On schemes of combinatorial transcription logic

Broccoli aptamer allows quantitative transcription regulation studies in vitro

Quantitative transcription regulation studies in vivo and in vitro often make use of reporter proteins. Here we show that using Broccoli aptamers, quantitative study of transcription in various regulatory scenarios is possible without a translational step. To explore the method we studied several regulatory scenarios that we analyzed using thermodynamic occupancy-based models, and found excellent agreement with previous studies. In the next step we show that non-coding DNA can have a dramatic effect on the level of transcription, similar to the influence of the lac repressor with a strong affinity to operator sites. Finally, we point out the limitations of the method in terms of delay times coupled to the folding of the aptamer. We conclude that the Broccoli aptamer is suitable for quantitative transcription measurements.

Dynamical and combinatorial coding by MAPK p38 and NFκB in the inflammatory response of macrophages

Macrophages sense pathogens and orchestrate specific immune responses. Stimulus specificity is thought to be achieved through combinatorial and dynamical coding by signaling pathways. While NFκB dynamics are known to encode stimulus information, dynamical coding in other signaling pathways and their combinatorial coordination remain unclear. Here, we established live-cell microscopy to investigate how NFκB and p38 dynamics interface in stimulated macrophages. Information theory and machine learning revealed that p38 dynamics distinguish cytokine TNF from pathogen-associated molecular patterns and high doses from low, but contributed little to information-rich NFκB dynamics when both pathways are considered. This suggests that immune response genes benefit from decoding immune signaling dynamics or combinatorics, but not both. We found that the heterogeneity of the two pathways is surprisingly uncorrelated. Mathematical modeling revealed potential sources of uncorrelated heterogeneity in the branched pathway network topology and predicted it to drive gene expression variability. Indeed, genes dependent on both p38 and NFκB showed high scRNAseq variability and bimodality. These results identify combinatorial signaling as a mechanism to restrict NFκB-AND-p38-responsive inflammatory cytokine expression to few cells.

A parameterized two-domain thermodynamic model explains diverse mutational effects on protein allostery

New experimental findings continue to challenge our understanding of protein allostery. Recent deep mutational scanning study showed that allosteric hotspots in the tetracycline repressor (TetR) and its homologous transcriptional factors are broadly distributed rather than spanning well-defined structural pathways as often assumed. Moreover, hotspot mutation-induced allostery loss was rescued by distributed additional mutations in a degenerate fashion. Here, we develop a two-domain thermodynamic model for TetR, which readily rationalizes these intriguing observations. The model accurately captures the in vivo activities of various mutants with changes in physically transparent parameters, allowing the data-based quantification of mutational effects using statistical inference. Our analysis reveals the intrinsic connection of intra- and inter-domain properties for allosteric regulation and illustrate epistatic interactions that are consistent with structural features of the protein. The insights gained from this study into the nature of two-domain allostery are expected to have broader implications for other multi-domain allosteric proteins.

A mathematical framework for understanding the spontaneous emergence of complexity applicable to growing multicellular systems

In embryonic development and organogenesis, cells sharing identical genetic codes acquire diverse gene expression states in a highly reproducible spatial distribution, crucial for multicellular formation and quantifiable through positional information. To understand the spontaneous growth of complexity, we constructed a one-dimensional division-decision model, simulating the growth of cells with identical genetic networks from a single cell. Our findings highlight the pivotal role of cell division in providing positional cues, escorting the system toward states rich in information. Moreover, we pinpointed lateral inhibition as a critical mechanism translating spatial contacts into gene expression. Our model demonstrates that the spatial arrangement resulting from cell division, combined with cell lineages, imparts positional information, specifying multiple cell states with increased complexity-illustrated through examples in C.elegans. This study constitutes a foundational step in comprehending developmental intricacies, paving the way for future quantitative formulations to construct synthetic multicellular patterns.

Regulatory properties of transcription factors with diverse mechanistic function

Transcription factors (TFs) regulate the process of transcription through the modulation of different kinetic steps. Although models can often describe the observed transcriptional output of a measured gene, predicting a TFs role on a given promoter requires an understanding of how the TF alters each step of the transcription process. In this work, we use a simple model of transcription to assess the role of promoter identity, and the degree to which TFs alter binding of RNAP (stabilization) and initiation of transcription (acceleration) on three primary characteristics: the range of steady-state regulation, cell-to-cell variability in expression, and the dynamic response time of a regulated gene. We find that steady state regulation and the response time of a gene behave uniquely for TFs that regulate incoherently, i.e that speed up one step but slow the other. We also find that incoherent TFs have dynamic implications, with one type of incoherent mode configuring the promoter to respond more slowly at intermediate TF concentrations. We also demonstrate that the noise of gene expression for these TFs is sensitive to promoter strength, with a distinct non-monotonic profile that is apparent under stronger promoters. Taken together, our work uncovers the coupling between promoters and TF regulatory modes with implications for understanding natural promoters and engineering synthetic gene circuits with desired expression properties.

The Blueprint of Logical Decisions in a NF-κB Signaling System

Nearly identical cells can exhibit substantially different responses to the same stimulus that causes phenotype diversity. Such interplay between phenotype diversity and the architecture of regulatory circuits is crucial since it determines the state of a biological cell. Here, we theoretically analyze how the circuit blueprints of NF-κB in cellular environments are formed and their role in determining the cells' metabolic state. The NF-κB is a collective name for a developmental conserved family of five different transcription factors that can form homodimers or heterodimers and often promote DNA looping to reprogram the inflammatory gene response. The NF-κB controls many biological functions, including cellular differentiation, proliferation, migration, and survival. Our model shows that nuclear localization of NF-κB differentially promotes logic operations such as AND, NAND, NOR, and OR in its regulatory network. Through the quantitative thermodynamic model of transcriptional regulation and systematic variation of promoter-enhancer interaction modes, we can account for the origin of various logic gates as formed in the NF-κB system. We further show that the interconversion or switching of logic gates yielded under systematic variations of the stimuli activity and DNA looping parameters. Such computation occurs in regulatory and signaling pathways in individual cells at a molecular scale, which one can exploit to design a biomolecular computer.

A domain swapping strategy to create modular transcriptional regulators for novel topology in genetic network

Transcriptional regulators generate connections between biological signals and genetic outputs. They are used robustly for sensing input signals in building genetic circuits. However, each regulator can only generate a fixed connection, which generates constraints in linking multiple signals for more complex processes. Recent studies discovered that a domain swapping strategy can be applied to various regulator families to create modular regulators for new signal-output connections, significantly broadening possibilities in circuit design. Here we review the development of this emerging strategy, the use of resulting modular regulators for creating novel genetic response behaviors, and current limitations and solutions for further advancing the design of modular regulators.

