Glycolysis model

Models for Oscillating Reactions in Glycolysis Model 1 Back Activation Model Reference Higgins (1967). 

Lactococcus lactis IL1403 Glycolysis model for primary metabolism regulation Voit et al. (2006)... 

Lactococcus lactis MG1363 Streptococcus pyogenes M49 Two glycolysis models revealing role of extracellular phosphate Levering et al. (2012)... 

Lactococcus lactis MG1363 Glycolysis model with mannitol and 2,3-Butanediol pathway Costa et al. (2014)... 

This is not the place to expose in detail the problems and the solutions already obtained in studying biochemical reaction networks. However, because of the importance of this problem and the great recent interest in understanding metabolic networks, we hope to throw a little light on this area. Figure 10.3-23 shows a model for the metabolic pathways involved in the central carbon metabolism of Escherichia coli through glycolysis and the pentose phosphate pathway [22]. 

Figure 10.3-23. Metabolic model of glycolysis and tbe pentose phosphate pathway in E. coli. Squares Indicate enzyme activities circles indicate regulatory effects,...

The glycolysis of PETP was studied in a batch reactor at 265C. The reaction extent in the initial period was determined as a function of reaction time using a thermogravimetric technique. The rate data were shown to fit a second order kinetic model at small reaction times. An initial glycolysis rate was calculated from the model and was found to be over four times greater than the initial rate of hydrolysis under the same reaction conditions. 4 refs. 

Figure 5. A minimal model of glycolysis One unit of glucose (G) is converted into two units of pyruvate (P), generating a net yield of 2 units of ATP for each unit of glucose. Gx, Px, and Glx are considered external and are not included into the stoichiometric matrix. A A graphical depiction of the network. B The stoichiometric matrix. Rows correspond to metabolites, columns correspond to reactions. C A list of individual reactions. D The corresponding system of differential equations. Abbreviations G, glucose (Glc) TP, triosephosphate, P, pyruvate.

Probably the most well-known pathway to exemplify the occurrence of complex dynamics in metabolic networks is the glycolytic pathway of yeast. Arguably one of the most modeled pathways ever, minimal models of yeast glycolysis were studied since the 1960s [94, 273, 305 308] and give rise to a rich spectrum of... 

The first reaction vi (Gx. ATP) describes the upper part of glycolysis, converting one (external) molecule of glucose (Gx) into two molecules of triosephosphate (TP), using two molecules of ATP. The second reaction v2 (TP, ADP) describes the synthesis of two molecules ATP from each molecule of TP. The third reaction v3 (ATP) describes a (lumped) overall ATP utilization. To obtain a minimal kinetic model for the glycolytic pathway, we adopt rate function similar to [96], using... 

Figure 21. The nullclines of the minimal model of glycolysis (schematic). The graphic analysis allows to deduce the qualitative dynamics of the system. Each area in the phasespace is characterized by the signs of the local derivatives, corresponding to increasing or decreasing concentration of the respective variable. The gray arrows indicate the direction a trajectory will go. Note that the trajectories may only intersect vertically or horizontally with the nullclines. For simplicity, the nullclines are depicted schematically only, for the actual nullclines corresponding to the rate equations see Fig. 22C.

Figure 22. The nullclines corresponding to the minimal model of glycolysis. Depending on the value of the maximal ATP utilization Vm3, the pathway either exhibits a unique steady state or allows for a bistable solution. Note that the nullcline for TP does not depend on VThe corresponding steady states are shown in Fig. 23. Parameters are Vm 3.1, K 0.57, ki 4.0, K i 0.06, and n 4 (the values do not correspond to a specific biological situation).

Figure 23. The steady state ATP concentration as a function of maximal ATP utilization Vmi for the minimal model of glycolysis. The letters denoted on the x axis correspond to the different scenarios shown in Fig. 22A D. Bold lines indicate stable steady states. Note that the physiologically feasible region is confined to the interval ATP0 e [0,Ar]. For low ATP usage (Vm3 small), there are three steady states, two of which are stable. However, both stable states are outside the feasible interval.

In addition to bistability and hysteresis, the minimal model of glycolysis also allows nonstationary solutions. Indeed, as noted above, one of the main rationales for the construction of kinetic models of yeast glycolysis is to account for metabolic oscillations observed experimentally for several decades [297, 305] and probably the model system for metabolic rhythms. In the minimal model considered here, oscillations arise due to the inhibition of the first reaction by its substrate ATP (a negative feedback). Figure 24 shows the time courses of oscillatory solutions for the minimal model of glycolysis. Note that for a large... 

Figure 24. The nullclines (upper panels, gray lines) and time courses (lower panels) for oscillatory solutions of the minimal model of glycolysis. Left panels Damped oscillations. The...

Figure 29 Bifurcation diagram of the minimal model of glycolysis as a function of feedback strength and saturation 6 of the ATPase reaction. Shown are the transitions to instability via a saddle node (SN) and a Hopf (HO) bifurcation (solid lines). In the regions (i) and (iv), the largest real part with in the spectrum of eigenvalues is positive > 0. Within region (ii), the metabolic state is a stable node, within region (iii) a stable focus, corresponding to damped transient oscillations.

Figure 30. A medium complexity model of yeast glycolysis [342], The model consists of nine metabolites and nine reactions. The main regulatory step is the phosphofructokinase (PFK), combined with the hexokinase (HK) reaction into a single reaction vi. As in the minimal model, we only consider the inhibition by its substrate ATP, although PFK is known to have several effectors. External glucose (Glc ) and ethanol (EtOH) are assumed to be constant. Additional abbreviations Glucose (Glc), fructose 1,6 biphosphate (FBP), pool of triosephosphates (TP), 1,3 biphosphogly cerate (BPG), and the pool of pyruvate and acetaldehyde (Pyr).

Figure 32. Bifurcation diagram of the medium complexity model of glycolysis, analogous to Fig. 29. A The largest real part of the eigenvalues as a function of the feedback strength 0 TP, depicted for increasing saturation of the overall ATPase reaction. B The metabolic state is stable only for an intermediate value of the feedback parameter. For increasing saturation of the ATPase reaction, the stable region decreases.

F. Hynne, S. Dan0, and R G. Sprensen, Full scale model of glycolysis in Saccharomyces cerevisiae. Biophys. Chem. 94, 121 163 (2001). 

---