Synapse Model
using PiecewiseDeterministicMarkovProcesses, JumpProcesses, OrdinaryDiffEq
using Catalyst, Parameters, LazySets, StaticArrays, Distributions, LinearAlgebra,
SparseArrays, RecursiveArrayTools
using Plots
using BenchmarkTools
const PDMP = PiecewiseDeterministicMarkovProcesses
const fmt = :png:pngThis benchmark implements the stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics from Rodrigues et al. [1]. The source code for the model was obtained from the GitHub repository SynapseElife that accompanies the paper. The original source code is licensed with the MIT license. We have added comments on the parts of the code that were directly borrowed from the repository.
Initial idea for benchmarking this model comes from a Discourse discussion.
Model and example solutions
Parameters and initial conditions
Presynaptic parameters
# adapted from SynapseElife/src/ParamsSynapse.jl
@with_kw struct PreSynapseParams
"recovery constant of pre calcium decay function."
τ_rec::Float64 = 20000
"fraction of decay constant of pre calcium decay f."
δ_ca::Float64 = 0.0004
"decay time constant of pre calcium."
τ_pre::Float64 = 20
"decay time constant for AP induced by EPSP."
τ_V::Float64 = 40
"delay to EPSPs onset and evoked AP."
δ_delay_AP::Float64 = 15.0
"initial conditions ready releaseble pool."
D_0::Int64 = 25
"initial conditions recovery pool."
R_0::Int64 = 30
"rate for `D -> R`."
τ_R::Float64 = 5000
"rate for `R -> D`."
τ_D::Float64 = 45000
"rate for `infinite reservoir -> R`."
τ_R_ref::Float64 = 40000
"sigmoid parameter for release probability."
s::Float64 = 2.0
"sigmoid parameter for release probability."
h::Float64 = 0.7 # this value changes given Ca external concentration
"sampling rate for plotting / printing."
sampling_rate::Float64 = 1.0
endMain.var"##WeaveSandBox#277".PreSynapseParamsPostsynaptic parameters
# adapted from SynapseElife/src/ParamsSynapse.jl
@with_kw struct SynapseParams{Tp}
"polygonal threshold."
LTP_region::Tp = VPolygon([[6.35, 1.4], [10, 1.4], [6.35, 29.5], [10, 29.5]]) # VPolygon([SVector(6.35,1.4), SVector(10,1.4),SVector(6.35,29.5), SVector(10,29.5)])
"polygonal threshold."
LTD_region::Tp = VPolygon([
[6.35, 1.4],
[6.35, 23.25],
[6.35, 29.5],
[1.85, 11.327205882352938],
[1.85, 23.25],
[3.7650354609929075, 1.4],
[5.650675675675676, 29.5]
]) # VPolygon([SVector(6.35,1.4),SVector(6.35,23.25),SVector(6.35,29.5),SVector(1.85,11.327205882352938),SVector(1.85,23.25),SVector(3.7650354609929075,1.4),SVector(5.650675675675676,29.5)])
"activation rates for thresholds."
a_D::Float64 = 0.1
"activation rates for thresholds."
b_D::Float64 = 0.00002
"activation rates for thresholds."
a_P::Float64 = 0.2
"activation rates for thresholds."
b_P::Float64 = 0.0001
"activation rates for thresholds."
t_D::Float64 = 18000
"activation rates for thresholds."
t_P::Float64 = 13000
"sigmoids controlling the rate of plasticity change."
K_D::Float64 = 80000.0
"sigmoids controlling the rate of plasticity change."
K_P::Float64 = 13000.0
"plasticity states."
rest_plstcty::Int64 = 100
"simulation."
t_end::Float64 = 100
"simulation."
sampling_rate::Float64 = 10
"biophysical and GHK parameters."
temp_rates::Float64 = 35.0
"biophysical and GHK parameters."
age::Float64 = 60.0
"biophysical and GHK parameters."
faraday::Float64 = 96485e-6 * 1e-3
"biophysical and GHK parameters."
Ca_ext::Float64 = 2.5e3
"biophysical and GHK parameters."
Ca_infty::Float64 = 50e-3
"biophysical and GHK parameters."
tau_ca::Float64 = 10.0
"biophysical and GHK parameters."
D_Ca::Float64 = 0.3338
"biophysical and GHK parameters."
f_Ca::Float64 = 0.1
"biophysical and GHK parameters."
perm::Float64 = -0.04583333333333333
"biophysical and GHK parameters."
z::Float64 = 2.0
"biophysical and GHK parameters."
gas::Float64 = 8.314e-6
"biophysical and GHK parameters."
p_release::NTuple{4,
Float64} = (
0.004225803293622208, 1708.4124496514878, 1.3499793762587964, 0.6540248201173222)
"backpropagation attenuation."
trec::Float64 = 2000
"backpropagation attenuation."
trec_soma::Float64 = 500
"backpropagation attenuation."
delta_decay::Float64 = 1.7279e-5
"backpropagation attenuation."
p_age_decay_bap::NTuple{
3, Float64} = (0.13525468256031167, 16.482800452454164, 5.564691354645679)
"backpropagation attenuation."
delta_soma::Float64 = 2.5e-5 *
(p_age_decay_bap[3] /
(1 + exp(p_age_decay_bap[1] * (age - p_age_decay_bap[2]))))
"backpropagation attenuation."
delta_aux::Float64 = 2.304e-5
"backpropagation attenuation."
injbap::Float64 = 2.0
"backpropagation attenuation."
soma_dist::Float64 = 200.0
"backpropagation attenuation."
p_dist::NTuple{4,
Float64} = (
0.019719018173341547, 230.3206470553394, 1.4313810030893268, 0.10406540965358434)
"backpropagation attenuation."
ϕ_dist::Float64 = (p_dist[4] +
p_dist[3] / (1 + exp(p_dist[1] * (soma_dist - p_dist[2]))))
"backpropagation attenuation."
I_clamp::Float64 = 0.0
"Na and K."
gamma_Na::Float64 = 8e2
"Na and K."
Erev_Na::Float64 = 50.0
"Na and K."
gamma_K::Float64 = 4e1
"Na and K."
Erev_K::Float64 = -90.0
"NMDAr temperature modification."
p_nmda_frwd::NTuple{4,
Float64} = (
-0.09991802053299291, -37.63132907014948, 1239.0673283348326, -1230.6805720050966)
"NMDAr temperature modification."
frwd_T_chng_NMDA::Float64 = (
p_nmda_frwd[4] +
p_nmda_frwd[3] / (1 + exp(p_nmda_frwd[1] * (temp_rates - p_nmda_frwd[2])))
)
"NMDAr temperature modification."
p_nmda_bcwd::NTuple{4,
Float64} = (
-0.10605060141396823, 98.99939433046647, 1621.6168608608068, 3.0368551011554143)
"NMDAr temperature modification."
bcwd_T_chng_NMDA::Float64 = (
p_nmda_bcwd[4] +
p_nmda_bcwd[3] / (1 + exp(p_nmda_bcwd[1] * (temp_rates - p_nmda_bcwd[2])))
) # 0.16031*temp_rates - 0.80775
"NMDAr kinetics (GluN2A type), uM-1ms-1."
NMDA_N2A_ka::Float64 = frwd_T_chng_NMDA * 34.0 * 1e-3
"NMDAr kinetics (GluN2A type), uM-1ms-1."
NMDA_N2A_kb::Float64 = frwd_T_chng_NMDA * 17.0 * 1e-3
"NMDAr kinetics (GluN2A type), uM-1ms-1."
NMDA_N2A_kc::Float64 = frwd_T_chng_NMDA * 127.0 * 1e-3
"NMDAr kinetics (GluN2A type), uM-1ms-1."
NMDA_N2A_kd::Float64 = frwd_T_chng_NMDA * 580.0 * 1e-3
"NMDAr kinetics (GluN2A type), uM-1ms-1."
NMDA_N2A_ke::Float64 = frwd_T_chng_NMDA * 2508.0 * 1e-3
"NMDAr kinetics (GluN2A type), uM-1ms-1."
NMDA_N2A_kf::Float64 = frwd_T_chng_NMDA * 3449.0 * 1e-3
"NMDAr kinetics (GluN2A type), ms-1."
NMDA_N2A_k_f::Float64 = bcwd_T_chng_NMDA * 662.0 * 1e-3
"NMDAr kinetics (GluN2A type), ms-1."
NMDA_N2A_k_e::Float64 = bcwd_T_chng_NMDA * 2167.0 * 1e-3
"NMDAr kinetics (GluN2A type), ms-1."
NMDA_N2A_k_d::Float64 = bcwd_T_chng_NMDA * 2610.0 * 1e-3
"NMDAr kinetics (GluN2A type), ms-1."
NMDA_N2A_k_c::Float64 = bcwd_T_chng_NMDA * 161.0 * 1e-3
"NMDAr kinetics (GluN2A type), ms-1."
NMDA_N2A_k_b::Float64 = bcwd_T_chng_NMDA * 120.0 * 1e-3
"NMDAr kinetics (GluN2A type), ms-1."
NMDA_N2A_k_a::Float64 = bcwd_T_chng_NMDA * 60.0 * 1e-3
"NMDAr kinetics (GluN2B type), uM-1ms-1."
NMDA_N2B_sa::Float64 = frwd_T_chng_NMDA * 0.25 * 34.0 * 1e-3
"NMDAr kinetics (GluN2B type), uM-1ms-1."
NMDA_N2B_sb::Float64 = frwd_T_chng_NMDA * 0.25 * 17.0 * 1e-3
"NMDAr kinetics (GluN2B type), uM-1ms-1."
NMDA_N2B_sc::Float64 = frwd_T_chng_NMDA * 0.25 * 127.0 * 1e-3
"NMDAr kinetics (GluN2B type), uM-1ms-1."
NMDA_N2B_sd::Float64 = frwd_T_chng_NMDA * 0.25 * 580.0 * 1e-3
"NMDAr kinetics (GluN2B type), uM-1ms-1."
NMDA_N2B_se::Float64 = frwd_T_chng_NMDA * 0.25 * 2508.0 * 1e-3
"NMDAr kinetics (GluN2B type), uM-1ms-1."
NMDA_N2B_sf::Float64 = frwd_T_chng_NMDA * 0.25 * 3449.0 * 1e-3
"NMDAr kinetics (GluN2B type), ms-1."
NMDA_N2B_s_f::Float64 = bcwd_T_chng_NMDA * 0.23 * 662.0 * 1e-3
"NMDAr kinetics (GluN2B type), ms-1."
NMDA_N2B_s_e::Float64 = bcwd_T_chng_NMDA * 0.23 * 2167.0 * 1e-3
"NMDAr kinetics (GluN2B type), ms-1."
NMDA_N2B_s_d::Float64 = bcwd_T_chng_NMDA * 0.23 * 2610.0 * 1e-3
"NMDAr kinetics (GluN2B type), ms-1."
NMDA_N2B_s_c::Float64 = bcwd_T_chng_NMDA * 0.23 * 161.0 * 1e-3
"NMDAr kinetics (GluN2B type), ms-1."
NMDA_N2B_s_b::Float64 = bcwd_T_chng_NMDA * 0.23 * 120.0 * 1e-3
"NMDAr kinetics (GluN2B type), ms-1."
NMDA_N2B_s_a::Float64 = bcwd_T_chng_NMDA * 0.23 * 60.0 * 1e-3
"NMDA details."
p_nmda::NTuple{4,
Float64} = (
0.004477162852447629, 2701.3929349701334, 58.38819453272428, 33.949463268365555)
"NMDA details."
gamma_nmda::Float64 = (p_nmda[4] +
p_nmda[3] / (1 + exp(p_nmda[1] * (Ca_ext - p_nmda[2])))) * 1e-3
"NMDA details."
p_age::NTuple{4,
Float64} = (
0.09993657672916968, 25.102347872464193, 0.9642137892004939, 0.5075183905839776)
"ratio N2B/N2A."
r_NMDA_age::Float64 = rand(Normal(0, 0.05)) + p_age[4] +
p_age[3] / (1 + exp(p_age[1] * (age - p_age[2]))) # 0.5+1.6*exp(-age/16.66) + rand(Normal(0,.05))
"ratio N2B/N2A."
N_NMDA::Int64 = 15
"ratio N2B/N2A."
N_N2B::Int64 = round(N_NMDA * r_NMDA_age / (r_NMDA_age + 1))
"ratio N2B/N2A, using Sinclair ratio."
N_N2A::Int64 = round(N_NMDA / (r_NMDA_age + 1))
"other NMDAr parameters."
Erev_nmda::Float64 = 0.0
"other NMDAr parameters."
