Biology subjects

Sontag, E. D.

Publications and source records attributed to Sontag, E. D..

14 recordsLinked to original sources

bioRxiv2025

Optimization of heuristic logic synthesis by iteratively reducing circuit substructures using a database of optimal implementations

Minimal synthesis of Boolean functions is an NP-hard problem, and heuristic approaches typically give suboptimal circuits. However, in the emergent field of synthetic biology, genetic logic designs that use even a single additional Boolean gate can render a circuit unimplementable in a cell. This has led to a renewed interest in the field of optimal multilevel Boolean synthesis. For small numbers (1-4) of inputs, an exhaustive search is possible, but this is impractical for large circuits. In this work, we demonstrate that even though it is challenging to build a database of optimal implementations for anything larger than 4-input Boolean functions, a database of 4-input optimal implementations can be used to greatly reduce the number of logical gates required in larger heuristic logic synthesis implementations. The proposed algorithm combines the heuristic results with an optimal implementation database and yields average improvements in fractional gate-count reduction relative to ABC of 5.16% for 5-input circuits and 4.54% for 6-input circuits on outputs provided by the logic synthesis tool ABC. In addition to the gains in the efficiency of the implemented circuits, this work also attests to the importance and practicality of the field of optimal synthesis, even if it cannot directly provide results for larger circuits. The focus of this work is on circuits made exclusively of 2-input NOR gates but the presented results are readily applicable to 2-input NAND circuits as well as (2-input) AND/NOT circuits. The framework proposed here is likely to be adaptable to other types of circuits. Moreover, a small computational pipeline is provided for integration with synthetic biology tools such as Cello. An implementation of the described algorithm, HLM (Hybrid Logic Minimizer), is available at https://github.com/sontaglab/HLM/.

synthetic biology↗

bioRxiv2025

Paradoxical gene regulation explained by competition for genomic sites

Understanding how opposing regulatory factors shape gene expression is essential for understanding complex biological systems. A motivating observation, drawn from cancer epigenetics, is that removing an activating factor can sometimes lead to higher, not lower, expression of a gene that is also subject to a repressing factor. Prior theoretical work explained this counterintuitive behavior by competition of repressors and activators for genomic binding sites. However, it has been difficult to test this directly in natural systems, where layers of regulation obscure causal relationships. This paper introduces a fully synthetic, tunable genetic platform in a prokaryotic model system that reconstitutes this competition mechanism in a controlled and isolated setting. The genetic platform contains a target gene with binding sites for both an activator and a repressor, together with separate overlapping decoy binding sites for the same regulators. Activator and repressor functions are implemented using CRISPRa and CRISPRi, which permit independent control of regulator expression levels, design of the binding sites, and modulation of the binding affinities. Using this minimal system, we demonstrate that increasing activator expression level can reduce expression of the target gene when both regulators are present, consistent with the hypothesis that additional activator molecules displace the repressor from decoy sites, which becomes available to repress the target. By demonstrating how competition for genomic binding sites can invert expected regulatory responses, this synthetic framework provides a system for understanding similar paradoxical behaviors in natural regulatory networks and establishes a foundation for future studies in more complex mammalian contexts. Significance StatementGene regulation is often described in terms of activators that increase expression and repressors that decrease it, yet biological systems frequently display counterintuitive behaviors. Here we show that competition between regulators for shared genomic binding sites can invert expected responses, so that increasing an activator can reduce target gene expression. Using a minimal, fully controllable synthetic system based on CRISPR activation and interference, we isolate and experimentally validate this mechanism. Our results demonstrate that such paradoxical effects arise not from changes in intrinsic regulatory roles but from redistribution of regulators across competing sites. This work provides a general, mechanistic framework for understanding nonintuitive gene-expression patterns observed in complex systems, including those relevant to disease.

synthetic biology↗

bioRxiv2025

Modeling and minimization of dCas9-induced competition in CRISPRi-based genetic circuits

Implementing logic functions in living cells is a fundamental area of interest among synthetic biologists. The goal of designing biochemical circuits in synthetic biology is to make modular and tractable systems that perform well with predictable behaviors. Developing formalisms towards the design of such systems has proven to be difficult with the diverse retroactive effects that appear with respect to the context of the cell. Repressor-based circuits have various applications in biosynthesis, therapeutics, and bioremediation. Particularly using CRISPRi, competition for components of the system (unbound dCas9) can affect the achievable dynamic range of repression. Moreover, the toxicity of dCas9 via non-specific binding inhibits high levels of expression and limits the performance of genetic circuits. In this work, we study the computation of Boolean functions through CRISPRi based circuits built out of NOT and NOR gates. We provide algebraic expressions that allow us to evaluate the steady-state behaviors of any realized circuit. Our mathematical analysis reveals that the effective non-cooperativity of any given gate is a major bottleneck for increasing the dynamic range of the outputs. Further, we find that under the condition of competition between promoters for dCas9, certain circuit architectures perform better than others depending on factors such as circuit depth, fan-in, and fan-out. We pose optimization problems to evaluate the effects engineerable parameter values to find regimes in which a given circuit performs best. This framework provides a mathematical template and computational library for evaluating the performance of repressor-based circuits with a focus on effective cooperativity.

