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Model Packages

File SBML : Minimal Mitotic Oscillator(Goldbeter, 1991)
This is a widely cited minimal (3-variable) model for a mitotic oscillator. The three variables represent Cyclin ( C), inactive cdc-2 Kinase (M) and an active cdc-2 Kinase (X).
File SBML : Lorenz equations: Deterministic nonperiodic flow
This file implements the famous 1963 Lorenz equations as a set of reactions.
File SBML : Cell Cycle Model - 6 variables(Tyson, 1991)
A model of the cell cycle based on the interactions between cdc2 and cyclin. The model has six dynamic variables: C2 (cdc2); CP (cdc2-P complex); pM (P- cyclin-cdc2-P complex); M (active MPF, P-cyclin- cdc2 complex); Y (cyclin); and YP (cyclin-P). Total cyclin concentration (YT) is the sum YT=Y+YP+pM+M4
File SBML : Novak and Tyson Cell Cycle Model (1997)
A cell cycle model with 13 dynamic variables (Cdc25, G1K, G1R = [Cig2/Cdc2/Rum1], G2K = [Cdc13/Cdc2], G2R = [Cdc13/Cdc2/Rum1], IE = [ Intermediary enzyme], mass, PG2 = [Cdc13/P-Cdc2], PG2R = [Cdc13/P-Cdc2/Rum1], R = [ Rum1], UbE, UbE2, Wee1} and two auxilllary variables MPF = G2K+ beta*PG2, SPF = MPF + alpha * G1K + Cig1, (alpha, beta, Cig1 constants). NOTE: The following switches in the published model are NOT described by the SBML: "Switches (i) When SPF crosses 0.1 from below, S phase is initiated (Start). (ii) When UbE crosses 0.1 from above, the cell divides functionally (mass->mass/2), although visible cytokinesis may be delayed. (iii) 60 min after Start,kp is divided by 2, and at cell division kp is multiplied by 2." ( from Table 1 of the cited reference).
File SBML : Cell Cycle Model; Tyson (1991, 2 variables)
This is a two variable reduction of the larger 6- variable model published in the same paper. The published equations are du/dt = k4 * (v - u) * (alpha + u2) - k6 * u dv/dt = Kappa - k6 * u In the present implementation, the change of variables z = v - u is made, so that the system becomes the more symmetric system du/dt = k4 * z * (alpha + u2) - k6 * u dz/dt = Kappa - z * (alpha + u2) The variables can be interpreted as follows: u = [activeMPF] / [CT] v = ([cyclin] + [preMPF] + [activeMPF]) / [CT] z = ([ cyclin] + [preMPF]) / [CT] where [CT] = [CDC2] + [CDC2P] + [preMPF] + [aMPF]
File SBML : A Minimal Model for Circadian Oscillations
A minimal model of genomically based oscillation, based on two mutually interacting genes, an activator and a repressor. Positive feedback is provided by the activator protein, which binds to the promotors of both the activator and the repressor genes. Negative feedback is provided by the repressor protein which binds to the activator protein.
File SBML : Interlocked Feedback Model of Drosophila Circadian Rhythm
A mechanism for generating circadian rhythms has been of major interest in recent years. After the discovery of per and tim, a model with a simple feedback loop involving per and tim has been proposed. However, it is recognized that the simple feedback model cannot account for phenotypes generated by various mutants. A recent report by Glossop, Lyons & Hardin [Science286, 766 (1999)] on Drosophila suggests involvement of another feedback loop by dClk that is interlocked with per-tim feedback loop. In order to examine whether interlocked feedback loops can be a basic mechanism for circadian rhythms, a mathematical model was created and examined. Through extensive simulation and mathematical analysis, it was revealed that the interlocked feedback model accounts for the observations that are not explained by the simple feedback model. Moreover, the interlocked feedback model has robust properties in oscillations.
File SBML : Minimal Mitotic Oscillator with Inhibitor(Gardner et al., 1998)
This is a modification of the widely cited Goldbeter (1991) minimal (3-variable) model for a mitotic oscillator. The three variables represent Cyclin ( C), inactive cdc-2 Kinase (M), and an active cdc-2 Kinase (X). Two additional variables Y, Z control the dynamics of the inhibitor.