Mg::Float64 = 1.0
"AMPAr temperature modification."
p_ampa_frwd::NTuple{
3, Float64} = (-0.4737773089201679, 31.7248285571622, 10.273135485873242)
"AMPAr temperature modification."
frwd_T_chng_AMPA::Float64 = (p_ampa_frwd[3] /
(1 + exp(p_ampa_frwd[1] * (temp_rates - p_ampa_frwd[2])))) # temp_rates*0.78-18.7
"AMPAr temperature modification."
p_ampa_bcwd::NTuple{
3, Float64} = (-0.36705555170278986, 28.976662403966674, 5.134547217640794)
"AMPAr temperature modification."
bcwd_T_chng_AMPA::Float64 = (p_ampa_bcwd[3] /
(1 + exp(p_ampa_bcwd[1] * (temp_rates - p_ampa_bcwd[2])))) # temp_rates*0.37-8.25
"AMPAr kinetics, uM-1ms-1."
AMPA_k1::Float64 = frwd_T_chng_AMPA * 1.6 * 1e7 * 1e-6 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_k_1::Float64 = bcwd_T_chng_AMPA * 7400 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_k_2::Float64 = bcwd_T_chng_AMPA * 0.41 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_alpha::Float64 = 2600 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_beta::Float64 = 9600 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_delta_1::Float64 = 1500 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_gamma_1::Float64 = 9.1 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_delta_2::Float64 = 170 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_gamma_2::Float64 = 42 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_delta_0::Float64 = 0.003 * 1e-3
"AMPAr kinetics, ms-1."
AMPA_gamma_0::Float64 = 0.83 * 1e-3
"AMPAr conductances, nS."
gamma_ampa1::Float64 = 0.5 * 31e-3
"AMPAr conductances, nS."
gamma_ampa2::Float64 = 0.5 * 52e-3
"AMPAr conductances, nS."
gamma_ampa3::Float64 = 0.5 * 73e-3
"AMPAr conductances, AMPAr number."
N_ampa::Int64 = 120
"AMPAr conductances, AMPAR reversal potential, mV."
Erev_ampa::Float64 = 0.0
"GABAr."
N_GABA::Int64 = 34
"GABAr."
p_Cl::NTuple{4,
Float64} = (
0.09151696057098718, 0.6919298240788684, 243.5159017060495, -92.6496083089155)
"GABAr, Cl reversal potential."
Erev_Cl::Float64 = (p_Cl[4] + p_Cl[3] / (1 + exp(p_Cl[1] * (age - p_Cl[2]))))
"GABAr, Cl reversal potential."
gamma_GABA::Float64 = 35e-3
"GABAr, Cl reversal potential."
GABA_r_b1::Float64 = 1e6 * 1e-6 * 1e-3 * 20
"GABAr, Cl reversal potential."
GABA_r_u1::Float64 = 1e3 * 4.6e-3
"GABAr, Cl reversal potential."
GABA_r_b2::Float64 = 1e6 * 1e-6 * 1e-3 * 10
"GABAr, Cl reversal potential."
GABA_r_u2::Float64 = 1e3 * 9.2e-3
"GABAr, Cl reversal potential."
GABA_r_ro1::Float64 = 1e3 * 3.3e-3
"GABAr, Cl reversal potential."
GABA_r_ro2::Float64 = 1e3 * 10.6e-3
"GABAr, Cl reversal potential."
p_GABA::NTuple{4,
Float64} = (
0.19127068198185954, 32.16771140618756, -1.2798050197287802, 1.470692263981145)
"GABAr, Cl reversal potential."
GABA_r_c1::Float64 = (p_GABA[4] +
p_GABA[3] / (1 + exp(p_GABA[1] * (temp_rates - p_GABA[2])))) *
1e3 *
9.8e-3
"GABAr, Cl reversal potential."
GABA_r_c2::Float64 = (p_GABA[4] +
p_GABA[3] / (1 + exp(p_GABA[1] * (temp_rates - p_GABA[2])))) *
400e-3
"passive electrical properties."
E_leak::Float64 = -70.0
"passive electrical properties."
g_leak::Float64 = 4e-6
"passive electrical properties."
Cm::Float64 = 0.6e-2
"passive electrical properties."
R_a::Float64 = 1e-2
"morphology, Dendritic properties, dendrite diameter, um."
D_dend::Float64 = 2.0
"morphology, Dendritic properties, dendrite length, chosen to tune attenuation, but not modified in BaP adaptation for simplicity sake, um."
L_dend::Float64 = 1400
"morphology, Dendritic properties, dendrite surface area, 500 gives dendrite input resistance of 200MOhm, um^2."
A_dend::Float64 = 2 * pi * (D_dend / 2) * L_dend
"morphology, Dendritic properties, dendrite volume, um^3."
Vol_dend::Float64 = pi * ((D_dend / 2)^2) * L_dend
"morphology, Dendritic properties, dendritic membrane capacitance."
Cdend::Float64 = Cm * A_dend
"morphology, Dendritic properties, dendrite cross-sectional area, um^2."
CS_dend::Float64 = pi * (D_dend / 2) .^ 2
"morphology, Dendritic properties, nS."
g_leakdend::Float64 = g_leak * A_dend
"morphology, Soma properties, soma diameter, um."
D_soma::Float64 = 30
"morphology, Soma properties, soma surface area, 500 gives dendrite input resistance of 200MOhm, um^2."
A_soma::Float64 = pi * D_soma^2
"morphology, Soma properties, soma membrane capacitance."
Csoma::Float64 = Cm * A_soma
"morphology, Soma properties, soma cross-sectional area, um^2."
CS_soma::Float64 = pi * (D_soma / 2) .^ 2
"morphology, Soma properties, nS."
g_leaksoma::Float64 = 15.0
"morphology, Soma properties, value subject to modifications due to BaP adaptation implementation."
g_diff::Float64 = D_dend / (4R_a)
"spine properties, spine head volume [bartol2015], um^3."
Vol_sp::Float64 = 0.03
"spine properties, spine head surface area."
A_sp::Float64 = 4 * pi * ((3 * Vol_sp) / (4 * pi))^(2.0 / 3.0)
"spine properties, spine membrane capacitance."
Csp::Float64 = Cm * A_sp
"spine properties, spine head leak conductance."
g_leaksp::Float64 = g_leak * A_sp
"neck properties, spine neck diameter [bartol2015], um."
D_neck::Float64 = 0.1
"neck properties, neck length [bartol2015], um."
L_neck::Float64 = 0.2
"neck properties, neck cross sectional area, um^2."
CS_neck::Float64 = pi * (D_neck / 2) .^ 2
"neck properties."
g_neck::Float64 = CS_neck / (L_neck * R_a)
"neck properties."
tau_diff::Float64 = ((Vol_sp / (2 * D_Ca * D_neck)) + (L_neck^2 / (2 * D_Ca)))
"synpatic glutamate transient parameters, arbitrary, ms."
glu_width::Float64 = 1.0 # 0.1 ms for synapse
"synpatic glutamate transient parameters, arbitrary, mM."
glu_amp::Float64 = 1e+3
"synpatic glutamate transient parameters [liu1999]."
glu_cv::Float64 = 0.5
"SK channels, number of SK channels."
N_SK::Int64 = 15
"SK channels [maylie2004], ns."
SK_gamma::Float64 = 10e-3
"SK channels [mellor2016annex], mv."
SK_Erev::Float64 = -90
"SK channels [mellor2016annex], uM."
SK_gating_half::Float64 = 0.33
"SK channels [mellor2016annex], ms."
SK_time::Float64 = 6.3
"SK channels [mellor2016annex], ms."
SK_hill::Float64 = 6
"SK channels."
p_SK_bcwd::NTuple{4,
Float64} = (
0.09391588258147192, 98.85165844770867, -147.61669527876904, 149.37767054612135)
"SK channels."
bcwd_SK::Float64 = (
p_SK_bcwd[4] + p_SK_bcwd[3] / (1 + exp(p_SK_bcwd[1] * (temp_rates - p_SK_bcwd[2])))
)
"SK channels."
p_SK_frwd::NTuple{4,
Float64} = (
-0.334167923607112, 25.590920461511878, 2.2052151559841193, 0.005904170174699533)
"SK channels."
frwd_SK::Float64 = (
p_SK_frwd[4] + p_SK_frwd[3] / (1 + exp(p_SK_frwd[1] * (temp_rates - p_SK_frwd[2])))
)
"CaM, CaMKII and CaN concentrations."
CaM_con::Float64 = 30.0
"CaM, CaMKII and CaN concentrations, renamed [feng2011], 100um."
mKCaM_con::Float64 = 70.0
"CaM, CaMKII and CaN concentrations [lisman?], uM."
mCaN_con::Float64 = 20.0
"Chang Pepke model - CaM reactions I."
kon_1C::Float64 = 5e-3
"Chang Pepke model - CaM reactions I."
koff_1C::Float64 = 50e-3
"Chang Pepke model - CaM reactions I."
kon_2C::Float64 = 10e-3
"Chang Pepke model - CaM reactions I."
koff_2C::Float64 = 10e-3
"Chang Pepke model - CaM reactions I."
kon_1N::Float64 = 100e-3
"Chang Pepke model - CaM reactions I."
koff_1N::Float64 = 2000e-3
"Chang Pepke model - CaM reactions I."
kon_2N::Float64 = 200e-3
"Chang Pepke model - CaM reactions I."
koff_2N::Float64 = 500e-3
"Chang Pepke model - CaM reactions II."
kf_CaM0::Float64 = 3.8e-6
"Chang Pepke model - CaM reactions II."
kb_CaM0::Float64 = 5.5e-3
"Chang Pepke model - CaM reactions II."
kf_CaM2C::Float64 = 0.92e-3
"Chang Pepke model - CaM reactions II."
kb_CaM2C::Float64 = 6.8e-3
"Chang Pepke model - CaM reactions II."
kf_CaM2N::Float64 = 0.12e-3
"Chang Pepke model - CaM reactions II."
kb_CaM2N::Float64 = 1.7e-3
"Chang Pepke model - CaM reactions II."
kf_CaM4::Float64 = 30e-3
"Chang Pepke model - CaM reactions II."
kb_CaM4::Float64 = 1.5e-3
"Chang Pepke model - CaMKII reactions."
kon_K1C::Float64 = 44e-3
"Chang Pepke model - CaMKII reactions."
koff_K1C::Float64 = 33e-3
"Chang Pepke model - CaMKII reactions."
kon_K2C::Float64 = 44e-3
"Chang Pepke model - CaMKII reactions."
koff_K2C::Float64 = 0.8e-3
"Chang Pepke model - CaMKII reactions."
kon_K1N::Float64 = 76e-3
"Chang Pepke model - CaMKII reactions."
koff_K1N::Float64 = 300e-3
"Chang Pepke model - CaMKII reactions."
kon_K2N::Float64 = 76e-3
"Chang Pepke model - CaMKII reactions."
koff_K2N::Float64 = 20e-3
"Chang Pepke model - autophosphorilation."
p_camkii_q10::NTuple{4,
Float64} = (
0.5118207068695309, 45.47503600542303, -161.42634157226917, 162.1718925882677)
"Chang Pepke model - autophosphorilation."
q10::Float64 = p_camkii_q10[4] +
p_camkii_q10[3] /
(1 + exp(p_camkii_q10[1] * (temp_rates - p_camkii_q10[2]))) # change of temp to fit chang 35C
"Chang Pepke model - autophosphorilation."
k1::Float64 = 12.6e-3
"Chang Pepke model - autophosphorilation."
k2::Float64 = q10 * 0.33e-3 # q10 * 0.33e-3
"Chang Pepke model - autophosphorilation."
k3::Float64 = 4 * q10 * 0.17e-3 # q10 * 0.17e-3
"Chang Pepke model - autophosphorilation."
k4::Float64 = 4 * 0.041e-3
"Chang Pepke model - autophosphorilation."
k5::Float64 = 4 * q10 * 2 * 0.017e-3 # q10 * 2* 0.017e-3
"CaM-CaN reactions."
p_CaN_frwd::NTuple{4,
Float64} = (
-0.29481489145354556, 29.999999999999968, 0.15940019940354327, 0.870299900298228)
"CaM-CaN reactions, 22C - 4.6e-2 [quintana2005]."
kcanf::Float64 = (
p_CaN_frwd[4] +
p_CaN_frwd[3] / (1 + exp(p_CaN_frwd[1] * (temp_rates - p_CaN_frwd[2])))
) * 1.75e-2
"CaM-CaN reactions."
p_CaN_bcwd::NTuple{4,
Float64} = (
-0.6833299932488973, 26.277500129849113, 0.7114524682690591, 0.29037766196937326)
"CaM-CaN reactions, 22C - 1.2e-6 [quintana2005]."
kcanb::Float64 = (
p_CaN_bcwd[4] +
p_CaN_bcwd[3] / (1 + exp(p_CaN_bcwd[1] * (temp_rates - p_CaN_bcwd[2])))
) * 2e-5
"VGCCs."
p_frwd_VGCC::NTuple{4,
Float64} = (
1.0485098341579628, 30.66869198447378, -0.3040010721391852, 2.5032059559264357)
"VGCCs."
frwd_VGCC::Float64 = (
p_frwd_VGCC[4] +
p_frwd_VGCC[3] / (1 + exp(p_frwd_VGCC[1] * (temp_rates - p_frwd_VGCC[2])))
)
"VGCCs."
p_bcwd_VGCC::NTuple{4,
Float64} = (
-0.3302682317933842, 36.279019647221226, 3.2259761593440155, 0.7298285671937866)
"VGCCs."
bcwd_VGCC::Float64 = (
p_bcwd_VGCC[4] +
p_bcwd_VGCC[3] / (1 + exp(p_bcwd_VGCC[1] * (temp_rates - p_bcwd_VGCC[2])))
)
"VGCCs, calcium channel reversal potential, mV."