synthetic biology↗

bioRxiv2025

Quantitative pharmacology methods for bispecific T cell engagers

T Cell Engager (TCE)s are an exciting therapeutic modality in immuno-oncology that acts to bypass antigen presentation and forms a direct link between cancer and immune cells in the Tumor Microenvironment (TME). TCEs are efficacious only when the drug is bound to both immune and cancer cell targets. Therefore, approaches that maximize the formation of the drug-target trimer in the TME are expected to increase the drugs efficacy. In this study, we quantitatively investigate how the concentration of ternary complex and its biodistribution depend on both the targets specific properties and the design characteristics of the TCE, and specifically on the binding kinetics of the drug to its targets. A simplified mathematical model of drug-target interactions is considered here, with insights from the "three-body" problem applied to the model. Parameter identifiability analysis performed on the model demonstrates that steady state data, which is often available at the early pre-clinical stages, is sufficient to estimate the binding affinity of the TCE molecule to both targets. We used the model to analyze several existing antibodies, both clinically approved and under development, to explore their common kinetic features. The manuscript concludes with an assessment of a full quantitative pharmacology model that accounts for drug disposition into the peripheral compartment.

systems biology↗

bioRxiv2024

Cumulative dose responses for adapting biological systems

This paper introduces the notion of cumulative dose response (cDR). The cDR is the area under the plot of a response variable, an integral taken over a fixed time interval and seen as a function of an input parameter. This work was motivated by the accumulation of cytokines resulting from T cell stimulation, where a non-monotonic cDR has been observed experimentally. However, the notion is of general applicability. A surprising conclusion is that incoherent feedforward loops studied in the systems biology literature, though capable of non-monotonic dose responses, can be mathematically shown to always result in monotonic cDR.

systems biology↗

bioRxiv2024

Understanding therapeutic tolerance through a mathematical model of drug-induced resistance

There is growing recognition that phenotypic plasticity enables cancer cells to adapt to various environmental conditions. An example of this adaptability is the persistence of an initially sensitive population of cancer cells in the presence of therapeutic agents. Understanding the implications of this druginduced resistance is essential for predicting transient and long-term tumor tumor dynamics subject to treatment. This paper introduces a mathematical model of this phenomenon of drug-induced resistance which provides excellent fits to time-resolved in vitro experimental data. From observational data of total numbers of cells, the model unravels the relative proportions of sensitive and resistance subpopulations, and quantifies their dynamics as a function of drug dose. The predictions are then validated using data on drug doses which were not used when fitting parameters. The model is then used, in conjunction with optimal control techniques, in order to discover dosing strategies that might lead to better outcomes as quantified by lower total cell volume.

systems biology↗

bioRxiv2021

Derivation of stationary distributions of biochemical reaction networks via structure transformation

Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing. Specifically, we merge nodes and edges of BRNs to match in- and out-flows of each node. This allows us to derive the stationary distributions of a large class of BRNs, including autophosphorylation networks of EGFR, PAK1, and Aurora B kinase and a genetic toggle switch. This reveals the unique properties of their stochastic dynamics such as robustness, sensitivity and multi-modality. Importantly, we provide a user-friendly computational package, CASTANET, that automatically derives symbolic expressions of the stationary distributions of BRNs to understand their long-term stochasticity.

systems biology↗

bioRxiv2019

Validation of a Mathematical Model of Cancer Incorporating Spontaneous and Induced Evolution to Drug Resistance

This paper continues the study of a model which was introduced in earlier work by the authors to study spontaneous and induced evolution to drug resistance under chemotherapy. The model is fit to existing experimental data, and is then validated on additional data that had not been used when fitting. In addition, an optimal control problem is studied numerically.

cancer biology↗

bioRxiv2019

Delicate balances in cancer chemotherapy: modeling immune recruitment and emergence of systemic drug resistance

Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the responsible mechanisms are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a fixed set of parameters, not adjusted for individuals nor for drug schedule, excellently recapitulates experimental data across various drug regimens, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. The validated model was then used to make predictions about expected tumor-immune dynamics for novel drug administration schedules. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.

systems biology↗

bioRxiv2019

Compact attractors of an antithetic integral feedback system have a simple structure

