Michaelis-Menten dynamics in protein subnetworks

Rubin, Katy J.; Sollich, Peter

doi:10.1063/1.4947478

Cited by 6 publications

(23 citation statements)

References 14 publications

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“…It only captures the dissipation due to the conversion of substrate into product. This reasoning can be made more rigorous: there are time-scale separation techniques for deterministic rate equations [25,51] frequently used in biochemical contexts [26], furthermore stochastic corrections due to small copy-numbers [52] and even effective memory effects [27,53] can be incorporated. However, these techniques do not explicitly address the question of thermodynamic consistency and we think that combining our coarse-graining with these techniques is a promising endeavor for the future.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

2018

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Starting from the detailed catalytic mechanism of a biocatalyst we provide a coarse-graining procedure which, by construction, is thermodynamically consistent. This procedure provides stoichiometries, reaction fluxes (rate laws), and reaction forces (Gibbs energies of reaction) for the coarse-grained level. It can treat active transporters and molecular machines, and thus extends the applicability of ideas that originated in enzyme kinetics. Our results lay the foundations for systematic studies of the thermodynamics of large-scale biochemical reaction networks. Moreover, we identify the conditions under which a relation between one-way fluxes and forces holds at the coarse-grained level as it holds at the detailed level. In doing so, we clarify the speculations and broad claims made in the literature about such a general flux-force relation. As a further consequence we show that, in contrast to common belief, the second law of thermodynamics does not require the currents and the forces of biochemical reaction networks to be always aligned.

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Section: Discussionmentioning

confidence: 99%

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

2018

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“…Michaelis-Menten (enzymatic) kinetics and Hill functions. To extend our formalism to such cases one could follow a procedure similar to the one used to treat Michaelis-Menten kinetics by projection methods [29]: introduce fast variables and binary reactions that in the limit of large rates reproduce the desired kinetics; apply the reduction method to this larger system; and finally take the large rate limit to get back to a reduced description for the original kinetics.…”

Section: Discussionmentioning

confidence: 99%

“…If we consider the fluctuating version of this quantity, namely r 1 GVA (t) = χ 1 (t) + ψ 1 (t) (E. 29) we can prove the equivalence with the projection formalism. m 4 has minus sign as it is a correction term needed for the substitution in the second line of (E.34) to be valid (in other words, to compensate for the use of (E.33) instead of (E.32)); namely In the second line of (E.44), we can apply the identity…”

Section: Appendix E3 Full Nonlinear Memory and Random Force In The Gvamentioning

confidence: 92%

Statistical physics approaches to subnetwork dynamics in biochemical systems

Bravi¹,

Sollich²

2017

Phys. Biol.

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We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally, embedded in a larger network (bulk). The key goal is to write dynamical equations reduced to the subnetwork but still retaining the effects of the bulk. As a result, the subnetwork-reduced dynamics contains a memory term and an extrinsic noise term with non-trivial temporal correlations. We first derive expressions for this memory and noise in the linearized (Gaussian) dynamics and then use a perturbative power expansion to obtain first order nonlinear corrections. For the case of vanishing intrinsic noise, our description is explicitly shown to be equivalent to projection methods up to quadratic terms, but it is applicable also in the presence of stochastic fluctuations in the original dynamics. An example from the epidermal growth factor receptor signalling pathway is provided to probe the increased prediction accuracy and computational efficiency of our method.

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“…Originally developed to allow the extraction of macroscopic equations from a microscopic description of the dynamics—a brief overview can be found in e.g. [ 19 ]—these methods have since been used to separate a network into an arbitarily chosen subnetwork and bulk in ways that preserve substantial features of the original temporal dynamics [ 20 , 21 ]. Used in this way, the approach describes the concentration of components in the subnetwork in detail, while the activities of the species in the bulk are replaced with so-called ‘memory functions’.…”

Section: Introductionmentioning

confidence: 99%

“…Evolving from its original applications to critical dynamics and supercooled liquids near the glass transition [ 22 ], this approach has been applied to biochemical networks [ 20 ], where it has been used to analyse the dynamics of signaling in the EGFR (epidermal growth factor receptor) network. It has since been developed further to include also enzymatic Michaelis-Menten reactions [ 21 ]. Here we apply the Zwanzig-Mori approach to the analysis of GRNs.…”

Section: Introductionmentioning

confidence: 99%

Memory functions reveal structural properties of gene regulatory networks

et al. 2018

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Gene regulatory networks (GRNs) control cellular function and decision making during tissue development and homeostasis. Mathematical tools based on dynamical systems theory are often used to model these networks, but the size and complexity of these models mean that their behaviour is not always intuitive and the underlying mechanisms can be difficult to decipher. For this reason, methods that simplify and aid exploration of complex networks are necessary. To this end we develop a broadly applicable form of the Zwanzig-Mori projection. By first converting a thermodynamic state ensemble model of gene regulation into mass action reactions we derive a general method that produces a set of time evolution equations for a subset of components of a network. The influence of the rest of the network, the bulk, is captured by memory functions that describe how the subnetwork reacts to its own past state via components in the bulk. These memory functions provide probes of near-steady state dynamics, revealing information not easily accessible otherwise. We illustrate the method on a simple cross-repressive transcriptional motif to show that memory functions not only simplify the analysis of the subnetwork but also have a natural interpretation. We then apply the approach to a GRN from the vertebrate neural tube, a well characterised developmental transcriptional network composed of four interacting transcription factors. The memory functions reveal the function of specific links within the neural tube network and identify features of the regulatory structure that specifically increase the robustness of the network to initial conditions. Taken together, the study provides evidence that Zwanzig-Mori projections offer powerful and effective tools for simplifying and exploring the behaviour of GRNs.

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Michaelis-Menten dynamics in protein subnetworks

Cited by 6 publications

References 14 publications

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

Statistical physics approaches to subnetwork dynamics in biochemical systems

Memory functions reveal structural properties of gene regulatory networks

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