On schemes of combinatorial transcription logic

Scaling of gene expression with transcription-factor fugacity

The proteins associated with gene regulation are often shared between multiple pathways simultaneously. By way of contrast, models in regulatory biology often assume these pathways act independently. We demonstrate a framework for calculating the change in gene expression for the interacting case by decoupling repressor occupancy across the cell from the gene of interest by way of a chemical potential. The details of the interacting regulatory architecture are encompassed in an effective concentration, and thus, a single scaling function describes a collection of gene expression data from diverse regulatory situations and collapses it onto a single master curve.

A framework for modelling gene regulation which accommodates non-equilibrium mechanisms

BACKGROUND

Gene regulation has, for the most part, been quantitatively analysed by assuming that regulatory mechanisms operate at thermodynamic equilibrium. This formalism was originally developed to analyse the binding and unbinding of transcription factors from naked DNA in eubacteria. Although widely used, it has made it difficult to understand the role of energy-dissipating, epigenetic mechanisms, such as DNA methylation, nucleosome remodelling and post-translational modification of histones and co-regulators, which act together with transcription factors to regulate gene expression in eukaryotes.

RESULTS

Here, we introduce a graph-based framework that can accommodate non-equilibrium mechanisms. A gene-regulatory system is described as a graph, which specifies the DNA microstates (vertices), the transitions between microstates (edges) and the transition rates (edge labels). The graph yields a stochastic master equation for how microstate probabilities change over time. We show that this framework has broad scope by providing new insights into three very different ad hoc models, of steroid-hormone responsive genes, of inherently bounded chromatin domains and of the yeast PHO5 gene. We find, moreover, surprising complexity in the regulation of PHO5, which has not yet been experimentally explored, and we show that this complexity is an inherent feature of being away from equilibrium. At equilibrium, microstate probabilities do not depend on how a microstate is reached but, away from equilibrium, each path to a microstate can contribute to its steady-state probability. Systems that are far from equilibrium thereby become dependent on history and the resulting complexity is a fundamental challenge. To begin addressing this, we introduce a graph-based concept of independence, which can be applied to sub-systems that are far from equilibrium, and prove that history-dependent complexity can be circumvented when sub-systems operate independently.

CONCLUSIONS

As epigenomic data become increasingly available, we anticipate that gene function will come to be represented by graphs, as gene structure has been represented by sequences, and that the methods introduced here will provide a broader foundation for understanding how genes work.

Heuristic identification of biological architectures for simulating complex hierarchical genetic interactions

Simulation plays an essential role in the development of new computational and statistical methods for the genetic analysis of complex traits. Most simulations start with a statistical model using methods such as linear or logistic regression that specify the relationship between genotype and phenotype. This is appealing due to its simplicity and because these statistical methods are commonly used in genetic analysis. It is our working hypothesis that simulations need to move beyond simple statistical models to more realistically represent the biological complexity of genetic architecture. The goal of the present study was to develop a prototype genotype–phenotype simulation method and software that are capable of simulating complex genetic effects within the context of a hierarchical biology-based framework. Specifically, our goal is to simulate multilocus epistasis or gene–gene interaction where the genetic variants are organized within the framework of one or more genes, their regulatory regions and other regulatory loci. We introduce here the Heuristic Identification of Biological Architectures for simulating Complex Hierarchical Interactions (HIBACHI) method and prototype software for simulating data in this manner. This approach combines a biological hierarchy, a flexible mathematical framework, a liability threshold model for defining disease endpoints, and a heuristic search strategy for identifying high-order epistatic models of disease susceptibility. We provide several simulation examples using genetic models exhibiting independent main effects and three-way epistatic effects.

Autocrine FGF feedback can establish distinct states of Nanog expression in pluripotent stem cells: a computational analysis

Background

The maintenance of stem cell pluripotency is controlled by a core cluster of transcription factors, NANOG, OCT4 and SOX2 – genes that jointly regulate each other’s expression. The expression of some of these genes, especially of Nanog, is heterogeneous in a population of undifferentiated stem cells in culture. Transient changes in expression levels, as well as heterogeneity of the population is not restricted to this core regulator, but involve a large number of other genes that include growth factors, transcription factors or signal transduction proteins.

Results

As the molecular mechanisms behind NANOG expression heterogeneity is not yet understood, we explore by computational modeling the core transcriptional regulatory circuit and its input from autocrine FGF signals that act through the MAP kinase cascade. We argue that instead of negative feedbacks within the core NANOG-OCT4-SOX2 transcriptional regulatory circuit, autocrine signaling loops such as the Esrrb - FGF - ERK feedback considered here are likely to generate distinct sub-states within the “ON” state of the core Nanog switch. Thus, the experimentally observed fluctuations in Nanog transcription levels are best explained as noise-induced transitions between negative feedback-generated sub-states. We also demonstrate that ERK phosphorilation is altered and being anti-correlated with fluctuating Nanog expression – in accord with model simulations. Our modeling approach assigns an empirically testable function to the transcriptional regulators Klf4 and Esrrb, and predict differential regulation of FGF family members.

Conclusions

We argue that slow fluctuations in Nanog expression likely reflect individual cell-specific changes in parameters of an autocrine feedback loop, such as changes in ligand capture efficiency, receptor numbers or the presence of crosstalks within the MAPK signal transduction pathway. We proposed a model that operates with binding affinities of multiple transcriptional regulators of pluripotency, and the activity of an autocrine signaling pathway. The resulting model produces varied expression levels of several components of pluripotency regulation, largely consistent with empirical observations reported previously and in this present work.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0112-4) contains supplementary material, which is available to authorized users.

Top-level dynamics and the regulated gene response of feed-forward loop transcriptional motifs

Feed-forward loops are hierarchical three-node transcriptional subnetworks, wherein a top-level protein regulates the activity of a target gene via two paths: a direct-regulatory path, and an indirect route, whereby the top-level proteins act implicitly through an intermediate transcription factor. Using a transcriptional network of the model bacterium Escherichia coli, we confirmed that nearly all types of feed-forward loop were significantly overrepresented in the bacterial network. We then used mathematical modeling to study their dynamics by manipulating the rise times of the top-level protein concentration, termed the induction time, through alteration of the protein destruction rates. Rise times of the regulated proteins exhibited two qualitatively different regimes, depending on whether top-level inductions were "fast" or "slow." In the fast regime, rise times were nearly independent of rapid top-level inductions, indicative of biological robustness, and occurred when RNA production rate-limits the protein yield. Alternatively, the protein rise times were dependent upon slower top-level inductions, greater than approximately one bacterial cell cycle. An equation is given for this crossover, which depends upon three parameters of the direct-regulatory path: transcriptional cooperation at the DNA-binding site, a protein-DNA dissociation constant, and the relative magnitude of the top-level protien concentration.