Erev_CaT::Float64 = 10.0
"VGCCs, calcium channel reversal potential, mV."
Erev_CaR::Float64 = 10.0
"VGCCs, calcium channel reversal potential, mV."
Erev_CaL::Float64 = 10.0
"VGCCs [magee1995], nS."
gamma_CaT::Float64 = 12e-3
"VGCCs [magee1995], nS."
gamma_CaR::Float64 = 17e-3
"VGCCs [magee1995], nS."
gamma_CaL::Float64 = 27e-3
"VGCCs."
N_caT::Int64 = 3
"VGCCs."
N_caR::Int64 = 3
"VGCCs."
N_caL::Int64 = 3
"calcium dye and buffers [zenisek2003,naraghi1997], uMms-1."
EGTA_kf::Float64 = 2.7e-3
"calcium dye and buffers, assuming Kd of 0.18uM [naraghi1997] ms-1."
EGTA_kb::Float64 = 0.18 * EGTA_kf
"calcium dye and buffers, 0.2 for imaging, 200 for elecrophysiology [tigaret2016] uM."
EGTA_con::Float64 = 0.0
"calcium dye and buffers [zenisek2003,naraghi1997], uM-1ms-1."
BAPTA_kf::Float64 = 0.45
"calcium dye and buffers, assuming Kd of 0.176uM [naraghi1997], ms-1."
BAPTA_kb::Float64 = 0.176 * BAPTA_kf
"calcium dye and buffers, uM."
BAPTA_con::Float64 = 0.0
"calcium dye and buffers [bartol2015], uM-1ms-1."
Imbuf_k_on::Float64 = 0.247
"calcium dye and buffers [bartol2015], ms-1."
Imbuf_k_off::Float64 = 0.524
"calcium dye and buffers."
K_buff_diss::Float64 = Imbuf_k_off / Imbuf_k_on
"calcium dye and buffers, 76.7 [bartol2015], uM."
Imbuf_con::Float64 = 62
"calcium dye and buffers."
Imbuf_con_dend::Float64 = Imbuf_con * 4
"calcium fluorescent dyes, assuming a [Ca] = 1um [bartol2015], ms-1."
ogb1_kf::Float64 = 0.8
"calcium fluorescent dyes [bartol2015], ms-1."
ogb1_kb::Float64 = 0.16
"calcium fluorescent dyes, assuming a [Ca] = 1um [bartol2015], ms-1."
fluo4_kf::Float64 = 0.8
"calcium fluorescent dyes [bartol2015], ms-1."
fluo4_kb::Float64 = 0.24
"calcium fluorescent dyes."
dye::Float64 = 0.0
"calcium fluorescent dyes [zenisek2003,naraghi1997], uMms-1."
fluo5f_kf::Float64 = dye * 0.01
"calcium fluorescent dyes assuming [Kd] = 1.3uM [yasuda2004]."
fluo5f_kb::Float64 = dye * 26 * fluo5f_kf
"calcium fluorescent dyes uM [tigaret2016]."
fluo5f_con::Float64 = dye * 200.0
endMain.var"##WeaveSandBox#277".SynapseParamsTransition matrices
We define some utilities to help us construct the transition matrices.
# adapted from SynapseElife/src/JumpMatrices.jl
get_stoichmatrix(model) = transpose(Catalyst.netstoichmat(model)) |> Matrix
# adapted from SynapseElife/src/JumpMatrices.jl
jump_matrix(matrix_list) = cat(matrix_list..., dims = (1, 2))jump_matrix (generic function with 1 method)Now we define each matrix one-by-one.
# adapted from SynapseElife/src/JumpMatrices.jl
const ampa_model = @reaction_network begin
#1line
#2line-GO
1, C0 → C1
1, C1 → C2
1, C2 → C3
1, C3 → C4
#2line-BAC
1, C4 → C3
1, C3 → C2
1, C2 → C1
1, C1 → C0
#3line-GO
1, D0 → D1
1, D1 → D2
1, D2 → D3
1, D3 → D4
#3line-BACK
1, D4 → D3
1, D3 → D2
1, D2 → D1
1, D1 → D0
#4line-GO
1, D22 → D23
1, D23 → D24
#4line-BACK
1, D24 → D23
1, D23 → D22
#1column-GO-BACK
1, C0 → D0
1, D0 → C0
#2column-GO-BACK
1, C1 → D1
1, D1 → C1
#3column-GO
1, O2 → C2
1, C2 → D2
1, D2 → D22
#3column-BACK
1, D22 → D2
1, D2 → C2
1, C2 → O2
#4column-GO
1, O3 → C3
1, C3 → D3
1, D3 → D23
#4column-BACK
1, D23 → D3
1, D3 → C3
1, C3 → O3
#5column-GO
1, O4 → C4
1, C4 → D4
1, D4 → D24
#5column-BACK
1, D24 → D4
1, D4 → C4
1, C4 → O4
end
# adapted from SynapseElife/src/JumpMatrices.jl
AMPA_matrix() = get_stoichmatrix(ampa_model)
# adapted from SynapseElife/src/JumpMatrices.jl
const nmda_model_v2 = @reaction_network begin #same structure for N2A and N2B
#1line-GO
1, A0 → A1
1, A1 → A2
1, A2 → A3
1, A3 → A4
1, A4 → AO1
1, AO1 → AO2
#2line-BACK
1, AO2 → AO1
1, AO1 → A4
1, A4 → A3
1, A3 → A2
1, A2 → A1
1, A1 → A0
end
# adapted from SynapseElife/src/JumpMatrices.jl
NMDA_matrix() = get_stoichmatrix(nmda_model_v2)
# adapted from SynapseElife/src/JumpMatrices.jl
function R_channel_matrix()
[[-1 1 0 0] # CaR m0h0 -> m1h0
[1 -1 0 0] # CaR m1h0 -> m0h0
[-1 0 1 0] # CaR m0h0 -> m0h1
[1 0 -1 0] # CaR m0h1 -> m0h0
[0 -1 0 1] # CaR m1h0 -> O
[0 1 0 -1] # CaR O -> m1h0
[0 0 -1 1] # CaR m0h1 -> O
[0 0 1 -1]]
end
# adapted from SynapseElife/src/JumpMatrices.jl
function T_channel_matrix()
[[-1 1 0 0] # CaT m0h0 -> m1h0
[1 -1 0 0] # CaT m1h0 -> m0h0
[-1 0 1 0] # CaT m0h0 -> m0h1
[1 0 -1 0] # CaT m0h1 -> m0h0
[0 -1 0 1] # CaT m1h0 -> O
[0 1 0 -1] # CaT O -> m1h0
[0 0 -1 1] # CaT m0h1 -> O
[0 0 1 -1]]
end
# adapted from SynapseElife/src/JumpMatrices.jl
L_channel_matrix() = [[-1 1 0] # CaL C -> O1
[1 -1 0] # CaL O1 -> C
[-1 0 1] # CaL C -> O2
[1 0 -1]]
# adapted from SynapseElife/src/JumpMatrices.jl
const plasticity = @reaction_network begin
1, NC → LTD
1, LTD → NC
1, NC → LTP
1, LTP → NC
end
# adapted from SynapseElife/src/JumpMatrices.jl
LTP_LTD_matrix() = get_stoichmatrix(plasticity)
# adapted from SynapseElife/src/JumpMatrices.jl
const gaba_destexhe = @reaction_network begin
#1line-GO
(1, 1), CO ↔ C1
(1, 1), C1 ↔ C2
(1, 1), C1 ↔ O1
(1, 1), C2 ↔ O2
end
# adapted from SynapseElife/src/JumpMatrices.jl
GABA_matrix() = get_stoichmatrix(gaba_destexhe)GABA_matrix (generic function with 1 method)Finally, we define a wrapper function to build the main transition matrix.
# adapted from SynapseElife/src/SynapseModel.jl
function buildTransitionMatrix()
matrix_list = [AMPA_matrix()]
push!(matrix_list, NMDA_matrix()) # for GluN2A
push!(matrix_list, Matrix{Int64}(I, 1, 1)) # print from Poisson Rate
push!(matrix_list, R_channel_matrix())
push!(matrix_list, T_channel_matrix())
push!(matrix_list, L_channel_matrix())
push!(matrix_list, LTP_LTD_matrix())
push!(matrix_list, NMDA_matrix()) # for GluN2B
push!(matrix_list, GABA_matrix())
return sparse(jump_matrix(matrix_list))
endbuildTransitionMatrix (generic function with 1 method)Assembling it all
Parameters.
const p_synapse = SynapseParams(t_end = 1000.0);
const glu = 0.0;
const events_sorted_times = [500.0];
const is_pre_or_post_event = [true];
const events_bap = events_sorted_times[is_pre_or_post_event .== false];
const bap_by_epsp = Float64[];
const nu = buildTransitionMatrix();Initial conditions.
# adapted from SynapseElife/src/UtilsData.jl
function initial_conditions_continuous_temp(param_synapse)
@unpack_SynapseParams param_synapse
if temp_rates <= 25
return vec(
[-70.10245699808998
-70.02736715107497
-70.01992573979436
1.0
5.251484030952095
0.17942311304488254
0.0
18.422417385628144
0.061182835845181506
0.007491230194287401
2.5601235159798556e-5
18.60768149870139
1.3923185018623478
47.943467158481965
0.33484901412981444
0.00873078540237604
0.26160543666353603
0.006945031752908706
5.28369636945184
4.008117080305045
0.11294478061086997
0.09967594670655765
4.656494469862573
7.283473926518337
0.0
0.0
0.0
0.0
0.012283139643655655
0.9999998289470913
0.00010811866849049202
0.09878906052566663
1.0
1.0],
)
end
if 25 < temp_rates <= 30.0
return vec(
[-70.0140727673961
-70.00177103943689
-70.00007589726667
1.0
3.48177628683147
0.11706193391209137
0.0
19.902059159951726
0.04813075789246737
0.0033156783870759324
1.3058864642411135e-5
19.473469645955362
0.5265303542539336
49.658388018645105
0.39979810740476907
0.005987535794514187
0.22114161049072126
0.003443459770906218
5.486877056572574
3.2429635679748126
0.0967411298498974
0.06299852278885718
4.315666798657558
6.505994192089851
0.0
0.0
0.0
0.0
0.0123167984282587
0.9999998268859568
0.00010833059621284
0.016112012029112062
1.0
1.0],
)
end
if temp_rates > 30
return vec(
[-70.02953996060384
-70.00364683510847
-70.0013995913228
1.0
3.3989773357494646
0.11430174346528181
0.0
25.14694054430742
0.048232611580821316
0.004340152415081933
6.8123069384392556e-6
19.865575695641734
0.13442430463415694
62.32357049746406
0.8459878113145832
0.009234347120412881
0.3607751119415231
0.003937688645035126
2.3440067259757305
1.0593952833042108
0.02913354160885602
0.013585064852268125
1.6677561415335218
1.3426177862569586
0.0
0.0
0.0
0.0
0.012314741437834478
0.999999826986425
0.00010831999489540837
0.03393795777123425
1.0
1.0],
)
end
end
# adapted from SynapseElife/src/UtilsData.jl
function initial_conditions_discrete(param_synapse)
@unpack_SynapseParams param_synapse
return vec([
N_ampa, # AMPA 1-16
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
N_N2A, # NMDA 17-23
0,
0,
0,
0,
0,
0,
0, # Print 24
0, # R-type 25-28
0,
N_caR,
0,
0, # T-type 29-32
0,
N_caT,
0,
N_caL, # L-type 33-35
0,
0,
rest_plstcty, # GLUN2B
0,
0,
N_N2B,
0,
0,
0,
0,
0,
0,
N_GABA, # GABA
0,
0,
0,
0
])
endinitial_conditions_discrete (generic function with 1 method)const xc0 = initial_conditions_continuous_temp(p_synapse);
const xd0 = initial_conditions_discrete(p_synapse);Model
Rodrigues et al. [1] synapse model that replaces NMDA model with fully state-based one from Jahr and Stevens, plus three types of VGCCs (R-type, T-type and L-type), from Magee and Johnston [2].
Continuous evolution
Helper functions.