Since its introduction by Briat, Gupta and Khammash, the antithetic feedback controller design has attracted considerable attention in both theoretical and experimental systems biology. The case in which the plant is a two-dimensional linear system (making the closed-loop system a nonlinear four-dimensional system) has been analyzed in much detail. This system has a unique equilibrium but, depending on parameters, it may exhibit periodic orbits. An interesting open question is whether other dynamical behaviors, such as chaotic attractors, might be possible for some parameter choices. This note shows that, for any parameter choices, every bounded trajectory satisfies a Poincare-Bendixson property. The analysis is based on the recently introduced notion of k-cooperative dynamical systems. It is shown that the model is a strongly 2-cooperative system, implying that the dynamics in the omega-limit set of any precompact solution is conjugate to the dynamics in a compact invariant subset of a two-dimensional Lipschitz dynamical system, thus precluding chaotic and other strange attractors.

bioengineering↗

bioRxiv2019

Inferring reaction network structure from single-cell, multiplex data, using toric systems theory

The goal of many single-cell studies on eukaryotic cells is to gain insight into the biochemical reactions that control cell fate and state. In this paper we introduce the concept of effective stoichiometric space (ESS) to guide the reconstruction of biochemical networks from multiplexed, fixed time-point, single-cell data. In contrast to methods based solely on statistical models of data, the ESS method leverages the power of the geometric theory of toric varieties to begin unraveling the structure of chemical reaction networks (CRN). This application of toric theory enables a data-driven mapping of covariance relationships in single cell measurements into stoichiometric information, one in which each cell subpopulation has its associated ESS interpreted in terms of CRN theory. In the development of ESS we reframe certain aspects of the theory of CRN to better match data analysis. As an application of our approach we process cytomery- and image-based single-cell datasets and identify differences in cells treated with kinase inhibitors. Our approach is directly applicable to data acquired using readily accessible experimental methods such as Fluorescence Activated Cell Sorting (FACS) and multiplex immunofluorescence.\n\nAuthor summaryWe introduce a new notion, which we call the effective stoichiometric space (ESS), that elucidates network structure from the covariances of single-cell multiplexed data. The ESS approach differs from methods that are based on purely statistical models of data: it allows a completely new and data-driven translation of the theory of toric varieties in geometry and specifically their role in chemical reaction networks (CRN). In the process, we reframe certain aspects of the theory of CRN. As illustrations of our approach, we find stoichiometry in different single-cell datasets, and pinpoint dose-dependence of network perturbations in drug-treated cells.

systems biology↗

bioRxiv2019

Mathematical models of protease-based enzymatic biosensors

An important goal of synthetic biology is to build biosensors and circuits with well-defined input-output relationships that operate at speeds found in natural biological systems. However, for molecular computation, most commonly used genetic circuit elements typically involve several steps from input detection to output signal production: transcription, translation, and post-translational modifications. These multiple steps together require up to several hours to respond to a single stimulus, and this limits the overall speed and complexity of genetic circuits. To address this gap, molecular frame-works that rely exclusively on post-translational steps to realize reaction networks that can process inputs at a timescale of seconds to minutes have been proposed. Here, we build mathematical models of fast biosensors capable of producing Boolean logic functionality. We employ protease-based chemical and light-induced switches, investigate their operation, and provide selection guidelines for their use as on-off switches. We then use these switches as elementary blocks, developing models for biosensors that can perform OR and XOR Boolean logic computation while using reaction conditions as tuning parameters. We use sensitivity analysis to determine the time-dependent sensitivity of the output to proteolytic and protein-protein binding reaction parameters. These fast protease-based biosensors can be used to implement complex molecular circuits with a capability of processing multiple inputs controllably and algorithmically. Our framework for evaluating and optimizing circuit performance can be applied to other molecular logic circuits.

synthetic biology↗

bioRxiv2019

In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller

Feedback mechanisms play a critical role in the maintenance of cell homeostasis in the presence of disturbances and uncertainties. Motivated by the need to tune the dynamics and improve the robustness of synthetic gene circuits, biological engineers have proposed various designs that mimic natural molecular feedback control mechanisms. However, practical and predictable implementations have proved challenging because of the complexity of synthesis and analysis of complex biomolecular networks. Here, we analyze and experimentally validate a first synthetic biomolecular controller executed in vitro. The controller is based on the interaction between a sigma and an anti-sigma factor, which ensures that gene expression tracks an externally imposed reference level, and achieves this goal even in the presence of disturbances. Our design relies upon an analog of the well-known principle of integral feedback in control theory. We implement the controller in an Escherichia coli cell-free transcription-translation (TXTL) system, a platform that allows rapid prototyping and implementation. Modeling and theory guide experimental implementation of the controller with well-defined operational predictability.

synthetic biology↗

bioRxiv2017

A mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment

Drug resistance is a major impediment to the success of cancer treatment. Resistance is typically thought to arise through random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that the progression to drug resistance need not occur randomly, but instead may be induced by the treatment itself, through either genetic changes or epigenetic alterations. This relatively novel notion of resistance complicates the already challenging task of designing effective treatment protocols. To better understand resistance, we have developed a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance. Our model demonstrates that the ability of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. We have also proven that the induction parameter in our model is theoretically identifiable, and proposed an in vitro protocol which could be used to determine a treatments propensity to induce resistance.

cancer biology↗