Directed acyclic graph-based technology mapping of genetic circuit models

As engineering foundations such as standards and abstraction begin to mature within synthetic biology, it is vital that genetic design automation (GDA) tools be developed to enable synthetic biologists to automatically select standardized DNA components from a library to meet the behavioral specification for a genetic circuit. To this end, we have developed a genetic technology mapping algorithm that builds on the directed acyclic graph (DAG) based mapping techniques originally used to select parts for digital electronic circuit designs and implemented it in our GDA tool, iBioSim. It is among the first genetic technology mapping algorithms to adapt techniques from electronic circuit design, in particular the use of a cost function to guide the search for an optimal solution, and perhaps that which makes the greatest use of standards for describing genetic function and structure to represent design specifications and component libraries. This paper demonstrates the use of our algorithm to map the specifications for three different genetic circuits against four randomly generated libraries of increasing size to evaluate its performance against both exhaustive search and greedy variants for finding optimal and near-optimal solutions.

Homotypic clusters of transcription factor binding sites: A model system for understanding the physical mechanics of gene expression

The organization of binding sites in cis-regulatory elements (CREs) can influence gene expression through a combination of physical mechanisms, ranging from direct interactions between TF molecules to DNA looping and transient chromatin interactions. The study of simple and common building blocks in promoters and other CREs allows us to dissect how all of these mechanisms work together. Many adjacent TF binding sites for the same TF species form homotypic clusters, and these CRE architecture building blocks serve as a prime candidate for understanding interacting transcriptional mechanisms. Homotypic clusters are prevalent in both bacterial and eukaryotic genomes, and are present in both promoters as well as more distal enhancer/silencer elements. Here, we review previous theoretical and experimental studies that show how the complexity (number of binding sites) and spatial organization (distance between sites and overall distance from transcription start sites) of homotypic clusters influence gene expression. In particular, we describe how homotypic clusters modulate the temporal dynamics of TF binding, a mechanism that can affect gene expression, but which has not yet been sufficiently characterized. We propose further experiments on homotypic clusters that would be useful in developing mechanistic models of gene expression.

Boolean networks with veto functions

Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give analytical expressions for the sensitivity of these functions and provide evidence for their role in natural systems. In an intracellular signal transduction network [Helikar et al., Proc. Natl. Acad. Sci. USA 105, 1913 (2008)], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. In Boolean networks for control of the yeast cell cycle [Li et al., Proc. Natl. Acad. Sci. USA 101, 4781 (2004); Davidich et al., PLoS ONE 3, e1672 (2008)], no or minimal changes to the wiring diagrams are necessary to formulate their dynamics in terms of the veto functions introduced here.

A Novel Synthesizing Genetic Logic Circuit: Frequency Multiplier

This paper presents a novel synthesizing genetic logic circuit design based on an existing synthetic genetic oscillator, which provides a function of frequency multiplier to synthesize a clock signal whose frequency is a multiple of that of the genetic oscillator. In the renowned literature, the synthetic genetic oscillator, known as a repressilator, has been successfully built in Escherichia coli to generate a periodic oscillating phenomenon through three repressive genes repress each other in a chain. On the basis of this fact, our proposed genetic frequency multiplier circuit utilizes genetic Buffers in series with a waveform-shaping circuit to reshape the genetic oscillation signal into a crisp logic clock signal. By regulating different threshold levels in the Buffer, the time length of logic high/low levels in a fundamental sinusoidal wave can be engineered to pulse-width-modulated (PWM) signals with various duty cycles. Integrating some of genetic logic XOR gates and PWM signals from the output of the Buffers, a genetic frequency multiplier circuit can be created and the clock signal with the integer-fold of frequency of the genetic oscillator is generated. The synthesized signal can be used in triggering the downstream digital genetic logic circuits. Simulation results show the applicability of the proposed idea.

Mutations in transcriptional regulators allow selective engineering of signal integration logic

Bacterial cells monitor their environment by sensing a set of signals. Typically, these environmental signals affect promoter activities by altering the activity of transcription regulatory proteins. Promoters are often regulated by more than one regulatory protein, and in these cases the relevant signals are integrated by certain logic. In this work, we study how single amino acid substitutions in a regulatory protein (GalR) affect transcriptional regulation and signal integration logic at a set of engineered promoters. Our results suggest that point mutations in regulatory genes allow independent evolution of regulatory logic at different promoters.

IMPORTANCE

Gene regulatory networks are built from simple building blocks, such as promoters, transcription regulatory proteins, and their binding sites on DNA. Many promoters are regulated by more than one regulatory input. In these cases, the inputs are integrated and allow transcription only in certain combinations of input signals. Gene regulatory networks can be easily rewired, because the function of cis-regulatory elements and promoters can be altered by point mutations. In this work, we tested how point mutations in transcription regulatory proteins can affect signal integration logic. We found that such mutations allow context-dependent engineering of signal integration logic at promoters, further contributing to the plasticity of gene regulatory networks.

Principles of genetic circuit design

Cells navigate environments, communicate and build complex patterns by initiating gene expression in response to specific signals. Engineers seek to harness this capability to program cells to perform tasks or create chemicals and materials that match the complexity seen in nature. This Review describes new tools that aid the construction of genetic circuits. Circuit dynamics can be influenced by the choice of regulators and changed with expression 'tuning knobs'. We collate the failure modes encountered when assembling circuits, quantify their impact on performance and review mitigation efforts. Finally, we discuss the constraints that arise from circuits having to operate within a living cell. Collectively, better tools, well-characterized parts and a comprehensive understanding of how to compose circuits are leading to a breakthrough in the ability to program living cells for advanced applications, from living therapeutics to the atomic manufacturing of functional materials.

Cellular noise and information transmission

The technological revolution in biological research, and in particular the use of molecular fluorescent labels, has allowed investigation of heterogeneity of cellular responses to stimuli on the single cell level. Computational, theoretical, and synthetic biology advances have allowed predicting and manipulating this heterogeneity with an exquisite precision previously reserved only for physical sciences. Functionally, this cell-to-cell variability can compromise cellular responses to environmental signals, and it can also enlarge the repertoire of possible cellular responses and hence increase the adaptive nature of cellular behaviors. And yet quantification of the functional importance of this response heterogeneity remained elusive. Recently the mathematical language of information theory has been proposed to address this problem. This opinion reviews the recent advances and discusses the broader implications of using information-theoretic tools to characterize heterogeneity of cellular behaviors.

Latent phenotypes pervade gene regulatory circuits

BACKGROUND

Latent phenotypes are non-adaptive byproducts of adaptive phenotypes. They exist in biological systems as different as promiscuous enzymes and genome-scale metabolic reaction networks, and can give rise to evolutionary adaptations and innovations. We know little about their prevalence in the gene expression phenotypes of regulatory circuits, important sources of evolutionary innovations.

