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CaMKII_plast.f95
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CaMKII_plast.f95
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! -*- f95 -*-
! (c) 2016 - Ilya Prokin - [email protected] - https://sites.google.com/site/ilyaprokin
! INRIA Rhone-Alpes
! STDP model : An implementation of bistable CaMKII model of Graupner, Michael, and Nicolas Brunel. “STDP in a Bistable Synapse Model Based on CaMKII and
! Associated Signaling Pathways.” Edited by Karl J Friston. PLoS Computational Biology 3, no. 11 (November 2007): e221–e221.
! doi:10.1371/journal.pcbi.0030221.
module CaMKII_plast
use pars_mod
implicit none
contains
real*8 function CaM_conc(Ca_cyt, pars)
implicit none
real*8 :: Ca_cyt
type(pars_type) :: pars
type(post_CaMKII_plast_type) :: p
p = pars%post_CaMKII_plast
CaM_conc = p%CaMT/(1 + p%Ka4/Ca_cyt + p%Ka3*p%Ka4/(Ca_cyt**2) + p%Ka2*p%Ka3*p%Ka4/(Ca_cyt**3) + p%Ka1*p%Ka2*p%Ka3*p%Ka4/(Ca_cyt**4))
end function CaM_conc
subroutine dy_CaMKII(y, PP1, CaM, pars, dy, phossum)
implicit none
real*8, intent(in) :: y(13), PP1, CaM
type(pars_type), intent(in) :: pars
real*8, intent(out) :: phossum
real*8, intent(out) :: dy(13)
type(post_CaMKII_plast_type) :: p
real*8 :: B0, sum_y23, sum_y24, sum_y57, sum_y58, sum_y911, rr
real*8 :: k10, gamma, gamma2, k6gamma2, k7gamma
dy = 0.0
p = pars%post_CaMKII_plast
rr=sum(y)
! B0 is whats left from total
B0=2*p%CaMKT-rr
! kinetic equations
sum_y23=sum(y(2:3))
sum_y24=sum_y23+y(4)
sum_y57=sum(y(5:7))
sum_y58=sum_y57+y(8)
sum_y911=sum(y(9:11))
phossum=y(1) + 2*sum_y24 + 3*sum_y58 + 4*sum_y911 + 5*y(12) + 6*y(13)
k10=p%k12*PP1/(p%KM + phossum)
gamma=CaM/(p%K5+CaM)
!dBi/dt
gamma2=gamma*gamma
k6gamma2=p%k6*gamma2
k7gamma=p%k7*gamma
dy(1) = 6*k6gamma2*B0 - (4*k6gamma2 + k7gamma + k10)*y(1) + 2*k10*sum_y24
dy(2) = (k7gamma + k6gamma2)*y(1) - (3*k6gamma2 + k7gamma + 2*k10)*y(2) + k10*(y(5) + sum_y57)
dy(3) = 2*k6gamma2*y(1) - 2*(k7gamma + k6gamma2 + k10)*y(3) + k10*(sum_y57 + 3*y(8))
dy(4) = k6gamma2*y(1) - 2*(k7gamma + k6gamma2 + k10)*y(4) + k10*(y(6) + y(7))
dy(5) = k7gamma*(sum_y23 - y(5)) + k6gamma2*(y(2) - 2*y(5)) + k10*(2*y(9) + y(10) - 3*y(5))
dy(6) = k6gamma2*(sum_y23 - y(6)) + k7gamma*(2*y(4) - 2*y(6)) +k10*(-3*y(6) + sum_y911 + y(11))
dy(7) = k6gamma2*(y(2) + 2*y(4) - y(7)) + k7gamma*(y(3) - 2*y(7)) +k10*(-3*y(7) + y(9) + y(10) + 2*y(11))
dy(8) = k6gamma2*y(3) - 3*k7gamma*y(8) + k10*(y(10)- 3*y(8))
dy(9) = k7gamma*(sum_y57 - y(9)) + k6gamma2*(y(5) - y(9)) +k10*(-4*y(9) + 2*y(12))
dy(10)= k6gamma2*y(5) + k6gamma2*y(6) + k7gamma*(y(7) + 3*y(8) - 2*y(10)) + k10*(2*y(12)- 4*y(10))
dy(11)= k7gamma*(y(6)- 2*y(11)) + k6gamma2*y(7) + k10*(y(12)- 4*y(11))
dy(12)= k6gamma2*y(9) +k7gamma*(2*sum_y911-y(9) - y(12)) + k10*(6*y(13)- 5*y(12))
dy(13)= k7gamma*y(12) - 6*k10*y(13)
end subroutine dy_CaMKII
pure real*8 function CaMKIIpho_func(y)
implicit none
real*8, intent(in) :: y(13)
real*8 :: sum_y24, sum_y58, sum_y911
sum_y24=sum(y(2:4))
sum_y58=sum(y(5:8))
sum_y911=sum(y(9:11))
CaMKIIpho_func = y(1) + 2*sum_y24 + 3*sum_y58 + 4*sum_y911 + 5*y(12) + 6*y(13)
end function CaMKIIpho_func
subroutine d_PP1_I1P(PP1, I1P, CaM, pars, dPP1, dI1P)
implicit none
real*8, intent(in) :: PP1, I1P, CaM
type(pars_type), intent(in) :: pars
real*8, intent(out) :: dPP1, dI1P
type(post_CaMKII_plast_type) :: p
real*8 :: vPKA, vCaN, k11, km11
p = pars%post_CaMKII_plast
vPKA = p%kpka0I1 + p%kpkaI1/(1 + (p%KdpkaI1/CaM)**p%npkaI1)
vCaN = p%kcan0I1 + p%kcanI1/(1 + (p%KdcanI1/CaM)**p%ncanI1)
k11=p%k11
km11=p%km11
dPP1= -k11*I1P*PP1 + km11*(p%PP10 - PP1) !RHS PP1
dI1P= dPP1 + vPKA*p%I10 - vCaN*I1P !RHS I1P
end subroutine d_PP1_I1P
end module CaMKII_plast