Biology subjects

Khammash, M.

Publications and source records attributed to Khammash, M..

At least 37 records · Page 2Linked to original sources

bioRxiv2021

DeepCME: A deep learning framework for solving the Chemical Master Equation

Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorovs forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for solving high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorovs backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) and is algorithmically based on reinforcement learning. It only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the "policy function". This allows not just the numerical approximation of the CME solution but also of its sensitivities to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

systems biology↗

bioRxiv2021

A Class of Simple Biomolecular Antithetic Proportional-Integral-Derivative Controllers

Proportional-Integral-Derivative (PID) feedback controllers have been the most widely used controllers in industry for almost a century due to their good performance, simplicity, and ease of tuning. Motivated by their success in various engineering disciplines, PID controllers recently found their way into synthetic biology, where the design of feedback molecular control systems has been identified as an important goal. In this paper, we consider the mathematical realization of PID controllers via biomolecular interactions. We propose an array of topologies that offer a compromise between simplicity and high performance. We first demonstrate that different Proportional-Integral (PI) controllers exhibit different capabilities for enhancing the dynamics and reducing variance (cell-to-cell variability). Next, we introduce several derivative controllers that are realized based on incoherent feedforward loops acting in a feedback configuration. Alternatively, we show that differentiators can be realized by placing molecular integrators in a negative feedback loop--an arrangement that can then be augmented by PI components to yield PID feedback controllers. We demonstrate that the derivative component can be exploited for enhancing system stability, dramatically increasing the molecular control systems dynamic performance, and for reducing the noise effect on the output of interest. The PID controller features are established through various deterministic and stochastic analyses as well as numerical simulations. Finally, we provide an experimental demonstration using a recently developed hybrid setup, the cyberloop, where the controller is implemented in silico to control a biological genetic circuit in vivo. The large array of novel biomolecular PID controllers introduced here forms a basis for the design and construction of advanced high-performance biomolecular control systems that robustly regulate the dynamics of living systems.

synthetic biology↗

bioRxiv2021

Synthetic gene networks recapitulate dynamic signal decoding and differential gene expression

Cells live in constantly changing environments and employ dynamic signaling pathways to transduce information about the signals they encounter. However, the mechanisms by which dynamic signals are decoded into appropriate gene expression patterns remain poorly understood. Here, we devise networked optogenetic pathways that achieve novel dynamic signal processing functions that recapitulate cellular information processing. Exploiting light-responsive transcriptional regulators with differing response kinetics, we build a falling-edge pulse-detector and show that this circuit can be employed to demultiplex dynamically encoded signals. We combine this demultiplexer with dCas9-based gene networks to construct pulsatile-signal filters and decoders. Applying information theory, we show that dynamic multiplexing significantly increases the information transmission capacity from signal to gene expression state. Finally, we use dynamic multiplexing for precise multidimensional regulation of a heterologous metabolic pathway. Our results elucidate design principles of dynamic information processing and provide original synthetic systems capable of decoding complex signals for biotechnological applications.

synthetic biology↗

bioRxiv2020

Genetically Engineered Integral Feedback Controllers for Robust Perfect Adaptation in Mammalian Cells

To support their survival, cells adapt to environmental disturbances by maintaining a constant internal milieu. Robust perfect adaptation is a strategy that utilizes integral feedback to promote adaptation by robustly driving regulated physiological variables to their pre-disturbance levels. Present in natural systems, this stringent regulatory strategy promises to enable the engineering of sophisticated genetic programs with diverse applications. Here, we present the first synthetic implementations of integral and proportional-integral feedback controllers in mammalian cells. We show that the integral controller robustly and precisely maintains a desired level of a transcription factor, in spite of induced disturbances and network perturbations. Augmenting proportional feedback reduces stochastic variability while maintaining robust perfect adaptation. We demonstrate the benefits of these controllers in mitigating the impact of resource burden and investigate their use in cell therapy. The synthetic biological realization of robust perfect adaptation holds promise for substantial advances in industrial biotechnology and cell-based therapies.