RESULTS

Here, we study a space of more than sixteen million three-gene model regulatory circuits, where each circuit is represented by a genotype, and has one or more functions embodied in one or more gene expression phenotypes. We find that the majority of circuits with single functions have latent expression phenotypes. Moreover, the set of circuits with a given spectrum of functions has a repertoire of latent phenotypes that is much larger than that of any one circuit. Most of this latent repertoire can be easily accessed through a series of small genetic changes that preserve a circuit's main functions. Both circuits and gene expression phenotypes that are robust to genetic change are associated with a greater number of latent phenotypes.

CONCLUSIONS

Our observations suggest that latent phenotypes are pervasive in regulatory circuits, and may thus be an important source of evolutionary adaptations and innovations involving gene regulation.

Synthesizing genetic sequential logic circuit with clock pulse generator

Background

Rhythmic clock widely occurs in biological systems which controls several aspects of cell physiology. For the different cell types, it is supplied with various rhythmic frequencies. How to synthesize a specific clock signal is a preliminary but a necessary step to further development of a biological computer in the future.

Results

This paper presents a genetic sequential logic circuit with a clock pulse generator based on a synthesized genetic oscillator, which generates a consecutive clock signal whose frequency is an inverse integer multiple to that of the genetic oscillator. An analogous electronic waveform-shaping circuit is constructed by a series of genetic buffers to shape logic high/low levels of an oscillation input in a basic sinusoidal cycle and generate a pulse-width-modulated (PWM) output with various duty cycles. By controlling the threshold level of the genetic buffer, a genetic clock pulse signal with its frequency consistent to the genetic oscillator is synthesized. A synchronous genetic counter circuit based on the topology of the digital sequential logic circuit is triggered by the clock pulse to synthesize the clock signal with an inverse multiple frequency to the genetic oscillator. The function acts like a frequency divider in electronic circuits which plays a key role in the sequential logic circuit with specific operational frequency.

Conclusions

A cascaded genetic logic circuit generating clock pulse signals is proposed. Based on analogous implement of digital sequential logic circuits, genetic sequential logic circuits can be constructed by the proposed approach to generate various clock signals from an oscillation signal.

Ligand-dependent Notch signaling strength orchestrates lateral induction and lateral inhibition in the developing inner ear

During inner ear development, Notch exhibits two modes of operation: lateral induction, which is associated with prosensory specification, and lateral inhibition, which is involved in hair cell determination. These mechanisms depend respectively on two different ligands, jagged 1 (Jag1) and delta 1 (Dl1), that rely on a common signaling cascade initiated after Notch activation. In the chicken otocyst, expression of Jag1 and the Notch target Hey1 correlates well with lateral induction, whereas both Jag1 and Dl1 are expressed during lateral inhibition, as are Notch targets Hey1 and Hes5. Here, we show that Jag1 drives lower levels of Notch activity than Dl1, which results in the differential expression of Hey1 and Hes5. In addition, Jag1 interferes with the ability of Dl1 to elicit high levels of Notch activity. Modeling the sensory epithelium when the two ligands are expressed together shows that ligand regulation, differential signaling strength and ligand competition are crucial to allow the two modes of operation and for establishing the alternate pattern of hair cells and supporting cells. Jag1, while driving lateral induction on its own, facilitates patterning by lateral inhibition in the presence of Dl1. This novel behavior emerges from Jag1 acting as a competitive inhibitor of Dl1 for Notch signaling. Both modeling and experiments show that hair cell patterning is very robust. The model suggests that autoactivation of proneural factor Atoh1, upstream of Dl1, is a fundamental component for robustness. The results stress the importance of the levels of Notch signaling and ligand competition for Notch function.

Comparison of the theoretical and real-world evolutionary potential of a genetic circuit

With the development of next-generation sequencing technologies, many large scale experimental efforts aim to map genotypic variability among individuals. This natural variability in populations fuels many fundamental biological processes, ranging from evolutionary adaptation and speciation to the spread of genetic diseases and drug resistance. An interesting and important component of this variability is present within the regulatory regions of genes. As these regions evolve, accumulated mutations lead to modulation of gene expression, which may have consequences for the phenotype. A simple model system where the link between genetic variability, gene regulation and function can be studied in detail is missing. In this article we develop a model to explore how the sequence of the wild-type lac promoter dictates the fold-change in gene expression. The model combines single-base pair resolution maps of transcription factor and RNA polymerase binding energies with a comprehensive thermodynamic model of gene regulation. The model was validated by predicting and then measuring the variability of lac operon regulation in a collection of natural isolates. We then implement the model to analyze the sensitivity of the promoter sequence to the regulatory output, and predict the potential for regulation to evolve due to point mutations in the promoter region.

A mixed incoherent feed-forward loop allows conditional regulation of response dynamics

Expression of the SodA superoxide dismutase (MnSOD) in Escherichia coli is regulated by superoxide concentration through the SoxRS system and also by Fur (Ferric uptake regulator) through a mixed incoherent feed forward loop (FFL) containing the RyhB small regulatory RNA. In this work I theoretically analyze the function of this feed forward loop as part of the network controlling expression of the two cytoplasmic superoxide dismutases, SodA and SodB. I find that feed forward regulation allows faster response to superoxide stress at low intracellular iron levels compared to iron rich conditions. That is, it can conditionally modulate the response time of a superimposed transcriptional control mechanism.

Generic Properties of Random Gene Regulatory Networks

Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In particular, it is not clear typically how attractors partition among the three types of orbits: steady state, periodic and chaotic, and how the dynamical properties change with network's topological characteristics. In this work, we first investigated these questions in random GRNs with different network sizes, connectivity, fraction of inhibitory links and transcription regulation rules. Then we searched for the core motifs that govern the dynamic behavior of large GRNs. We show that the stability of a random GRN is typically governed by a few embedding motifs of small sizes, and therefore can in general be understood in the context of these short motifs. Our results provide insights for the study and design of genetic networks.

The transcription factor titration effect dictates level of gene expression

Models of transcription are often built around a picture of RNA polymerase and transcription factors (TFs) acting on a single copy of a promoter. However, most TFs are shared between multiple genes with varying binding affinities. Beyond that, genes often exist at high copy number-in multiple identical copies on the chromosome or on plasmids or viral vectors with copy numbers in the hundreds. Using a thermodynamic model, we characterize the interplay between TF copy number and the demand for that TF. We demonstrate the parameter-free predictive power of this model as a function of the copy number of the TF and the number and affinities of the available specific binding sites; such predictive control is important for the understanding of transcription and the desire to quantitatively design the output of genetic circuits. Finally, we use these experiments to dynamically measure plasmid copy number through the cell cycle.

