arXiv subjects

Mustafa Khammash

Publications and source records attributed to Mustafa Khammash.

At least 19 recordsLinked to original sources

arXiv2026

GenAI-Net: A Generative AI Framework for Automated Biomolecular Network Design

Biomolecular networks underpin emerging technologies in synthetic biology-from robust biomanufacturing and metabolic engineering to smart therapeutics and cell-based diagnostics-and also provide a mechanistic language for understanding complex dynamics in natural and ecological systems. Yet designing chemical reaction networks (CRNs) that implement a desired dynamical function remains largely manual: while a proposed network can be checked by simulation, the reverse problem of discovering a network from a behavioral specification is difficult, requiring substantial human insight to navigate a vast space of topologies and kinetic parameters with nonlinear and possibly stochastic dynamics. Here we introduce GenAI-Net, a generative AI framework that automates CRN design by coupling an agent that proposes reactions to simulation-based evaluation defined by a user-specified objective. GenAI-Net efficiently produces novel, topologically diverse solutions across multiple design tasks, including dose responses, complex logic gates, classifiers, oscillators, and robust perfect adaptation in deterministic and stochastic settings (including noise reduction). By turning specifications into families of circuit candidates and reusable motifs, GenAI-Net provides a general route to programmable biomolecular circuit design and accelerates the translation from desired function to implementable mechanisms.

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arXiv2025

Interpretable Neural Approximation of Stochastic Reaction Dynamics with Guaranteed Reliability

Stochastic Reaction Networks (SRNs) are a fundamental modeling framework for systems ranging from chemical kinetics and epidemiology to ecological and synthetic biological processes. A central computational challenge is the estimation of expected outputs across initial conditions and times, a task that is rarely solvable analytically and becomes computationally prohibitive with current methods such as Finite State Projection or the Stochastic Simulation Algorithm. Existing deep learning approaches offer empirical scalability, but provide neither interpretability nor reliability guarantees, limiting their use in scientific analysis and in applications where model outputs inform real-world decisions. Here we introduce DeepSKA, a neural framework that jointly achieves interpretability, guaranteed reliability, and substantial computational gains. DeepSKA yields mathematically transparent representations that generalise across states, times, and output functions, and it integrates this structure with a small number of stochastic simulations to produce unbiased, provably convergent, and dramatically lower-variance estimates than classical Monte Carlo. We demonstrate these capabilities across nine SRNs, including nonlinear and non-mass-action models with up to ten species, where DeepSKA delivers accurate predictions and orders-of-magnitude efficiency improvements. This interpretable and reliable neural framework offers a principled foundation for developing analogous methods for other Markovian systems, including stochastic differential equations.

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arXiv2025

A Spectral Koopman Approximation Framework for Stochastic Reaction Networks

Stochastic reaction networks (SRNs) are a general class of continuous-time Markov jump processes used to model a wide range of systems, including biochemical dynamics in single cells, ecological and epidemiological populations, and queueing or communication networks. Yet analyzing their dynamics remains challenging because these processes are high-dimensional and their transient behavior can vary substantially across different initial molecular or population states. Here we introduce a spectral framework for the stochastic Koopman operator that provides a tractable, low-dimensional representation of SRN dynamics over continuous time, together with computable error estimates. By exploiting the compactness of the Koopman operator, we recover dominant spectral modes directly from simulated or experimental data, enabling efficient prediction of moments, event probabilities, and other summary statistics across all initial states. We further derive continuous-time parameter sensitivities and cross-spectral densities, offering new tools for probing noise structure and frequency-domain behavior. We demonstrate the approach on biologically relevant systems, including synthetic intracellular feedback controllers, stochastic oscillators, and inference of initial-state distributions from high-temporal-resolution flow cytometry. Together, these results establish spectral Koopman analysis as a powerful and general framework for studying stochastic dynamical systems across the biological, ecological, and computational sciences.

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arXiv2025

Realizing Reduced and Sparse Biochemical Reaction Networks from Dynamics

We propose a direct optimization framework for learning reduced and sparse chemical reaction networks (CRNs) from time-series trajectory data. In contrast to widely used indirect methods-such as those based on sparse identification of nonlinear dynamics (SINDy)-which infer reaction dynamics by fitting numerically estimated derivatives, our approach fits entire trajectories by solving a dynamically constrained optimization problem. This formulation enables the construction of reduced CRNs that are both low-dimensional and sparse, while preserving key dynamical behaviors of the original system. We develop an accelerated proximal gradient algorithm to efficiently solve the resulting non-convex optimization problem. Through illustrative examples, including a Drosophila circadian oscillator and a glycolytic oscillator, we demonstrate the ability of our method to recover accurate and interpretable reduced-order CRNs. Notably, the direct approach avoids the derivative estimation step and mitigates error accumulation issues inherent in indirect methods, making it a robust alternative for data-driven CRN realizations.