synthetic biology↗

bioRxiv2020

Stability and Control of Biomolecular Circuits through Structure

Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely invariant despite uncertainties, and building feedback control through such structures. In this work, we develop the tool of log derivatives to capture structures in how the production and degradation rates of molecules depend on concentrations of reactants. We show that log derivatives could establish stability of fixed points based on structure, despite large variations in rates and functional forms of models. Furthermore, we demonstrate how control objectives, such as robust perfect adaptation (i.e. step disturbance rejection), could be implemented through the structures captured. Due to the methods simplicity, structural properties for analysis and design of biomolecular circuits can often be determined by a glance at the equations.

systems biology↗

bioRxiv2020

Frequency Spectra and the Color of Cellular Noise

The invention of the Fourier integral in the 19th century laid the foundation for modern spectral analysis methods. By decomposing a (time) signal into its essential frequency components, these methods uncovered deep insights into the signal and its generating process, precipitating tremendous inventions and discoveries in many fields of engineering, technology, and physical science. In systems and synthetic biology, however, the impact of frequency methods has been far more limited despite their huge promise. This is in large part due to the difficulties encountered in connecting the underlying stochastic reaction network in the living cell, whose dynamics is typically modelled as a continuous-time Markov chain (CTMC), to the frequency content of the observed, distinctively noisy single-cell trajectories. Here we draw on stochastic process theory to develop a spectral theory and computational methodologies tailored specifically to the computation and analysis of frequency spectra of noisy cellular networks. Specifically, we develop a generic method to obtain accurate Pade approximations of the spectrum from a handful of trajectory simulations. Furthermore, for linear networks, we present a novel decomposition result that expresses the frequency spectrum in terms of its sources. Our results provide new conceptual and practical methods for the analysis and design of noisy cellular networks based on their output frequency spectra. We illustrate this through diverse case studies in which we show that the single-cell frequency spectrum facilitates topology discrimination, synthetic oscillator optimization, cybergenetic controller design, systematic investigation of stochastic entrainment, and even parameter inference from single-cell trajectory data.

synthetic biology↗

bioRxiv2020

An inducible AraC that responds to blue light instead of arabinose

In Escherichia coli, the operon responsible for the catabolism of L-arabinose is regulated by the dimeric DNA-binding protein AraC. In the absence of L-arabinose, AraC binds to the distal I1 and O2 half-sites, leading to repression of the downstream PBAD promoter. In the presence of the sugar, the dimer changes conformation and binds to the adjacent I1 and I2 half-sites, resulting in the activation of PBAD. Here we engineer blue light-inducible AraC dimers in Escherichia coli (BLADE) by swapping the dimerization domain of AraC with blue light-inducible dimerization domains. Using BLADE to overexpress proteins important for cell shape and division site selection, we reversibly control cell morphology with light. We demonstrate the exquisite light responsiveness of BLADE by employing it to create bacteriographs with an unprecedented quality. We then employ it to perform a medium-throughput characterization of 39 E. coli genes with poorly defined or completely unknown function. Finally, we expand the initial library and create a whole family of BLADE transcription factors (TFs), which we characterize using a novel 96-well light induction setup. Since the PBAD promoter is commonly used by microbiologists, we envisage that the BLADE TFs will bring the many advantages of optogenetic gene expression to the field of microbiology.

microbiology↗

bioRxiv2019

Characterization, modelling and mitigation of gene expression burden in mammalian cells

Despite recent advances in genome engineering, the design of genetic circuits in mammalian cells is still painstakingly slow and fraught with inexplicable failures. Here we demonstrate that competition for limited transcriptional and translational resources dynamically couples otherwise independent co-expressed exogenous genes, leading to diminished performance and contributing to the divergence between intended and actual function. We also show that the expression of endogenous genes is likewise impacted when genetic payloads are expressed in the host cells. Guided by a resource-aware mathematical model and our experimental finding that post-transcriptional regulators have a large capacity for resource redistribution, we identify and engineer natural and synthetic miRNA-based incoherent feedforward loop (iFFL) circuits that mitigate gene expression burden. The implementation of these circuits features the novel use of endogenous miRNAs as integral components of the engineered iFFL device, a versatile hybrid design that allows burden mitigation to be achieved across different cell-lines with minimal resource requirements. This study establishes the foundations for context-aware prediction and improvement of in vivo synthetic circuit performance, paving the way towards more rational synthetic construct design in mammalian cells.