Quantitative modeling of a gene's expression from its intergenic sequence

Modeling a gene's expression from its intergenic locus and trans-regulatory context is a fundamental goal in computational biology. Owing to the distributed nature of cis-regulatory information and the poorly understood mechanisms that integrate such information, gene locus modeling is a more challenging task than modeling individual enhancers. Here we report the first quantitative model of a gene's expression pattern as a function of its locus. We model the expression readout of a locus in two tiers: 1) combinatorial regulation by transcription factors bound to each enhancer is predicted by a thermodynamics-based model and 2) independent contributions from multiple enhancers are linearly combined to fit the gene expression pattern. The model does not require any prior knowledge about enhancers contributing toward a gene's expression. We demonstrate that the model captures the complex multi-domain expression patterns of anterior-posterior patterning genes in the early Drosophila embryo. Altogether, we model the expression patterns of 27 genes; these include several gap genes, pair-rule genes, and anterior, posterior, trunk, and terminal genes. We find that the model-selected enhancers for each gene overlap strongly with its experimentally characterized enhancers. Our findings also suggest the presence of sequence-segments in the locus that would contribute ectopic expression patterns and hence were "shut down" by the model. We applied our model to identify the transcription factors responsible for forming the stripe boundaries of the studied genes. The resulting network of regulatory interactions exhibits a high level of agreement with known regulatory influences on the target genes. Finally, we analyzed whether and why our assumption of enhancer independence was necessary for the genes we studied. We found a deterioration of expression when binding sites in one enhancer were allowed to influence the readout of another enhancer. Thus, interference between enhancer activities was a possible factor necessitating enhancer independence in our model.

Training an asymmetric signal perceptron through reinforcement in an artificial chemistry

State-of-the-art biochemical systems for medical applications and chemical computing are application-specific and cannot be reprogrammed or trained once fabricated. The implementation of adaptive biochemical systems that would offer flexibility through programmability and autonomous adaptation faces major challenges because of the large number of required chemical species as well as the timing-sensitive feedback loops required for learning. In this paper, we begin addressing these challenges with a novel chemical perceptron that can solve all 14 linearly separable logic functions. The system performs asymmetric chemical arithmetic, learns through reinforcement and supports both Michaelis-Menten as well as mass-action kinetics. To enable cascading of the chemical perceptrons, we introduce thresholds that amplify the outputs. The simplicity of our model makes an actual wet implementation, in particular by DNA-strand displacement, possible.

FOUNDATIONS FOR MODELING THE DYNAMICS OF GENE REGULATORY NETWORKS: A MULTILEVEL-PERSPECTIVE REVIEW

A promising alternative for unraveling the principles under which the dynamic interactions among genes lead to cellular phenotypes relies on mathematical and computational models at different levels of abstraction, from the molecular level of protein-DNA interactions to the system level of functional relationships among genes. This review article presents, under a bottom–up perspective, a hierarchy of approaches to modeling gene regulatory network dynamics, from microscopic descriptions at the single-molecule level in the spatial context of an individual cell to macroscopic models providing phenomenological descriptions at the population-average level. The reviewed modeling approaches include Molecular Dynamics, Particle-Based Brownian Dynamics, the Master Equation approach, Ordinary Differential Equations, and the Boolean logic abstraction. Each of these frameworks is motivated by a particular biological context and the nature of the insight being pursued. The setting of gene network dynamic models from such frameworks involves assumptions and mathematical artifacts often ignored by the non-specialist. This article aims at providing an entry point for biologists new to the field and computer scientists not acquainted with some recent biophysically-inspired models of gene regulation. The connections promoting intuition between different abstraction levels and the role that approximations play in the modeling process are highlighted throughout the paper.

Synthesising periodic triggering signals with genetic oscillators

The potential of the clock lies in its role of triggering logic reaction for sequential biological circuits. This research introduces an idea of designing a genetic clock generator by Fourier series based on the genetic oscillators. The authors generalise the design idea using a combination of fundamental sinusoidal signals. Since biochemical reaction of the biological system is extremely slow, however, transition between minimal and maximal levels is instantaneous for an ideal clock signal; it is thus not directly realisable in biological systems. That means it would be hard to directly synthesize a square wave generator for use as a genetic clock. They apply Fourier series to represent a square wave as a finite summation of sinusoidal waves generated by some genetic oscillators with different harmonic oscillating frequencies, in which the amplitude alternates at a constant frequency between the fixed minimal and maximal levels with the same duration of time.

A multi-scale model of hepcidin promoter regulation reveals factors controlling systemic iron homeostasis

Systemic iron homeostasis involves a negative feedback circuit in which the expression level of the peptide hormone hepcidin depends on and controls the iron blood levels. Hepcidin expression is regulated by the BMP6/SMAD and IL6/STAT signaling cascades. Deregulation of either pathway causes iron-related diseases such as hemochromatosis or anemia of inflammation. We quantitatively analyzed how BMP6 and IL6 control hepcidin expression. Transcription factor (TF) phosphorylation and reporter gene expression were measured under co-stimulation conditions, and the promoter was perturbed by mutagenesis. Using mathematical modeling, we systematically analyzed potential mechanisms of cooperative and competitive promoter regulation by the transcription factors, and experimentally validated the model predictions. Our results reveal that hepcidin cross-regulation primarily occurs by combinatorial transcription factor binding to the promoter, whereas signaling crosstalk is insignificant. We find that the presence of two BMP-responsive elements enhances the steepness of the promoter response towards the iron-sensing BMP signaling axis, which promotes iron homeostasis in vivo. IL6 co-stimulation reduces the promoter sensitivity towards the BMP signal, because the SMAD and STAT transcription factors compete for recruiting RNA polymerase to the transcription start site. This may explain why inflammatory signals disturb iron homeostasis in anemia of inflammation. Taken together, our results reveal why the iron homeostasis circuit is sensitive to perturbations implicated in disease.

The nutritional iron uptake is tightly regulated because the body has limited capacity of iron excretion. Mammals maintain iron homeostasis by a negative feedback loop, in which the peptide hepcidin senses the iron blood level and controls iron resorption. Molecular perturbations in the homeostasis loop lead to iron-related diseases such as hemochromatosis or anemia of inflammation. Quantitative studies are required to understand the dynamics of the iron homeostasis circuitry in health and disease. We investigated how the biological activity of hepcidin is regulated by combining experiments with mathematical modeling. We present a multi-scale model that describes the signaling network and the gene promoter controlling hepcidin expression. Possible scenarios of hepcidin regulation were systematically tested against experimental data, and interpreted using a network model of iron metabolism in vivo. The analysis showed that the presence of multiple redundant regulatory elements in the hepcidin gene promoter facilitates homeostasis, because changes in iron blood levels are sensed with high sensitivity. We further suggest that inflammatory signals establish molecular competition at the hepcidin promoter, thereby reducing its iron sensitivity and leading to a loss of homeostasis in anemia of inflammation. We conclude that quantitative insights into hepcidin expression regulation explain features of systemic iron homeostasis.