A logic-incorporated gene regulatory network deciphers principles in cell fate decisions

Organisms utilize gene regulatory networks (GRN) to make fate decisions, but the regulatory mechanisms of transcription factors (TF) in GRNs are exceedingly intricate. A longstanding question in this field is how these tangled interactions synergistically contribute to decision-making procedures. To comprehensively understand the role of regulatory logic in cell fate decisions, we constructed a logic-incorporated GRN model and examined its behavior under two distinct driving forces (noise-driven and signal-driven). Under the noise-driven mode, we distilled the relationship among fate bias, regulatory logic, and noise profile. Under the signal-driven mode, we bridged regulatory logic and progression-accuracy trade-off, and uncovered distinctive trajectories of reprogramming influenced by logic motifs. In differentiation, we characterized a special logic-dependent priming stage by the solution landscape. Finally, we applied our findings to decipher three biological instances: hematopoiesis, embryogenesis, and trans-differentiation. Orthogonal to the classical analysis of expression profile, we harnessed noise patterns to construct the GRN corresponding to fate transition. Our work presents a generalizable framework for top-down fate-decision studies and a practical approach to the taxonomy of cell fate decisions.

Governing principles of transcriptional logic out of equilibrium

To survive, adapt, and develop, cells respond to external and internal stimuli by tightly regulating transcription. Transcriptional regulation involves the combinatorial binding of a repertoire of transcription factors to DNA, which often results in switch-like binary outputs akin to Boolean logic gates. Recent experimental studies have demonstrated that in eukaryotes, transcription factor binding to DNA often involves energy expenditure, thereby driving the system out of equilibrium. The governing principles of transcriptional logic operations out of equilibrium remain unexplored. Here, we employ a simple two-input, single-locus model of transcription that can accommodate both equilibrium and nonequilibrium mechanisms. Using this model, we find that nonequilibrium regimes can give rise to all the logic operations accessible in equilibrium. Strikingly, energy expenditure alters the regulatory function of the two transcription factors in a mutually exclusive manner. This allows for the emergence of new logic operations that are inaccessible in equilibrium. Overall, our results show that energy expenditure can expand the range of cellular decision-making without the need for more complex promoter architectures.

Interaction models matter: an efficient, flexible computational framework for model-specific investigation of epistasis

PURPOSE

Epistasis, the interaction between two or more genes, is integral to the study of genetics and is present throughout nature. Yet, it is seldom fully explored as most approaches primarily focus on single-locus effects, partly because analyzing all pairwise and higher-order interactions requires significant computational resources. Furthermore, existing methods for epistasis detection only consider a Cartesian (multiplicative) model for interaction terms. This is likely limiting as epistatic interactions can evolve to produce varied relationships between genetic loci, some complex and not linearly separable.

METHODS

We present new algorithms for the interaction coefficients for standard regression models for epistasis that permit many varied models for the interaction terms for loci and efficient memory usage. The algorithms are given for two-way and three-way epistasis and may be generalized to higher order epistasis. Statistical tests for the interaction coefficients are also provided. We also present an efficient matrix based algorithm for permutation testing for two-way epistasis. We offer a proof and experimental evidence that methods that look for epistasis only at loci that have main effects may not be justified. Given the computational efficiency of the algorithm, we applied the method to a rat data set and mouse data set, with at least 10,000 loci and 1,000 samples each, using the standard Cartesian model and the XOR model to explore body mass index.

RESULTS

This study reveals that although many of the loci found to exhibit significant statistical epistasis overlap between models in rats, the pairs are mostly distinct. Further, the XOR model found greater evidence for statistical epistasis in many more pairs of loci in both data sets with almost all significant epistasis in mice identified using XOR. In the rat data set, loci involved in epistasis under the XOR model are enriched for biologically relevant pathways.

CONCLUSION

Our results in both species show that many biologically relevant epistatic relationships would have been undetected if only one interaction model was applied, providing evidence that varied interaction models should be implemented to explore epistatic interactions that occur in living systems.

Compact RNA sensors for increasingly complex functions of multiple inputs

Designing single molecules that compute general functions of input molecular partners represents a major unsolved challenge in molecular design. Here, we demonstrate that high-throughput, iterative experimental testing of diverse RNA designs crowdsourced from Eterna yields sensors of increasingly complex functions of input oligonucleotide concentrations. After designing single-input RNA sensors with activation ratios beyond our detection limits, we created logic gates, including challenging XOR and XNOR gates, and sensors that respond to the ratio of two inputs. Finally, we describe the OpenTB challenge, which elicited 85-nucleotide sensors that compute a score for diagnosing active tuberculosis, based on the ratio of products of three gene segments. Building on OpenTB design strategies, we created an algorithm Nucleologic that produces similarly compact sensors for the three-gene score based on RNA and DNA. These results open new avenues for diverse applications of compact, single molecule sensors previously limited by design complexity.

The Drosophila ecdysone receptor promotes or suppresses proliferation according to ligand level

The steroid hormone 20-hydroxy-ecdysone (20E) promotes proliferation in Drosophila wing precursors at low titer but triggers proliferation arrest at high doses. Remarkably, wing precursors proliferate normally in the complete absence of the 20E receptor, suggesting that low-level 20E promotes proliferation by overriding the default anti-proliferative activity of the receptor. By contrast, 20E needs its receptor to arrest proliferation. Dose-response RNA sequencing (RNA-seq) analysis of ex vivo cultured wing precursors identifies genes that are quantitatively activated by 20E across the physiological range, likely comprising positive modulators of proliferation and other genes that are only activated at high doses. We suggest that some of these "high-threshold" genes dominantly suppress the activity of the pro-proliferation genes. We then show mathematically and with synthetic reporters that combinations of basic regulatory elements can recapitulate the behavior of both types of target genes. Thus, a relatively simple genetic circuit can account for the bimodal activity of this hormone.

Cooperative assembly confers regulatory specificity and long-term genetic circuit stability

A ubiquitous feature of eukaryotic transcriptional regulation is cooperative self-assembly between transcription factors (TFs) and DNA cis-regulatory motifs. It is thought that this strategy enables specific regulatory connections to be formed in gene networks between otherwise weakly interacting, low-specificity molecular components. Here, using synthetic gene circuits constructed in yeast, we find that high regulatory specificity can emerge from cooperative, multivalent interactions among artificial zinc-finger-based TFs. We show that circuits "wired" using the strategy of cooperative TF assembly are effectively insulated from aberrant misregulation of the host cell genome. As we demonstrate in experiments and mathematical models, this mechanism is sufficient to rescue circuit-driven fitness defects, resulting in genetic and functional stability of circuits in long-term continuous culture. Our naturally inspired approach offers a simple, generalizable means for building high-fidelity, evolutionarily robust gene circuits that can be scaled to a wide range of host organisms and applications.