File SBML : Repressilator
This file describes the repressilator system. The authors of this model (see reference) use three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network that they called the repressilator. The model system was induced in Escherichia coli. In this system, LacI (variable X is the mRNA, variable PX is the protein) inhibits the tetracycline-resistance transposon tetR (Y, PY describe mRNA and protein). Protein tetR inhibits the gene Cl from phage Lambda (Z, PZ: mRNA, protein), and protein Cl inhibits lacI expression. With appropriate parameter values this system oscillates.
File SBML : MAPK in solution (no scaffold)
This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) cascade in solution. This cascade is typically expressed as RAF ==> MEK ==> MAPK (alternative forms are K3 ==> K2 ==> K1 and KKK ==> KK ==> K). The input signal is RAFK (RAF Kinase) and the output signal is MAPKpp (doubly phosphorylated form of MAPK). RAFK phosphorylates RAF once to RAFp. RAFp, the phosphorylated form of RAF induces two phoshporylations of MEK, to MEKp and MEKpp. MEKpp, the doubly phosphorylated form of MEK, induces two phosphorylations of MAPK to MAPKp and MAPKpp.
File SBML : MAPK in solution on a scaffold
This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) . Kinases in solution are written as K[ 3,J], K[2,J], K[1,J] for MAPKKK, MAPKK, and MAPK, respectively, J indicates the phosphorylation level, J=0, 1 for K3 and J=0,1, 2 for K2 and K1. Scaffolds have three slots, for MAPK, MAPKK, and MAPKK, respectively. Bound and free scaffold are denoted as S[ i,j,k], where i, j, and k indicate the binding of K[1,i], K[2,j] and K[3,k] in their respective slots. Here i,j=-1,0,1,or, 2 and k=-1,0,or,1. A value of - 1 means the slot is empty, 0 means the unphorphorylated kinase is bound, 1 means the singly phosphorylated kinase is bound, and 2 means the doubly phosporylated kinase is bound. Thus S[ 1,-1,2] is a scaffold with K[1,1] bound in the first slot and K[3,2] in the third slot, while the second slot is empty.Note: Indices X[I,J,K] are translated into the unindexed variable X_I_J_K and so forth in the SBML. Negative indices are translated as mI, etc, thus S[1,-1,2] becomes S_1_m1_2.
File Glycolysis in Saccharomyces cerevisiae(.eml)
The paper in which this model of glycolysis in bakers yeast was presented "examines whether the in vivo behaviour of yeast glycolysis can be understood in terms of the in vitro kinetic properties of the constituent enzymes. In non-growing, anaerobic, compressed Saccharomyces cerevisiae the values of the kinetic parameters of most glycolytic enzymes were determined. For the other enzymes appropriate literature values were collected. By inserting these values into a kinetic model for glycolysis, fluxes and metabolites were calculated. Under the same conditions fluxes and metabolite levels were measured. In our first model, branch reactions were ignored. This model failed to reach the stable steady state that was observed in the experimental flux measurements. Introduction of branches towards trehalose, glycogen, glycerol and succinate did allow such a steady state. The predictions of this branched model were compared with the empirical behaviour. Half of the enzymes matched their predicted flux in vivo within a factor of 2. For the other enzymes it was calculated what deviation between in vivo and in vitro kinetic characteristics could explain the discrepancy between in vitro rate and in vivo flux."
File Glycogenolysis in skeletal muscle(.eml)
Abstract of the paper in which the results of modelling glycogenolysis in skeletal muscle was described: "A dynamic model of the glycogenolytic pathway to lactate in skeletal muscle was constructed with mammalian kinetic parameters obtained from the literature. Energetic buffers relevant to muscle were included. The model design features stoichiometric constraints, mass balance, and fully reversible thermodynamics as defined by the Haldane relation. We employed a novel method of validating the thermodynamics of the model by allowing the closed system to come to equilibrium; the combined mass action ratio of the pathway equalled the product of the individual enzymes’ equilibrium constants. Adding features physiologically relevant to muscle - a fixed glycogen concentration, efflux of lactate, and coupling to an ATPase - allowed for a steady-state flux far from equilibrium. The main result of our analysis is that coupling of the glycogenolytic network to the ATPase transformed the entire complex into an ATPase driven system. This steady-state system was most sensitive to the external ATPase activity and not to internal pathway mechanisms. The control distribution among the internal pathway enzymes - although small compared to control by ATPase - depended on the flux level and fraction of glycogen phosphorylase a. This model of muscle glycogenolysis thus has unique features compared to models developed for other cell types."