Statistical mechanical model of coupled transcription from multiple promoters due to transcription factor titration

Transcription factors (TFs) with regulatory action at multiple promoter targets is the rule rather than the exception, with examples ranging from the cAMP receptor protein (CRP) in E. coli that regulates hundreds of different genes simultaneously to situations involving multiple copies of the same gene, such as plasmids, retrotransposons, or highly replicated viral DNA. When the number of TFs heavily exceeds the number of binding sites, TF binding to each promoter can be regarded as independent. However, when the number of TF molecules is comparable to the number of binding sites, TF titration will result in correlation ("promoter entanglement") between transcription of different genes. We develop a statistical mechanical model which takes the TF titration effect into account and use it to predict both the level of gene expression for a general set of promoters and the resulting correlation in transcription rates of different genes. Our results show that the TF titration effect could be important for understanding gene expression in many regulatory settings.

Time-scale separation--Michaelis and Menten's old idea, still bearing fruit

Michaelis and Menten introduced to biochemistry the idea of time-scale separation, in which part of a system is assumed to be operating sufficiently fast compared to the rest so that it may be taken to have reached a steady state. This allows, in principle, the fast components to be eliminated, resulting in a simplified description of the system's behaviour. Similar ideas have been widely used in different areas of biology, including enzyme kinetics, protein allostery, receptor pharmacology, gene regulation and post-translational modification. However, the methods used have been independent and ad hoc. In the present study, we review the use of time-scale separation as a means to simplify the description of molecular complexity and discuss recent work setting out a single framework that unifies these separate calculations. The framework offers new capabilities for mathematical analysis and helps to do justice to Michaelis and Menten's insights about individual enzymes in the context of multi-enzyme biological systems.

Understanding variation in transcription factor binding by modeling transcription factor genome-epigenome interactions

Despite explosive growth in genomic datasets, the methods for studying epigenomic mechanisms of gene regulation remain primitive. Here we present a model-based approach to systematically analyze the epigenomic functions in modulating transcription factor-DNA binding. Based on the first principles of statistical mechanics, this model considers the interactions between epigenomic modifications and a cis-regulatory module, which contains multiple binding sites arranged in any configurations. We compiled a comprehensive epigenomic dataset in mouse embryonic stem (mES) cells, including DNA methylation (MeDIP-seq and MRE-seq), DNA hydroxymethylation (5-hmC-seq), and histone modifications (ChIP-seq). We discovered correlations of transcription factors (TFs) for specific combinations of epigenomic modifications, which we term epigenomic motifs. Epigenomic motifs explained why some TFs appeared to have different DNA binding motifs derived from in vivo (ChIP-seq) and in vitro experiments. Theoretical analyses suggested that the epigenome can modulate transcriptional noise and boost the cooperativity of weak TF binding sites. ChIP-seq data suggested that epigenomic boost of binding affinities in weak TF binding sites can function in mES cells. We showed in theory that the epigenome should suppress the TF binding differences on SNP-containing binding sites in two people. Using personal data, we identified strong associations between H3K4me2/H3K9ac and the degree of personal differences in NFκB binding in SNP-containing binding sites, which may explain why some SNPs introduce much smaller personal variations on TF binding than other SNPs. In summary, this model presents a powerful approach to analyze the functions of epigenomic modifications. This model was implemented into an open source program APEG (Affinity Prediction by Epigenome and Genome, http://systemsbio.ucsd.edu/apeg).

Discrimination between thermodynamic models of cis-regulation using transcription factor occupancy data

Many studies have identified binding preferences for transcription factors (TFs), but few have yielded predictive models of how combinations of transcription factor binding sites generate specific levels of gene expression. Synthetic promoters have emerged as powerful tools for generating quantitative data to parameterize models of combinatorial cis-regulation. We sought to improve the accuracy of such models by quantifying the occupancy of TFs on synthetic promoters in vivo and incorporating these data into statistical thermodynamic models of cis-regulation. Using chromatin immunoprecipitation-seq, we measured the occupancy of Gcn4 and Cbf1 in synthetic promoter libraries composed of binding sites for Gcn4, Cbf1, Met31/Met32 and Nrg1. We measured the occupancy of these two TFs and the expression levels of all promoters in two growth conditions. Models parameterized using only expression data predicted expression but failed to identify several interactions between TFs. In contrast, models parameterized with occupancy and expression data predicted expression data, and also revealed Gcn4 self-cooperativity and a negative interaction between Gcn4 and Nrg1. Occupancy data also allowed us to distinguish between competing regulatory mechanisms for the factor Gcn4. Our framework for combining occupancy and expression data produces predictive models that better reflect the mechanisms underlying combinatorial cis-regulation of gene expression.

DNA sequence-dependent mechanics and protein-assisted bending in repressor-mediated loop formation

As the chief informational molecule of life, DNA is subject to extensive physical manipulations. The energy required to deform double-helical DNA depends on sequence, and this mechanical code of DNA influences gene regulation, such as through nucleosome positioning. Here we examine the sequence-dependent flexibility of DNA in bacterial transcription factor-mediated looping, a context for which the role of sequence remains poorly understood. Using a suite of synthetic constructs repressed by the Lac repressor and two well-known sequences that show large flexibility differences in vitro, we make precise statistical mechanical predictions as to how DNA sequence influences loop formation and test these predictions using in vivo transcription and in vitro single-molecule assays. Surprisingly, sequence-dependent flexibility does not affect in vivo gene regulation. By theoretically and experimentally quantifying the relative contributions of sequence and the DNA-bending protein HU to DNA mechanical properties, we reveal that bending by HU dominates DNA mechanics and masks intrinsic sequence-dependent flexibility. Such a quantitative understanding of how mechanical regulatory information is encoded in the genome will be a key step towards a predictive understanding of gene regulation at single-base pair resolution.

Design of synthetic biological logic circuits based on evolutionary algorithm

The construction of an artificial biological logic circuit using systematic strategy is recognised as one of the most important topics for the development of synthetic biology. In this study, a real-structured genetic algorithm (RSGA), which combines general advantages of the traditional real genetic algorithm with those of the structured genetic algorithm, is proposed to deal with the biological logic circuit design problem. A general model with the cis-regulatory input function and appropriate promoter activity functions is proposed to synthesise a wide variety of fundamental logic gates such as NOT, Buffer, AND, OR, NAND, NOR and XOR. The results obtained can be extended to synthesise advanced combinational and sequential logic circuits by topologically distinct connections. The resulting optimal design of these logic gates and circuits are established via the RSGA. The in silico computer-based modelling technology has been verified showing its great advantages in the purpose.