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline alpha_m(V) = 0.4 * (V + 30) / (1 - exp(-(V + 30) / 7.2))
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline beta_m(V) = 0.124 * (V + 30) / (exp((V + 30) / 7.2) - 1)
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline alpha_h(V) = 0.01 * (V + 45) / (exp((V + 45) / 1.5) - 1)
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline beta_h(V) = 0.03 * (V + 45) / (1 - exp(-(V + 45) / 1.5))
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline alpha_n(V, nspeedfactor = 1) = nspeedfactor * exp(-0.11 * (V - 13))
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline beta_n(V, nspeedfactor = 1) = nspeedfactor * exp(-0.08 * (V - 13))
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function ghk(V, Ca_int, Ca_ext, p_synapse)
# Kelvin physiological temp.
@unpack_SynapseParams p_synapse
x = z * V * faraday / (gas * (temp_rates + 273.15))
v = z * x * faraday * ((Ca_int) - (Ca_ext) * exp(-x)) / (1 - exp(-x))
return v
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline SK_chnnl(Ca) = Ca^6 / (Ca^6 + 0.333^6) # 0.333
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function mollifier(t, duration::T; pw = 20) where {T}
if abs(t/duration) > 10
return zero(T)
else
return one(T) / (one(T) + (t/duration)^pw)
end
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function inputBaP(t, bapTimes::Vector, duration::T, amp::T) where {T}
if isempty(bapTimes)
return zero(T)
end
res = zero(T)
Δ = duration / 2
for ts in bapTimes
res += mollifier(t - (ts + Δ), Δ)
end
return res * amp
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline rates_adapt(a, b, c, d, Ca) = a * b / (c + d * Ca)
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline B(v, Mg) = 1 / (1 + exp(-0.062 * v) * (Mg / 3.57)) #Jahr StevensB (generic function with 1 method)The continuous evolution.
# adapted from SynapseElife/src/SynapseModel.jl
function F_synapse(dxc, xc, xd, p_synapse::SynapseParams, t, events_bap, bap_by_epsp)
@unpack_SynapseParams p_synapse
# Stochastic channels/receptors
n1_ampa = xd[14] # ampa subconductance 1
n2_ampa = xd[15] # ampa subconductance 2
n3_ampa = xd[16] # ampa subconductance 3
n1_nmda_A = xd[22] # nmda subconductance 1
n2_nmda_A = xd[23] # nmda subconductance 2
n1_nmda_B = xd[44] # nmda subconductance 1
n2_nmda_B = xd[45] # nmda subconductance 2
n_car = xd[28] # vgcc-R opened state
n_cat = xd[32] # vgcc-T opened state
n_cal = xd[34] + xd[35] # vgcc-L opened states
n_gaba1 = xd[49] # GABA opened state
n_gaba2 = xd[50] # GABA opened state
# Continuous variables
Vsp,
Vdend,
Vsoma,
λ,
ImbufCa,
Ca,
Dye,
CaM0,
CaM2C,
CaM2N,
CaM4,
mCaN,
CaN4,
mKCaM,
KCaM0,
KCaM2N,
KCaM2C,
KCaM4,
PCaM0,
PCaM2C,
PCaM2N,
PCaM4,
P,
P2,
LTD,
LTP,
act_D,
act_P,
m,
h,
n,
SK,
λ_age,
λ_aux = xc
# Plasticity prediction regions
CaMKII = KCaM0 + KCaM2C + KCaM2N + KCaM4 + PCaM0 + PCaM2C + PCaM2N + PCaM4 + P + P2
CaN = CaN4
# Activation when it is inside the region
# this following line allocates 74.779 ns (3 allocations: 144 bytes). The 2 lines count for 25% of the performance
∂LTD = SVector(CaN, CaMKII) ∈ LTD_region
∂LTP = SVector(CaN, CaMKII) ∈ LTP_region
∂act_D = a_D * ∂LTD - b_D * act_D * (1 - ∂LTD)
∂act_P = a_P * ∂LTP - b_P * act_P * (1 - ∂LTP)
# Na channel
m_inf = alpha_m(Vsoma) / (alpha_m(Vsoma) + beta_m(Vsoma))
m_tau = 1 / (alpha_m(Vsoma) + beta_m(Vsoma))
∂m = (m_inf - m) / m_tau
∂h = alpha_h(Vsoma) * (1 - h) - beta_h(Vsoma) * h
I_Na = gamma_Na * (m^3) * h * (Erev_Na - Vsoma)
# K channel
n_inf = 1 / (1 + alpha_n(Vsoma))
n_tau = max(50 * beta_n(Vsoma) / (1 + alpha_n(Vsoma)), 2.0)
∂n = (n_inf - n) / n_tau
I_K = gamma_K * n * (Erev_K - Vsoma)
# NMDA
NMDA = (n1_nmda_A + n2_nmda_A + n1_nmda_B + n2_nmda_B) * B(Vsp, Mg) * gamma_nmda
Inmda = (Erev_nmda - Vsp) * NMDA # current nmda
# AMPA
Iampa = (Erev_ampa - Vsp) *
(gamma_ampa1 * n1_ampa + gamma_ampa2 * n2_ampa + gamma_ampa3 * n3_ampa) # current ampa
# GABA
Igaba = (n_gaba1 + n_gaba2) * (Erev_Cl - Vdend) * gamma_GABA
# Calcium sources (VGCCs currents, and NMDA calcium contribution)
ΦCa = perm * ghk(Vsp, Ca, Ca_ext, p_synapse) #GHK factor
Ica_nmda = f_Ca * ΦCa * NMDA
Icar = gamma_CaR * n_car * ΦCa
Icat = gamma_CaT * n_cat * ΦCa
Ical = gamma_CaL * n_cal * ΦCa
# SK channel (not stochastic)
∂SK = (SK_chnnl(Ca) * frwd_SK - SK) / (SK_time * bcwd_SK) #SK spine
Isk = SK_gamma * (SK_Erev - Vsp) * SK * N_SK
# Backpropgation
# Post input - for experimentally induced BaPs and those induced by EPSPs
I_BaP = inputBaP(t, bap_by_epsp, injbap, I_clamp) +
inputBaP(t, events_bap, injbap, I_clamp)
# Bap decay/attenuation - two component for adaptation in the Bap
∂λ = (1 - λ) / trec - delta_decay * (1 / λ_aux) * λ * I_BaP
∂λ_aux = (1 - λ_aux) / trec - delta_aux * λ_aux * I_BaP
gadapt = λ * g_diff * ϕ_dist
# Bap decay/attenuation - age dependent modification factor
∂λ_age = (1 - λ_age) / trec_soma - delta_soma * λ_age * I_BaP
# Voltage
# Spine
∂Vsp = (
Isk +
Inmda +
Iampa +
Icat +
Icar +
Ical +
g_neck * (Vdend - Vsp) +
g_leak * (E_leak - Vsp)
) / (Csp)
# Dendrite
∂Vdend = (
g_neck * (Vsp - Vdend) +
Igaba +
g_leakdend * (E_leak - Vdend) +
gadapt * (Vsoma - Vdend)
) / Cdend
# Soma
∂Vsoma = (
(I_BaP + I_Na) * λ_age +
I_K +
g_leaksoma * (E_leak - Vsoma) +
gadapt * (Vdend - Vsoma)
) / Csoma
# Buffer and dye (spine only - no neck diffusion)
∂ImbufCa = Imbuf_k_on * (Imbuf_con - ImbufCa) * Ca - Imbuf_k_off * ImbufCa
∂Dye = 4 * fluo5f_kf * (fluo5f_con - Dye) * Ca - 8 * fluo5f_kb * Dye
# Ca Downstream
# CaM-KCaM-rates (coarsed model) from Pepke adapted by
kf_2C = rates_adapt(kon_1C, kon_2C, koff_1C, kon_2C, Ca)
kb_2C = rates_adapt(koff_1C, koff_2C, koff_1C, kon_2C, Ca)
kf_2N = rates_adapt(kon_1N, kon_2N, koff_1N, kon_2N, Ca)
kb_2N = rates_adapt(koff_1N, koff_2N, koff_1N, kon_2N, Ca)
kf_K2C = rates_adapt(kon_K1C, kon_K2C, koff_K1C, kon_K2C, Ca)
kb_K2C = rates_adapt(koff_K1C, koff_K2C, koff_K1C, kon_K2C, Ca)
kf_K2N = rates_adapt(kon_K1N, kon_K2N, koff_K1N, kon_K2N, Ca)
kb_K2N = rates_adapt(koff_K1N, koff_K2N, koff_K1N, kon_K2N, Ca)
F = CaMKII / mKCaM_con
∂CaM0 = k2 * PCaM0 +
kb_2C * CaM2C +
kb_2N * CaM2N +
kb_CaM0 * KCaM0 +
-(1 // 2) * kf_2C * (Ca^2) * CaM0 - (1 // 2) * kf_2N * (Ca^2) * CaM0 +
-kf_CaM0 * CaM0 * mKCaM
∂CaM2C = kb_2N * CaM4 + kb_CaM2C * KCaM2C + k2 * PCaM2C +
+(1 // 2) * kf_2C * (Ca^2) * CaM0 -
kb_2C * CaM2C - (1 // 2) * kf_2N * (Ca^2) * CaM2C + -kf_CaM2C * CaM2C * mKCaM
∂CaM2N = kb_2C * CaM4 + kb_CaM2N * KCaM2N + k2 * PCaM2N +
+(1 // 2) * kf_2N * (Ca^2) * CaM0 -
kb_2N * CaM2N - (1 // 2) * kf_2C * (Ca^2) * CaM2N + -kf_CaM2N * CaM2N * mKCaM
∂CaM4 = k2 * PCaM4 +
kcanb * CaN4 +
kb_CaM4 * KCaM4 +
+(1 // 2) * kf_2N * (Ca^2) * CaM2C +
(1 // 2) * kf_2C * (Ca^2) * CaM2N - kb_2C * CaM4 + -kb_2N * CaM4 -
kcanf * CaM4 * mCaN - kf_CaM4 * CaM4 * mKCaM
∂mCaN = kcanb * CaN4 - kcanf * CaM4 * mCaN
∂CaN4 = kcanf * CaM4 * mCaN - kcanb * CaN4
∂mKCaM = kb_CaM0 * KCaM0 +
k3 * P +
kb_CaM2C * KCaM2C +
kb_CaM2N * KCaM2N +
+kb_CaM4 * KCaM4 - kf_CaM0 * CaM0 * mKCaM - kf_CaM2C * CaM2C * mKCaM +
-kf_CaM2N * CaM2N * mKCaM - kf_CaM4 * CaM4 * mKCaM
∂KCaM0 = kb_K2C * KCaM2C + kb_K2N * KCaM2N + kf_CaM0 * CaM0 * mKCaM + -kb_CaM0 * KCaM0 -
(1 // 2) * kf_K2C * (Ca^2) * KCaM0 - F * k1 * KCaM0 +
-(1 // 2) * kf_K2N * (Ca^2) * KCaM0
∂KCaM2N = kb_K2C * KCaM4 + kf_CaM2N * CaM2N * mKCaM +
+(1 // 2) * kf_K2N * (Ca^2) * KCaM0 -
kb_CaM2N * KCaM2N - kb_K2N * KCaM2N + -(1 // 2) * kf_K2C * (Ca^2) * KCaM2N -
F * k1 * KCaM2N
∂KCaM2C = kb_K2N * KCaM4 + kf_CaM2C * CaM2C * mKCaM +
+(1 // 2) * kf_K2C * (Ca^2) * KCaM0 -
kb_CaM2C * KCaM2C - kb_K2C * KCaM2C + -F * k1 * KCaM2C -
(1 // 2) * kf_K2N * (Ca^2) * KCaM2C
∂KCaM4 = kf_CaM4 * CaM4 * mKCaM +
(1 // 2) * kf_K2C * (Ca^2) * KCaM2N +
+(1 // 2) * kf_K2N * (Ca^2) * KCaM2C - kb_CaM4 * KCaM4 - kb_K2C * KCaM4 +
-kb_K2N * KCaM4 - F * k1 * KCaM4
∂PCaM0 = F * k1 * KCaM0 - k2 * PCaM0
∂PCaM2N = F * k1 * KCaM2N - k2 * PCaM2N
∂PCaM2C = F * k1 * KCaM2C - k2 * PCaM2C
∂PCaM4 = F * k1 * KCaM4 - k2 * PCaM4
∂P = k2 * PCaM0 + k5 * P2 + k2 * PCaM2C + k2 * PCaM2N + k2 * PCaM4 - k3 * P - k4 * P
∂P2 = k4 * P - k5 * P2
# Postsynaptic Ca
∂Ca = (Ca_infty - Ca) / tau_ca +
+(Ica_nmda + Icar + Ical + Icat) / (2 * faraday * A_sp) +
+(max(Ca_infty, Ca / 3) - Ca) / tau_diff +
-∂ImbufCa +
-∂Dye +
+2kb_2C * CaM2C +
2kb_2C * CaM4 +
2kb_2N * CaM2N +
2kb_2N * CaM4 +
+2kb_K2C * KCaM2C +
2kb_K2N * KCaM2N +
2kb_K2C * KCaM4 +
2kb_K2N * KCaM4 +
-kf_2C * (Ca^2) * CaM0 - kf_2N * (Ca^2) * CaM0 - kf_2N * (Ca^2) * CaM2C +
-kf_2C * (Ca^2) * CaM2N - kf_K2C * (Ca^2) * KCaM0 - kf_K2C * (Ca^2) * KCaM2N +
-kf_K2N * (Ca^2) * KCaM0 - kf_K2N * (Ca^2) * KCaM2C
# dxc update
dxc[1] = ∂Vsp
dxc[2] = ∂Vdend
dxc[3] = ∂Vsoma
dxc[4] = ∂λ
dxc[5] = ∂ImbufCa
dxc[6] = ∂Ca
dxc[7] = ∂Dye
dxc[8] = ∂CaM0
dxc[9] = ∂CaM2C
dxc[10] = ∂CaM2N
dxc[11] = ∂CaM4
dxc[12] = ∂mCaN
dxc[13] = ∂CaN4
dxc[14] = ∂mKCaM
dxc[15] = ∂KCaM0
dxc[16] = ∂KCaM2N
dxc[17] = ∂KCaM2C
dxc[18] = ∂KCaM4
dxc[19] = ∂PCaM0
dxc[20] = ∂PCaM2C
dxc[21] = ∂PCaM2N
dxc[22] = ∂PCaM4
dxc[23] = ∂P
dxc[24] = ∂P2
dxc[25] = ∂LTD
dxc[26] = ∂LTP
dxc[27] = ∂act_D
dxc[28] = ∂act_P
dxc[29] = ∂m
dxc[30] = ∂h
dxc[31] = ∂n
dxc[32] = ∂SK
dxc[33] = ∂λ_age
dxc[34] = ∂λ_aux
endF_synapse (generic function with 1 method)Discrete jumps
For the PDMP package we need to define the rates in which the jumps occur.
