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Hello everyone,

I'll attach my script here, in case you want to run the simulation yourself.

My task is to find two values x and y so that if I multiply them by G_max_chl2 and G_max_glu2 (two scalar values that I pre-defined in previous parts of the code) respectively, this:

CPSC_2 = ((G_max_chl2 * x) .* (1 - exp(-t / tau_rise_In2)) .* (exp(-t / tau_decay_In2)) * (Vm - EChl2)) + ((G_max_glu2 * y) .* (1 - exp(-t / tau_rise_Ex2)) .* exp(-t / tau_decay_Ex2) * (Vm - EGlu2))

becomes the same as this:

CPSC_1 = ((G_max_chl) .* (1 - exp(-t / tau_rise_In)) .* (exp(-t / tau_decay_In)) * (Vm - EChl)) + (G_max_glu .* (1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex) * (Vm - EGlu))

1 All the variables above are the same for the two equations, except for the four "G_max" values. The only two variables that change are G_max_chl2 and G_max_glu2, so that they become the same as G_max_chl and G_max_glu.

2 Some of these variables are matrices, but in this case they are not involved and should remain the same (only the two scalars G_max_chl2 and G_max_glu2 should change)

I solved the task setting up a nonlinear equation:

% This is the difference that has to be minimized

Diff_CPSC = abs((((G_max_chl2) .* ((1 - exp(-t / tau_rise_In2)) .* ...

(exp(-t / tau_decay_In2))) * (Vm - EChl2)) + ((G_max_glu2) .* ...

((1 - exp(-t / tau_rise_Ex2)) .* exp(-t / tau_decay_Ex2)) * (Vm - EGlu2))) - (((G_max_chl) .* ...

((1 - exp(-t / tau_rise_In)) .* exp(-t / tau_decay_In)) * ...

(Vm - EChl)) + ((G_max_glu) .* ((1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex)) * (Vm - EGlu))));

% EQUATION

% Create a nonlinear equation

x = optimvar('x',1);

y = optimvar('y',1);

% Define function to minimize

eq1 = (((G_max_chl2 * x) .* ((1 - exp(-t / tau_rise_In2)) .* ...

(exp(-t / tau_decay_In2))) * (Vm - EChl2)) + ((G_max_glu2 * y) .* ...

((1 - exp(-t / tau_rise_Ex2)) .* exp(-t / tau_decay_Ex2))* ...

(Vm - EGlu2))) == ((G_max_chl) .* ((1 - exp(-t / tau_rise_In)) .* ...

exp(-t / tau_decay_In)) * (Vm - EChl)) + ((G_max_glu) .* ...

((1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex)) * (Vm - EGlu));

% Create an equation problem, and place the equation in the problem

prob = eqnproblem;

prob.Equations.eq1 = eq1;

% Show the problem

show(prob);

% Specify the initial point as a structure

x0.x = G_max_chl / G_max_chl2;

x0.y = G_max_glu / G_max_glu2;

[sol,fval,exitflag] = solve(prob,x0);

% View the solution point and convert to double

disp(sol.x);

disp(sol.y);

x = sol.x;

y = sol.y;

However, I find this procedure a bit laborious because, if I wanted to optimize other variables, I'd have to hard code the unknown variables everytime. My question is:

- This procedure forces me to know all of the values of CPSC_2, which in this case is true because I generated the simulation. However, if it were coming from experimental recordings, it wouldn't be the case anymore. Is there a way to fit a CPSC_2 (whose variables are unknown) to CPSC_1 (whose variables are known)?

Matt J
on 16 Feb 2021

Edited: Matt J
on 16 Feb 2021

Your problem appears to be a linear fit. I see no non-linear dependence on x or y. You should therefore use lsqlin, if you also have bounds or linear constraints.

Otherwise, you could just use mldivide() or linsolve().

Matt J
on 19 Feb 2021

You could use fmincon if you want more control over the cost function,

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