NFAT and NF-κB dynamically co-regulate TCR and CAR signaling responses in human T cells

While it has been established that the responses of T cells to antigens are combinatorially regulated by multiple signaling pathways, it remains elusive what mechanisms cells utilize to quantitatively modulate T cell responses during pathway integration. Here, we show that two key pathways in T cell signaling, calcium/nuclear factor of activated T cells (NFAT) and protein kinase C (PKC)/nuclear factor κB (NF-κB), integrate through a dynamic and combinatorial strategy to fine-tune T cell response genes. At the cis-regulatory level, the two pathways integrate through co-binding of NFAT and NF-κB to immune response genes. Pathway integration is further regulated temporally, where T cell receptor (TCR) and chimeric antigen receptor (CAR) activation signals modulate the temporal relationships between the nuclear localization dynamics of NFAT and NF-κB. Such physical and temporal integrations together contribute to distinct modes of expression modulation for genes. Thus, the temporal relationships between regulators can be modulated to affect their co-targets during immune responses, underscoring the importance of dynamic combinatorial regulation in cellular signaling.

Theoretical investigation of functional responses of bio-molecular assembly networks

Cooperative protein-protein and protein-DNA interactions form programmable complex assemblies, often performing non-linear gene regulatory operations involved in signal transductions and cell fate determination. The apparent structure of those complex assemblies is very similar, but their functional response strongly depends on the topology of the protein-DNA interaction networks. Here, we demonstrate how the coordinated self-assembly creates gene regulatory network motifs that corroborate the existence of a precise functional response at the molecular level using thermodynamic and dynamic analyses. Our theoretical and Monte Carlo simulations show that a complex network of interactions can form a decision-making loop, such as feedback and feed-forward circuits, only by a few molecular mechanisms. We characterize each possible network of interactions by systematic variations of free energy parameters associated with the binding among biomolecules and DNA looping. We also find that the higher-order networks exhibit alternative steady states from the stochastic dynamics of each network. We capture this signature by calculating stochastic potentials and attributing their multi-stability features. We validate our findings against the Gal promoter system in yeast cells. Overall, we show that the network topology is vital in phenotype diversity in regulatory circuits.

Minimal synthetic enhancers reveal control of the probability of transcriptional engagement and its timing by a morphogen gradient

How enhancers interpret morphogen gradients to generate gene expression patterns is a central question in developmental biology. Recent studies have proposed that enhancers can dictate whether, when, and at what rate promoters engage in transcription, but the complexity of endogenous enhancers calls for theoretical models with too many free parameters to quantitatively dissect these regulatory strategies. To overcome this limitation, we established a minimal promoter-proximal synthetic enhancer in embryos of Drosophila melanogaster. Here, a gradient of the Dorsal activator is read by a single Dorsal DNA binding site. Using live imaging to quantify transcriptional activity, we found that a single binding site can regulate whether promoters engage in transcription in a concentration-dependent manner. By modulating the binding-site affinity, we determined that a gene's decision to transcribe and its transcriptional onset time can be explained by a simple model where the promoter traverses multiple kinetic barriers before transcription can ensue.

Combinatorial protein dimerization enables precise multi-input synthetic computations

Bacterial transcription factors (TFs) with helix-turn-helix (HTH) DNA-binding domains have been widely explored to build orthogonal transcriptional regulation systems in mammalian cells. Here we capitalize on the modular structure of these proteins to build a framework for multi-input logic gates relying on serial combinations of inducible protein-protein interactions. We found that for some TFs, their HTH domain alone is sufficient for DNA binding. By fusing the HTH domain to TFs, we established dimerization dependent rather than DNA-binding-dependent activation. This enabled us to convert gene switches from OFF-type into more widely applicable ON-type systems and to create mammalian gene switches responsive to new inducers. By combining both OFF and ON modes of action, we built a compact, high-performance bandpass filter. Furthermore, we were able to show cytosolic and extracellular dimerization. Cascading up to five pairwise fusion proteins yielded robust multi-input AND logic gates. Combinations of different pairwise fusion proteins afforded a variety of 4-input 1-output AND and OR logic gate configurations.

Multi-modular structure of the gene regulatory network for specification and commitment of murine T cells

T cells develop from multipotent progenitors by a gradual process dependent on intrathymic Notch signaling and coupled with extensive proliferation. The stages leading them to T-cell lineage commitment are well characterized by single-cell and bulk RNA analyses of sorted populations and by direct measurements of precursor-product relationships. This process depends not only on Notch signaling but also on multiple transcription factors, some associated with stemness and multipotency, some with alternative lineages, and others associated with T-cell fate. These factors interact in opposing or semi-independent T cell gene regulatory network (GRN) subcircuits that are increasingly well defined. A newly comprehensive picture of this network has emerged. Importantly, because key factors in the GRN can bind to markedly different genomic sites at one stage than they do at other stages, the genes they significantly regulate are also stage-specific. Global transcriptome analyses of perturbations have revealed an underlying modular structure to the T-cell commitment GRN, separating decisions to lose "stem-ness" from decisions to block alternative fates. Finally, the updated network sheds light on the intimate relationship between the T-cell program, which depends on the thymus, and the innate lymphoid cell (ILC) program, which does not.

Predictive modeling reveals that higher-order cooperativity drives transcriptional repression in a synthetic developmental enhancer

A challenge in quantitative biology is to predict output patterns of gene expression from knowledge of input transcription factor patterns and from the arrangement of binding sites for these transcription factors on regulatory DNA. We tested whether widespread thermodynamic models could be used to infer parameters describing simple regulatory architectures that inform parameter-free predictions of more complex enhancers in the context of transcriptional repression by Runt in the early fruit fly embryo. By modulating the number and placement of Runt binding sites within an enhancer, and quantifying the resulting transcriptional activity using live imaging, we discovered that thermodynamic models call for higher-order cooperativity between multiple molecular players. This higher-order cooperativity captures the combinatorial complexity underlying eukaryotic transcriptional regulation and cannot be determined from simpler regulatory architectures, highlighting the challenges in reaching a predictive understanding of transcriptional regulation in eukaryotes and calling for approaches that quantitatively dissect their molecular nature.

Deduction of signaling mechanisms from cellular responses to multiple cues

Cell signaling networks are complex and often incompletely characterized, making it difficult to obtain a comprehensive picture of the mechanisms they encode. Mathematical modeling of these networks provides important clues, but the models themselves are often complex, and it is not always clear how to extract falsifiable predictions. Here we take an inverse approach, using experimental data at the cell level to deduce the minimal signaling network. We focus on cells' response to multiple cues, specifically on the surprising case in which the response is antagonistic: the response to multiple cues is weaker than the response to the individual cues. We systematically build candidate signaling networks one node at a time, using the ubiquitous ingredients of (i) up- or down-regulation, (ii) molecular conversion, or (iii) reversible binding. In each case, our method reveals a minimal, interpretable signaling mechanism that explains the antagonistic response. Our work provides a systematic way to deduce molecular mechanisms from cell-level data.

