parameters for the FitzHugh-Nagumo
model, starts with gamf=5, which is overdamped. Try gamf=2 for underdamped,
and gamf=1 for oscillatory. |
| GFitz_Nag.m - Runs the model based on global parameters in the
system. Operator has the option of erasing graphs or letting them
build up.
Calls “GFNfun” to do the simulation. Calls GFitz_Jac
to get nullclines and eigenvalues (which calls “Intersect” – though
not necessary since intersection is at origin with no applied current) |
| GFitz_Nag_Jac.m - Called by GFitz_Nag_Init to do phase plane and
nullcline stuff. |
| GFNfun.m - Simulation program for FitzHugh-Nagumo model |
Chapter 3 - Transporters and Pumps
| P3_9.m - Simulates the 4 state glucose model in Figure 3.1 for
the Eadie-Hofstee plots. Does it both with analytical solutions based
on linear system and with simulations. Calls “glucfun” to
do simulations |
| glucfun.m - Simulation program for exercise 3.9 or 4 state glucose
model |
| P3_10.m - Shows using analytic method the 11 directed diagrams
needed for this problem. |
Chapter 4 - Reduction of Scale
| F4_3.m - Demos the concepts in early part of chapter
based on L-type calcium channels. Calls LCfullfun to compute second
order
model as
well as the first order “fast” and “slow” modifications.
Calls Lctsfun to demonstrate time scaling, ie, 1 dimensionless unit
for 200 seconds of real time. A plot of calcium current is shown
to compare to figure 4.1. Values come from E 4_3. |
| LCfullfun.m - Matlab ODE simulation for 3 models (full, fast, slow)
for L-Type channels. |
| LCtsfun.m - Matlab ODE Simulation
for time scaled L-Type channels |
| F4_6.m - Demonstrates the concept of figure 4.6 using a range of
glucose values – goes through whole range of states. Each iteration
calls GlucInsModel_Init to initiate the variables and GlucInsModel
to run the model. |
| GlucInsModel_Init.m - Routine that initializes all the variables
for the glucose model in figure 4.5 |
| GlucInsModel.m - This is the model for F4.5. It calls three functions
and compares results: glucfun4 is full model, glucfun2 is reduced
two equation model, glucfunnorm is the normalized model. |
| glucfun4.m - Matlab ODE simulation of the full 4 equation model
of glucose-dependent insulin secretion |
| glucfun2.m - Matlab ODE simulation of the reduced 2 equation model
of glucose-dependent insulin secretion |
| glucfunnorm.m - Matlab ODE simulation of the normalized version
of glucfun2 |
| F4_11.m - Demonstration of figure 4.11 |
| P4_1.m - Problem 4.1. Shows analytic and simulated solutions. Calls
P4_1fun for ODE |
| P4_1fun.m - ODE for system in P 4_1 |
| P4_5.m - Simulation for Problem 4.5. Calls LcfullE5fun for ODE |
| LcfullE5fun.m - ODE function for P4_5 |
Chapter 5 - Whole Cell Models
| Fanal.m - Function called to pick out beats (frequency analysis)
from vector x. Uses simple zero crossing technique. Returned variables
are: beat = length of time for the beat, tb=time selected for start
of beat, xvalue at that time |
| F5_6A.m - Demonstrates Figure 5.6A for full model with jumps in
C. Call subroutine klfun. |
| klfun.m - Full Keizer-Levine Model. Called by F5_6A and F5_6A_Full_Reduced.
Allows a jump in Calcium. cfinal is the height of the step jump.
tjump is the time of the jump. |
| F5_6A_Full_Reduced.m - Comparison of full Keizer-Levine Model
and reduced model for Figure 5.6A. Calls klfun and klfunpo. |
| klfunpo.m - Reduced Keizer-Levine Model. Comparable to klfun with
jump capabilities. |
| F5_6B.m - Does the steady-state analysis of Keizer-Levine (reduced)
for a range of Ca valules. |
| F5_7A.m - Generates nullclines for three different values of
CT – as
shown in Figure 5.7A. Calls on klclosejac to produce graphs – one
at a time and then the composite. Calls klclose_anal to do simulations. |
| klclosejac.m - Subroutine to get nullclines (nullC, nullw), crossing
points(Cs,Ws) and eigenvalues (lams) of system and plots, based on
the a passed CT value. |
| klclose_anal.m - Subroutine called by F5_7A to demonstrate time
and phase plots (with nullclines from klclosejac) for a selected
set
of initial values of Ca, w, and CT. Calls klclosefun to do the simulation |
| klclosefun.m - ODE function for closed cell Keizer-Levine model |
| F5_7B.m - Generates Figure 5.7B |
| F5_8.m - Generates Figure 5.8 for open-cell Keizer-Levine model.
