Stochastic dynamics of macromolecular-assembly networks

The unreasonable effectiveness of equilibrium gene regulation through the cell cycle

Systems like the prototypical lac operon can reliably hold repression of transcription upon DNA replication across cell cycles with just 10 repressor molecules per cell and behave as if they were at equilibrium. The origin of this phenomenology is still an unresolved question. Here, we develop a general theory to analyze strong perturbations in quasi-equilibrium systems and use it to quantify the effects of DNA replication in gene regulation. We find a scaling law linking actual with predicted equilibrium transcription via a single kinetic parameter. We show that even the lac operon functions beyond the physical limits of naive regulation through compensatory mechanisms that suppress non-equilibrium effects. Synthetic systems without adjuvant activators, such as the cAMP receptor protein (CRP), lack this reliability. Our results provide a rationale for the function of CRP, beyond just being a tunable activator, as a mitigator of cell cycle perturbations.

Modeling reveals the strength of weak interactions in stacked-ring assembly

Cells employ many large macromolecular machines for the execution and regulation of processes that are vital for cell and organismal viability. Interestingly, cells cannot synthesize these machines as functioning units. Instead, cells synthesize the molecular parts that must then assemble into the functional complex. Many important machines, including chaperones such as GroEL and proteases such as the proteasome, comprise protein rings that are stacked on top of one another. While there is some experimental data regarding how stacked-ring complexes such as the proteasome self-assemble, a comprehensive understanding of the dynamics of stacked-ring assembly is currently lacking. Here, we developed a mathematical model of stacked-trimer assembly and performed an analysis of the assembly of the stacked homomeric trimer, which is the simplest stacked-ring architecture. We found that stacked rings are particularly susceptible to a form of kinetic trapping that we term "deadlock," in which the system gets stuck in a state where there are many large intermediates that are not the fully assembled structure but that cannot productively react. When interaction affinities are uniformly strong, deadlock severely limits assembly yield. We thus predicted that stacked rings would avoid situations where all interfaces in the structure have high affinity. Analysis of available crystal structures indicated that indeed the majority-if not all-of stacked trimers do not contain uniformly strong interactions. Finally, to better understand the origins of deadlock, we developed a formal pathway analysis and showed that, when all the binding affinities are strong, many of the possible pathways are utilized. In contrast, optimal assembly strategies utilize only a small number of pathways. Our work suggests that deadlock is a critical factor influencing the evolution of macromolecular machines and provides general principles for understanding the self-assembly efficiency of existing machines.

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.

It is time to crowd your cell culture media - Physicochemical considerations with biological consequences

In vivo, the interior and exterior of cells is populated by various macromolecules that create an extremely crowded milieu. Yet again, in vitro eukaryotic cell culture is conducted in dilute culture media that hardly imitate the native tissue density. Herein, the concept of macromolecular crowding is discussed in both intracellular and extracellular context. Particular emphasis is given on how the physicochemical properties of the crowding molecules govern and determine kinetics, equilibria and mechanism of action of biochemical and biological reactions, processes and functions. It is evidenced that we are still at the beginning of appreciating, let alone effectively implementing, the potential of macromolecular crowding in permanently differentiated and stem cell culture systems.

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.

Extraction and Refolding Determinants of Chaperone-Driven Aggregated Protein Reactivation

Reactivation of protein aggregates plays a fundamental role in numerous situations, including essential cellular processes, hematological and neurological disorders, and biotechnological applications. The molecular details of the chaperone systems involved are known to a great extent but how the overall reactivation process is achieved has remained unclear. Here, we quantified reactivation over time through a predictive mechanistic model and identified the key parameters that control the overall dynamics. We performed new targeted experiments and analyzed classical data, covering multiple types of non-ordered aggregates, chaperone combinations, and experimental conditions. We found that, irrespective of the behavior observed, the balance of surface disaggregation and refolding in solution universally determines the reactivation dynamics, which is broadly described by two characteristic times. This characterization makes it possible to use activity measurements to accurately infer the underlying loss of aggregated protein and to quantify, for the first time, the refolding rates of the soluble intermediates.