Helper functions.
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function rates_m_r(Vsp)
beta_m_r_star = 1 / (4e-1) # /ms
minf_m_r_star = 1 / (1 + exp((3 - 10) / 8))
alpha_m_r_star = beta_m_r_star * minf_m_r_star / (1 - minf_m_r_star)
tau_m_r = 1 / (alpha_m_r_star + beta_m_r_star)
minf_r = 1 / (1 + exp((3 - Vsp) / 8))
alpha_m_r = minf_r / tau_m_r
beta_m_r = (1 - minf_r) / tau_m_r
return alpha_m_r, beta_m_r
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function rates_h_r(Vsp)
tau_h_r = 100 # ms
hinf_r = 1 / (1 + exp((Vsp + 39) / 9.2))
alpha_h_r = hinf_r / tau_h_r
beta_h_r = (1 - hinf_r) / tau_h_r
return alpha_h_r, beta_h_r
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function rates_m_t(Vsp)
beta_m_t_star = 1 # /ms
minf_m_t_star = 1 / (1 + exp((-32 + 20) / 7))
alpha_m_t_star = beta_m_t_star * minf_m_t_star / (1 - minf_m_t_star)
tau_m_t = 1 / (alpha_m_t_star + beta_m_t_star)
minf_t = 1 / (1 + exp((-32 - Vsp) / 7))
alpha_m_t = minf_t / tau_m_t
beta_m_t = (1 - minf_t) / tau_m_t
return alpha_m_t, beta_m_t
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function rates_h_t(Vsp)
tau_h_t = 50 # ms
hinf_t = 1 / (1 + exp((Vsp + 70) / 6.5))
alpha_h_t = hinf_t / tau_h_t
beta_h_t = (1 - hinf_t) / tau_h_t
return alpha_h_t, beta_h_t
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function rates_l(Vsp)
return 0.83 / (1 + exp((13.7 - Vsp) / 6.1)),
0.53 / (1 + exp((Vsp - 11.5) / 6.4)),
1.86 / (1 + exp((Vsp - 18.8) / 6.17))
end
# adapted from SynapseElife/src/UtilsDynamics.jl
@inline function plasticityRate(p, nhill, K)
Pmax = 1
r = p^nhill
return Pmax * r / (r + K^nhill)
endplasticityRate (generic function with 1 method)The rate function.
# adapted from SynapseElife/src/SynapseModel.jl
function R_synapse(rate, xc, xd, p_synapse::SynapseParams, t, sum_rate, glu = 0)
@unpack_SynapseParams p_synapse
# Voltage
Vsp = xc[1]
# Glutamate & GABA
Glu = glu_amp * glu
# AMPA
#2line-GO
rate[1] = 4 * AMPA_k1 * Glu * xd[1]
rate[2] = 3 * AMPA_k1 * Glu * xd[2]
rate[3] = 2 * AMPA_k1 * Glu * xd[3]
rate[4] = 1 * AMPA_k1 * Glu * xd[4]
#2line-BACK
rate[5] = 4 * AMPA_k_1 * xd[5]
rate[6] = 3 * AMPA_k_1 * xd[4]
rate[7] = 2 * AMPA_k_1 * xd[3]
rate[8] = 1 * AMPA_k_1 * xd[2]
#3line-GO
rate[9] = 3 * AMPA_k1 * Glu * xd[6]
rate[10] = 3 * AMPA_k1 * Glu * xd[7]
rate[11] = 2 * AMPA_k1 * Glu * xd[8]
rate[12] = 1 * AMPA_k1 * Glu * xd[9]
#3line-BACK
rate[13] = 3 * AMPA_k_1 * xd[10]
rate[14] = 2 * AMPA_k_1 * xd[9]
rate[15] = 1 * AMPA_k_1 * xd[8]
rate[16] = 1 * AMPA_k_2 * xd[7]
#4line-GO
rate[17] = 2 * AMPA_k1 * Glu * xd[11]
rate[18] = 1 * AMPA_k1 * Glu * xd[12]
#4line-BACK
rate[19] = 2 * AMPA_k_1 * xd[13]
rate[20] = 1 * AMPA_k_1 * xd[12]
#1column-GO-BACK
rate[21] = 4 * AMPA_delta_0 * xd[1]
rate[22] = 1 * AMPA_gamma_0 * xd[6]
#2column-GO-BACK
rate[23] = 1 * AMPA_delta_1 * xd[2]
rate[24] = 1 * AMPA_gamma_1 * xd[7]
#3column-GO
rate[25] = 1 * AMPA_alpha * xd[14]
rate[26] = 2 * AMPA_delta_1 * xd[3]
rate[27] = 1 * AMPA_delta_2 * xd[8]
#3column-BACK
rate[28] = 1 * AMPA_gamma_2 * xd[11]
rate[29] = 1 * AMPA_gamma_1 * xd[8]
rate[30] = 2 * AMPA_beta * xd[3]
#4column-GO
rate[31] = 1 * AMPA_alpha * xd[15]
rate[32] = 3 * AMPA_delta_1 * xd[4]
rate[33] = 2 * AMPA_delta_2 * xd[9]
#4column-BACK
rate[34] = 1 * AMPA_gamma_2 * xd[12]
rate[35] = 1 * AMPA_gamma_1 * xd[9]
rate[36] = 2 * AMPA_beta * xd[4]
#5column-GO
rate[37] = 1 * AMPA_alpha * xd[16]
rate[38] = 4 * AMPA_delta_1 * xd[5]
rate[39] = 3 * AMPA_delta_2 * xd[10]
#5column-BACK
rate[40] = 1 * AMPA_gamma_2 * xd[13]
rate[41] = 1 * AMPA_gamma_1 * xd[10]
rate[42] = 4 * AMPA_beta * xd[5]
# NMDA
#1line-GO
rate[43] = NMDA_N2A_ka * xd[17] * Glu
rate[44] = NMDA_N2A_kb * xd[18] * Glu
rate[45] = NMDA_N2A_kc * xd[19]
rate[46] = NMDA_N2A_kd * xd[20]
rate[47] = NMDA_N2A_ke * xd[21]
rate[48] = NMDA_N2A_kf * xd[22]
#1line-BACK
rate[49] = NMDA_N2A_k_f * xd[23]
rate[50] = NMDA_N2A_k_e * xd[22]
rate[51] = NMDA_N2A_k_d * xd[21]
rate[52] = NMDA_N2A_k_c * xd[20]
rate[53] = NMDA_N2A_k_b * xd[19]
rate[54] = NMDA_N2A_k_a * xd[18]
# Sampling
rate[55] = sampling_rate
# R-type VGCC
alpha_m_r, beta_m_r = rates_m_r(Vsp)
alpha_h_r, beta_h_r = rates_h_r(Vsp)
rate[56] = xd[25] * alpha_m_r * frwd_VGCC
rate[57] = xd[26] * beta_m_r * bcwd_VGCC
rate[58] = xd[25] * alpha_h_r * frwd_VGCC
rate[59] = xd[27] * beta_h_r * bcwd_VGCC
rate[60] = xd[26] * alpha_h_r * frwd_VGCC
rate[61] = xd[28] * beta_h_r * bcwd_VGCC
rate[62] = xd[27] * alpha_m_r * frwd_VGCC
rate[63] = xd[28] * beta_m_r * bcwd_VGCC
# T-type VGCC
alpha_m_t, beta_m_t = rates_m_t(Vsp)
alpha_h_t, beta_h_t = rates_h_t(Vsp)
rate[64] = xd[29] * alpha_m_t * frwd_VGCC
rate[65] = xd[30] * beta_m_t * bcwd_VGCC # this one can have a high rate
rate[66] = xd[29] * alpha_h_t * frwd_VGCC
rate[67] = xd[31] * beta_h_t * bcwd_VGCC
rate[68] = xd[30] * alpha_h_t * frwd_VGCC
rate[69] = xd[32] * beta_h_t * bcwd_VGCC
rate[70] = xd[31] * alpha_m_t * frwd_VGCC
rate[71] = xd[32] * beta_m_t * bcwd_VGCC # this one can have a high rate
# L-type VGCC
alpha_l, beta_1_l, beta_2_l = rates_l(Vsp)
rate[72] = xd[33] * alpha_l * frwd_VGCC
rate[73] = xd[34] * beta_1_l * bcwd_VGCC
rate[74] = xd[33] * alpha_l * frwd_VGCC
rate[75] = xd[35] * beta_2_l * bcwd_VGCC
# LTD/LTP
#the 6 lines take 50ns on 200ns, 1/4 of computations are here!!
D_rate = plasticityRate(xc[27], 2, K_D) / t_D
P_rate = plasticityRate(xc[28], 2, K_P) / t_P
rate[76] = xd[36] * D_rate
rate[77] = xd[37] * P_rate
rate[78] = xd[36] * P_rate
rate[79] = xd[38] * D_rate
# NMDA GLUN2B
#1line-GO
rate[80] = NMDA_N2B_sa * xd[39] * Glu
rate[81] = NMDA_N2B_sb * xd[40] * Glu
rate[82] = NMDA_N2B_sc * xd[41]
rate[83] = NMDA_N2B_sd * xd[42]
rate[84] = NMDA_N2B_se * xd[43]
rate[85] = NMDA_N2B_sf * xd[44]
#1line-BACK
rate[86] = NMDA_N2B_s_f * xd[45]
rate[87] = NMDA_N2B_s_e * xd[44]
rate[88] = NMDA_N2B_s_d * xd[43]
rate[89] = NMDA_N2B_s_c * xd[42]
rate[90] = NMDA_N2B_s_b * xd[41]
rate[91] = NMDA_N2B_s_a * xd[40]
# GABA
rate[92] = GABA_r_b1 * xd[46] * Glu #to simplify, we use the same amount at the same time
rate[93] = GABA_r_u1 * xd[47]
rate[94] = GABA_r_b2 * xd[47] * Glu
rate[95] = GABA_r_u2 * xd[48]
rate[96] = GABA_r_ro1 * xd[47]
rate[97] = GABA_r_c1 * xd[49]
rate[98] = GABA_r_ro2 * xd[48]
rate[99] = GABA_r_c2 * xd[50]
bound = 0.0
if sum_rate == false
return 0.0, bound
else
return sum(rate), bound
end
endR_synapse (generic function with 2 methods)Alternatively, for the JumpProcesses package we need to define the jumps. First we define a macro to aid us in the definition of the jumps.
"""
Macro to help with defining the Synapse problem for the JumpProcesses package, used in the `J_synapse` function body.
