A minimal model

This is a (minimal) model including the formation of the complex R1-R2, the active precursor complex APC that interconverts to those states belonging to the active successor complex ASC, as discussed in the previous section. The chemical reaction, in this model, ends up with the formation of the products PI and P2. The kinetic parameters k+ and k- hide the effects of quantum interconversions via the intermediate Hamiltonian Hc(ij). Let us introduce this feature in the kinetic model, so that... 

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.

The rate expression described in Sect. 2, Fermi s golden rule, is commonly derived from a minimal model of two interacting quantum states plus environmental (bath) states which serve to provide the localizing fluctuations. As the... 

Fig. 1. Construction of a computational model for TauD. (A) the solvated TauD enzyme (PDB code 1GY9, solvating water molecules in red) (B) the desolvated enzyme (C) the active site with the substrate and a-ketoglutarate bound to the iron centre, and the most important amino acids in the first and second coordination sphere (D) a minimal model for TauD including only the first coordination sphere and the substrate.

In the following we use a minimal model for the low energy, long wave length excitations of the condensed charge density wave. Since fluctuations in the amplitude Z are suppressed, because they are massive, we take only fluctuations of the phase cp (cf. eq. 2) into account. Clearly, such an approach breaks down sufficiently close to the mean-field transition temperature TCMF. Neglecting fluctuations in Z, the Hamiltonian for our model is given by... 

A minimal model for self-replication is shown in Scheme 12.23. The replicator (R) must be able to recognise and bind at least two different precursor components (Cl and C2) in a ternary (three component) complex, and to accelerate their chemical reaction with each other to produce a product that is a copy of the original R. Such a simple system will always be in competition with the uncatalysed binary reaction of Cl and C2. 

In an attempt to better understand the role of receptor internalization, a minimal model has been developed using hypothesis testing [10]. The model is based on experimental data on autophosphorylation of the IR. Upon addition of insulin to intact adipocytes, the IR rapidly autophosphorylates with an overshoot peak before t = 0.9 min, and then slowly declines to a quasi-steady state at around 15 min. 

This subsection summarizes what is known about exciton-vibration coupling in general. Thereafter, specific cases will be treated. We restrict our discussion to a minimal model of coupling characterized by the following approximations50 ... 

In order to model the oscillatory waveform and to predict the p-T locus for the (Hopf) bifurcation from oscillatory ignition to steady flame accurately, it is in fact necessary to include more reaction steps. Johnson et al. [45] examined the 35 reaction Baldwin-Walker scheme and obtained a number of reduced mechanisms from this in order to identify a minimal model capable of semi-quantitative p-T limit prediction and also of producing the complex, mixed-mode waveforms observed experimentally. The minimal scheme depends on the rate coefficient data used, with an updated set beyond that used by Chinnick et al. allowing reduction to a 10-step scheme. It is of particular interest, however, that not even the 35 reaction mechanism can predict complex oscillations unless the non-isothermal character of the reaction is included explicitly. (In computer integrations it is easy to examine the isothermal system by setting the reaction enthalpies equal to zero this allows us, in effect, to examine the behaviour supported by the chemical feedback processes in this system in isolation... 

Of course, it is impossible to include all possible chemicals in a model. Because our constructive biology is aimed at neither making a complicated realistic model for a cell nor imitating a specific cellular function, we set up a minimal model with reaction network, to answer the questions raised in Section I. Now, there are several levels of modeling, depending on what question we are trying to answer. 

Fantacci, S Migani, A., Olivucci, M., CASPT2/CASSCF and TDDFT/CASSCF Mapping of the Excited State Isomerization Path of a Minimal Model of the Retinal Chromophore, J. Phys. Chem. A 2004, 108, 1208 1213. 

For some reactions [e.g., Co(phen)3 + oxidation of plastocyanin (Cu )] the expected linear plot of kobs vs. [complex] is not observed. Instead, the rate is observed to saturate (Figure 6.27). A minimal model used to explain this behavior involves the two pathways for electron transfer shown in Equation... 

Li Rinzel, 1994). The latter reductions therefore yield a minimal model for Ca oscillations, like the earlier, two-pool minimal model considered below, which takes into account only CICR and not the inhibition of Ca " release at high levels of cytosolic Ca. A one-pool version of this model in which Ca and IP3 behave as co-agonists for Ca " release is presented in section 9.4. A model based on the bellshaped calcium dependence of the ryanodine-sensitive calcium channel was recently proposed for calcium dynamics in cardiac myocytes (Tang Othmer, 1994b). 

These results have opened the way to the construction of more realistic models for the mitotic oscillator. The purpose of this chapter is briefly to present these models and to classify them according to the type of regulation responsible for oscillatory behaviour. The way sustained oscillations are generated is examined in detail in a minimal model based on the cascade of phosphorylation-dephosphorylation cycles that controls the onset of mitosis in embryonic cells. Extensions of the cascade model taking into account additional, recently uncovered phosphorylation-dephosphorylation cycles are considered. Ways of arresting the cell division cycle in that model and the control of the mitotic oscillator by growth factors are also discussed. 

The inversion symmetry with respect to the x — z plane implies that the equations must he invariant under the transformation S Ai, Bi —Ai,Bi, so that only odd powers of the Aj-s can appear in the first set of equations and only even powers in the second set. In a linear approximation, only the A-s have to he taken into account, as they are the ones driven hy the light directly. Thus for a minimal model the three modes A, A2,Bi have been kept. The resulting set of ODEs has been solved numerically, and the nature of the solutions has been analyzed as a function of the two control parameters of the problem the angle of incidence a and the intensity of the light normalized by the OFT threshold p. 

Respiratory rhythmicity is an emergent property of the RCPG resulting from mutual inhibition of inspiratory and expiratory related neurons. A minimal model due to Duffin [1991] postulated the early-burst inspiratory (I) neurons and Botzinger complex expiratory (E) neurons to be the mutually inhibiting pair. Adaptation of the I neurons (e.g., by calcium-activated potassium conductance) results in sustained relaxation oscillation in the network under constant chemical excitation. Both neuron groups are assumed to have monosynaptic inhibitory projections to bulbospinal inspiratory (Ir) output neurons (Figure 11.3). The model equations are ... 

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