/* * Nucleocytoplasmic oscillations of the yeast transcription factor * Msn2: evidence for periodic PKA activation * * Model Status * * This model has been built using the expressions found in the * supplemental data of Garmendia-Torres's 2007 paper on oscillations * of Msn2 due to PKA activation. This model reproduces the curves * on Figure 3, page 1047, using the corresponding initial values * and the parameters found in Table S2. The variable Str has been * given a value of 1 in order to show oscillatory behavior but * may be changed to 0 or 2.5 for low and high values. This file * is known to run on COR 0.9 and OpenCell. * * Model Structure * * At intermediate intensities, stress induces oscillations in * the nucleocytoplasmic shuttling of the transcription factor * Msn2 in budding yeast. Activation by stress results in a reversible * translocation of Msn2 from the cytoplasm to the nucleus. This * translocation is negatively controlled by the cAMP-PKA pathway * through Msn2 phosphorylation. Here we show that the nuclear * localization signal (NLS) of Msn2 is necessary and sufficient * to promote the nucleocytoplasmic oscillations of the transcription * factor. Because the NLS is controlled by protein kinase A (PKA) * phosphorylation, we use a computational model to investigate * the possibility that the cAMP-PKA pathway could function as * an oscillator driving the periodic shuttling of Msn2. The model * indicates that sustained oscillations of cAMP can indeed occur * in a range bounded by two critical values of stress intensity, * owing to the negative feedback exerted by PKA on cAMP accumulation. * We verify the predictions of the model in mutants by showing * that suppressing this negative-feedback loop prevents the oscillatory * shuttling but still promotes the stress-induced nuclear localization * of Msn2. The physiological significance of Msn2 oscillations * is discussed in the light of the frequency encoding of cellular * rhythms. * * Nucleocytoplasmic oscillations of the yeast transcription factor * Msn2: evidence for periodic PKA activation, Garmendia-Torres * C, Goldbeter A, Jacquet M Current Biology, 17, 1044-1049PubMed * ID: 17570669 * * Model Diagram * * [[Image file: garmendiatorres_2007.png]] * * (A) Time evolution of RGTP, cAMP, active PKA, and nuclear Msn2 * predicted by the model for three different values of Str, the * dimensionless parameter measuring stress intensity. At low value, * Str = 0 (dotted blue curves), and at high value, Str = 2.5 (dotted * red curves), a steady-state level is observed for the different * components, whereas at intermediate value, Str = 1 (green curves), * sustained oscillations occur. The curves show the oscillatory * behavior after the elimination of transients. (B) Envelope of * cAMP oscillations as a function of stress intensity showing * the maximum (red curve) and the minimum (blue curve) values * during sustained oscillations. The variation of periodicity * (green dots) is also shown. (C) Envelope of oscillations in * Msn2 subcellular localization. The curves show the maximumvalues * (Max) and minimum values (Min) for cytoplasmic Msn2 (in blue) * and nuclear Msn2 (in red). Outside of the oscillatory range, * the system reaches a stable steady state. The curves have been * obtained with the Berkeley Madonna program, by numerical integration * of Equations S1-S4. Parameter values are given in Table S2. * Initial conditions were as follows: GEFa 0.36, GAPa 0.5, RGTP * 0.1, CYCLa 0.1, cAMP 1, R2C2 0.5,MC 0.25, MN 0.25, MCP 0.25, * MNP 0.25, and PDEa 0.5. */ import nsrunit; unit conversion on; unit minute=60 second^1; unit per_minute=.01666667 second^(-1); unit per_litre=1E3 meter^(-3); // unit micromolar predefined unit micromolar_per_minute=1.6666667E-5 meter^(-3)*second^(-1)*mole^1; unit per_micromolar_minute=16.66666667 meter^3*second^(-1)*mole^(-1); unit per_micromolar_squared_minute=1.6666667E4 meter^6*second^(-1)*mole^(-2); unit