# Arguments
- i : Jump index
- p_synapse : Synapse parameters
- rate_ex : Rate as Julia expression
- urate_ex : Rate upper bound as a Julia expression
- rateinterval_ex : Rate interval as a Julia expression
"""
macro j_jump(i, p_synapse, nu, rate_ex, urate_ex = nothing, rateinterval_ex = nothing)
assignments = Expr[]
alpha_beta_regex = r"(alpha|beta)_(m_r|h_r|m_t|h_t|l|1_l|2_l)"
alpha_beta_matches = Set([m.match for m in eachmatch(alpha_beta_regex, "$rate_ex")])
if length(alpha_beta_matches) > 0
for m in ("alpha_1_l", "alpha_2_l", "beta_l")
if m in alpha_beta_matches
throw(DomainError(m, "this variable does not exist in the model."))
end
end
push!(assignments, :(Vsp = u[1]))
if "alpha_m_r" in alpha_beta_matches || "beta_m_r" in alpha_beta_matches
push!(assignments, :((alpha_m_r, beta_m_r) = rates_m_r(Vsp)))
end
if "alpha_h_r" in alpha_beta_matches || "beta_h_r" in alpha_beta_matches
push!(assignments, :((alpha_h_r, beta_h_r) = rates_h_r(Vsp)))
end
if "alpha_m_t" in alpha_beta_matches || "beta_m_t" in alpha_beta_matches
push!(assignments, :((alpha_m_t, beta_m_t) = rates_m_t(Vsp)))
end
if "alpha_h_t" in alpha_beta_matches || "beta_h_t" in alpha_beta_matches
push!(assignments, :((alpha_h_t, beta_h_t) = rates_h_t(Vsp)))
end
if "alpha_l" in alpha_beta_matches ||
"beta_1_l" in alpha_beta_matches ||
"beta_2_l" in alpha_beta_matches
push!(assignments, :((alpha_l, beta_1_l, beta_2_l) = rates_l(Vsp)))
end
end
if occursin("D_rate", "$rate_ex")
push!(assignments, :(D_rate = plasticityRate(u[27], 2, K_D) / t_D))
end
if occursin("P_rate", "$rate_ex")
push!(assignments, :(P_rate = plasticityRate(u[28], 2, K_D) / t_P))
end
ex = Expr[]
push!(
ex,
quote
@unpack_SynapseParams $(esc(p_synapse))
@inline @inbounds function rate(u, p, t)
$(assignments...)
return $rate_ex
end
@inline @inbounds function affect!(integrator)
for (j, a) in zip(findnz($(esc(nu))[$(esc(i)), :])...)
integrator.p.xd[j] += a
end
end
end
)
if !isnothing(urate_ex)
push!(ex, quote
max_m_r = rates_m_r(1_000.0)[1]
max_h_r = rates_h_r(1_000.0)[2]
max_m_t = rates_m_t(1_000.0)[1]
max_h_t = rates_h_t(1_000.0)[2]
max_alpha_l = rates_l(1_000)[1]
max_beta_1_l, max_beta_2_l = rates_l(-1_000)[2:3]
@inline @inbounds function urate(u, p, t)
return $urate_ex
end
@inline @inbounds function rateinterval(u, p, t)
return $rateinterval_ex
end
end)
end
if isnothing(urate_ex)
push!(ex, :(ConstantRateJump(rate, affect!)))
else
push!(
ex,
:(VariableRateJump(rate, affect!; urate = urate, rateinterval = rateinterval))
)
end
quote
$(ex...)
end
endMain.var"##WeaveSandBox#277".@j_jumpNext, we define the jumps themselves.
function J_synapse(p_synapse::SynapseParams, nu)
# we order the jumps in their order they appear in the dependency graph
jumps = JumpSet(;
constant_jumps = (
# AMPA
#2line-GO
@j_jump(1, p_synapse, nu, 4 * AMPA_k1 * p.Glu * p.xd[1]), # 1
@j_jump(2, p_synapse, nu, 3 * AMPA_k1 * p.Glu * p.xd[2]), # 2
@j_jump(3, p_synapse, nu, 2 * AMPA_k1 * p.Glu * p.xd[3]), # 3
@j_jump(4, p_synapse, nu, 1 * AMPA_k1 * p.Glu * p.xd[4]), # 4
#2line-BACK
@j_jump(5, p_synapse, nu, 4 * AMPA_k_1 * p.xd[5]), # 5
@j_jump(6, p_synapse, nu, 3 * AMPA_k_1 * p.xd[4]), # 6
@j_jump(7, p_synapse, nu, 2 * AMPA_k_1 * p.xd[3]), # 7
@j_jump(8, p_synapse, nu, 1 * AMPA_k_1 * p.xd[2]), # 8
#3line-GO
@j_jump(9, p_synapse, nu, 3 * AMPA_k1 * p.Glu * p.xd[6]), # 9
@j_jump(10, p_synapse, nu, 3 * AMPA_k1 * p.Glu * p.xd[7]), # 10
@j_jump(11, p_synapse, nu, 2 * AMPA_k1 * p.Glu * p.xd[8]), # 11
@j_jump(12, p_synapse, nu, 1 * AMPA_k1 * p.Glu * p.xd[9]), # 12
#3line-BACK
@j_jump(13, p_synapse, nu, 3 * AMPA_k_1 * p.xd[10]), # 13
@j_jump(14, p_synapse, nu, 2 * AMPA_k_1 * p.xd[9]), # 14
@j_jump(15, p_synapse, nu, 1 * AMPA_k_1 * p.xd[8]), # 15
@j_jump(16, p_synapse, nu, 1 * AMPA_k_2 * p.xd[7]), # 16
#4line-GO
@j_jump(17, p_synapse, nu, 2 * AMPA_k1 * p.Glu * p.xd[11]), # 17
@j_jump(18, p_synapse, nu, 1 * AMPA_k1 * p.Glu * p.xd[12]), # 18
#4line-BACK
@j_jump(19, p_synapse, nu, 2 * AMPA_k_1 * p.xd[13]), # 19
@j_jump(20, p_synapse, nu, 1 * AMPA_k_1 * p.xd[12]), # 20
#1column-GO-BACK
@j_jump(21, p_synapse, nu, 4 * AMPA_delta_0 * p.xd[1]), # 21
@j_jump(22, p_synapse, nu, 1 * AMPA_gamma_0 * p.xd[6]), # 22
#2column-GO-BACK
@j_jump(23, p_synapse, nu, 1 * AMPA_delta_1 * p.xd[2]), # 23
@j_jump(24, p_synapse, nu, 1 * AMPA_gamma_1 * p.xd[7]), # 24
#3column-GO
@j_jump(25, p_synapse, nu, 1 * AMPA_alpha * p.xd[14]), # 25
@j_jump(26, p_synapse, nu, 2 * AMPA_delta_1 * p.xd[3]), # 26
@j_jump(27, p_synapse, nu, 1 * AMPA_delta_2 * p.xd[8]), # 27
#3column-BACK
@j_jump(28, p_synapse, nu, 1 * AMPA_gamma_2 * p.xd[11]), # 28
@j_jump(29, p_synapse, nu, 1 * AMPA_gamma_1 * p.xd[8]), # 29
@j_jump(30, p_synapse, nu, 2 * AMPA_beta * p.xd[3]), # 30
#4column-GO
@j_jump(31, p_synapse, nu, 1 * AMPA_alpha * p.xd[15]), # 31
@j_jump(32, p_synapse, nu, 3 * AMPA_delta_1 * p.xd[4]), # 32
@j_jump(33, p_synapse, nu, 2 * AMPA_delta_2 * p.xd[9]), # 33
#4column-BACK
@j_jump(34, p_synapse, nu, 1 * AMPA_gamma_2 * p.xd[12]), # 34
@j_jump(35, p_synapse, nu, 1 * AMPA_gamma_1 * p.xd[9]), # 35
@j_jump(36, p_synapse, nu, 2 * AMPA_beta * p.xd[4]), # 36
#5column-GO
@j_jump(37, p_synapse, nu, 1 * AMPA_alpha * p.xd[16]), # 37
@j_jump(38, p_synapse, nu, 4 * AMPA_delta_1 * p.xd[5]), # 38
@j_jump(39, p_synapse, nu, 3 * AMPA_delta_2 * p.xd[10]), # 39
#5column-BACK
@j_jump(40, p_synapse, nu, 1 * AMPA_gamma_2 * p.xd[13]), # 40
@j_jump(41, p_synapse, nu, 1 * AMPA_gamma_1 * p.xd[10]), # 41
@j_jump(42, p_synapse, nu, 4 * AMPA_beta * p.xd[5]), # 42
# NMDA
#1line-GO
@j_jump(43, p_synapse, nu, NMDA_N2A_ka * p.xd[17] * p.Glu), # 43
@j_jump(44, p_synapse, nu, NMDA_N2A_kb * p.xd[18] * p.Glu), # 44
@j_jump(45, p_synapse, nu, NMDA_N2A_kc * p.xd[19]), # 45
@j_jump(46, p_synapse, nu, NMDA_N2A_kd * p.xd[20]), # 46
@j_jump(47, p_synapse, nu, NMDA_N2A_ke * p.xd[21]), # 47
@j_jump(48, p_synapse, nu, NMDA_N2A_kf * p.xd[22]), # 48
#1line-BACK
@j_jump(49, p_synapse, nu, NMDA_N2A_k_f * p.xd[23]), # 49
@j_jump(50, p_synapse, nu, NMDA_N2A_k_e * p.xd[22]), # 50
@j_jump(51, p_synapse, nu, NMDA_N2A_k_d * p.xd[21]), # 51
@j_jump(52, p_synapse, nu, NMDA_N2A_k_c * p.xd[20]), # 52
@j_jump(53, p_synapse, nu, NMDA_N2A_k_b * p.xd[19]), # 53
@j_jump(54, p_synapse, nu, NMDA_N2A_k_a * p.xd[18]), # 54
# NMDA GLUN2B
#1line-GO
@j_jump(80, p_synapse, nu, NMDA_N2B_sa * p.xd[39] * p.Glu), # 80
@j_jump(81, p_synapse, nu, NMDA_N2B_sb * p.xd[40] * p.Glu), # 81
@j_jump(82, p_synapse, nu, NMDA_N2B_sc * p.xd[41]), # 82
@j_jump(83, p_synapse, nu, NMDA_N2B_sd * p.xd[42]), # 83
@j_jump(84, p_synapse, nu, NMDA_N2B_se * p.xd[43]), # 84
@j_jump(85, p_synapse, nu, NMDA_N2B_sf * p.xd[44]), # 85
#1line-BACK
@j_jump(86, p_synapse, nu, NMDA_N2B_s_f * p.xd[45]), # 86
@j_jump(87, p_synapse, nu, NMDA_N2B_s_e * p.xd[44]), # 87
@j_jump(88, p_synapse, nu, NMDA_N2B_s_d * p.xd[43]), # 88
@j_jump(89, p_synapse, nu, NMDA_N2B_s_c * p.xd[42]), # 89
@j_jump(90, p_synapse, nu, NMDA_N2B_s_b * p.xd[41]), # 90
@j_jump(91, p_synapse, nu, NMDA_N2B_s_a * p.xd[40]), # 91
# GABA
@j_jump(92, p_synapse, nu, GABA_r_b1 * p.xd[46] * p.Glu), # 92 to simplify, we use the same amount at the same time)
@j_jump(93, p_synapse, nu, GABA_r_u1 * p.xd[47]), # 93
@j_jump(94, p_synapse, nu, GABA_r_b2 * p.xd[47] * p.Glu), # 94
@j_jump(95, p_synapse, nu, GABA_r_u2 * p.xd[48]), # 95
@j_jump(96, p_synapse, nu, GABA_r_ro1 * p.xd[47]), # 96
@j_jump(97, p_synapse, nu, GABA_r_c1 * p.xd[49]), # 97
@j_jump(98, p_synapse, nu, GABA_r_ro2 * p.xd[48]), # 98
@j_jump(99, p_synapse, nu, GABA_r_c2 * p.xd[50]), # 99
),
variable_jumps = (
# R-type VGCC
@j_jump(56,
p_synapse,
nu,
p.xd[25] * alpha_m_r * frwd_VGCC,
p.xd[25] * max_m_r * frwd_VGCC,
typemax(Float64)), # 56
@j_jump(57,
p_synapse,
nu,
p.xd[26] * beta_m_r * bcwd_VGCC,
p.xd[26] * max_m_r * frwd_VGCC,
typemax(Float64)), # 57
@j_jump(58,
p_synapse,
nu,
p.xd[25] * alpha_h_r * frwd_VGCC,
p.xd[25] * max_h_r * frwd_VGCC,
typemax(Float64)), # 58
@j_jump(59,
p_synapse,
nu,
p.xd[27] * beta_h_r * bcwd_VGCC,
p.xd[27] * max_h_r * bcwd_VGCC,
typemax(Float64)), # 59
@j_jump(60,
p_synapse,
nu,
p.xd[26] * alpha_h_r * frwd_VGCC,
p.xd[26] * max_h_r * frwd_VGCC,
typemax(Float64)), # 60
@j_jump(61,
p_synapse,
nu,
p.xd[28] * beta_h_r * bcwd_VGCC,
p.xd[28] * max_h_r * bcwd_VGCC,
typemax(Float64)), # 61
@j_jump(62,
p_synapse,
nu,
p.xd[27] * alpha_m_r * frwd_VGCC,
p.xd[27] * max_m_r * frwd_VGCC,
typemax(Float64)), # 62
@j_jump(63,
p_synapse,
nu,
p.xd[28] * beta_m_r * bcwd_VGCC,
p.xd[28] * max_m_r * bcwd_VGCC,
typemax(Float64)), # 63
# T-type VGCC
@j_jump(64,
p_synapse,
nu,
p.xd[29] * alpha_m_t * frwd_VGCC,
p.xd[29] * max_m_t * frwd_VGCC,
typemax(Float64)), # 64
@j_jump(65,
p_synapse,
nu,
p.xd[30] * beta_m_t * bcwd_VGCC,
p.xd[30] * max_m_t * bcwd_VGCC,
typemax(Float64)), # 65 this one can have a high rate
@j_jump(66,
p_synapse,
nu,
p.xd[29] * alpha_h_t * frwd_VGCC,
p.xd[29] * max_h_t * frwd_VGCC,
typemax(Float64)), # 66
@j_jump(67,
p_synapse,
nu,
p.xd[31] * beta_h_t * bcwd_VGCC,
p.xd[31] * max_h_t * bcwd_VGCC,
typemax(Float64)), # 67
@j_jump(68,
p_synapse,
nu,
p.xd[30] * alpha_h_t * frwd_VGCC,
p.xd[30] * max_h_t * frwd_VGCC,
typemax(Float64)), # 68
@j_jump(69,