synthetic biology↗

bioRxiv2019

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.

synthetic biology↗

bioRxiv2019

Cell-in-the-loop pattern formation with optogenetically emulated cell-to-cell signaling

1Designing and implementing synthetic biological pattern formation remains a challenge due to underlying theoretical complexity as well as the difficulty of engineering multicellular networks bio-chemically. Here, we introduce a \"cell-in-the-loop\" approach where living cells interact through in silico signaling, establishing a new testbed to interrogate theoretical principles when internal cell dynamics are incorporated rather than modeled. We present a theory that offers an easy-to-use test to predict the emergence of contrasting patterns in gene expression among laterally inhibiting cells. Guided by the theory, we experimentally demonstrated spontaneous checkerboard patterning in an optogenetic setup where cell-to-cell signaling was emulated with light inputs calculated in silico from real-time gene expression measurements. The scheme successfully produced spontaneous, persistent checkerboard patterns for systems of sixteen patches, in quantitative agreement with theoretical predictions. Our research highlights how tools from dynamical systems theory may inform our understanding of patterning, and illustrates the potential of cell-in-the-loop for engineering synthetic multicellular systems.

synthetic biology↗

bioRxiv2019

The probability distribution of the reconstructed phylogenetic tree with occurrence data

We consider a homogeneous birth-death process with incomplete sampling. Three successive sampling schemes are considered. First, individuals can be sampled through time and included in the tree. Second, they can be occurrences which are sampled through time and not included in the tree. Third, individuals reaching present day can be sampled and included in the tree. Upon sampling, individuals are removed (i.e. die).\n\nThe outcome of the process is thus composed of the reconstructed evolutionary tree spanning all individuals sampled and included in the tree, and a timeline of occurrence events which are not placed along the tree. We derive a formula allowing one to compute the joint probability density of these, which can readily be used to perform maximum likelihood or Bayesian estimation of the parameters of the model.\n\nIn the context of epidemiology, our probability density allows us to estimate transmission rates through a joint analysis of epidemiological case count data and phylogenetic trees reconstructed from pathogen sequences. Within macroevolution, our equations are the basis for taking into account fossil occurrences from paleontological databases together with extant species phylogenies for estimating speciation and extinction rates. Thus, we provide the theoretical framework for bridging not only the gap between phylogenetics and epidemiology, but also the gap between phylogenetics and paleontology.

evolutionary biology↗

bioRxiv2019

Temporal perturbation of Erk dynamics reveals network architecture of FGF2-MAPK signaling

Stimulation of PC-12 cells with epidermal (EGF) versus nerve (NGF) growth factors (GFs) biases the distribution between transient and sustained single-cell ERK activity states, and between proliferation and differentiation fates within a cell population. We report that fibroblast GF (FGF2) evokes a distinct behavior that consists of a gradually changing population distribution of transient/sustained ERK signaling states in response to increasing inputs in a dose response. Temporally-controlled GF perturbations of MAPK signaling dynamics applied using microfluidics reveals that this wider mix of ERK states emerges through the combination of an intracellular feedback, and competition of FGF2 binding to FGF receptors (FGFR) and heparan-sulfate proteoglycans (HSPGs) co-receptors. We show that the latter experimental modality is instructive for model selection using a Bayesian parameter inference. Our results provide novel insights into how different receptor tyrosine kinase (RTK) systems differentially wire the MAPK network to fine tune fate decisions at the cell population-level.\n\nMicrofluidics, Erk Signaling Dynamics, Mechanistic Modelling, Parameter Estimation, Cell Fate Determination