Calls ODE klopenfun_red |
| klopenfun_red.m - ODE for reduced open-cell Keizer-Levine. Enables
a jump in jin between starting and ending times. |
| F5_9.m - Generates Figure 5.9 by simulating the reduced open-cell
Keizer Levine model and superimposing the phase plot on the bifurcation
diagram (Figure 5.7B) of the closed-cell model. Calls klopenfun_red. |
| F5_12.m - Generates plots as seen in Figure 5.12. The process
starts by simulating the closed-cell gonadotroph model over a range
of [IP3]
values from .6 to 1.6, focusing with focus around the bifurcation
points. The program calls the ODE lrclosefun and a subroutine lrclose_intersect
to calculate the intersection of the nullclines. |
| lrclosefun.m - ODE for closed-cell gonadotroph model. Passes L,
Vserca and [IP3] |
| lrclose_intersect.m - calculated the intersection of the nullclines
for closed_cell gonadotroph model |
| F5_13.m - Generates Figure 5.3 by calling the ODE lrclosefun numerous
times. |
| F5_14.m - Generates figures applicable to Figures 5.14 and 5.15.
Calls ODE lropenfun |
| lropenfun.m - ODE for open-cell gonadotroph model as shown in
Figure 5.14, i.e., Jin is 1200 for first 40 seconds then goes to
0. |
| F5_16.m - Demonstrates Figure 5.16 – full gonadotroph model:
Morris-Lecar + Li-Rinzel model, calls ODE lrpmlfun |
| lrpmlfun.m - ODE for F5_16 |
| F5_19.m - Demonstration for Figure 5.19 and part of 5.20. Chay-Keizer
model. ODE is mlbetafun |
| mlbetafun.m - ODE for F5_19. |
Chapter 6 - Intercellular Communication
| F6_2_3.m - Morris-Lecar neurons
interacting. Figures 2 and 3 for gap junctions (calls ode ‘mlgapfun’).
Also calls ‘fanal’ to get beat durations. |
| mlgapfun.m - Morris-Lecar model
of two cells interacting between gap junctions. Gap strength – gc – is
a passed variable. |
| F6_6_7.m - Morris-Lecar neurons
interacting. Figures 6 and 7 for synaptic transmission (calls ode ‘mlsynfun’).
Also calls ‘fanal’ to get beat durations. |
| mlsynfun.m - Morris-Lecar model
of two cells interacting through synaptic transmission. Rate constants
and when they go into effect (switch) are passed parameters. |
| F6_9.m - Coincidence detection
for excitatory inputs at different offset times. Calls ode ‘mlcdfun’ with
time delays between -40 and +40 milliseconds. |
| mlcdfun.m - Morris-Lecar model
for two excitatory receptors acting at time offsets passed to the
routine. |
| F6_10.m - Demonstration program
for Figure 6.10. Voltages are shown for both neurons 1 and 2 (target
neuron) over delalys between -40 and +40 milliseconds. Calls the
ODE mlds2cellfun |
| mlds2cellfun.m - ODE for
network shown in Figiure 6.8C |
| F6_11.m - Figure 6_11, Steady
State determination for populations at different a weights. |
| F6_12_13.m - Large scale population
simulations from Figures 12 and 13. Calls ‘netcall’ which
calls ‘netfun’ for ode and adds nullclines and phase
plane plots. |
| netcall.m - Calls ‘netfun’ for
ode simulation, passing different inputs to the excitatory population. |
| netfun.m - ODE for Large population
model, input to excitatory model is a passed variable. |
| P6_1Call.m - Calls subroutines
for Problem 6_1. Calls P6_1 for control and P6_1fun for ODE. |
| P6_1.m - General Call for parameters
for Problem 6_1. Calls ODE P6_1fun. |
| P6_1fun.m - ODE for Problem
6_1. |
| P6_2Call.m - Calls subroutines
for Problem 6_2. Calls P6_2 for control and P6_2fun for ODE. |
| P6_2.m - General Call for parameters
for Problem 6_2. Calls ODE P6_2fun. |
| P6_2fun.m - ODE for Problem
6_2. |
| P6_3Call.m - Calls subroutines
for Problem 6_3. Calls P6_3 for control and P6_3fun for ODE. |
| P6_3Call.m - General Call for
parameters for Problem 6_3. Calls ODE P6_3fun. |
| P6_3fun.m - ODE for Problem
6_3. |
Chapter 9 - Biochemical Oscillations
Goldbeter5_fct.m - The five-variable
Goldbeter circadian rhythm oscillator.
Goldbeter5.m - Script for running Goldbeter5_fct.
Contributed by Maxime Dechesne at Montefiore
Institute,
University of Liège.
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Goldbeter5_sim.m - Simulink version of the five-variable Goldbeter
circadian rhythm oscillator. This version includes a delay in the
feedback loop, that allows to have the bifurcation for a lower value
of the parameter Vs (this idea comes from a paper of D. Angeli and
E. Sontag). Under that value of the parameter, no delay can cause
oscillations in the system.
Goldbeter5_simscript.m - Script for running Goldbeter5_sim.
Contributed by Maxime Dechesne at Montefiore Institute, University of Liège.
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