p_synapse,
nu,
p.xd[32] * beta_h_t * bcwd_VGCC,
p.xd[32] * max_h_t * bcwd_VGCC,
typemax(Float64)), # 69
@j_jump(70,
p_synapse,
nu,
p.xd[31] * alpha_m_t * frwd_VGCC,
p.xd[31] * max_m_t * frwd_VGCC,
typemax(Float64)), # 70
@j_jump(71,
p_synapse,
nu,
p.xd[32] * beta_m_t * bcwd_VGCC,
p.xd[32] * max_m_t * bcwd_VGCC,
typemax(Float64)), # 71, this one can have a high rate
# L-type VGCC
@j_jump(72,
p_synapse,
nu,
p.xd[33] * alpha_l * frwd_VGCC,
p.xd[33] * max_alpha_l * frwd_VGCC,
typemax(Float64)), # 72
@j_jump(73,
p_synapse,
nu,
p.xd[34] * beta_1_l * bcwd_VGCC,
p.xd[34] * max_beta_1_l * bcwd_VGCC,
typemax(Float64)), # 73
@j_jump(74,
p_synapse,
nu,
p.xd[33] * alpha_l * frwd_VGCC,
p.xd[33] * max_alpha_l * frwd_VGCC,
typemax(Float64)), # 74
@j_jump(75,
p_synapse,
nu,
p.xd[35] * beta_2_l * bcwd_VGCC,
p.xd[35] * max_beta_2_l * bcwd_VGCC,
typemax(Float64)), # 75
# LTD/LTP
@j_jump(76, p_synapse, nu, p.xd[36] * D_rate, 1, typemax(Float64)), # 76
@j_jump(77, p_synapse, nu, p.xd[37] * P_rate, 1, typemax(Float64)), # 77
@j_jump(78, p_synapse, nu, p.xd[36] * P_rate, 1, typemax(Float64)), # 78
@j_jump(79, p_synapse, nu, p.xd[38] * D_rate, 1, typemax(Float64)), # 79
),
)
return jumps
endJ_synapse (generic function with 1 method)R_synapse and J_synapse define the exact same discrete problem. The comments at the end of the line in J_synapse correspond to the rate index defined in R_synapse. For example, in R_synapse we have rate[1]
rate[1] = 4 * AMPA_k1 * Glu * xd[1]Equivalently, in J_synapse we have the equivalent formulation in terms of a jump using our macro.
@j_jump(1, p_synapse, nu, 4 * AMPA_k1 * p.Glu * p.xd[1]), # 1Also, note that we modify the order of jumps in J_synapse compared to R_synapse because we bundle ConstantRateJump and VariableRateJump separately. Algorithms in JumpProcesses will approach each of these jumps in a different way.
We also remove the sampling rate from J_synapse (rate[55] in R_synapse) as it is not needed for JumpProcesses. The package can take a snapshot of the evolution at any point desired.
Problem wrappers
We define wrappers for setting up and solving problems involving synapses.
First, we define the problem for the PDMP package.
function SynapseProblem(
xc,
xd,
t1,
t2,
events_bap,
bap_by_epsp,
glu,
p_synapse,
nu,
algo::T,
agg = nothing;
vr_agg = VR_FRM(),
saveat = [],
save_everystep = isempty(saveat),
kwargs...,
) where {T<:CHV}
problem = PDMP.PDMPProblem(
(dxc, xc, xd, p, t) -> F_synapse(dxc, xc, xd, p, t, events_bap, bap_by_epsp),
(rate, xc, xd, p, t, sum_rate) -> R_synapse(rate, xc, xd, p, t, sum_rate, glu),
nu,
xc,
xd,
p_synapse,
(t1, t2);
Ncache = 12 # this option is for AD in PreallocationTools
)
sol = solve(problem, algo; kwargs...)
return sol
endSynapseProblem (generic function with 2 methods)Second, we define the problem for the JumpProcesses package.
We define a custom saving callback for the JumpProcesses problem to bring the saving behaviour as close as possible to the PDMP problem. Our callback will save jumps whenever the integrator steps and save_modified == true.
using DiffEqCallbacks: SavedValues, SavingAffect
import DataStructures
# adapted from DiffEqCallbacks.jl/src/saving.jl
function (affect!::SavingAffect)(integrator, force_save = false)
just_saved = false
# see OrdinaryDiffEq.jl -> integrator_utils.jl, function savevalues!
while !isempty(affect!.saveat) &&
integrator.tdir * first(affect!.saveat) <= integrator.tdir * integrator.t # Perform saveat
affect!.saveiter += 1
curt = pop!(affect!.saveat) # current time
if curt != integrator.t # If <t, interpolate
if integrator isa SciMLBase.AbstractODEIntegrator
# Expand lazy dense for interpolation
SciMLBase.addsteps!(integrator)
end
if !SciMLBase.isinplace(integrator.sol.prob)
curu = integrator(curt)
else
curu = first(SciMLBase.get_tmp_cache(integrator))
integrator(curu, curt) # inplace since save_func allocates
end
copyat_or_push!(affect!.saved_values.t, affect!.saveiter, curt)
copyat_or_push!(affect!.saved_values.saveval, affect!.saveiter,
affect!.save_func(curu, curt, integrator), Val{false})
else # ==t, just save
just_saved = true
copyat_or_push!(affect!.saved_values.t, affect!.saveiter, integrator.t)
copyat_or_push!(affect!.saved_values.saveval, affect!.saveiter,
affect!.save_func(integrator.u, integrator.t, integrator),
Val{false})
end
end
if !just_saved && affect!.save_everystep ||
force_save ||
(
affect!.save_end &&
# ensures we don't save twice; this the only difference from the original source
affect!.saved_values.t[affect!.saveiter] != integrator.t &&
integrator.t == integrator.sol.prob.tspan[end]
)
affect!.saveiter += 1
copyat_or_push!(affect!.saved_values.t, affect!.saveiter, integrator.t)
copyat_or_push!(
affect!.saved_values.saveval,
affect!.saveiter,
affect!.save_func(integrator.u, integrator.t, integrator),
Val{false}
)
end
if isdefined(SciMLBase, :derivative_discontinuity!)
return SciMLBase.derivative_discontinuity!(integrator, false)
end
return SciMLBase.u_modified!(integrator, false)
end
# adapted from DiffEqCallbacks.jl/src/saving.jl
function saving_initialize!(cb, u, t, integrator, last_modified_value)
integrator.p.xd .= integrator.p.xd0
last_modified_value[] = copy(integrator.p.xd)
saveat = deepcopy(integrator.opts.saveat)
while !isempty(cb.affect!.saveat)
pop!(cb.affect!.saveat)
end
while !isempty(saveat)
push!(cb.affect!.saveat, pop!(saveat))
end
cb.affect!.save_everystep = integrator.opts.save_everystep
cb.affect!.save_start = integrator.opts.save_start
cb.affect!.save_end = integrator.opts.save_end
cb.affect!.saveiter = 0
return cb.affect!.save_start && cb.affect!(integrator, true)
end
# adapted from DiffEqCallbacks.jl/src/saving.jl
function SavingCallback(save_func, saved_values::SavedValues; save_modified = true)
saveat_internal = DataStructures.BinaryHeap{eltype(saved_values.t)}(DataStructures.FasterForward())
last_modified_value = Ref{eltype(saved_values.saveval)}()
affect! = SavingAffect(
save_func,
saved_values,
saveat_internal,
nothing,
false,
false,
false,
0
)
# only save when save_modified is true; SavingCallback from DiffEqCallbacks
# saves every step regardless of save_modified
condition = if save_modified
function (u, t, integrator)
if integrator.p.xd != last_modified_value[]
copyto!(last_modified_value[], integrator.p.xd)
push!(affect!.saveat, t)
end
return true
end
else
function (u, t, integrator)
return true
end
end
return DiscreteCallback(
condition,
affect!;
initialize = (cb, u, t, integrator) ->
saving_initialize!(cb, u, t, integrator, last_modified_value),
save_positions = (false, false)
)
endSavingCallback (generic function with 1 method)Next, we define our problem wrapper that uses our custom saving callback.
function buildRxDependencyGraph(nu)
numrxs, _ = size(nu)
dep_graph = [Vector{Int}() for n in 1:(numrxs - 1)]
for rx in 1:numrxs
if rx == 55 # no need to track the Poisson process
continue
end
rx_ix = rx
if 56 <= rx < 80
rx_ix += 19
elseif rx >= 80
rx_ix -= 25
end
for (spec, _) in zip(findnz(nu[rx, :])...)
# we need to reorder the indices according to the order
# they apper in the problem
for (dependent_rx, _) in zip(findnz(nu[:, spec])...)
# we need to reorder the indices according to the order
# they apper in the problem
dependent_rx_ix = dependent_rx
if 56 <= dependent_rx < 80
dependent_rx_ix += 19
elseif dependent_rx >= 80
dependent_rx_ix -= 25
end
push!(dep_graph[rx_ix], dependent_rx_ix)
end
end
end
return dep_graph
end
function SynapseProblem(
xc,
xd,
t1,
t2,
events_bap,
bap_by_epsp,
glu,
p_synapse,
nu,
algo,
agg;
vr_agg = VR_FRM(),
jumps = nothing,
save_positions = (false, true),
saveat = [],
save_everystep = isempty(saveat),
kwargs...,
)
p = (
xd0 = copy(xd),
xd = copy(xd),
Glu = p_synapse.glu_amp * glu,
p_synapse = p_synapse
)
oprob = ODEProblem(
(dxc, xc, p,
t) -> F_synapse(dxc, xc, p.xd, p.p_synapse, t, events_bap, bap_by_epsp),
xc,
(t1, t2),
p
)
xdsol = SavedValues(typeof(t1), typeof(xd))
dep_graph = buildRxDependencyGraph(nu)
callback = SavingCallback(
(u, t, integrator) -> copy(integrator.p.xd),
xdsol;
save_modified = typeof(save_positions) <: Bool ? save_positions : save_positions[2]
)
jprob = JumpProblem(
oprob,
agg,
jumps;
vr_aggregator = vr_agg,
dep_graph,
save_positions,
saveat,
save_everystep,
callback
)
sol = (xcsol = solve(jprob, algo; saveat, save_everystep, kwargs...), xdsol = xdsol)
return sol
endSynapseProblem (generic function with 3 methods)Assembling it all
We define functions to run the evolution of the whole synapse. The evolution includes a period before glutamate is released and after.
# adapted from SynapseElife/src/SynapseModel.jl
function evolveSynapse(
xc0::Vector{T},
xd0,
p_synapse::SynapseParams,
events_sorted_times,
is_pre_or_post_event,
bap_by_epsp,
is_glu_released,
nu,
algos,
agg = nothing;
vr_agg,
progress = false,
abstol = 1e-8,
reltol = 1e-7,
save_positions = (false, true),
saveat = [],
kwargs...,
) where {T}
tt, XC,
XD = evolveSynapse_noformat(
xc0,
xd0,
p_synapse,
events_sorted_times,
is_pre_or_post_event,
bap_by_epsp,
is_glu_released,
nu,
algos,
agg;
vr_agg,
progress,
abstol,
reltol,
save_positions,
saveat,
kwargs...
