Modeling Stochastic Dynamics in Biochemical Systems with Feedback Using Maximum Caliber

Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A.

doi:10.1021/jp111112s

Cited by 32 publications

(57 citation statements)

References 39 publications

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“…This was demonstrated in two synthetic gene circuits: (i) in a positive feedback (PF) circuit in which a gene autoactivates itself 62 and (ii) in genetic toggle switch (TS) in which two genes repress each other. 30,63 The information input was (1) protein synthesis, (2) protein turnover, and (3) effective coupling between species (positive feedback in the case of PF and negative feedback in the case of a TS; see Fig. 4 for the PF circuit).…”

Section: Modeling Network That Are Biochemical or Socialmentioning

confidence: 99%

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Perspective: Maximum caliber is a general variational principle for dynamical systems

Dixit

Wagoner

Weistuch

et al. 2018

The Journal of Chemical Physics

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A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations The Journal of Chemical Physics 148, 014103 (2018) We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

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Section: Modeling Network That Are Biochemical or Socialmentioning

confidence: 99%

“…In such cases, we can use first or higher moments or other knowledge. 62,63,67,77,80 If constraints beyond first moment are negligible it will be seen from the data which will make Lagrange multipliers vanishing for these higher moments. However we cannot assume that apriori.…”

Section: A Accounting For Measurement Errors In the Constraintsmentioning

confidence: 99%

Perspective: Maximum caliber is a general variational principle for dynamical systems

Dixit

Wagoner

Weistuch

et al. 2018

The Journal of Chemical Physics

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“…[15,16,17], and applications to discrete master equations have been explored in Refs. [18,19], and from another perspective in Ref. [20].…”

Section: Maximum Calibermentioning

confidence: 99%

Irreversible Thermodynamics

Rogers

Rempe

2012

J. Phys.: Conf. Ser.

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“…We have recently introduced an alternate top-down approach based on the principle of Maximum Caliber (MaxCal) to analyze genetic circuits. [32][33][34][35] MaxCal maximizes the path/trajectory entropy subject to minimal constraints to predict the trajectory probability distribution 33,36 and circumvents both of the challenges mentioned above. First, MaxCal is built in the language of trajectories, thus it starts directly with the raw data.…”

Section: Introductionmentioning

confidence: 99%

Maximum Caliber can build and infer models of oscillation in a three-gene feedback network

Firman

Amgalan

Ghosh

2018

Preprint

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Single-cell protein expression time trajectories provide rich temporal data quantifying cellular variability and its role in dictating fitness. However, theoretical models to analyze and fully extract information from these measurements remain limited for three reasons: i) gene expression profiles are noisy, rendering models of averages inapplicable, ii) experiments typically measure only a few protein species while leaving other molecular actors -necessary to build traditional bottom-up models -unnoticed, and iii) measured data is in fluorescence, not particle number. We have recently addressed these challenges in an alternate top-down approach using the principle of Maximum Caliber (MaxCal) to model genetic switches with one and two protein species. In the present work we address scalability and broader applicability of MaxCal by extending to a three-gene (A, B, C) feedback network that exhibits oscillation, commonly known as the repressilator. We test MaxCal's inferential power by using synthetic data of noisy protein number time traces -serving as a proxy for experimental data -generated from a known underlying model. We notice that the minimal MaxCal model -accounting for production, degradation, and only one type of symmetric coupling between all three species -reasonably infers several underlying features of the circuit such as the effective production rate, degradation rate, frequency of oscillation, and protein number distribution. Next, we build models of higher complexity including different levels of coupling between A, B, and C and rigorously assess their relative performance. While the minimal model (with four parameters) performs remarkably well, we note that the most complex model (with six parameters) allowing all possible forms of crosstalk between A, B, and C slightly improves prediction of rates, but avoids ad-hoc assumption of all the other models. It is also the model of choice based on Bayesian Information Criteria. We further analyzed time trajectories in arbitrary fluorescence (using synthetic trajectories) to mimic realistic data. We conclude that even with a three-protein system including both fluorescence noise and intrinsic gene expression fluctuations, MaxCal can faithfully infer underlying details of the network, opening up future directions to model other network motifs with many species.

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Modeling Stochastic Dynamics in Biochemical Systems with Feedback Using Maximum Caliber

Cited by 32 publications

References 39 publications

Perspective: Maximum caliber is a general variational principle for dynamical systems

Perspective: Maximum caliber is a general variational principle for dynamical systems

Irreversible Thermodynamics

Maximum Caliber can build and infer models of oscillation in a three-gene feedback network

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