Stochasticity, bistability and the wisdom of crowds: a model for associative learning in genetic regulatory networks

It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations, a power that is substantially enhanced when these cells form a population.

Cross talk and interference enhance information capacity of a signaling pathway

A recurring motif in gene regulatory networks is transcription factors (TFs) that regulate each other and then bind to overlapping sites on DNA, where they interact and synergistically control transcription of a target gene. Here, we suggest that this motif maximizes information flow in a noisy network. Gene expression is an inherently noisy process due to thermal fluctuations and the small number of molecules involved. A consequence of multiple TFs interacting at overlapping binding sites is that their binding noise becomes correlated. Using concepts from information theory, we show that in general a signaling pathway transmits more information if 1), noise of one input is correlated with that of the other; and 2), input signals are not chosen independently. In the case of TFs, the latter criterion hints at upstream cross-regulation. We demonstrate these ideas for competing TFs and feed-forward gene-regulatory modules, and discuss generalizations to other signaling pathways. Our results challenge the conventional approach of treating biological noise as uncorrelated fluctuations, and present a systematic method for understanding TF cross-regulation networks either from direct measurements of binding noise or from bioinformatic analysis of overlapping binding sites.

FOXO transcription factors control E2F1 transcriptional specificity and apoptotic function

The transcription factor E2F1 is a key regulator of proliferation and apoptosis but the molecular mechanisms that mediate these cell fate decisions remain unclear. Here, we identify FOXO transcription factors as E2F1 target genes that act in a feed-forward regulatory loop to reinforce gene induction of multiple apoptotic genes. We found that E2F1 forms a complex with FOXO1 and FOXO3. RNAi-mediated silencing of FOXO impaired E2F1 binding to the promoters of cooperative target genes. A FOXO3 mutant insensitive to inactivation by survival kinases rescued the inhibitory effect of growth factor signaling on E2F1-mediated transcription and apoptosis. The E2F1/FOXO axis is frequently blocked in cancer, as evidenced by the specific downregulation of the FOXO-dependent E2F1 transcriptional program in multiple cancer types and by the association of a reduced E2F1/FOXO transcriptional program with poor prognosis. HDAC and phosphoinositide 3-kinase (PI3K) inhibitors were identified as specific activators of E2F1/FOXO transcription, acting to enhance E2F1-induced apoptosis in a FOXO3-dependent manner. Notably, combining the histone deacetylase inhibitor vorinostat with a PI3K inhibitor led to enhanced FOXO-dependent apoptosis. Collectively, our results identify E2F1/FOXO cooperation as a regulatory mechanism that places E2F1 apoptotic activity under the control of survival signaling. Therapeutic reactivation of this tumor suppressive mechanism may offer a novel broad-acting therapy for cancer.

The evolution of complex gene regulation by low-specificity binding sites

Requirements for gene regulation vary widely both within and among species. Some genes are constitutively expressed, whereas other genes require complex regulatory control. Transcriptional regulation is often controlled by a module of multiple transcription factor binding sites that, in combination, mediate the expression of a target gene. Here, we study how such regulatory modules evolve in response to natural selection. Using a population-genetic model, we show that complex regulatory modules which contain a larger number of binding sites must employ binding motifs that are less specific, on average, compared with smaller regulatory modules. This effect is extremely general, and it holds regardless of the selected binding logic that a module experiences. We attribute this phenomenon to the inability of stabilizing selection to maintain highly specific sites in large regulatory modules. Our analysis helps to explain broad empirical trends in the Saccharomyces cerevisiae regulatory network: those genes with a greater number of distinct transcriptional regulators feature less-specific binding motifs, compared with genes with fewer regulators. Our results also help to explain empirical trends in module size and motif specificity across species, ranging from prokaryotes to single-cellular and multi-cellular eukaryotes.

DNA-binding-protein inhomogeneity in E. coli modeled as biphasic facilitated diffusion

We have recently shown that nonspecifically bound lac repressors are spatially inhomogeneous in E. coli cells and depends upon the location of its encoding gene and the DNA compaction state [Kuhlman and Cox, Mol. Syst. Biol. 8, 610 (2012)]. Here we model this inhomogeneity as a consequence of diffusion within and exchange between two distinct intracellular phases: the condensed chromosomal DNA and an extrachromosomal compartment, the cytoplasm. We discuss the consequences of this model for the target search process.

Propagation of genetic variation in gene regulatory networks

A future quantitative genetics theory should link genetic variation to phenotypic variation in a causally cohesive way based on how genes actually work and interact. We provide a theoretical framework for predicting and understanding the manifestation of genetic variation in haploid and diploid regulatory networks with arbitrary feedback structures and intra-locus and inter-locus functional dependencies. Using results from network and graph theory, we define propagation functions describing how genetic variation in a locus is propagated through the network, and show how their derivatives are related to the network's feedback structure. Similarly, feedback functions describe the effect of genotypic variation of a locus on itself, either directly or mediated by the network. A simple sign rule relates the sign of the derivative of the feedback function of any locus to the feedback loops involving that particular locus. We show that the sign of the phenotypically manifested interaction between alleles at a diploid locus is equal to the sign of the dominant feedback loop involving that particular locus, in accordance with recent results for a single locus system. Our results provide tools by which one can use observable equilibrium concentrations of gene products to disclose structural properties of the network architecture. Our work is a step towards a theory capable of explaining the pleiotropy and epistasis features of genetic variation in complex regulatory networks as functions of regulatory anatomy and functional location of the genetic variation.

Computational identification of diverse mechanisms underlying transcription factor-DNA occupancy

ChIP-based genome-wide assays of transcription factor (TF) occupancy have emerged as a powerful, high-throughput method to understand transcriptional regulation, especially on a global scale. This has led to great interest in the underlying biochemical mechanisms that direct TF-DNA binding, with the ultimate goal of computationally predicting a TF's occupancy profile in any cellular condition. In this study, we examined the influence of various potential determinants of TF-DNA binding on a much larger scale than previously undertaken. We used a thermodynamics-based model of TF-DNA binding, called “STAP,” to analyze 45 TF-ChIP data sets from Drosophila embryonic development. We built a cross-validation framework that compares a baseline model, based on the ChIP'ed (“primary”) TF's motif, to more complex models where binding by secondary TFs is hypothesized to influence the primary TF's occupancy. Candidates interacting TFs were chosen based on RNA-SEQ expression data from the time point of the ChIP experiment. We found widespread evidence of both cooperative and antagonistic effects by secondary TFs, and explicitly quantified these effects. We were able to identify multiple classes of interactions, including (1) long-range interactions between primary and secondary motifs (separated by ≤150 bp), suggestive of indirect effects such as chromatin remodeling, (2) short-range interactions with specific inter-site spacing biases, suggestive of direct physical interactions, and (3) overlapping binding sites suggesting competitive binding. Furthermore, by factoring out the previously reported strong correlation between TF occupancy and DNA accessibility, we were able to categorize the effects into those that are likely to be mediated by the secondary TF's effect on local accessibility and those that utilize accessibility-independent mechanisms. Finally, we conducted in vitro pull-down assays to test model-based predictions of short-range cooperative interactions, and found that seven of the eight TF pairs tested physically interact and that some of these interactions mediate cooperative binding to DNA.