Synthetic neuromorphic computing in living cells

Computational properties of neuronal networks have been applied to computing systems using simplified models comprising repeated connected nodes, e.g., perceptrons, with decision-making capabilities and flexible weighted links. Analogously to their revolutionary impact on computing, neuro-inspired models can transform synthetic gene circuit design in a manner that is reliable, efficient in resource utilization, and readily reconfigurable for different tasks. To this end, we introduce the perceptgene, a perceptron that computes in the logarithmic domain, which enables efficient implementation of artificial neural networks in Escherichia coli cells. We successfully modify perceptgene parameters to create devices that encode a minimum, maximum, and average of analog inputs. With these devices, we create multi-layer perceptgene circuits that compute a soft majority function, perform an analog-to-digital conversion, and implement a ternary switch. We also create a programmable perceptgene circuit whose computation can be modified from OR to AND logic using small molecule induction. Finally, we show that our approach enables circuit optimization via artificial intelligence algorithms.

Repetitive DNA symmetry elements negatively regulate gene expression in embryonic stem cells

Transcription factor (TF) binding to genomic DNA elements constitutes one of the key mechanisms that regulates gene expression program in cells. Both consensus and nonconsensus DNA sequence elements influence the recognition specificity of TFs. Based on the analysis of experimentally determined c-Myc binding preferences to genomic DNA, here we statistically predict that certain repetitive, nonconsensus DNA symmetry elements can relatively reduce TF-DNA binding preferences. This is in contrast to a different set of repetitive, nonconsensus symmetry elements that can increase the strength of TF-DNA binding. Using c-Myc enhancer reporter system containing consensus motif flanked by nonconsensus sequences in embryonic stem cells, we directly demonstrate that the enrichment in such negatively regulating repetitive symmetry elements is sufficient to reduce the gene expression level compared with native genomic sequences. Negatively regulating repetitive symmetry elements around consensus c-Myc motif and DNA sequences containing consensus c-Myc motif flanked by entirely randomized sequences show similar expression baseline. A possible explanation for this observation is that rather than complete repression, negatively regulating repetitive symmetry elements play a regulatory role in fine-tuning the reduction of gene expression, most probably by binding TFs other than c-Myc.

Thermodynamic Modelling of Transcriptional Control: A Sensitivity Analysis

Modelling is a tool used to decipher the biochemical mechanisms involved in transcriptional control. Experimental evidence in genetics is usually supported by theoretical models in order to evaluate the effects of all the possible interactions that can occur in these complicated processes. Models derived from the thermodynamic method are critical in this labour because they are able to take into account multiple mechanisms operating simultaneously at the molecular micro-scale and relate them to transcriptional initiation at the tissular macro-scale. This work is devoted to adapting computational techniques to this context in order to theoretically evaluate the role played by several biochemical mechanisms. The interest of this theoretical analysis relies on the fact that it can be contrasted against those biological experiments where the response to perturbations in the transcriptional machinery environment is evaluated in terms of genetically activated/repressed regions. The theoretical reproduction of these experiments leads to a sensitivity analysis whose results are expressed in terms of the elasticity of a threshold function determining those activated/repressed regions. The study of this elasticity function in thermodynamic models already proposed in the literature reveals that certain modelling approaches can alter the balance between the biochemical mechanisms considered, and this can cause false/misleading outcomes. The reevaluation of classical thermodynamic models gives us a more accurate and complete picture of the interactions involved in gene regulation and transcriptional control, which enables more specific predictions. This sensitivity approach provides a definite advantage in the interpretation of a wide range of genetic experimental results.

Programming and training rate-independent chemical reaction networks

To program complex behavior in environments incompatible with electronic controllers such as within bioreactors or engineered cells, we turn to chemical information processors. While chemical reactions can perform computation in the stoichiometric exchange of reactants for products (how many molecules of which reactants result in how many molecules of which products), the control of reaction rates is usually thought to allow more complex computation. Motivated by the fact that correct stoichiometry is easier to ensure than reaction rates, we provide a method for programming and training chemical computation by stoichiometry. We show that such computation can be straightforwardly programmed in a manner analogous to sequential programming, and demonstrate the execution of neural networks capable of complex machine learning tasks.

Embedding computation in biochemical environments incompatible with traditional electronics is expected to have a wide-ranging impact in synthetic biology, medicine, nanofabrication, and other fields. Natural biochemical systems are typically modeled by chemical reaction networks (CRNs) which can also be used as a specification language for synthetic chemical computation. In this paper, we identify a syntactically checkable class of CRNs called noncompetitive (NC) whose equilibria are absolutely robust to reaction rates and kinetic rate law, because their behavior is captured solely by their stoichiometric structure. In spite of the inherently parallel nature of chemistry, the robustness property allows for programming as if each reaction applies sequentially. We also present a technique to program NC-CRNs using well-founded deep learning methods, showing a translation procedure from rectified linear unit (ReLU) neural networks to NC-CRNs. In the case of binary weight ReLU networks, our translation procedure is surprisingly tight in the sense that a single bimolecular reaction corresponds to a single ReLU node and vice versa. This compactness argues that neural networks may be a fitting paradigm for programming rate-independent chemical computation. As proof of principle, we demonstrate our scheme with numerical simulations of CRNs translated from neural networks trained on traditional machine learning datasets, as well as tasks better aligned with potential biological applications including virus detection and spatial pattern formation.

The nonequilibrium mechanism of noise-enhanced drug synergy in HIV latency reactivation

Noise-modulating chemicals can synergize with transcriptional activators in reactivating latent HIV to eliminate latent HIV reservoirs. To understand the underlying biomolecular mechanism, we investigate a previous two-gene-state model and identify two necessary conditions for the synergy: an assumption of the inhibition effect of transcription activators on noise enhancers; and frequent transitions to the gene non-transcription-permissive state. We then develop a loop-four-gene-state model with Tat transcription/translation and find that drug synergy is mainly determined by the magnitude and direction of energy input into the genetic regulatory kinetics of the HIV promoter. The inhibition effect of transcription activators is actually a phenomenon of energy dissipation in the nonequilibrium gene transition system. Overall, the loop-four-state model demonstrates that energy dissipation plays a crucial role in HIV latency reactivation, which might be useful for improving drug effects and identifying other synergies on lentivirus latency reactivation.