per_micromolar_squared=1E6 meter^6*mole^(-2); math main { realDomain time minute; time.min=0; extern time.max; extern time.delta; real V_max1 micromolar_per_minute; V_max1=1; real GEFt micromolar; GEFt=4; real V_1 per_minute; real Str dimensionless; Str=1; real V_max2 micromolar_per_minute; V_max2=1; real V_2 per_minute; real k_c3 per_minute; k_c3=3.5; real PKAt micromolar; PKAt=0.3; real GAPt micromolar; GAPt=1.5; real V_3 per_minute; real V_max4 micromolar_per_minute; V_max4=1.3; real V_4 per_minute; real k_gef per_minute; k_gef=240; real RASt micromolar; RASt=250; real V_5 per_minute; real k_gap per_minute; k_gap=600; real V_6 per_minute; real k_c7 per_minute; k_c7=3.333; real PDEt micromolar; PDEt=0.5; real V_7 per_minute; real V_max8 micromolar_per_minute; V_max8=1.5; real V_8 per_minute; real a per_micromolar_squared_minute; a=1; real r per_minute; r=1; real R2C2(time) dimensionless; when(time=time.min) R2C2=0.5; real cAMP(time) micromolar; when(time=time.min) cAMP=1; real C(time) dimensionless; real R2cAMP2(time) dimensionless; real V_PKAact(time) per_minute; real K_1 dimensionless; K_1=0.05; real K_2 dimensionless; K_2=0.05; real GEFa(time) dimensionless; when(time=time.min) GEFa=0.36; real K_3 dimensionless; K_3=0.01; real K_4 dimensionless; K_4=0.01; real GAPa(time) dimensionless; when(time=time.min) GAPa=0.5; real K_5 dimensionless; K_5=0.001; real K_6 dimensionless; K_6=0.001; real RGTP(time) dimensionless; when(time=time.min) RGTP=0.1; real k_a per_micromolar_minute; k_a=0.01; real k_i per_minute; k_i=1; real CYCLa(time) dimensionless; when(time=time.min) CYCLa=0.1; real K_7 dimensionless; K_7=0.01; real K_8 dimensionless; K_8=0.01; real PDEa(time) dimensionless; when(time=time.min) PDEa=0.5; real k_s per_minute; k_s=4; real k_d per_minute; k_d=100; real CYCLt micromolar; CYCLt=0.7; real K_md micromolar; K_md=20; real k_c9 per_minute; k_c9=3.333; real MSNt micromolar; MSNt=1; real V_9 per_minute; real V_max10 micromolar_per_minute; V_max10=0.6; real V_10 per_minute; real k_c11 per_minute; k_c11=3.333; real V_11 per_minute; real V_max12 micromolar_per_minute; V_max12=2; real V_12 per_minute; real k_t1 per_minute; k_t1=10; real k_t2 per_minute; k_t2=0.001; real K_11 dimensionless; K_11=0.05; real K_12 dimensionless; K_12=0.05; real MN(time) dimensionless; when(time=time.min) MN=0.25; real MCP(time) dimensionless; when(time=time.min) MCP=0.25; real MC(time) dimensionless; when(time=time.min) MC=0.25; real K_9 dimensionless; K_9=0.05; real K_10 dimensionless; K_10=0.05; real MNP(time) dimensionless; when(time=time.min) MNP=0.25; real k_t3 per_minute; k_t3=0.001; real k_t4 per_minute; k_t4=10; real M_cyto(time) dimensionless; real M_nucl(time) dimensionless; // // V_1=(V_max1/GEFt); // V_2=(Str*V_max2/GEFt); // V_3=(k_c3*PKAt/GAPt); // V_4=(V_max4/GAPt); // V_5=(k_gef*GEFt/RASt); // V_6=(k_gap*GAPt/RASt); // V_7=(k_c7*PKAt/PDEt); // V_8=(V_max8/PDEt); // V_PKAact=(a*R2C2*cAMP^2-r*C*R2cAMP2*PKAt^2*(1 per_micromolar_squared)); // R2cAMP2=(1-R2C2); // C=(2*(1-R2C2)); // GEFa:time=(V_1*(1-GEFa)/(K_1+(1-GEFa))-V_2*GEFa/(K_2+GEFa)); // GAPa:time=(V_3*C*(1-GAPa)/(K_3+(1-GAPa))-V_4*GAPa/(K_4+GAPa)); // RGTP:time=(V_5*GEFa*(1-RGTP)/(K_5+(1-RGTP))-V_6*GAPa*RGTP/(K_6+RGTP)); // CYCLa:time=(k_a*RGTP*RASt*(1-CYCLa)-k_i*CYCLa); // PDEa:time=(V_7*C*(1-PDEa)/(K_7+(1-PDEa))-V_8*PDEa/(K_8+PDEa)); // cAMP:time=(k_s*CYCLa*CYCLt-k_d*PDEt*PDEa*cAMP/(K_md+cAMP)-2*V_PKAact*PKAt); // R2C2:time=((-1)*a*R2C2*cAMP^2+r*C^2*R2cAMP2*PKAt^2*(1 per_micromolar_squared)); // V_9=(k_c9*PKAt/MSNt); // V_10=(Str*V_max10/MSNt); // V_11=(k_c11*PKAt/MSNt); // V_12=(Str*V_max12/MSNt); // MC:time=((-1)*k_t1*MC+k_t2*MN-V_11*C*MC/(K_11+MC)+V_12*MCP/(K_12+MCP)); // MN:time=(k_t1*MC-k_t2*MN-V_9*C*MN/(K_9+MN)+V_10*MNP/(K_10+MNP)); // MNP:time=(V_9*C*MN/(K_9+MN)-V_10*MNP/(K_10+MNP)+k_t3*MCP-k_t4*MNP); // MCP:time=((-1)*k_t3*MCP+k_t4*MNP+V_11*C*MC/(K_11+MC)-V_12*MCP/(K_12+MCP)); // M_cyto=(MC+MCP); // M_nucl=(MN+MNP); }