Mathematical modeling identifies potential gene structure determinants of co-transcriptional control of alternative pre-mRNA splicing

The spliceosome catalyzes the removal of introns from pre-messenger RNA (mRNA) and subsequent pairing of exons with remarkable fidelity. Some exons are known to be skipped or included in the mature mRNA in a cell type- or context-dependent manner (cassette exons), thereby contributing to the diversification of the human proteome. Interestingly, splicing is initiated (and sometimes completed) co-transcriptionally. Here, we develop a kinetic mathematical modeling framework to investigate alternative co-transcriptional splicing (CTS) and, specifically, the control of cassette exons' inclusion. We show that when splicing is co-transcriptional, default splice patterns of exon inclusion are more likely than when splicing is post-transcriptional, and that certain exons are more likely to be regulatable (i.e. cassette exons) than others, based on the exon-intron structure context. For such regulatable exons, transcriptional elongation rates may affect splicing outcomes. Within the CTS paradigm, we examine previously described hypotheses of co-operativity between splice sites of short introns (i.e. 'intron definition') or across short exons (i.e. 'exon definition'), and find that models encoding these faithfully recapitulate observations in the fly and human genomes, respectively.

Specifically bound lambda repressor dimers promote adjacent non-specific binding

Genetic switches frequently include DNA loops secured by proteins. Recent studies of the lambda bacteriophage repressor (CI), showed that this arrangement in which the protein links two sets of three operators separated by approximately 2.3 kbp, optimizes both the stability and dynamics of DNA loops, compared to an arrangement with just two sets of two operators. Because adjacent dimers interact pairwise, we hypothesized that the odd number of operators in each set of the lambda regulatory system might have evolved to allow for semi-specific, pair-wise interactions that add stability to the loop while maintaining it dynamic. More generally, additional CI dimers may bind non-specifically to flanking DNA sequences making the genetic switch more sensitive to CI concentration. Here, we tested this hypothesis using spectroscopic and imaging approaches to study the binding of the lambda repressor (CI) dimer protein to DNA fragments. For fragments with only one operator and a short flanking sequence, fluorescence correlation spectroscopy measurements clearly indicated the presence of two distinct DNA-CI complexes; one is thought to have a non-specifically bound CI dimer on the flanking sequence. Scanning force micrographs of CI bound to DNA with all six operators revealed wild-type or mutant proteins bound at operator positions. The number of bound, wild-type proteins increased with CI concentration and was larger than expected for strictly specific binding to operators. In contrast, a mutant that fails to oligomerize beyond a dimer, D197G, only bound to operators. These data are evidence that CI cooperativity promotes oligomerization that extends from operator sites to influence the thermodynamics and kinetics of CI-mediated looping.

A general model for predicting the binding affinity of reversibly and irreversibly dimerized ligands

Empirical data has shown that bivalent inhibitors can bind a given target protein significantly better than their monomeric counterparts. However, predicting the corresponding theoretical fold improvements has been challenging. The current work builds off the reacted-site probability approach to provide a straightforward baseline reference model for predicting fold-improvements in effective affinity of dimerized ligands over their monomeric counterparts. For the more familiar irreversibly linked bivalents, the model predicts a weak dependence on tether length and a scaling of the effective affinity with the 3/2 power of the monomer’s affinity. For the previously untreated case of the emerging technology of reversibly linking dimers, the effective affinity is also significantly improved over the affinity of the non-dimerizing monomers. The model is related back to experimental quantities, such as EC₅₀s, and the approaches to fully characterize the system given the assumptions of the model. Because of the predicted significant potency gains, both irreversibly and reversibly linked bivalent ligands offer the potential to be a disruptive technology in pharmaceutical research.