File Sporulation control network in Physarum polycephalum(.eml)
Mutants of Physarum polycephalum can be complemented by fusion of plasmodial cells followed by cytoplasmic mixing. Complementation between strains carrying different mutational defects in the sporulation control network may depend on the signalling state of the network components. Time-resolved somatic complementation (TRSC) analysis with such mutants may be used to probe network architecture and dynamics. The model presented here was used to show how and under which conditions the regulatory hierarchy of genes can be determined experimentally. It demonstrates how the mechanisms of TRSC can be understood and simulated at the kinetic level. The theoretical framework provided may be used to systematically analyze network structure and dynamics through time-resolved somatic complementation studies.
File Glycogenolysis in skeletal muscle(.xml)
Abstract of the paper in which the results of modelling glycogenolysis in skeletal muscle was described: "A dynamic model of the glycogenolytic pathway to lactate in skeletal muscle was constructed with mammalian kinetic parameters obtained from the literature. Energetic buffers relevant to muscle were included. The model design features stoichiometric constraints, mass balance, and fully reversible thermodynamics as defined by the Haldane relation. We employed a novel method of validating the thermodynamics of the model by allowing the closed system to come to equilibrium; the combined mass action ratio of the pathway equalled the product of the individual enzymes’ equilibrium constants. Adding features physiologically relevant to muscle - a fixed glycogen concentration, efflux of lactate, and coupling to an ATPase - allowed for a steady-state flux far from equilibrium. The main result of our analysis is that coupling of the glycogenolytic network to the ATPase transformed the entire complex into an ATPase driven system. This steady-state system was most sensitive to the external ATPase activity and not to internal pathway mechanisms. The control distribution among the internal pathway enzymes - although small compared to control by ATPase - depended on the flux level and fraction of glycogen phosphorylase a. This model of muscle glycogenolysis thus has unique features compared to models developed for other cell types."
File Cell Cycle Model; Tyson (1991, 6 variables) (.eml)
A model of the cell cycle based on the interactions between cdc2 and cyclin. The model has six dynamic variables: C2 (cdc2); CP (cdc2-P complex); pM (P- cyclin-cdc2-P complex); M (active MPF, P-cyclin- cdc2 complex); Y (cyclin); and YP (cyclin-P). Total cyclin concentration (YT) is the sum YT=Y+YP+pM+M4
File Pyruvate branches in Lactococcus lactis(.eml)
This model of glycolysis in Lactococcus lactis was set up in parallel with metabolic engineering experiments aimed at optimization of the production of di-acetyl, a by-product of glycolysis, but an important flavour component of dairy products such as butter. Metabolic modelling and analysis clearly indicated that the enzymes with the greatest effect on the flux to acetoin and di-acetyl reside outside the acetolacetate branch itself, and the predictions were confirmed experimentally. In this model, the steps of the actual glycolysis (glucose to pyruvate) are lumped together into an overall 'glycolysis' step.
File SBML : IP3 dependent Calcium Channel
This model describes the IP3- sensitive Calcium channel. The receptor has three binding sites, denoted by three indices S[i,j,k],where i,j, k are 0 or 1. A 0 indicates the binding site is empty;a 1 indicates the binding site is occupied. The first site ( index i) binds IP3 (Inositol 1,4,5-Trisphosphate) ; the second site (j) binds Calcium and activates the channel; the third site (k) binds Calcium and inactivates the channel. The open channel probability can be computed as ( S[1,1,0]/(Sum of all S[i,j,k]))^ 3 as described in the reference. The differential equations shown below treate C and P as dynamic variables. To reproduce the results in the original paper both C and P should be treated as constants and not as dynamic variables.