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The inhibition of Activator on Noise enhancer is necessary for their synergy in reactivating HIV

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The drug synergy is a nonequilibrium phenomenon in the gene regulatory system

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The magnitude and direction of energy input determine the drug synergy

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This nonequilibrium mechanism is general without regarding molecular details

Robust boundary formation in a morphogen gradient via cell-cell signaling

Establishing sharp and correctly positioned boundaries in spatial gene expression patterns is a central task in both developmental and synthetic biology. We consider situations where a global morphogen gradient provides positional information to cells but is insufficient to ensure the required boundary precision, due to different types of noise in the system. In a conceptual model, we quantitatively compare three mechanisms, which combine the global signal with local signaling between neighboring cells, to enhance the boundary formation process. These mechanisms differ with respect to the way in which they combine the signals by following either an AND, an OR, or a SUM rule. Within our model, we analyze the dynamics of the boundary formation process, and the fuzziness of the resulting boundary. Furthermore, we consider the tunability of the boundary position and its scaling with system size. We find that all three mechanisms produce less fuzzy boundaries than the purely gradient-based reference mechanism, even in the regime of high noise in the local signals relative to the noise in the global signal. Among the three mechanisms, the SUM rule produces the most accurate boundary. However, in contrast to the other two mechanisms, it requires noise to exit metastable states and rapidly reach the stable boundary pattern.

DNA Memristors and Their Application to Reservoir Computing

This paper introduces memristors realized by molecular and DNA reactions. Molecular memristors process one input molecule, generate two output molecules, and are realized using two molecular reactions with two different rate constants. The DNA memristors are realized using five DNA strand displacement (DSD) reactions with two effective rate constants. The hysteresis behavior is preserved in the proposed memristors, and this behavior can be altered by changing the ratios of the rate constants. The state of the memristor can be computed from the concentrations of the two output molecules using bipolar fractional coding. We describe how the proposed memristors can be used to learn the spatial and temporal properties of data via the reservoir computing (RC) model. An RC system can be divided into two parts: reservoir and readout layer. The first part transfers the information from the input space to a high-dimensional spatiotemporal feature space represented by the state of reservoirs. The connectivity structure of the reservoir will remain fixed through the dynamical evaluations. The readout layer effectively maps the projected features to the target output. A dynamical memristor array is used to implement an RC system that exploits the internal dynamical processes of the memristors. The readout layer implements a matrix-vector multiplication using molecular reactions, also based on bipolar fractional coding. All molecular reactions are mapped to DSD reactions. The RC system based on the DNA reservoir and the DNA readout layer is used to solve a handwritten digit recognition task and a second-order time series prediction task. The performance of the DNA RC system is comparable to that of an electronic memristor RC system for both tasks.

Synthetic nonlinear computation for genetic circuit design

Computation frameworks have been studied in synthetic biology to achieve biosignals integration and processing, for biosensing and therapeutics applications. Biological systems exhibit nonlinearity across scales from the molecular level, to biochemical network and intercellular systems. At the molecular level, cooperative bindings contribute to nonlinear molecular signal processing in a way similar to weight variables. At the intracellular network level, feedback and feedforward regulations result in cell behaviors such as multistability and adaptation. When biochemical networks are distributed in different cell groups, intercelluar networks can generate population dynamics. Here, we review works that highlight nonlinear computations in synthetic biology. We group the works according to the scale of implementations, from the cis-transcription level, to biochemical circuit level and cellular networks.

Minimum complexity drives regulatory logic in Boolean models of living systems

The properties of random Boolean networks have been investigated extensively as models of regulation in biological systems. However, the Boolean functions (BFs) specifying the associated logical update rules should not be expected to be random. In this contribution, we focus on biologically meaningful types of BFs, and perform a systematic study of their preponderance in a compilation of 2,687 functions extracted from published models. A surprising feature is that most of these BFs have odd "bias", that is they produce "on" outputs for a total number of input combinations that is odd. Upon further analysis, we are able to explain this observation, along with the enrichment of read-once functions (RoFs) and its nested canalyzing functions (NCFs) subset, in terms of 2 complexity measures: Boolean complexity based on string lengths in formal logic, which is yet unexplored in biological contexts, and the so-called average sensitivity. RoFs minimize Boolean complexity and all such functions have odd bias. Furthermore, NCFs minimize not only the Boolean complexity but also the average sensitivity. These results reveal the importance of minimum complexity in the regulatory logic of biological networks.

Cellular Computational Logic Using Toehold Switches

The development of computational logic that carries programmable and predictable features is one of the key requirements for next-generation synthetic biological devices. Despite considerable progress, the construction of synthetic biological arithmetic logic units presents numerous challenges. In this paper, utilizing the unique advantages of RNA molecules in building complex logic circuits in the cellular environment, we demonstrate the RNA-only bitwise logical operation of XOR gates and basic arithmetic operations, including a half adder, a half subtractor, and a Feynman gate, in Escherichia coli. Specifically, de-novo-designed riboregulators, known as toehold switches, were concatenated to enhance the functionality of an OR gate, and a previously utilized antisense RNA strategy was further optimized to construct orthogonal NIMPLY gates. These optimized synthetic logic gates were able to be seamlessly integrated to achieve final arithmetic operations on small molecule inputs in cells. Toehold-switch-based ribocomputing devices may provide a fundamental basis for synthetic RNA-based arithmetic logic units or higher-order systems in cells.

Principles for the design of multicellular engineered living systems

Remarkable progress in bioengineering over the past two decades has enabled the formulation of fundamental design principles for a variety of medical and non-medical applications. These advancements have laid the foundation for building multicellular engineered living systems (M-CELS) from biological parts, forming functional modules integrated into living machines. These cognizant design principles for living systems encompass novel genetic circuit manipulation, self-assembly, cell-cell/matrix communication, and artificial tissues/organs enabled through systems biology, bioinformatics, computational biology, genetic engineering, and microfluidics. Here, we introduce design principles and a blueprint for forward production of robust and standardized M-CELS, which may undergo variable reiterations through the classic design-build-test-debug cycle. This Review provides practical and theoretical frameworks to forward-design, control, and optimize novel M-CELS. Potential applications include biopharmaceuticals, bioreactor factories, biofuels, environmental bioremediation, cellular computing, biohybrid digital technology, and experimental investigations into mechanisms of multicellular organisms normally hidden inside the "black box" of living cells.

Complex effects of kinase localization revealed by compartment-specific regulation of protein kinase A activity

Kinase activity in signaling networks frequently depends on regulatory subunits that can both inhibit activity by interacting with the catalytic subunits and target the kinase to distinct molecular partners and subcellular compartments. Here, using a new synthetic molecular interaction system, we show that translocation of a regulatory subunit of the protein kinase A (PKA-R) to the plasma membrane has a paradoxical effect on the membrane kinase activity. It can both enhance it at lower translocation levels, even in the absence of signaling inputs, and inhibit it at higher translocation levels, suggesting its role as a linker that can both couple and decouple signaling processes in a concentration-dependent manner. We further demonstrate that superposition of gradients of PKA-R abundance across single cells can control the directionality of cell migration, reversing it at high enough input levels. Thus, complex in vivo patterns of PKA-R localization can drive complex phenotypes, including cell migration.