Chromatin Immunoprecipitation (ChIP)-based genome-wide assays of transcription factor (TF) occupancy have emerged as a powerful, high throughput method to understand transcriptional regulation, especially on a global scale. Here, we utilize 45 ChIP-chip and ChIP-SEQ data sets from Drosophila to explore the underlying mechanisms of TF-DNA binding. For this, we employ a biophysically motivated computational model, in conjunction with over 300 TF motifs (binding specificities) as well as gene expression and DNA accessibility data from different developmental stages in Drosophila embryos. Our findings provide robust statistical evidence of the role played by TF-TF interactions in shaping genome-wide TF-DNA binding profiles, and thus in directing gene regulation. Our method allows us to go beyond simply recognizing the existence of such interactions, to quantifying their effects on TF occupancy. We are able to categorize the probable mechanisms of these effects as involving direct physical interactions versus accessibility-mediated indirect interactions, long-range versus short-range interactions, and cooperative versus antagonistic interactions. Our analysis reveals widespread evidence of combinatorial regulation present in recently generated ChIP data sets, and sets the stage for rich integrative models of the future that will predict cell type-specific TF occupancy values from sequence and expression data.

Biological signal processing with a genetic toggle switch

Complex gene regulation requires responses that depend not only on the current levels of input signals but also on signals received in the past. In digital electronics, logic circuits with this property are referred to as sequential logic, in contrast to the simpler combinatorial logic without such internal memory. In molecular biology, memory is implemented in various forms such as biochemical modification of proteins or multistable gene circuits, but the design of the regulatory interface, which processes the input signals and the memory content, is often not well understood. Here, we explore design constraints for such regulatory interfaces using coarse-grained nonlinear models and stochastic simulations of detailed biochemical reaction networks. We test different designs for biological analogs of the most versatile memory element in digital electronics, the JK-latch. Our analysis shows that simple protein-protein interactions and protein-DNA binding are sufficient, in principle, to implement genetic circuits with the capabilities of a JK-latch. However, it also exposes fundamental limitations to its reliability, due to the fact that biological signal processing is asynchronous, in contrast to most digital electronics systems that feature a central clock to orchestrate the timing of all operations. We describe a seemingly natural way to improve the reliability by invoking the master-slave concept from digital electronics design. This concept could be useful to interpret the design of natural regulatory circuits, and for the design of synthetic biological systems.

Global parameter estimation for thermodynamic models of transcriptional regulation

Deciphering the mechanisms involved in gene regulation holds the key to understanding the control of central biological processes, including human disease, population variation, and the evolution of morphological innovations. New experimental techniques including whole genome sequencing and transcriptome analysis have enabled comprehensive modeling approaches to study gene regulation. In many cases, it is useful to be able to assign biological significance to the inferred model parameters, but such interpretation should take into account features that affect these parameters, including model construction and sensitivity, the type of fitness calculation, and the effectiveness of parameter estimation. This last point is often neglected, as estimation methods are often selected for historical reasons or for computational ease. Here, we compare the performance of two parameter estimation techniques broadly representative of local and global approaches, namely, a quasi-Newton/Nelder-Mead simplex (QN/NMS) method and a covariance matrix adaptation-evolutionary strategy (CMA-ES) method. The estimation methods were applied to a set of thermodynamic models of gene transcription applied to regulatory elements active in the Drosophila embryo. Measuring overall fit, the global CMA-ES method performed significantly better than the local QN/NMS method on high quality data sets, but this difference was negligible on lower quality data sets with increased noise or on data sets simplified by stringent thresholding. Our results suggest that the choice of parameter estimation technique for evaluation of gene expression models depends both on quality of data, the nature of the models [again, remains to be established] and the aims of the modeling effort.

The biological microprocessor, or how to build a computer with biological parts

Systemics, a revolutionary paradigm shift in scientific thinking, with applications in systems biology, and synthetic biology, have led to the idea of using silicon computers and their engineering principles as a blueprint for the engineering of a similar machine made from biological parts. Here we describe these building blocks and how they can be assembled to a general purpose computer system, a biological microprocessor. Such a system consists of biological parts building an input / output device, an arithmetic logic unit, a control unit, memory, and wires (busses) to interconnect these components. A biocomputer can be used to monitor and control a biological system.

Temporal expression program of quorum sensing-based transcription regulation in Sinorhizobium meliloti

The Sin quorum sensing (QS) system of S. meliloti activates exopolysaccharide and represses flagellum production. The system consists of an N-acyl-homoserine lactone (AHL) synthase, SinI, and at least two LuxR-type regulators, SinR and ExpR. SinR appears to be independent of AHLs for its control of sinI expression, while ExpR is almost completely dependent upon AHLs. In this study, we confirmed 7 previously detected ExpR-DNA binding sites and used the consensus sequence to identify another 26 sites, some of which regulate genes previously not known to be members of the ExpR/AHL regulon. The activities of promoters dependent upon ExpR/AHL were titrated against AHL levels, with varied outcomes in AHL sensitivity. The data suggest a type of temporal expression program whereby the activity of each promoter is subject to a specific range of AHL concentrations. For example, genes responsible for exopolysaccharide production are activated at lower concentrations of AHLs than those required for the repression of genes controlling flagellum production. Several features of ExpR-regulated promoters appear to determine their response to AHLs. The location of the ExpR-binding site with respect to the relevant transcription start within each promoter region determines whether ExpR/AHL activates or represses promoter activity. Furthermore, the strength of the response is dependent upon the concentration of AHLs. We propose that this differential sensitivity to AHLs provides a bacterial colony with a transcription control program that is dynamic and precise.