File Processivity of Myosin-V(.eml)
Myosin-V is a two-headed molecular motor that facilitates transport of organelles and vesicles inside cells. The motor hydrolyses ATP to generate the energy for its processive walk along actin filaments. Myosin-V takes steps of about 36 nm. This model describes the Myosin-V processivity as a simple, reversible two-step process. The rate of the first forward step is mainly determined by the ATP binding kinetics, the rate of the second step by ADP dissociation. All rates are dependent on the force that is generated by the load, but the dependence is different for each sub-step. Fitting the model to experimental observations lead to the conclusion that the backward steps are highly force dependent, whereas the forward rates are hardly affected by the load.
File Circadian Oscillator involving PER and TIM(.eml)
In Drosophila, circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these proteins. per (Mp) and tim (Mt) are synthesized in the nucleus and transferred into the cytoson, where they accumulate at the maximum rates vsp and vst, respectively, and are degraded enzymatically at maximum rates vmp and vmt, with Michaelis constants Kmp and Kmt. The rates of synthesis of the PER and TIM proteins, respectively proportional to Mp and Mt, are characterized by the apparent first-order rate constants ksp and kst. Parameters Vip, Vit and Kip, Kit (i = 1,..4) denote the maximum rates and Michaelis constants of the kinase(s) and phosphatase(s) involved in the reversible phosphorylation of P0(T0) into P1(T1), and P1(T1) into P2(T2), respectively. The fully phosphorylated forms (P2 and T2) are degraded by enzymes of maximum rate Vdp, Vdt, and Michaelis constants Kdp, Kdt, and reversibly form a complex C (with forward and reverse rate constants k3, k4) which is transported into the nucleus at a rate characterized by the apparent first-order rate constant k1. Transport of the nuclear form of the PER-TIM complex (Cn) into the cytosol is characterized by the apparent first-order rate constant k2. The negative feedback exerted by the nuclear PER-TIM complex on per and tim transcription is described by an equation of the Hill type, in which n denotes the degree of cooperativity, and KIp and KIt the thresholds constants for repression. This model is capable of sustained oscillations (e.g. at parameter values as in the accompanying SBML file), chaotic behaviour ( e.g. at vmt = 0.28, vdt = 4.8 nM/hr, other parameters as in the SBML file), and bi-rhythmicity (e.g. at vmt = 0.99, vdt = 2.0, or vmt = 0.4, vdt = 3.8 nM/hr).
File Interlocked Feedback Model of Drosophila Circadian Rhythm (.eml)
A mechanism for generating circadian rhythms has been of major interest in recent years. After the discovery of per and tim, a model with a simple feedback loop involving per and tim has been proposed. However, it is recognized that the simple feedback model cannot account for phenotypes generated by various mutants. A recent report by Glossop, Lyons & Hardin [Science286, 766 (1999)] on Drosophila suggests involvement of another feedback loop by dClk that is interlocked with per-tim feedback loop. In order to examine whether interlocked feedback loops can be a basic mechanism for circadian rhythms, a mathematical model was created and examined. Through extensive simulation and mathematical analysis, it was revealed that the interlocked feedback model accounts for the observations that are not explained by the simple feedback model. Moreover, the interlocked feedback model has robust properties in oscillations.
File Minimal Mitotic Oscillator with Inhibitor (.eml)
This is a modification of the widely cited Goldbeter (1991) minimal (3-variable) model for a mitotic oscillator. The three variables represent Cyclin ( C), inactive cdc-2 Kinase (M), and an active cdc-2 Kinase (X). Two additional variables Y, Z control the dynamics of the inhibitor.
