First results for the dynamics of C elegans

Eigenvectors and eigenvalues MUST be complex. Still, real solution for the voltage is possible (each eigenvector/value has another one which is complex conjugate. If the modulus of the coefficient of both is the same, the final linear combination is real).

With no membrane conductance:

>> M=conectividad2matrizsistema(todas.A_chem’,todas.A_ej,todas.GABA,1,1,0);
>> V0=zeros(279,1);
>> solucion=matrizsistema2solucion(M,V0);
>> plot(solucion.autovalores,’.’)

This figure matches with Figure 8 of Mitya’s paper (y axis is imaginary part)

We see that there are positive eigenvalues. This has two consequences:
– Diverging voltage.
– Apparently some computations are not performed correctly. I get non-negligible imaginary parts in the voltages.

I see that I need about 30 in the membrane conductance to get all eigenvalues negative:

>> M=conectividad2matrizsistema(todas.A_chem’,todas.A_ej,todas.GABA,1,1,30);
>> solucion=matrizsistema2solucion(M,V0);
>> plot(solucion.autovalores,’.’)

 

FIRST EXAMPLE: Excitation of neuron 1.

>> V0=zeros(279,1);
>> V0(1)=1;
>> solucion=matrizsistema2solucion(M,V0);
>> V=solucion2voltajes(solucion,0:.001:.5);
>> plot(V(1,:))

>> plot(V(2,:))

And so on…

SECOND EXAMPLE: Random excitation

>> V0=rand(279,1);
>> solucion=matrizsistema2solucion(M,V0);
>> V=solucion2voltajes(solucion,0:.001:.5);
>> imagesc(V)

What are those ‘rough’ zones?

>> plot(V(149,:))

What the…?

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