systems biology↗

bioRxiv2019

Likelihood-free nested sampling for biochemical reaction networks

The development of mechanistic models of biological systems is a central part of Systems Biology. One major challenge in developing these models is the accurate inference of the model parameters. In the past years, nested sampling methods have gained an increasing amount of attention in the Systems Biology community. Some of the rather attractive features of these methods include that they are easily parallelizable and give an estimation of the variance of the final Bayesian evidence estimate from a single run. Still, the applicability of these methods is limited as they require the likelihood to be available and thus cannot be applied to stochastic systems with intractable likelihoods. In this paper, we present a likelihood-free nested sampling formulation that gives an unbiased estimator of the Bayesian evidence as well as samples from the posterior. Unlike most common nested sampling schemes we propose to use the information about the samples from the final prior volume to aid in the approximation of the Bayesian evidence and show how this allows us to formulate a lower bound on the variance of the obtained estimator. We proceed and use this lower bound to formulate a novel termination criterion for nested sampling approaches. We illustrate how our approach is applied to several realistically sized models with simulated data as well as recently published biological data. The presented method provides a viable alternative to other likelihood-free inference schemes such as Sequential Monte Carlo or Approximate Bayesian Computations methods. We also provide an intuitive and performative C++ implementation of our method.

bioinformatics↗

bioRxiv2018

Robust and Structural Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks

Controlling stochastic reactions networks is a challenging problem with important implications in various fields such as systems and synthetic biology. Various regulation motifs have been discovered or posited over the recent years, a very recent one being the so-called Antithetic Integral Control (AIC) motif [3]. Several appealing properties for the AIC motif have been demonstrated for classes of reaction networks that satisfy certain irreducibility, ergodicity and output controllability conditions. Here we address the problem of verifying these conditions for large sets of reaction networks with time-invariant topologies, either from a robust or a structural viewpoint, using three different approaches. The first one adopts a robust viewpoint and relies on the notion of interval matrices. The second one adopts a structural viewpoint and is based on sign properties of matrices. The last one is a direct approach where the parameter dependence is exactly taken into account and can be used to obtain both robust and structural conditions. The obtained results lie in the same spirit as those obtained in [3] where properties of reaction networks are independently characterized in terms of control theoretic concepts, linear programs, and graph-theoretic/algebraic conditions. Alternatively, those conditions can be cast as convex optimization problems that can be checked efficiently using modern optimization methods. Several examples are given for illustration.

systems biology↗

bioRxiv2018

Ergodicity analysis and antithetic integral control of a class of stochastic reaction networks with delays

Delays are important phenomena arising in a wide variety of real world systems, including biological ones, because of diffusion/propagation effects or as simplifying modeling elements. We propose here to consider delayed stochastic reaction networks, a class of networks that has been relatively few studied until now. The difficulty in analyzing them resides in the fact that their state-space is infinite-dimensional. We demonstrate here that by restricting the delays to be phase-type distributed, one can represent the associated delayed reaction network as a reaction network with finite-dimensional state-space. This can be achieved by suitably adding chemical species and reactions to the delay-free network following a simple algorithm which is fully characterized. Since phase-type distributions are dense in the set of probability distributions, they can approximate any distribution arbitrarily closely and this makes their consideration only a bit restrictive. As the state-space remains finite-dimensional, usual tools developed for non-delayed reaction network directly apply. In particular, we prove, for unimolecular mass-action reaction networks, that the delayed stochastic reaction network is ergodic if and only if the delay-free network is ergodic as well. Bimolecular reactions are more difficult to consider but slightly stronger analogous results are nevertheless obtained. These results demonstrate that delays have little to no harm to the ergodicity property of reaction networks as long as the delays are phase-type distributed, and this holds regardless the complexity of their distribution. We also prove that the presence of those delays adds convolution terms in the moment equation but does not change the value of the stationary means compared to the delay-free case. The covariance, however, is influenced by the presence of the delays. Finally, the control of a certain class of delayed stochastic reaction network using a delayed antithetic integral controller is considered. It is proven that this controller achieves its goal provided that the delay-free network satisfy the conditions of ergodicity and output-controllability.