File Circadian Oscillator involving PER and TIM(.xml)
In Drosophila, circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these proteins. per (Mp) and tim (Mt) are synthesized in the nucleus and transferred into the cytoson, where they accumulate at the maximum rates vsp and vst, respectively, and are degraded enzymatically at maximum rates vmp and vmt, with Michaelis constants Kmp and Kmt. The rates of synthesis of the PER and TIM proteins, respectively proportional to Mp and Mt, are characterized by the apparent first-order rate constants ksp and kst. Parameters Vip, Vit and Kip, Kit (i = 1,..4) denote the maximum rates and Michaelis constants of the kinase(s) and phosphatase(s) involved in the reversible phosphorylation of P0(T0) into P1(T1), and P1(T1) into P2(T2), respectively. The fully phosphorylated forms (P2 and T2) are degraded by enzymes of maximum rate Vdp, Vdt, and Michaelis constants Kdp, Kdt, and reversibly form a complex C (with forward and reverse rate constants k3, k4) which is transported into the nucleus at a rate characterized by the apparent first-order rate constant k1. Transport of the nuclear form of the PER-TIM complex (Cn) into the cytosol is characterized by the apparent first-order rate constant k2. The negative feedback exerted by the nuclear PER-TIM complex on per and tim transcription is described by an equation of the Hill type, in which n denotes the degree of cooperativity, and KIp and KIt the thresholds constants for repression. This model is capable of sustained oscillations (e.g. at parameter values as in the accompanying SBML file), chaotic behaviour ( e.g. at vmt = 0.28, vdt = 4.8 nM/hr, other parameters as in the SBML file), and bi-rhythmicity (e.g. at vmt = 0.99, vdt = 2.0, or vmt = 0.4, vdt = 3.8 nM/hr).
File Glycolysis in Saccharomyces cerevisiae(.xml)
The paper in which this model of glycolysis in bakers yeast was presented "examines whether the in vivo behaviour of yeast glycolysis can be understood in terms of the in vitro kinetic properties of the constituent enzymes. In non-growing, anaerobic, compressed Saccharomyces cerevisiae the values of the kinetic parameters of most glycolytic enzymes were determined. For the other enzymes appropriate literature values were collected. By inserting these values into a kinetic model for glycolysis, fluxes and metabolites were calculated. Under the same conditions fluxes and metabolite levels were measured. In our first model, branch reactions were ignored. This model failed to reach the stable steady state that was observed in the experimental flux measurements. Introduction of branches towards trehalose, glycogen, glycerol and succinate did allow such a steady state. The predictions of this branched model were compared with the empirical behaviour. Half of the enzymes matched their predicted flux in vivo within a factor of 2. For the other enzymes it was calculated what deviation between in vivo and in vitro kinetic characteristics could explain the discrepancy between in vitro rate and in vivo flux."
File Sporulation control network in Physarum polycephalum(.xml)
Mutants of Physarum polycephalum can be complemented by fusion of plasmodial cells followed by cytoplasmic mixing. Complementation between strains carrying different mutational defects in the sporulation control network may depend on the signalling state of the network components. Time-resolved somatic complementation (TRSC) analysis with such mutants may be used to probe network architecture and dynamics. The model presented here was used to show how and under which conditions the regulatory hierarchy of genes can be determined experimentally. It demonstrates how the mechanisms of TRSC can be understood and simulated at the kinetic level. The theoretical framework provided may be used to systematically analyze network structure and dynamics through time-resolved somatic complementation studies.
File MAPK in solution (no scaffold) (.eml)
This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) cascade in solution. This cascade is typically expressed as RAF ==> MEK ==> MAPK (alternative forms are K3 ==> K2 ==> K1 and KKK ==> KK ==> K). The input signal is RAFK (RAF Kinase) and the output signal is MAPKpp (doubly phosphorylated form of MAPK). RAFK phosphorylates RAF once to RAFp. RAFp, the phosphorylated form of RAF induces two phoshporylations of MEK, to MEKp and MEKpp. MEKpp, the doubly phosphorylated form of MEK, induces two phosphorylations of MAPK to MAPKp and MAPKpp.
File A Minimal Model for Circadian Oscillations (.eml)
A minimal model of genomically based oscillation, based on two mutually interacting genes, an activator and a repressor. Positive feedback is provided by the activator protein, which binds to the promotors of both the activator and the repressor genes. Negative feedback is provided by the repressor protein which binds to the activator protein.
File Pyruvate branches in Lactococcus lactis(.xml)
This model of glycolysis in Lactococcus lactis was set up in parallel with metabolic engineering experiments aimed at optimization of the production of di-acetyl, a by-product of glycolysis, but an important flavour component of dairy products such as butter. Metabolic modelling and analysis clearly indicated that the enzymes with the greatest effect on the flux to acetoin and di-acetyl reside outside the acetolacetate branch itself, and the predictions were confirmed experimentally. In this model, the steps of the actual glycolysis (glucose to pyruvate) are lumped together into an overall 'glycolysis' step.