)
out = formatSynapseResult(tt, XC, XD)
end
# adapted from SynapseElife/src/SynapseModel.jl
function evolveSynapse_noformat(
xc0::Vector{T},
xd0,
p_synapse::SynapseParams,
events_sorted_times,
is_pre_or_post_event,
bap_by_epsp,
is_glu_released,
nu,
algos,
agg = nothing;
vr_agg,
progress = false,
abstol = 1e-8,
reltol = 1e-7,
save_positions = (false, true),
saveat = [],
kwargs...,
) where {T}
if save_positions isa Tuple{Bool, Bool}
save_positionsON = save_positions
save_positionsOFF = save_positions
else
save_positionsON = save_positions[1]
save_positionsOFF = save_positions[2]
end
@assert eltype(is_pre_or_post_event) == Bool "Provide booleans for glutamate releases."
@assert eltype(is_glu_released) == Bool "Provide booleans for glutamate indices."
XC = VectorOfArray([xc0]) # vector to hold continuous variables
if isnothing(agg)
XD = VectorOfArray([xd0]) # vector to hold discrete variables
jumps = nothing
else
XD = VectorOfArray([xd0])
jumps = J_synapse(p_synapse, nu)
end
tt = [0.0] # vector of times
# we collect which external events correspond to BaPs
events_bap = events_sorted_times[is_pre_or_post_event .== false]
# function to simulate the synapse when Glutamate is ON
SimGluON =
(xc, xd, t1, t2, glu) -> SynapseProblem(
xc,
xd,
t1,
t2,
events_bap,
bap_by_epsp,
glu,
p_synapse,
nu,
algos[1],
agg;
vr_agg,
jumps,
reltol,
abstol,
saveat,
save_positions = save_positionsON,
kwargs...,
)
# function to simulate the synapse when Glutamate is OFF
SimGluOFF =
(xc, xd, t1, t2) -> SynapseProblem(
xc,
xd,
t1,
t2,
events_bap,
bap_by_epsp,
zero(T),
p_synapse,
nu,
algos[2],
agg;
vr_agg,
jumps,
reltol,
abstol,
saveat,
save_positions = save_positionsOFF,
kwargs...,
)
# random variable for Glutamate concentration
gluDist = Gamma(1 / p_synapse.glu_cv^2, p_synapse.glu_cv^2)
# we loop over the external events, simulate them and append to res
for (eveindex, eve) in enumerate(events_sorted_times)
if is_pre_or_post_event[eveindex] == true # it is a pre-synaptic event
# we simulate the synapse with Glutamate OFF until event time
# then we put Glutamate ON for dt = p_synapse.glu_width with variable amplitude (concentration)
# simulate the event with Glutamate OFF
res = SimGluOFF(XC[:, end], XD[:, end], tt[end], eve)
formatSimResult!(res, XC, XD, tt)
gluamp = rand(gluDist)
# simulate the event with Glutamate ON
# variability here
res = SimGluON(
XC[:, end],
XD[:, end],
eve,
eve + p_synapse.glu_width,
ifelse(is_glu_released[eveindex], gluamp, zero(T))
)
formatSimResult!(res, XC, XD, tt)
end
end
# reaching tend: we simulate the synapse with Glutamate OFF until simulation end time required
# by the user. In most protocol, this is taking most of the time.
res = SimGluOFF(XC[:, end], XD[:, end], tt[end], p_synapse.t_end)
formatSimResult!(res, XC, XD, tt)
if isnothing(agg)
@info "last bit" agg length(res.time) tt[end] p_synapse.t_end
else
@info "last bit" agg length(res.xcsol.t) tt[end] p_synapse.t_end
end
if tt[end] != p_synapse.t_end
@warn "The simulation did not reach requested simulated time."
end
return (t = tt, XC = XC, XD = XD)
end
function formatSimResult!(res::PDMP.PDMPResult, XC, XD, tt)
append!(XC, res.xc)
append!(XD, res.xd)
append!(tt, res.time)
nothing
end
function formatSimResult!(res::NamedTuple, XC, XD, tt)
append!(XC, VectorOfArray(res.xcsol.u))
append!(XD, VectorOfArray(res.xdsol.saveval))
append!(tt, res.xcsol.t)
nothing
end
# adapted from SynapseElife/src/SynapseModel.jl
function formatSynapseResult(tt, XC, XD)
namesC = (
:Vsp,
:Vdend,
:Vsoma,
:λ,
:ImbufCa,
:Ca,
:Dye,
:CaM0,
:CaM2C,
:CaM2N,
:CaM4,
:mCaN,
:CaN4,
:mKCaM,
:KCaM0,
:KCaM2N,
:KCaM2C,
:KCaM4,
:PCaM0,
:PCaM2C,
:PCaM2N,
:PCaM4,
:P,
:P2,
:LTD,
:LTP,
:act_D,
:act_P,
:m,
:h,
:n,
:SK,
:λ_age,
:λ_aux
)
values = (XC[i, :] for i in 1:length(namesC))
return (t = tt, XD = XD, XC = XC, zip(namesC, values)...)
endformatSynapseResult (generic function with 1 method)Algorithms to benchmark
The JumpProcesses algorithms allow us to save at regular intervals with saveat. Thus, rather than saving when a jump occurs, we save at the same average frequency as obtained with PDMP.
const solver = AutoTsit5(Rosenbrock23());
const algorithms = (
(
label = "PDMP",
agg = nothing,
vr_agg = VR_FRM(),
solver = (CHV(solver), CHV(solver)),
saveat = [],
),
(
label = "Coevolve",
agg = Coevolve(),
vr_agg = VR_FRM(),
solver = (solver, solver),
saveat = 1 / p_synapse.sampling_rate,
),
(
label = "Direct(VR_FRM)",
agg = Direct(),
vr_agg = VR_FRM(),
solver = (solver, solver),
saveat = 1 / p_synapse.sampling_rate,
),
(
label = "Direct(VR_Direct)",
agg = Direct(),
vr_agg = VR_Direct(),
solver = (solver, solver),
saveat = 1 / p_synapse.sampling_rate,
),
(
label = "Direct(VR_DirectFW)",
agg = Direct(),
vr_agg = VR_DirectFW(),
solver = (solver, solver),
saveat = 1 / p_synapse.sampling_rate,
),
);Example solutions
results = []
for algo in algorithms
push!(
results,
evolveSynapse(
xc0,
xd0,
p_synapse,
events_sorted_times,
is_pre_or_post_event,
bap_by_epsp,
[true],
nu,
algo.solver,
algo.agg;
algo.vr_agg,
save_positions = (false, true),
saveat = algo.saveat,
save_everystep = false
)
)
endfig = plot(xlabel = "Time", ylabel = "Voltage");
for (i, algo) in enumerate(algorithms)
res = results[i]
plot!(res.t, res.Vsp, label = algo.label)
end
title!("Vsp")
fig = plot(xlabel = "Time", ylabel = "N");
for (i, algo) in enumerate(algorithms)
res = results[i]
xd_arr = Array(res.XD)
n_xd = size(xd_arr, 2)
plot!(res.t[1:n_xd], xd_arr[1, :], label = algo.label)
end
title!("2line-Go, AMPA")
Benchmarking performance
bs = Vector{BenchmarkTools.Trial}()
for algo in algorithms
push!(
bs,
@benchmark(evolveSynapse(
xc0,
xd0,
p_synapse,
events_sorted_times,
is_pre_or_post_event,
bap_by_epsp,
[true],
nu,
$(algo).solver,
$(algo).agg;
$(algo).vr_agg,
save_positions = (false, true),
saveat = $(algo).saveat,
save_everystep = false
),
samples=50,
evals=1,
seconds=500,)
)
endlabels = [a.label for a in algorithms]
medtimes = [text(string(round(median(b).time/1e9, digits = 3), "s"), :center, 12)
for b in bs]
relmedtimes = [median(b).time for b in bs]
relmedtimes ./= relmedtimes[1]
bar(labels, relmedtimes, markeralpha = 0, series_annotation = medtimes, fmt = fmt)
title!("evolveSynapse (Median time)")
medmem = [text(string(round(median(b).memory/1e6, digits = 3), "Mb"), :center, 12)
for b in bs]
relmedmem = Float64[median(b).memory for b in bs]
relmedmem ./= relmedmem[1]
bar(labels, relmedmem, markeralpha = 0, series_annotation = medmem, fmt = fmt)
title!("evolveSynapse (Median memory)")
References
[1] Y. E. Rodrigues, C. M. Tigaret, H. Marie, C. O’Donnell, and R. Veltz, "A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics." bioRxiv, p. 2021.03.30.437703, Mar. 30, 2021. doi: 10.1101/2021.03.30.437703.
[2] Magee, J.C., Johnston, D., 1995. Characterization of single voltage-gated na+ and ca2+ channels in apical dendrites of rat ca1 pyramidal neurons. The Journal of physiology 487, 67–90.
Appendix
These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this benchmark, do the following commands:
using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/HybridJumps","Synapse.jmd")Computer Information:
Julia Version 1.12.7
Commit 6d172b025e4 (2026-08-15 08:05 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-18.1.7 (ORCJIT, znver2)
GC: Built with stock GC
Threads: 128 default, 1 interactive, 128 GC (on 128 virtual cores)
Environment:
JULIA_NUM_THREADS = auto
Package Information:
Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/HybridJumps/Project.toml`
[6e4b80f9] BenchmarkTools v1.8.0
⌃ [479239e8] Catalyst v16.4.3
[8f4d0f93] Conda v1.10.3
[864edb3b] DataStructures v0.19.6
⌃ [2b5f629d] DiffEqBase v7.21.2
[459566f4] DiffEqCallbacks v4.19.4
[31c24e10] Distributions v0.25.131
[86223c79] Graphs v1.15.0
[ccbc3e58] JumpProcesses v9.33.1
⌅ [b4f0291d] LazySets v5.3.0
⌃ [7ed4a6bd] LinearSolve v5.18.1
[1dea7af3] OrdinaryDiffEq v7.8.1
⌅ [d96e819e] Parameters v0.12.3
[86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12
[91a5bcdd] Plots v1.41.7
[438e738f] PyCall v1.96.4
⌃ [731186ca] RecursiveArrayTools v4.5.2
[31c91b34] SciMLBenchmarks v0.2.1 [loaded: `/home/crackauc/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/src/SciMLBenchmarks.jl` (v0.2.1) expected `/home/crackauc/.julia/packages/SciMLBenchmarks/ceJyd/src/SciMLBenchmarks.jl` (v0.2.1)]
[a6db7da4] SciMLLogging v2.1.0
⌃ [860ef19b] StableRNGs v1.0.4
⌃ [90137ffa] StaticArrays v1.9.22
[789caeaf] StochasticDiffEq v7.2.0
[37e2e46d] LinearAlgebra v1.12.0
[2f01184e] SparseArrays v1.12.0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`And the full manifest:
Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/HybridJumps/Manifest.toml`
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[a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
[cc61e674] Xorg_libxkbfile_jll v1.2.0+0
[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
[12413925] Xorg_xcb_util_image_jll v0.4.1+0
[2def613f] Xorg_xcb_util_jll v0.4.1+0
[975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
[35661453] Xorg_xkbcomp_jll v1.4.7+0
[33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[3161d3a3] Zstd_jll v1.5.7+1
[35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
[a4ae2306] libaom_jll v3.15.1+0
[0ac62f75] libass_jll v0.17.5+0
[1183f4f0] libdecor_jll v0.2.2+0
[8e53e030] libdrm_jll v2.4.134+0
[2db6ffa8] libevdev_jll v1.13.4+0
[f638f0a6] libfdk_aac_jll v2.0.4+0
[36db933b] libinput_jll v1.28.1+0
⌃ [b53b4c65] libpng_jll v1.6.58+0
[9a156e7d] libva_jll v2.23.0+0
[f27f6e37] libvorbis_jll v1.3.8+0
[009596ad] mtdev_jll v1.1.7+0
[1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
[dfaa095f] x265_jll v4.1.0+0
[d8fb68d0] xkbcommon_jll v1.13.0+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.7.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.12.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.3.0
[44cfe95a] Pkg v1.12.1
[de0858da] Printf v1.11.0
[9abbd945] Profile v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.12.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.3.1+2
[781609d7] GMP_jll v6.3.0+2
[deac9b47] LibCURL_jll v8.15.0+0
[e37daf67] LibGit2_jll v1.9.0+0
[29816b5a] LibSSH2_jll v1.11.3+1
[14a3606d] MozillaCACerts_jll v2025.11.4
[4536629a] OpenBLAS_jll v0.3.29+0
[05823500] OpenLibm_jll v0.8.7+0
[458c3c95] OpenSSL_jll v3.5.6+0
[efcefdf7] PCRE2_jll v10.44.0+1
[bea87d4a] SuiteSparse_jll v7.8.3+2
[83775a58] Zlib_jll v1.3.1+2
[8e850b90] libblastrampoline_jll v5.15.0+0
[8e850ede] nghttp2_jll v1.64.0+1
[3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`