/* * Role for G protein G-beta-gamma isoform specificity in synaptic * signal processing: a computational study * * Model Status * * This CellML model represents the pre-synaptic cell. The model * runs in both OpenCell and COR, but the membrane only depolarises * to -5 mV as opposed to ~40 mV. The units have been checked and * there are no inconsistencies (just equivalences). * * Model Structure * * ABSTRACT: Computational modeling is used to investigate the * functional impact of G protein-mediated presynaptic autoinhibition * on synaptic filtering properties. It is demonstrated that this * form of autoinhibition, which is relieved by depolarization, * acts as a high-pass filter. This contrasts with vesicle depletion, * which acts as a low-pass filter. Model parameters are adjusted * to reproduce kinetic slowing data from different Gbetagamma * dimeric isoforms, which produce different degrees of slowing. * With these sets of parameter values, we demonstrate that the * range of frequencies filtered out by the autoinhibition varies * greatly depending on the Gbetagamma isoform activated by the * autoreceptors. It is shown that G protein autoinhibition can * enhance the spatial contrast between a spatially distributed * high-frequency signal and surrounding low-frequency noise, providing * an alternate mechanism to lateral inhibition. It is also shown * that autoinhibition can increase the fidelity of coincidence * detection by increasing the signal-to-noise ratio in the postsynaptic * cell. The filter cut, the input frequency below which signals * are filtered, depends on several biophysical parameters in addition * to those related to Gbetagamma binding and unbinding. By varying * one such parameter, the rate at which transmitter unbinds from * autoreceptors, we show that the filter cut can be adjusted up * or down for several of the Gbetagamma isoforms. This allows * for great synapse-to-synapse variability in the distinction * between signal and noise. * * The original paper reference is cited below: * * Role for G Protein G-Beta-Gamma Isoform Specificity in Synaptic * Signal Processing: A Computational Study, Richard Bertram, Michelle * I. Arnot, and Gerald W. Zamponi, 2002,Journal of Neurophysiology * , 87, 2612-2623. PubMed ID: 11976397 * * reaction diagram * * [[Image file: bertram_2002.png]] * * Schematic diagram of the presynaptic model. */ import nsrunit; unit conversion on; unit s=1 second^1; unit ms=.001 second^1; unit uM=1E-3 meter^(-3)*mole^1; unit uA=1E-6 ampere^1; unit pS=1E-12 kilogram^(-1)*meter^(-2)*second^3*ampere^2; unit mV=.001 kilogram^1*meter^2*second^(-3)*ampere^(-1); unit cm2=1E-4 meter^2; unit per_cm2=1E4 meter^(-2); unit per_ms=1E3 second^(-1); unit uM_per_ms=1 meter^(-3)*second^(-1)*mole^1; unit per_uM_per_ms=1E6 meter^3*second^(-1)*mole^(-1); unit per_mV_per_ms=1E6 kilogram^(-1)*meter^(-2)*second^2*ampere^1; unit uM2_per_ms=.001 meter^(-6)*second^(-1)*mole^2; unit mV_per_uM=1 kilogram^1*meter^5*second^(-3)*ampere^(-1)*mole^(-1); unit uF_per_cm2=.01 kilogram^(-1)*meter^(-4)*second^4*ampere^2; unit uA_per_cm2=.01 meter^(-2)*ampere^1; unit pS_per_cm2=1E-8 kilogram^(-1)*meter^(-4)*second^3*ampere^2; unit mS_per_cm2=10 kilogram^(-1)*meter^(-4)*second^3*ampere^2; unit nm=1E-9 meter^1; unit uM2_nm=1E-15 meter^(-5)*mole^2; unit uM_per_cm2=10 meter^(-5)*mole^1; unit millijoule_per_mole_kelvin=.001 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit coulomb_per_mole=1 second^1*ampere^1*mole^(-1); unit uM_per_coulomb=1E-3 meter^(-3)*second^(-1)*ampere^(-1)*mole^1; unit um2_per_second=1E-12 meter^2*second^(-1); unit per_um3=1E18 meter^(-3); math main { realDomain time ms; time.min=0; extern