File Processivity of Myosin-V(.xml)
Myosin-V is a two-headed molecular motor that facilitates transport of organelles and vesicles inside cells. The motor hydrolyses ATP to generate the energy for its processive walk along actin filaments. Myosin-V takes steps of about 36 nm. This model describes the Myosin-V processivity as a simple, reversible two-step process. The rate of the first forward step is mainly determined by the ATP binding kinetics, the rate of the second step by ADP dissociation. All rates are dependent on the force that is generated by the load, but the dependence is different for each sub-step. Fitting the model to experimental observations lead to the conclusion that the backward steps are highly force dependent, whereas the forward rates are hardly affected by the load.
File Cell Cycle Model; Tyson (1991, 2 variables) (.eml)
This is a two variable reduction of the larger 6- variable model published in the same paper. The published equations are du/dt = k4 * (v - u) * (alpha + u2) - k6 * u dv/dt = Kappa - k6 * u In the present implementation, the change of variables z = v - u is made, so that the system becomes the more symmetric system du/dt = k4 * z * (alpha + u2) - k6 * u dz/dt = Kappa - z * (alpha + u2) The variables can be interpreted as follows: u = [activeMPF] / [CT] v = ([cyclin] + [preMPF] + [activeMPF]) / [CT] z = ([ cyclin] + [preMPF]) / [CT] where [CT] = [CDC2] + [CDC2P] + [preMPF] + [aMPF]
File MAPK in solution on a scaffold (.eml)
This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) . Kinases in solution are written as K[ 3,J], K[2,J], K[1,J] for MAPKKK, MAPKK, and MAPK, respectively, J indicates the phosphorylation level, J=0, 1 for K3 and J=0,1, 2 for K2 and K1. Scaffolds have three slots, for MAPK, MAPKK, and MAPKK, respectively. Bound and free scaffold are denoted as S[ i,j,k], where i, j, and k indicate the binding of K[1,i], K[2,j] and K[3,k] in their respective slots. Here i,j=-1,0,1,or, 2 and k=-1,0,or,1. A value of - 1 means the slot is empty, 0 means the unphorphorylated kinase is bound, 1 means the singly phosphorylated kinase is bound, and 2 means the doubly phosporylated kinase is bound. Thus S[ 1,-1,2] is a scaffold with K[1,1] bound in the first slot and K[3,2] in the third slot, while the second slot is empty.Note: Indices X[I,J,K] are translated into the unindexed variable X_I_J_K and so forth in the SBML. Negative indices are translated as mI, etc, thus S[1,-1,2] becomes S_1_m1_2.
File Novak and Tyson Cell Cycle Model (1997) (.eml)
A cell cycle model with 13 dynamic variables (Cdc25, G1K, G1R = [Cig2/Cdc2/Rum1], G2K = [Cdc13/Cdc2], G2R = [Cdc13/Cdc2/Rum1], IE = [ Intermediary enzyme], mass, PG2 = [Cdc13/P-Cdc2], PG2R = [Cdc13/P-Cdc2/Rum1], R = [ Rum1], UbE, UbE2, Wee1} and two auxilllary variables MPF = G2K+ beta*PG2, SPF = MPF + alpha * G1K + Cig1, (alpha, beta, Cig1 constants). NOTE: The following switches in the published model are NOT described by the SBML: "Switches (i) When SPF crosses 0.1 from below, S phase is initiated (Start). (ii) When UbE crosses 0.1 from above, the cell divides functionally (mass->mass/2), although visible cytokinesis may be delayed. (iii) 60 min after Start,kp is divided by 2, and at cell division kp is multiplied by 2." ( from Table 1 of the cited reference).
File IP3 dependent Calcium Channel (.eml)
This model describes the IP3- sensitive Calcium channel. The receptor has three binding sites, denoted by three indices S[i,j,k],where i,j, k are 0 or 1. A 0 indicates the binding site is empty;a 1 indicates the binding site is occupied. The first site ( index i) binds IP3 (Inositol 1,4,5-Trisphosphate) ; the second site (j) binds Calcium and activates the channel; the third site (k) binds Calcium and inactivates the channel. The open channel probability can be computed as ( S[1,1,0]/(Sum of all S[i,j,k]))^ 3 as described in the reference. The differential equations shown below treate C and P as dynamic variables. To reproduce the results in the original paper both C and P should be treated as constants and not as dynamic variables.
