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1. Absolutely robust controllers for chemical reaction networks

   https://doi.org/10.1098/rsif.2020.0031  

   Kim, Jinsu ; Enciso, German ( May 2020 , Journal of The Royal Society Interface)

   null (Ed.)

   In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor–ligand signalling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions. 

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2. Metastable spiking networks in the replica-mean-field limit

   https://doi.org/10.1371/journal.pcbi.1010215  

   Yu, Luyan ; Taillefumier, Thibaud O. ( June 2022 , PLOS Computational Biology)

   Beck, Jeff (Ed.)

   Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. In this limit, networks are made of infinitely many replicas of the finite network of interest, but with randomized interactions across replicas. Such randomization renders certain excitatory networks fully tractable at the cost of neglecting activity correlations, but with explicit dependence on the finite size of the neural constituents. However, metastable dynamics typically unfold in networks with mixed inhibition and excitation. Here, we extend the RMF computational framework to point-process-based neural network models with exponential stochastic intensities, allowing for mixed excitation and inhibition. Within this setting, we show that metastable finite-size networks admit multistable RMF limits, which are fully characterized by stationary firing rates. Technically, these stationary rates are determined as the solutions of a set of delayed differential equations under certain regularity conditions that any physical solutions shall satisfy. We solve this original problem by combining the resolvent formalism and singular-perturbation theory. Importantly, we find that these rates specify probabilistic pseudo-equilibria which accurately capture the neural variability observed in the original finite-size network. We also discuss the emergence of metastability as a stochastic bifurcation, which can be interpreted as a static phase transition in the RMF limits. In turn, we expect to leverage the static picture of RMF limits to infer purely dynamical features of metastable finite-size networks, such as the transition rates between pseudo-equilibria. 

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3. Replica-mean-field limits of fragmentation-interaction-aggregation processes

   https://doi.org/10.1017/jpr.2021.31  

   Baccelli, François ; Davydov, Michel ; Taillefumier, Thibaud ( March 2022 , Journal of Applied Probability)

   Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called ‘Poisson hypothesis’. However, in most applications this hypothesis is only conjectured. In this paper we establish the Poisson hypothesis for a general class of discrete-time, point-process-based dynamics that we propose to call fragmentation-interaction-aggregation processes, and which are introduced here. These processes feature a network of nodes, each endowed with a state governing their random activation. Each activation triggers the fragmentation of the activated node state and the transmission of interaction signals to downstream nodes. In turn, the signals received by nodes are aggregated to their state. Our main contribution is a proof of the Poisson hypothesis for the replica-mean-field version of any network in this class. The proof is obtained by establishing the propagation of asymptotic independence for state variables in the limit of an infinite number of replicas. Discrete-time Galves–Löcherbach neural networks are used as a basic instance and illustration of our analysis.

    

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4. Identifiability of stochastically modelled reaction networks

   https://doi.org/10.1017/S0956792520000492  

   ENCISO, GERMAN ; ERBAN, RADEK ; KIM, JINSU ( February 2021 , European Journal of Applied Mathematics)

   null (Ed.)

   Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous-time Markov processes. In this manuscript, the identifiability of the underlying network structure with a given stochastic system dynamics is studied. It is shown that some data types related to the associated stochastic dynamics can uniquely identify the underlying network structure as well as the system parameters. The accuracy of the presented network inference is investigated when given dynamical data are obtained via stochastic simulations. 

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5. Reducing the complexity of chemical networks via interpretable autoencoders

   https://doi.org/10.1051/0004-6361/202039956  

   Grassi, T. ; Nauman, F. ; Ramsey, J. P. ; Bovino, S. ; Picogna, G. ; Ercolano, B. ( December 2022 , Astronomy & Astrophysics)

   In many astrophysical applications, the cost of solving a chemical network represented by a system of ordinary differential equations (ODEs) grows significantly with the size of the network and can often represent a significant computational bottleneck, particularly in coupled chemo-dynamical models. Although standard numerical techniques and complex solutions tailored to thermochemistry can somewhat reduce the cost, more recently, machine learning algorithms have begun to attack this challenge via data-driven dimensional reduction techniques. In this work, we present a new class of methods that take advantage of machine learning techniques to reduce complex data sets (autoencoders), the optimization of multiparameter systems (standard backpropagation), and the robustness of well-established ODE solvers to to explicitly incorporate time dependence. This new method allows us to find a compressed and simplified version of a large chemical network in a semiautomated fashion that can be solved with a standard ODE solver, while also enabling interpretability of the compressed, latent network. As a proof of concept, we tested the method on an astrophysically relevant chemical network with 29 species and 224 reactions, obtaining a reduced but representative network with only 5 species and 12 reactions, and an increase in speed by a factor 65. 

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