Functional network motifs defined through integration of protein-protein and genetic interactions

Cells are enticingly complex systems. The identification of feedback regulation is critically important for understanding this complexity. Network motifs defined as small graphlets that occur more frequently than expected by chance have revolutionized our understanding of feedback circuits in cellular networks. However, with their definition solely based on statistical over-representation, network motifs often lack biological context, which limits their usefulness. Here, we define functional network motifs (FNMs) through the systematic integration of genetic interaction data that directly inform on functional relationships between genes and encoded proteins. Occurring two orders of magnitude less frequently than conventional network motifs, we found FNMs significantly enriched in genes known to be functionally related. Moreover, our comprehensive analyses of FNMs in yeast showed that they are powerful at capturing both known and putative novel regulatory interactions, thus suggesting a promising strategy towards the systematic identification of feedback regulation in biological networks. Many FNMs appeared as excellent candidates for the prioritization of follow-up biochemical characterization, which is a recurring bottleneck in the targeting of complex diseases. More generally, our work highlights a fruitful avenue for integrating and harnessing genomic network data.

Reservoir Computing Using DNA Oscillators

This paper presents novel implementations for reservoir computing (RC) using DNA oscillators. An RC system consists of two parts: reservoir and readout layer. The reservoir projects input signals into a high-dimensional feature space which is formed by the state of the reservoir. The internal connectivity structure of the reservoir remains unchanged throughout computation. After training, the readout layer maps the projected features into the desired output. It has been shown in prior work that coupled deoxyribozyme oscillators can be used as the reservoir. In this paper, we utilize the n-phase molecular oscillator (n ≥ 3) presented in our prior work. The readout layer implements a matrix-vector multiplication using molecular reactions based on molecular analog multiplication. All molecular reactions are mapped to DNA strand displacement (DSD) reactions. We also introduce a novel encoding method that can significantly reduce the reaction time. The feasibility of the proposed RC systems based on the DNA oscillator is demonstrated for the handwritten digit recognition task and a second-order nonlinear prediction task.

Sensory Systems and Transcriptional Regulation in Escherichia coli

In free-living bacteria, the ability to regulate gene expression is at the core of adapting and interacting with the environment. For these systems to have a logic, a signal must trigger a genetic change that helps the cell to deal with what implies its presence in the environment; briefly, the response is expected to include a feedback to the signal. Thus, it makes sense to think of genetic sensory mechanisms of gene regulation. Escherichia coli K-12 is the bacterium model for which the largest number of regulatory systems and its sensing capabilities have been studied in detail at the molecular level. In this special issue focused on biomolecular sensing systems, we offer an overview of the transcriptional regulatory corpus of knowledge for E. coli that has been gathered in our database, RegulonDB, from the perspective of sensing regulatory systems. Thus, we start with the beginning of the information flux, which is the signal's chemical or physical elements detected by the cell as changes in the environment; these signals are internally transduced to transcription factors and alter their conformation. Signals transduced to effectors bind allosterically to transcription factors, and this defines the dominant sensing mechanism in E. coli. We offer an updated list of the repertoire of known allosteric effectors, as well as a list of the currently known different mechanisms of this sensing capability. Our previous definition of elementary genetic sensory-response units, GENSOR units for short, that integrate signals, transport, gene regulation, and the biochemical response of the regulated gene products of a given transcriptional factor fit perfectly with the purpose of this overview. We summarize the functional heterogeneity of their response, based on our updated collection of GENSORs, and we use them to identify the expected feedback as part of their response. Finally, we address the question of multiple sensing in the regulatory network of E. coli. This overview introduces the architecture of sensing and regulation of native components in E.coli K-12, which might be a source of inspiration to bioengineering applications.

Analytical kinetic model of native tandem promoters in E. coli

Closely spaced promoters in tandem formation are abundant in bacteria. We investigated the evolutionary conservation, biological functions, and the RNA and single-cell protein expression of genes regulated by tandem promoters in E. coli. We also studied the sequence (distance between transcription start sites ‘d_TSS’, pause sequences, and distances from oriC) and potential influence of the input transcription factors of these promoters. From this, we propose an analytical model of gene expression based on measured expression dynamics, where RNAP-promoter occupancy times and d_TSS are the key regulators of transcription interference due to TSS occlusion by RNAP at one of the promoters (when d_TSS ≤ 35 bp) and RNAP occupancy of the downstream promoter (when d_TSS > 35 bp). Occlusion and downstream promoter occupancy are modeled as linear functions of occupancy time, while the influence of d_TSS is implemented by a continuous step function, fit to in vivo data on mean single-cell protein numbers of 30 natural genes controlled by tandem promoters. The best-fitting step is at 35 bp, matching the length of DNA occupied by RNAP in the open complex formation. This model accurately predicts the squared coefficient of variation and skewness of the natural single-cell protein numbers as a function of d_TSS. Additional predictions suggest that promoters in tandem formation can cover a wide range of transcription dynamics within realistic intervals of parameter values. By accurately capturing the dynamics of these promoters, this model can be helpful to predict the dynamics of new promoters and contribute to the expansion of the repertoire of expression dynamics available to synthetic genetic constructs.

Tandem promoters are common in nature, but investigations on their dynamics have so far largely relied on synthetic constructs. Thus, their regulation and potentially unique dynamics remain unexplored. We first performed a comprehensive exploration of the conservation of genes regulated by these promoters in E. coli and the properties of their input transcription factors. We then measured protein and RNA levels expressed by 30 Escherichia coli tandem promoters, to establish an analytical model of the expression dynamics of genes controlled by such promoters. We show that start site occlusion and downstream RNAP occupancy can be realistically captured by a model with RNAP binding affinity, the time length of open complex formation, and the nucleotide distance between transcription start sites. This study contributes to a better understanding of the unique dynamics tandem promoters can bring to the dynamics of gene networks and will assist in their use in synthetic genetic circuits.