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arXiv2024

Unbiased estimation of second-order parameter sensitivities for stochastic reaction networks

Stochastic models for chemical reaction networks are increasingly popular in systems and synthetic biology. These models formulate the reaction dynamics as Continuous-Time Markov Chains (CTMCs) whose propensities are parameterized by a vector $\theta$ and parameter sensitivities are introduced as derivatives of their expected outputs with respect to components of the parameter vector. Sensitivities characterise key properties of the output like robustness and are also at the heart of numerically efficient optimisation routines like Newton-type algorithms used in parameter inference and the design of of control mechanisms. Currently the only unbiased estimator for second-order sensitivities is based on the Girsanov transform and it often suffers from high estimator variance. We develop a novel estimator for second-order sensitivities by first rigorously deriving an integral representation of these sensitivities. We call the resulting method the Double Bernoulli Path Algorithm and illustrate its efficiency through numerical examples.

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arXiv2024

The generator gradient estimator is an adjoint state method for stochastic differential equations

Motivated by the increasing popularity of overparameterized Stochastic Differential Equations (SDEs) like Neural SDEs, Wang, Blanchet and Glynn recently introduced the generator gradient estimator, a novel unbiased stochastic gradient estimator for SDEs whose computation time remains stable in the number of parameters. In this note, we demonstrate that this estimator is in fact an adjoint state method, an approach which is known to scale with the number of states and not the number of parameters in the case of Ordinary Differential Equations (ODEs). In addition, we show that the generator gradient estimator is a close analogue to the exact Integral Path Algorithm (eIPA) estimator which was introduced by Gupta, Rathinam and Khammash for a class of Continuous-Time Markov Chains (CTMCs) known as stochastic chemical reactions networks (CRNs).

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arXiv2023

Effective filtering approach for joint parameter-state estimation in SDEs via Rao-Blackwellization and modularization

Stochastic filtering is a vibrant area of research in both control theory and statistics, with broad applications in many scientific fields. Despite its extensive historical development, there still lacks an effective method for joint parameter-state estimation in SDEs. The state-of-the-art particle filtering methods suffer from either sample degeneracy or information loss, with both issues stemming from the dynamics of the particles generated to represent system parameters. This paper provides a novel and effective approach for joint parameter-state estimation in SDEs via Rao-Blackwellization and modularization. Our method operates in two layers: the first layer estimates the system states using a bootstrap particle filter, and the second layer marginalizes out system parameters explicitly. This strategy circumvents the need to generate particles representing system parameters, thereby mitigating their associated problems of sample degeneracy and information loss. Moreover, our method employs a modularization approach when integrating out the parameters, which significantly reduces the computational complexity. All these designs ensure the superior performance of our method. Finally, a numerical example is presented to illustrate that our method outperforms existing approaches by a large margin.

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arXiv2023

Complete characterization of robust perfect adaptation in biochemical reaction networks

Perfect adaptation is a phenomenon whereby the output variables of a system can maintain certain values despite external disturbances. Robust perfect adaptation (RPA) refers to an adaptation property that does not require fine-tuning of system parameters. RPA plays a vital role for the survival of living systems in unpredictable environments. However, complex interaction patterns in biochemical systems pose a significant challenge in identifying RPA and associated regulatory mechanisms. The goal of this paper is to present a novel approach for finding all RPA properties that are realized for a generic choice of kinetics for general deterministic chemical reaction systems. This is accomplished by proving that an RPA property is represented by a subnetwork with certain topological features. This connection is exploited to show that these structures generate all kinetics-independent RPA properties, allowing us to systematically identify all RPA properties by enumerating these subnetworks. An efficient method is developed for this enumeration, and we provide a computational package for this purpose. We pinpoint the integral feedback controllers that work in concert to realize each RPA property, casting our results into the familiar control-theoretic paradigm of the Internal Model Principle. We further generalize the regulation problem to the multi-output scenario where the target values belong to a manifold of nonzero dimension, and provide a sufficient condition for this. The present work significantly advances our understanding of regulatory mechanisms that lead to RPA in endogenous biochemical systems, and it also provides rational design principles for synthetic controllers. The present results indicate that an RPA property is essentially equivalent to the existence of a "topological invariant", which is an instance of what we call the "Robust Adaptation is Topological"(RAT) principle.