File Repressilator (.eml)
This file describes the repressilator system. The authors of this model (see reference) use three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network that they called the repressilator. The model system was induced in Escherichia coli. In this system, LacI (variable X is the mRNA, variable PX is the protein) inhibits the tetracycline-resistance transposon tetR (Y, PY describe mRNA and protein). Protein tetR inhibits the gene Cl from phage Lambda (Z, PZ: mRNA, protein), and protein Cl inhibits lacI expression. With appropriate parameter values this system oscillates.
File Lorenz equations: Deterministic nonperiodic flow (.eml)
This file implements the famous 1963 Lorenz equations as a set of reactions.
Document ElectroPhys-1952Hod (Hodgkin & Huxley, 1952)
The changes in sodium and potassium permeability which underlie the nerve impulse can be described quantitatively by equations which are consistent with the idea that movement of membrane charges or dipoles, produced by changes in electric field, control gates to Na+ and K+ . When these equations are solved, they account quantitatively for the shape and velocity of the propagated impulse and the associated conductance change and ionic movements, as well as several puzzling subthreshold phenomena. [The SCI® indicates that this paper has been cited over 1,970 times since 1961.]
File MAPKcasc-2000Kho (Kholodenko, 2000) (xml)
Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.
File Metabolism-2002Hoe-2 (Hoefnagel et al., 2002) (xml)
Everyone who has ever tried to radically change metabolic fluxes knows that it is often harder to determine which enzymes have to be modified than it is to actually implement these changes. In the more traditional genetic engineering approaches ’bottle-necks’ are pinpointed using qualitative, intuitive approaches, but the alleviation of suspected ’rate-limiting’ steps has not often been successful. Here the authors demonstrate that a model of pyruvate distribution in Lactococcus lactis based on enzyme kinetics in combination with metabolic control analysis clearly indicates the key control points in the flux to acetoin and diacetyl, important flavour compounds. The model presented here (available at http://jjj.biochem.sun.ac.za/wcfs.html) showed that the enzymes with the greatest effect on this flux resided outside the acetolactate synthase branch itself. Experiments confirmed the predictions of the model, i.e. knocking out lactate dehydrogenase and overexpressing NADH oxidase increased the flux through the acetolactate synthase branch from 0 to 75% of measured product formation rates.
File ElectroPhys-1952Hod (Hodgkin & Huxley, 1952) (xml)
The changes in sodium and potassium permeability which underlie the nerve impulse can be described quantitatively by equations which are consistent with the idea that movement of membrane charges or dipoles, produced by changes in electric field, control gates to Na+ and K+ . When these equations are solved, they account quantitatively for the shape and velocity of the propagated impulse and the associated conductance change and ionic movements, as well as several puzzling subthreshold phenomena. [The SCI® indicates that this paper has been cited over 1,970 times since 1961.]
File MAPKcasc-2000Kho (Kholodenko, 2000) (eml)
Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.
File Metabolism-2002Hoe-2 (Hoefnagel et al., 2002) (eml)
Everyone who has ever tried to radically change metabolic fluxes knows that it is often harder to determine which enzymes have to be modified than it is to actually implement these changes. In the more traditional genetic engineering approaches ’bottle-necks’ are pinpointed using qualitative, intuitive approaches, but the alleviation of suspected ’rate-limiting’ steps has not often been successful. Here the authors demonstrate that a model of pyruvate distribution in Lactococcus lactis based on enzyme kinetics in combination with metabolic control analysis clearly indicates the key control points in the flux to acetoin and diacetyl, important flavour compounds. The model presented here (available at http://jjj.biochem.sun.ac.za/wcfs.html) showed that the enzymes with the greatest effect on this flux resided outside the acetolactate synthase branch itself. Experiments confirmed the predictions of the model, i.e. knocking out lactate dehydrogenase and overexpressing NADH oxidase increased the flux through the acetolactate synthase branch from 0 to 75% of measured product formation rates.