A primer on thermodynamic-based models for deciphering transcriptional regulatory logic

A rigorous analysis of transcriptional regulation at the DNA level is crucial to the understanding of many biological systems. Mathematical modeling has offered researchers a new approach to understanding this central process. In particular, thermodynamic-based modeling represents the most biophysically informed approach aimed at connecting DNA level regulatory sequences to the expression of specific genes. The goal of this review is to give biologists a thorough description of the steps involved in building, analyzing, and implementing a thermodynamic-based model of transcriptional regulation. The data requirements for this modeling approach are described, the derivation for a specific regulatory region is shown, and the challenges and future directions for the quantitative modeling of gene regulation are discussed.

Evaluating thermodynamic models of enhancer activity on cellular resolution gene expression data

With the advent of high throughput sequencing and high resolution transcriptomic technologies, there exists today an unprecedented opportunity to understand gene regulation at a quantitative level. State of the art models of the relationship between regulatory sequence and gene expression have shown great promise, but also suffer from some major shortcomings. In this paper, we identify and address methodological challenges pertaining to quantitative modeling of gene expression from sequence, and test our models on the anterior-posterior patterning system in the Drosophila embryo. We first develop a framework to process cellular resolution three-dimensional gene expression data from the Drosophila embryo and create data sets on which quantitative models can be trained. Next we propose a new score, called 'weighted pattern generating potential' (w-PGP), to evaluate model predictions, and show its advantages over the two most common scoring schemes in use today. The model building exercise uses w-PGP as the evaluation score and adopts a systematic strategy to increase a model's complexity while guarding against over-fitting. Our model identifies three transcription factors--ZELDA, SLOPPY-PAIRED, and NUBBIN--that have not been previously incorporated in quantitative models of this system, as having significant regulatory influence. Finally, we show how fitting quantitative models on data sets comprising a handful of enhancers, as reported in earlier work, may lead to unreliable models.

Dissecting specific and global transcriptional regulation of bacterial gene expression

Gene expression is regulated by specific transcriptional circuits but also by the global expression machinery as a function of growth. Simultaneous specific and global regulation thus constitutes an additional--but often neglected--layer of complexity in gene expression. Here, we develop an experimental-computational approach to dissect specific and global regulation in the bacterium Escherichia coli. By using fluorescent promoter reporters, we show that global regulation is growth rate dependent not only during steady state but also during dynamic changes in growth rate and can be quantified through two promoter-specific parameters. By applying our approach to arginine biosynthesis, we obtain a quantitative understanding of both specific and global regulation that allows accurate prediction of the temporal response to simultaneous perturbations in arginine availability and growth rate. We thereby uncover two principles of joint regulation: (i) specific regulation by repression dominates the transcriptional response during metabolic steady states, largely repressing the biosynthesis genes even when biosynthesis is required and (ii) global regulation sets the maximum promoter activity that is exploited during the transition between steady states.

Design principles of regulatory networks: searching for the molecular algorithms of the cell

A challenge in biology is to understand how complex molecular networks in the cell execute sophisticated regulatory functions. Here we explore the idea that there are common and general principles that link network structures to biological functions, principles that constrain the design solutions that evolution can converge upon for accomplishing a given cellular task. We describe approaches for classifying networks based on abstract architectures and functions, rather than on the specific molecular components of the networks. For any common regulatory task, can we define the space of all possible molecular solutions? Such inverse approaches might ultimately allow the assembly of a design table of core molecular algorithms that could serve as a guide for building synthetic networks and modulating disease networks.

Taking into account nucleosomes for predicting gene expression

The eukaryotic genome is organized in a chain of nucleosomes that consist of 145-147 bp of DNA wrapped around a histone octamer protein core. Binding of transcription factors (TF) to nucleosomal DNA is frequently impeded, which makes it a challenging task to calculate TF occupancy at a given regulatory genomic site for predicting gene expression. Here, we review methods to calculate TF binding to DNA in the presence of nucleosomes. The main theoretical problems are (i) the computation speed that is becoming a bottleneck when partial unwrapping of DNA from the nucleosome is considered, (ii) the perturbation of the binding equilibrium by the activity of ATP-dependent chromatin remodelers, which translocate nucleosomes along the DNA, and (iii) the model parameterization from high-throughput sequencing data and fluorescence microscopy experiments in living cells. We discuss strategies that address these issues to efficiently compute transcription factor binding in chromatin.

Online learning in a chemical perceptron

Autonomous learning implemented purely by means of a synthetic chemical system has not been previously realized. Learning promotes reusability and minimizes the system design to simple input-output specification. In this article we introduce a chemical perceptron, the first full-featured implementation of a perceptron in an artificial (simulated) chemistry. A perceptron is the simplest system capable of learning, inspired by the functioning of a biological neuron. Our artificial chemistry is deterministic and discrete-time, and follows Michaelis-Menten kinetics. We present two models, the weight-loop perceptron and the weight-race perceptron, which represent two possible strategies for a chemical implementation of linear integration and threshold. Both chemical perceptrons can successfully identify all 14 linearly separable two-input logic functions and maintain high robustness against rate-constant perturbations. We suggest that DNA strand displacement could, in principle, provide an implementation substrate for our model, allowing the chemical perceptron to perform reusable, programmable, and adaptable wet biochemical computing.

Statistical mechanics of Monod-Wyman-Changeux (MWC) models

The 50th anniversary of the classic Monod-Wyman-Changeux (MWC) model provides an opportunity to survey the broader conceptual and quantitative implications of this quintessential biophysical model. With the use of statistical mechanics, the mathematical implementation of the MWC concept links problems that seem otherwise to have no ostensible biological connection including ligand-receptor binding, ligand-gated ion channels, chemotaxis, chromatin structure and gene regulation. Hence, a thorough mathematical analysis of the MWC model can illuminate the performance limits of a number of unrelated biological systems in one stroke. The goal of our review is twofold. First, we describe in detail the general physical principles that are used to derive the activity of MWC molecules as a function of their regulatory ligands. Second, we illustrate the power of ideas from information theory and dynamical systems for quantifying how well the output of MWC molecules tracks their sensory input, giving a sense of the "design" constraints faced by these receptors.

Using topology to tame the complex biochemistry of genetic networks

Living cells are controlled by networks of interacting genes, proteins and biochemicals. Cells use the emergent collective dynamics of these networks to probe their surroundings, perform computations and generate appropriate responses. Here, we consider genetic networks, interacting sets of genes that regulate one another's expression. It is possible to infer the interaction topology of genetic networks from high-throughput experimental measurements. However, such experiments rarely provide information on the detailed nature of each interaction. We show that topological approaches provide powerful means of dealing with the missing biochemical data. We first discuss the biochemical basis of gene regulation, and describe how genes can be connected into networks. We then show that, given weak constraints on the underlying biochemistry, topology alone determines the emergent properties of certain simple networks. Finally, we apply these approaches to the realistic example of quorum-sensing networks: chemical communication systems that coordinate the responses of bacterial populations.