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arXiv2022

Noise in Biomolecular Systems: Modeling, Analysis, and Control Implications

While noise is generally associated with uncertainties and often has a negative connotation in engineering, living organisms have evolved to adapt to (and even exploit) such uncertainty to ensure the survival of a species or implement certain functions that would have been difficult or even impossible otherwise. In this article, we review the role and impact of noise in systems and synthetic biology, with a particular emphasis on its role in the genetic control of biological systems, an area we refer to as Cybergenetics. The main modeling paradigm is that of stochastic reaction networks, whose applicability goes beyond biology, as these networks can represent any population dynamics system, including ecological, epidemiological, and opinion dynamics networks. We review different ways to mathematically represent these systems, and we notably argue that the concept of ergodicity presents a particularly suitable way to characterize their stability. We then discuss noise-induced properties and show that noise can be both an asset and a nuisance in this setting. Finally, we discuss recent results on (stochastic) Cybergenetics and explore their relationships to noise. Along the way, we detail the different technical and biological constraints that need to be respected when designing synthetic biological circuits. Finally, we discuss the concepts, problems, and solutions exposed in the article; raise criticisms and concerns about current ideas and approaches; suggest current (open) problems with potential solutions; and provide some ideas for future research directions.

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arXiv2022

Structural Stability Properties of Antithetic Integral (Rein) Control with Output Inhibition

Perfect adaptation is a well-studied biochemical homeostatic behavior lying at the core of biochemical regulation. While the concepts of homeostasis and perfect adaptation are not new, their underlying mechanisms and associated biochemical regulation motifs are not yet fully understood. Insights from control theory unraveled the connections between perfect adaptation and integral control, a prevalent engineering control strategy. In particular, the recently introduced Antithetic Integral Controller (AIC) has been shown to successfully ensure perfect adaptation properties to the network it is connected to. The complementary structure of the two molecules the AIC relies upon allows for a versatile way to control biochemical networks, a property which gave rise to an important body of literature pertaining to mathematically elucidating its properties, generalizing its structure, and developing experimental methods for its implementation. The Antithetic Integral Rein Controller (AIRC), an extension of the AIC in which both controller molecules are used for control, holds many promises as it supposedly overcomes certain limitations of the AIC. We focus here on an AIRC structure with output inhibition that combines two AICs in a single structure. We demonstrate that rhis controller ensure structural stability and structural perfect adaptation properties for the controlled network under mild assumptions, meaning that this property is independent of the parameters of the network and the controller. The results are very general and valid for the class of unimolecular mass-action networks as well as more general networks, including cooperative and Michaelis-Menten networks. We also provide a systematic and accessible computational way for verifying whether a given network satisfies the conditions under which the structural property would hold.

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arXiv2021

Design of a synthetic integral feedback circuit: dynamic analysis and DNA implementation

The design and implementation of regulation motifs ensuring robust perfect adaptation are challenging problems in synthetic biology. Indeed, the design of high-yield robust metabolic pathways producing, for instance, drug precursors and biofuels, could be easily imagined to rely on such a control strategy in order to optimize production levels and reduce production costs, despite the presence of environmental disturbance and model uncertainty. We propose here a motif that ensures tracking and robust perfect adaptation for the controlled reaction network through integral feedback. Its metabolic load on the host is fully tunable and can be made arbitrarily close to the constitutive limit, the universal minimal metabolic load of all possible controllers. A DNA implementation of the controller network is finally provided. Computer simulations using realistic parameters demonstrate the good agreement between the DNA implementation and the ideal controller dynamics.

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arXiv2021

Optimal and $H_\infty$ Control of Stochastic Reaction Networks

Stochastic reaction networks is a powerful class of models for the representation a wide variety of population models including biochemistry. The control of such networks has been recently considered due to their important implications for the control of biological systems. Their optimal control, however, has been relatively few studied until now. The continuous-time finite-horizon optimal control problem is formulated first and explicitly solved in the case of unimolecular reaction networks. The problems of the optimal sampled-data control, the continuous $H_\infty$ control, and the sampled-data $H_\infty$ control of such networks are addressed next. The results in the unimolecular case take the form of nonstandard Riccati differential equations or differential Lyapunov equations coupled with difference Riccati equations, which can all be solved numerically by backward-in-time integration.

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arXiv2021

Convergence of regularized particle filters for stochastic reaction networks

Filtering for stochastic reaction networks (SRNs) is an important problem in systems/synthetic biology aiming to estimate the state of unobserved chemical species. A good solution to it can provide scientists valuable information about the hidden dynamic state and enable optimal feedback control. Usually, the model parameters need to be inferred simultaneously with state variables, and a conventional particle filter can fail to solve this problem accurately due to sample degeneracy. In this case, the regularized particle filter (RPF) is preferred to the conventional ones, as the RPF can mitigate sample degeneracy by perturbing particles with artificial noise. However, the artificial noise introduces an additional bias to the estimate, and, thus, it is questionable whether the RPF can provide reliable results for SRNs. In this paper, we aim to identify conditions under which the RPF converges to the exact filter in the filtering problem determined by a bimolecular network. First, we establish computationally efficient RPFs for SRNs on different scales using different dynamical models, including the continuous-time Markov process, tau-leaping model, and piecewise deterministic process. Then, by parameter sensitivity analyses, we show that the established RPFs converge to the exact filters if all reactions leading to an increase of the molecular population have linearly growing propensities and some other mild conditions are satisfied simultaneously. This ensures the performance of the RPF for a large class of SRNs, and several numerical examples are presented to illustrate our results.