systems biology↗

bioRxiv2018

Tuning gene expression variability and multi-gene regulation by dynamic transcription factor control

Many natural transcription factors are regulated in a pulsatile fashion, but it remains unknown whether synthetic gene expression systems can benefit from such dynamic regulation. Using a fast-acting, light-responsive transcription factor in Saccharomyces cerevisiae, we show that dynamic pulsatile signals reduce cell-to-cell variability in gene expression. We then show that by encoding such signals into a single input, expression mean and variability can be precisely and independently tuned. Further, we construct a light-responsive promoter library and demonstrate how pulsatile signaling also enables graded multi-gene regulation at fixed expression ratios, despite differences in promoter dose-response characteristics. Pulsatile regulation can thus lead to highly beneficial functional behaviors in synthetic biological systems, which previously required laborious optimization of genetic parts or complex construction of synthetic gene networks.

synthetic biology↗

bioRxiv2017

Variance reduction for antithetic integral control of stochastic reaction networks

The antithetic integral feedback motif recently introduced in [6] is known to ensure robust perfect adaptation for the mean dynamics of a given molecular species involved in a complex stochastic biomolecular reaction network. However, it was observed that it also leads to a higher variance in the controlled network than that obtained when using a constitutive (i.e. open-loop) control strategy. This was interpreted as the cost of the adaptation property and may be viewed as a performance deterioration for the overall controlled network. To decrease this variance and improve the performance, we propose to combine the antithetic integral feedback motif with a negative feedback strategy. Both theoretical and numerical results are obtained. The theoretical ones are based on a tailored moment closure method allowing one to obtain approximate expressions for the stationary variance for the controlled network and predict that the variance can indeed be decreased by increasing the strength of the negative feedback. Numerical results verify the accuracy of this approximation and show that the controlled species variance can indeed be decreased, sometimes below its constitutive level. Three molecular networks are considered in order to verify the wide applicability of two types of negative feedback strategies. The main conclusion is that there is a trade-off between the speed of the settling-time of the mean trajectories and the stationary variance of the controlled species; i.e. smaller variance is associated with larger settling-time.\n\nAuthor summaryHomeostasis, the ability of living organisms to regulate their internal state, is of fundamental importance for their adaptation to environmental changes and their survival. This is the reason why complex regulatory genetic networks evolved and allowed for the emergence of more and more complex organisms. Recently, the theoretical study of those regulatory networks using ideas and concepts from control theory and the design of novel ones have gained a lot of attention. Synthetic regulatory circuits are seen as elementary building blocks for the design of complex networks that need to incorporate some regulating elements to be fully functional. This is for instance the case in metabolic engineering where the production of biomolecules, such as drugs or biofuels, need to be optimized and tightly regulated. A particular circuit, the so-called antithetic integral controller, is now known to ensure homeostasis even when regulatory circuits are subject to randomness. However, it is also known that this circuit increases variability in the network. The effects of a correcting negative feedback loop on the variance are discussed here and it is shown that variability can be reduced this way. Notably, we show that there is a tradeoff between speed of the network and variability.

systems biology↗

bioRxiv2017

A synthetic integral feedback controller for robust tunable regulation in bacteria

We report on the first engineered integral feedback control system in a living cell. The controller is based on the recently published antithetic integral feedback motif [1] which has been analytically shown to have favorable regulation properties. It is implemented along with test circuitry in Escherichia coli using seven genes and three small-molecule inducers. The closed-loop system is highly tunable, allowing a regulated protein of interest to be driven to a desired level and maintained there with precision. Realized using a sigma/anti-sigma protein pair, the integral controller ensures that regulation is maintained in the face of perturbations that lead to the regulated proteins degradation, thus serving as a proof-of-concept prototype of integral feedback implementation in living cells. When suitably optimized, this integral controller may be utilized as a general-purpose robust regulator for genetic circuits with unknown or partially-known topologies and parameters.

synthetic biology↗