Predictive landscapes hidden beneath biological cellular automata

To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious "parameter problem": models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive "landscapes" whose shapes are described by Lyapunov functions and yield "equations of motion" for a "pseudo-particle." The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

Quantifying the regulatory role of individual transcription factors in Escherichia coli

Gene regulation often results from the action of multiple transcription factors (TFs) acting at a promoter, obscuring the individual regulatory effect of each TF on RNA polymerase (RNAP). Here we measure the fundamental regulatory interactions of TFs in E. coli by designing synthetic target genes that isolate individual TFs' regulatory effects. Using a thermodynamic model, each TF's regulatory interactions are decoupled from TF occupancy and interpreted as acting through (de)stabilization of RNAP and (de)acceleration of transcription initiation. We find that the contribution of each mechanism depends on TF identity and binding location; regulation immediately downstream of the promoter is insensitive to TF identity, but the same TFs regulate by distinct mechanisms upstream of the promoter. These two mechanisms are uncoupled and can act coherently, to reinforce the observed regulatory role (activation/repression), or incoherently, wherein the TF regulates two distinct steps with opposing effects.

Competitive dCas9 binding as a mechanism for transcriptional control

Catalytically dead Cas9 (dCas9) is a programmable transcription factor that can be targeted to promoters through the design of small guide RNAs (sgRNAs), where it can function as an activator or repressor. Natural promoters use overlapping binding sites as a mechanism for signal integration, where the binding of one can block, displace, or augment the activity of the other. Here, we implemented this strategy in Escherichia coli using pairs of sgRNAs designed to repress and then derepress transcription through competitive binding. When designed to target a promoter, this led to 27-fold repression and complete derepression. This system was also capable of ratiometric input comparison over two orders of magnitude. Additionally, we used this mechanism for promoter sequence-independent control by adopting it for elongation control, achieving 8-fold repression and 4-fold derepression. This work demonstrates a new genetic control mechanism that could be used to build analog circuit or implement cis-regulatory logic on CRISPRi-targeted native genes.

Stimulus-specific responses in innate immunity: Multilayered regulatory circuits

Immune sentinel cells initiate immune responses to pathogens and tissue injury and are capable of producing highly stimulus-specific responses. Insight into the mechanisms underlying such specificity has come from the identification of regulatory factors and biochemical pathways, as well as the definition of signaling circuits that enable combinatorial and temporal coding of information. Here, we review the multi-layered molecular mechanisms that underlie stimulus-specific gene expression in macrophages. We categorize components of inflammatory and anti-pathogenic signaling pathways into five layers of regulatory control and discuss unifying mechanisms determining signaling characteristics at each layer. In this context, we review mechanisms that enable combinatorial and temporal encoding of information, identify recurring regulatory motifs and principles, and present strategies for integrating experimental and computational approaches toward the understanding of signaling specificity in innate immunity.

Adaptive gene misregulation

Because gene expression is important for evolutionary adaptation, its misregulation is an important cause of maladaptation. A misregulated gene can be incorrectly silent ("off") when a transcription factor (TF) that is required for its activation does not binds its regulatory region. Conversely, a misregulated gene can be incorrectly active ("on") when a TF not normally involved in its activation binds its regulatory region, a phenomenon also known as regulatory crosstalk. DNA mutations that destroy or create TF binding sites on DNA are an important source of misregulation and crosstalk. Although misregulation reduces fitness in an environment to which an organism is well-adapted, it may become adaptive in a new environment. Here, I derive simple yet general mathematical expressions that delimit the conditions under which misregulation can be adaptive. These expressions depend on the strength of selection against misregulation, on the fraction of DNA sequence space filled with TF binding sites, and on the fraction of genes that must be expressed for optimal adaptation. I then use empirical data from RNA sequencing, protein-binding microarrays, and genome evolution, together with population genetic simulations to ask when these conditions are likely to be met. I show that they can be met under realistic circumstances, but these circumstances may vary among organisms and environments. My analysis provides a framework in which improved theory and data collection can help us demonstrate the role of misregulation in adaptation. It also shows that misregulation, like DNA mutation, is one of life's many imperfections that can help propel Darwinian evolution.

Beyond the adiabatic limit in systems with fast environments: A τ-leaping algorithm

We propose a τ-leaping simulation algorithm for stochastic systems subject to fast environmental changes. Similar to conventional τ-leaping the algorithm proceeds in discrete time steps, but as a principal addition it captures environmental noise beyond the adiabatic limit. The key idea is to treat the input rates for the τ-leaping as (clipped) Gaussian random variables with first and second moments constructed from the environmental process. In this way, each step of the algorithm retains environmental stochasticity to subleading order in the timescale separation between system and environment. We test the algorithm on several toy examples with discrete and continuous environmental states and find good performance in the regime of fast environmental dynamics. At the same time, the algorithm requires significantly less computing time than full simulations of the combined system and environment. In this context we also discuss several methods for the simulation of stochastic population dynamics in time-varying environments with continuous states.

Nonequilibrium model of short-range repression in gene transcription regulation

Transcription factors are proteins that regulate gene activity by activating or repressing gene transcription. A special class of transcriptional repressors operates via a short-range mechanism, making local DNA regions inaccessible to binding by activators, and thus providing an indirect repressive action on the target gene. This mechanism is commonly modeled assuming that repressors interact with DNA under thermodynamic equilibrium and neglecting some configurations of the gene regulatory region. We elaborate on a more general nonequilibrium model of short-range repression using the graph formalism for transitions between gene states, and we apply analytical calculations to compare it with the equilibrium model in terms of the repression strength and expression noise. In contrast to the equilibrium approach, the new model allows us to separate two basic mechanisms of short-range repression. The first mechanism is associated with the recruiting of factors that mediate chromatin condensation, and the second one concerns the blocking of factors that mediate chromatin loosening. The nonequilibrium model demonstrates better performance on previously published gene expression data obtained for transcription factors controlling Drosophila development, and furthermore it predicts that the first repression mechanism is the most favorable in this system. The presented approach can be scaled to larger gene networks and can be used to infer specific modes and parameters of transcriptional regulation from gene expression data.

Predicting synchronized gene coexpression patterns from fibration symmetries in gene regulatory networks in bacteria

BACKGROUND

Gene regulatory networks coordinate the expression of genes across physiological states and ensure a synchronized expression of genes in cellular subsystems, critical for the coherent functioning of cells. Here we address the question whether it is possible to predict gene synchronization from network structure alone. We have recently shown that synchronized gene expression can be predicted from symmetries in the gene regulatory networks described by the concept of symmetry fibrations. We showed that symmetry fibrations partition the genes into groups called fibers based on the symmetries of their 'input trees', the set of paths in the network through which signals can reach a gene. In idealized dynamic gene expression models, all genes in a fiber are perfectly synchronized, while less idealized models-with gene input functions differencing between genes-predict symmetry breaking and desynchronization.

RESULTS

To study the functional role of gene fibers and to test whether some of the fiber-induced coexpression remains in reality, we analyze gene fibrations for the gene regulatory networks of E. coli and B. subtilis and confront them with expression data. We find approximate gene coexpression patterns consistent with symmetry fibrations with idealized gene expression dynamics. This shows that network structure alone provides useful information about gene synchronization, and suggest that gene input functions within fibers may be further streamlined by evolutionary pressures to realize a coexpression of genes.