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arXiv2021

Stochastic filtering for multiscale stochastic reaction networks based on hybrid approximations

In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate with these advanced technologies, i.e., how to estimate latent dynamic states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. A good solution to this problem can further improve scientists' ability to extract information about intracellular systems from time-course experiments. A straightforward approach to this filtering problem is to use a particle filter where particles are generated by simulation of the full model and weighted according to observations. However, the exact simulation of the full dynamic model usually takes an impractical amount of computational time and prevents this type of particle filters from being used for real-time applications, such as transcription regulation networks. Inspired by the recent development of hybrid approximations to multiscale chemical reaction networks, we approach the filtering problem in an alternative way. We first prove that accurate solutions to the filtering problem can be constructed by solving the filtering problem for a reduced model that represents the dynamics as a hybrid process. The model reduction is based on exploiting the time-scale separations in the original network and, therefore, can greatly reduce the computational effort required to simulate the dynamics. As a result, we are able to develop efficient particle filters to solve the filtering problem for the original model by applying particle filters to the reduced model. We illustrate the accuracy and the computational efficiency of our approach using several numerical examples.

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arXiv2020

Stochastic filters based on hybrid approximations of multiscale stochastic reaction networks

We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering problem can be constructed by solving the filtering problem for a reduced model that represents the dynamics as a hybrid process. The model reduction is based on exploiting the time-scale separations in the original network, and it can greatly reduce the computational effort required to simulate the dynamics. This enables us to develop efficient particle filters to solve the filtering problem for the original model by applying particle filters to the reduced model. We illustrate the accuracy and the computational efficiency of our approach using a numerical example.

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arXiv2020

Ergodicity, Output-Controllability, and Antithetic Integral Control of Uncertain Stochastic Reaction Networks

The ergodicity and the output-controllability of stochastic reaction networks have been shown to be essential properties to fulfill to enable their control using, for instance, antithetic integral control. We propose here to extend those properties to the case of uncertain networks. To this aim, the notions of interval, robust, sign, and structural ergodicity/output-controllability are introduced. The obtained results lie in the same spirit as those obtained in [Briat, Gupta & Khammash, Cell Systems, 2016] where those properties are characterized in terms of control theoretic concepts, linear algebraic conditions, linear programs, and graph-theoretic/algebraic conditions. An important conclusion is that all those properties can be characterized by linear programs. Two examples are given for illustration.

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arXiv2020

In-Silico Proportional-Integral Moment Control of Stochastic Gene Expression

The problem of controlling the mean and the variance of a species of interest in a simple gene expression is addressed. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a simple PI controller that satisfies certain sufficient conditions. Controlling both the mean and variance however requires an additional control input, e.g. the mRNA degradation rate, and local robust tracking of mean and variance is proved to be achievable using multivariable PI control, provided that the reference point satisfies necessary conditions imposed by the system. Even more importantly, it is shown that there exist PI controllers that locally, robustly and simultaneously stabilize all the equilibrium points inside the admissible region. The results are then extended to the mean control of a gene expression with protein dimerization. It is shown that the moment closure problem can be circumvented without invoking any moment closure technique. Local stabilization and convergence of the average dimer population to any desired reference value is ensured using a pure integral control law. Explicit bounds on the controller gain are provided and shown to be valid for any reference value. As a byproduct, an explicit upper-bound of the variance of the monomer species, acting on the system as unknown input due to the moment openness, is obtained. The results are illustrated by simulation.

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arXiv2019

A hidden integral structure endows Absolute Concentration Robust systems with resilience to dynamical concentration disturbances

Biochemical systems that express certain chemical species of interest at the same level at any positive equilibrium are called "absolute concentration robust" (ACR). These species behave in a stable, predictable way, in the sense that their expression is robust with respect to sudden changes in the species concentration, regardless the new positive equilibrium reached by the system. Such a property has been proven to be fundamentally important in certain gene regulatory networks and signaling systems. In the present paper, we mathematically prove that a well-known class of ACR systems studied by Shinar and Feinberg in 2010 hides an internal integral structure. This structure confers these systems with a higher degree of robustness that what was previously unknown. In particular, disturbances much more general than sudden changes in the species concentrations can be rejected, and robust perfect adaptation is achieved. Significantly, we show that these properties are maintained when the system is interconnected with other chemical reaction networks. This key feature enables design of insulator devices that are able to buffer the loading effect from downstream systems - a crucial requirement for modular circuit design in synthetic biology.

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