File Receptor-1996Ede (Edelstein et al, 1996) (xml)
Nicotinic acetylcholine receptors are transmembrane oligomeric proteins that mediate interconversions between open and closed channel states under the control of neurotransmitters. Fast in vitro chemical kinetics and in vivo electrophysiological recordings are consistent with the following multi-step scheme. Upon binding of agonists, receptor molecules in the closed but activatable resting state (the Basal state, B) undergo rapid transitions to states of higher affinities with either open channels (the Active state, A) or closed channels (the initial Inactivatable and fully Desensitized states, I and D). In order to represent the functional properties of such receptors, we have developed a kinetic model that links conformational interconversion rates to agonist binding and extends the general principles of the Monod-Wyman-Changeux model of allosteric transitions. The crucial assumption is that the linkage is controlled by the position of the interconversion transition states on a hypothetical linear reaction coordinate. Application of the model to the peripheral nicotine acetylcholine receptor (nAChR) accounts for the main properties of ligand-gating, including single-channel events, and several new relationships are predicted. Kinetic simulations reveal errors inherent in using the dose-response analysis, but justify its application under defined conditions. The model predicts that (in order to overcome the intrinsic stability of the B state and to produce the appropriate cooperativity) channel activation is driven by an A state with a Kd in the 50 nM range, hence some 140-fold stronger than the apparent affinity of the open state deduced previously. According to the model, recovery from the desensitized states may occur via rapid transit through the A state with minimal channel opening, thus without necessarily undergoing a distinct recovery pathway, as assumed in the standard 'cycle' model. Transitions to the desensitized states by low concentration 'pre-pulses' are predicted to occur without significant channel opening, but equilibrium values of IC50 can be obtained only with long pre-pulse times. Predictions are also made concerning allosteric effectors and their possible role in coincidence detection. In terms of future developments, the analysis presented here provides a physical basis for constructing more biologically realistic models of synaptic modulation that may be applied to artificial neural networks
File Receptor-1996Ede (Edelstein et al, 1996) (eml)
Nicotinic acetylcholine receptors are transmembrane oligomeric proteins that mediate interconversions between open and closed channel states under the control of neurotransmitters. Fast in vitro chemical kinetics and in vivo electrophysiological recordings are consistent with the following multi-step scheme. Upon binding of agonists, receptor molecules in the closed but activatable resting state (the Basal state, B) undergo rapid transitions to states of higher affinities with either open channels (the Active state, A) or closed channels (the initial Inactivatable and fully Desensitized states, I and D). In order to represent the functional properties of such receptors, we have developed a kinetic model that links conformational interconversion rates to agonist binding and extends the general principles of the Monod-Wyman-Changeux model of allosteric transitions. The crucial assumption is that the linkage is controlled by the position of the interconversion transition states on a hypothetical linear reaction coordinate. Application of the model to the peripheral nicotine acetylcholine receptor (nAChR) accounts for the main properties of ligand-gating, including single-channel events, and several new relationships are predicted. Kinetic simulations reveal errors inherent in using the dose-response analysis, but justify its application under defined conditions. The model predicts that (in order to overcome the intrinsic stability of the B state and to produce the appropriate cooperativity) channel activation is driven by an A state with a Kd in the 50 nM range, hence some 140-fold stronger than the apparent affinity of the open state deduced previously. According to the model, recovery from the desensitized states may occur via rapid transit through the A state with minimal channel opening, thus without necessarily undergoing a distinct recovery pathway, as assumed in the standard 'cycle' model. Transitions to the desensitized states by low concentration 'pre-pulses' are predicted to occur without significant channel opening, but equilibrium values of IC50 can be obtained only with long pre-pulse times. Predictions are also made concerning allosteric effectors and their possible role in coincidence detection. In terms of future developments, the analysis presented here provides a physical basis for constructing more biologically realistic models of synaptic modulation that may be applied to artificial neural networks.
File Minimal Mitotic Oscillator (.eml)
This is a widely cited minimal (3-variable) model for a mitotic oscillator. The three variables represent Cyclin ( C), inactive cdc-2 Kinase (M) and an active cdc-2 Kinase (X).
File ElectroPhys-1952Hod (Hodgkin & Huxley, 1952) (eml)
 
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