CONCLUSIONS

Thus, gene fibrations provide a sound conceptual tool to describe tunable coexpression induced by network topology and shaped by mechanistic details of gene expression.

First-principles prediction of the information processing capacity of a simple genetic circuit

Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to survive in changing environments. Recent work has explored the use of information theory as a framework to understand the accuracy with which cells can ascertain the state of their surroundings. Yet the predictive power of these approaches is limited and has not been rigorously tested using precision measurements. To that end, we generate a minimal model for a simple genetic circuit in which all parameter values for the model come from independently published data sets. We then predict the information processing capacity of the genetic circuit for a suite of biophysical parameters such as protein copy number and protein-DNA affinity. We compare these parameter-free predictions with an experimental determination of protein expression distributions and the resulting information processing capacity of E. coli cells. We find that our minimal model captures the scaling of the cell-to-cell variability in the data and the inferred information processing capacity of our simple genetic circuit up to a systematic deviation.

Identifying the combinatorial control of signal-dependent transcription factors

The effectiveness of immune responses depends on the precision of stimulus-responsive gene expression programs. Cells specify which genes to express by activating stimulus-specific combinations of stimulus-induced transcription factors (TFs). Their activities are decoded by a gene regulatory strategy (GRS) associated with each response gene. Here, we examined whether the GRSs of target genes may be inferred from stimulus-response (input-output) datasets, which remains an unresolved model-identifiability challenge. We developed a mechanistic modeling framework and computational workflow to determine the identifiability of all possible combinations of synergistic (AND) or non-synergistic (OR) GRSs involving three transcription factors. Considering different sets of perturbations for stimulus-response studies, we found that two thirds of GRSs are easily distinguishable but that substantially more quantitative data is required to distinguish the remaining third. To enhance the accuracy of the inference with timecourse experimental data, we developed an advanced error model that avoids error overestimates by distinguishing between value and temporal error. Incorporating this error model into a Bayesian framework, we show that GRS models can be identified for individual genes by considering multiple datasets. Our analysis rationalizes the allocation of experimental resources by identifying most informative TF stimulation conditions. Applying this computational workflow to experimental data of immune response genes in macrophages, we found that a much greater fraction of genes are combinatorially controlled than previously reported by considering compensation among transcription factors. Specifically, we revealed that a group of known NFκB target genes may also be regulated by IRF3, which is supported by chromatin immuno-precipitation analysis. Our study provides a computational workflow for designing and interpreting stimulus-response gene expression studies to identify underlying gene regulatory strategies and further a mechanistic understanding.

Anticipating response function in gene regulatory networks

The origin of an ordered genetic response of a complex and noisy biological cell is intimately related to the detailed mechanism of protein-DNA interactions present in a wide variety of gene regulatory (GR) systems. However, the quantitative prediction of genetic response and the correlation between the mechanism and the response curve is poorly understood. Here, we report in silico binding studies of GR systems to show that the transcription factor (TF) binds to multiple DNA sites with high cooperativity spreads from specific binding sites into adjacent non-specific DNA and bends the DNA. Our analysis is not limited only to the isolated model system but also can be applied to a system containing multiple interacting genes. The controlling role of TF oligomerization, TF-ligand interactions, and DNA looping for gene expression has been also characterized. The predictions are validated against detailed grand canonical Monte Carlo simulations and published data for the lac operon system. Overall, our study reveals that the expression of target genes can be quantitatively controlled by modulating TF-ligand interactions and the bending energy of DNA.

A cis-regulatory atlas in maize at single-cell resolution

cis-regulatory elements (CREs) encode the genomic blueprints of spatiotemporal gene expression programs enabling highly specialized cell functions. Using single-cell genomics in six maize organs, we determined the cis- and trans-regulatory factors defining diverse cell identities and coordinating chromatin organization by profiling transcription factor (TF) combinatorics, identifying TFs with non-cell-autonomous activity, and uncovering TFs underlying higher-order chromatin interactions. Cell-type-specific CREs were enriched for enhancer activity and within unmethylated long terminal repeat retrotransposons. Moreover, we found cell-type-specific CREs are hotspots for phenotype-associated genetic variants and were targeted by selection during modern maize breeding, highlighting the biological implications of this CRE atlas. Through comparison of maize and Arabidopsis thaliana developmental trajectories, we identified TFs and CREs with conserved and divergent chromatin dynamics, showcasing extensive evolution of gene regulatory networks. In addition to this rich dataset, we developed single-cell analysis software, Socrates, which can be used to understand cis-regulatory variation in any species.

From Bench to Keyboard and Back Again: A Brief History of Lambda Phage Modeling

Cellular decision making is the process whereby cells choose one developmental pathway from multiple possible ones, either spontaneously or due to environmental stimuli. Examples in various cell types suggest an almost inexhaustible plethora of underlying molecular mechanisms. In general, cellular decisions rely on the gene regulatory network, which integrates external signals to drive cell fate choice. The search for general principles of such a process benefits from appropriate biological model systems that reveal how and why certain gene regulatory mechanisms drive specific cellular decisions according to ecological context and evolutionary outcomes. In this article, we review the historical and ongoing development of the phage lambda lysis-lysogeny decision as a model system to investigate all aspects of cellular decision making. The unique generality, simplicity, and richness of phage lambda decision making render it a constant source ofmathematical modeling-aided inspiration across all of biology. We discuss the origins and progress of quantitative phage lambda modeling from the 1950s until today, as well as its possible future directions. We provide examples of how modeling enabled methods and theory development, leading to new biological insights by revealing gaps in the theory and pinpointing areas requiring further experimental investigation. Overall, we highlight the utility of theoretical approaches both as predictive tools, to forecast the outcome of novel experiments, and as explanatory tools, to elucidate the natural processes underlying experimental data.

On reaction network implementations of neural networks

This paper is concerned with the utilization of deterministically modelled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differential equations (ODEs) associated with certain reaction network implementations of neural networks have desirable properties including (i) existence of unique positive fixed points that are smooth in the parameters of the model (necessary for gradient descent) and (ii) fast convergence to the fixed point regardless of initial condition (necessary for efficient implementation). We do so by first making a connection between neural networks and fixed points for systems of ODEs, and then by constructing reaction networks with the correct associated set of ODEs. We demonstrate the theory by constructing a reaction network that implements a neural network with a smoothed ReLU activation function, though we also demonstrate how to generalize the construction to allow for other activation functions (each with the desirable properties listed previously). As there are multiple types of 'networks' used in this paper, we also give a careful introduction to both reaction networks and neural networks, in order to disambiguate the overlapping vocabulary in the two settings and to clearly highlight the role of each network's properties.