time.max; extern time.delta; real R_gas_const millijoule_per_mole_kelvin; R_gas_const=8314.41; real Temp kelvin; Temp=310; real F coulomb_per_mole; F=96485; real V(time) mV; when(time=time.min) V=-65; real Cm uF_per_cm2; Cm=1; real i_app(time) uA_per_cm2; real i_Na(time) uA_per_cm2; real i_K(time) uA_per_cm2; real i_leak(time) uA_per_cm2; real IstimStart ms; IstimStart=10; real IstimEnd ms; IstimEnd=50000; real IstimAmplitude uA_per_cm2; IstimAmplitude=40.0; real IstimPeriod ms; IstimPeriod=100; real IstimPulseDuration ms; IstimPulseDuration=1; real x_infinity(time) dimensionless; real alpha_x(time) dimensionless; real beta_x(time) dimensionless; real n(time) dimensionless; when(time=time.min) n=0; real alpha_n(time) per_ms; real beta_n(time) per_ms; real T(time) uM; real T_bar uM; T_bar=4000.0; real R(time) dimensionless; when(time=time.min) R=0; real kr_plus per_uM_per_ms; kr_plus=0.15; real kr_minus per_ms; kr_minus=2.5; real Ca(time) uM; real Ca_ex uM; Ca_ex=2000.0; real Ca_open(time) uM; real Dc um2_per_second; Dc=220; real r nm; r=10; real sigma(time) uM_per_ms; real i_V(time) uA; real g_Ca pS; g_Ca=1.2; real P mV_per_uM; P=0.006; real O(time) dimensionless; real alpha(time) per_ms; real alpha_(time) per_ms; real beta(time) per_ms; real beta_(time) per_ms; real kG_plus(time) per_ms; real kG_minus per_ms; kG_minus=0.00025; real kG2_minus per_ms; kG2_minus=0.016; real kG3_minus per_ms; kG3_minus=1.024; real a(time) dimensionless; when(time=time.min) a=0; real ka_plus per_uM_per_ms; ka_plus=200.0; real ka_minus per_ms; ka_minus=0.0015; real C1(time) dimensionless; when(time=time.min) C1=1; real C2(time) dimensionless; when(time=time.min) C2=0; real C_G1(time) dimensionless; when(time=time.min) C_G1=0; real C3(time) dimensionless; when(time=time.min) C3=0; real C_G2(time) dimensionless; when(time=time.min) C_G2=0; real C4(time) dimensionless; when(time=time.min) C4=0; real C_G3(time) dimensionless; when(time=time.min) C_G3=0; real C_G(time) dimensionless; // // // V:time=((-1)*(i_Na+i_K+i_leak-i_app)/Cm); // i_app=(if (((time>=IstimStart) and (time<=IstimEnd)) and ((time-IstimStart-floor((time-IstimStart)/IstimPeriod)*IstimPeriod)<=IstimPulseDuration)) IstimAmplitude else (0 uA_per_cm2)); // i_Na=((120 pS_per_cm2)*x_infinity^3*(1-n)*(V-(120 mV))); x_infinity=(alpha_x/(alpha_x+beta_x)); alpha_x=(.2*(V+(40 mV))/((1 mV)-(1 mV)*exp((-1)*(V+(40 mV))/(10 mV)))); beta_x=(8*exp((1 mV)/((-1)*(V+(65 mV)/18)))); // i_K=((36 pS)*n^4*(V+(77 mV))/(1 cm2)); // n:time=(alpha_n*(1-n)-beta_n*n); alpha_n=((.02 per_mV_per_ms)*(V+(55 mV))/(1-exp((-1)*(V+(55 mV))/(10 mV)))); beta_n=((.25 per_ms)*exp((-1)*(V+(65 mV))/(80 mV))); // i_leak=((.3 pS_per_cm2)*(V+(54 mV))); // R:time=(kr_plus*Ca*(1-R)-kr_minus*R); T=(T_bar*R); // Ca_open=(sigma/((2 per_um3)*Dc*r*3.141592653589793)); sigma=((-1)*(5.182 uM_per_coulomb)*i_V); i_V=(g_Ca*P*2*F*V/(R_gas_const*Temp)*Ca_ex/(1-exp(2*F*V/(R_gas_const*Temp)))); Ca=(O*Ca_open+(.1 uM)); // alpha=((.45 per_ms)*exp(V/(22 mV))); alpha_=(alpha/8); beta=((.015 per_ms)*exp((-1)*V/(14 mV))); beta_=(beta*8); a:time=(ka_plus*T*(1-a)-ka_minus*a); kG_plus=((3 per_ms)*a/(680+320*a)); // C1:time=(beta*C2+kG_minus*C_G1-C1*(4*alpha+kG_plus)); // C2:time=(4*alpha*C1+2*beta*C3+kG2_minus*C_G2-C2*(beta+3*alpha+kG_plus)); // C3:time=(3*alpha*C2+3*beta*C4+kG3_minus*C_G3-C3*(2*beta+2*alpha+kG_plus)); // C4:time=(2*alpha*C3+4*beta*O-C4*(3*beta+alpha)); // O=(1-C1-C2-C3-C4-C_G1-C_G2-C_G3); C_G=(C_G1+C_G2+C_G3); // C_G1:time=(beta_*C_G2+kG_plus*C1-C_G1*(4*alpha_+kG_minus)); // C_G2:time=(4*alpha_*C_G1+2*beta_*C_G3+kG_plus*C2-C_G2*(beta_+3*alpha_+kG2_minus)); // C_G3:time=(3*alpha_*C_G2+kG_plus*C3-C_G3*(2*beta_+kG3_minus)); }