Modular Organization of Residue-Level Contacts Shapes the Selection Pressure on Individual Amino Acid Sites of Ribosomal Proteins

Understanding the molecular evolution of macromolecular complexes in the light of their structure, assembly, and stability is of central importance. Here, we address how the modular organization of native molecular contacts shapes the selection pressure on individual residue sites of ribosomal complexes. The bacterial ribosomal complex is represented as a residue contact network where nodes represent amino acid/nucleotide residues and edges represent their van der Waals interactions. We find statistically overrepresented native amino acid-nucleotide contacts (OaantC, one amino acid contacts one or multiple nucleotides, internucleotide contacts are disregarded). Contact number is defined as the number of nucleotides contacted. Involvement of individual amino acids in OaantCs with smaller contact numbers is more random, whereas only a few amino acids significantly contribute to OaantCs with higher contact numbers. An investigation of structure, stability, and assembly of bacterial ribosome depicts the involvement of these OaantCs in diverse biophysical interactions stabilizing the complex, including high-affinity protein-RNA contacts, interprotein cooperativity, intersubunit bridge, packing of multiple ribosomal RNA domains, etc. Amino acid-nucleotide constituents of OaantCs with higher contact numbers are generally associated with significantly slower substitution rates compared with that of OaantCs with smaller contact numbers. This evolutionary rate heterogeneity emerges from the strong purifying selection pressure that conserves the respective amino acid physicochemical properties relevant to the stabilizing interaction with OaantC nucleotides. An analysis of relative molecular orientations of OaantC residues and their interaction energetics provides the biophysical ground of purifying selection conserving OaantC amino acid physicochemical properties.

Assembly constraints drive co-evolution among ribosomal constituents

Ribosome biogenesis, a central and essential cellular process, occurs through sequential association and mutual co-folding of protein-RNA constituents in a well-defined assembly pathway. Here, we construct a network of co-evolving nucleotide/amino acid residues within the ribosome and demonstrate that assembly constraints are strong predictors of co-evolutionary patterns. Predictors of co-evolution include a wide spectrum of structural reconstitution events, such as cooperativity phenomenon, protein-induced rRNA reconstitutions, molecular packing of different rRNA domains, protein-rRNA recognition, etc. A correlation between folding rate of small globular proteins and their topological features is known. We have introduced an analogous topological characteristic for co-evolutionary network of ribosome, which allows us to differentiate between rRNA regions subjected to rapid reconstitutions from those hindered by kinetic traps. Furthermore, co-evolutionary patterns provide a biological basis for deleterious mutation sites and further allow prediction of potential antibiotic targeting sites. Understanding assembly pathways of multicomponent macromolecules remains a key challenge in biophysics. Our study provides a 'proof of concept' that directly relates co-evolution to biophysical interactions during multicomponent assembly and suggests predictive power to identify candidates for critical functional interactions as well as for assembly-blocking antibiotic target sites.

Effects of promoter leakage on dynamics of gene expression

Background

Quantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes. As network motifs occurring recurrently in complex biological networks, gene auto-regulatory circuits have been extensively studied but gene expression dynamics remain to be fully understood, e.g., how promoter leakage affects expression noise is unclear.

Results

In this work, we analyze a gene model with auto regulation, where the promoter is assumed to have one active state with highly efficient transcription and one inactive state with very lowly efficient transcription (termed as promoter leakage). We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics. Interestingly, we find that promoter leakage always reduces expression noise and that increasing the leakage rate tends to simplify phenotypes. In addition, higher leakage results in fewer bursts.

Conclusions

Our results reveal the essential role of promoter leakage in controlling expression dynamics and further phenotype. Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0157-z) contains supplementary material, which is available to authorized users.

Maturation of the proteasome core particle induces an affinity switch that controls regulatory particle association

Proteasome assembly is a complex process, requiring 66 subunits distributed over several subcomplexes to associate in a coordinated fashion. Ten proteasome-specific chaperones have been identified that assist in this process. For two of these, the Pba1-Pba2 dimer, it is well established that they only bind immature core particles (CP) in vivo. In contrast, the regulatory particle (RP) utilizes the same binding surface but only interacts with the mature CP in vivo. It is unclear how these binding events are regulated. Here, we show that Pba1-Pba2 binds tightly to immature CP, preventing RP binding. Changes in the CP that occur upon maturation significantly reduce its affinity for Pba1-Pba2, enabling the RP to displace the chaperone. Mathematical modeling indicates that this “affinity switch” mechanism has likely evolved to improve assembly efficiency by preventing the accumulation of stable, non-productive intermediates. Our work thus provides mechanistic insights into a crucial step in proteasome biogenesis.

An assembly funnel makes biomolecular complex assembly efficient

Like protein folding and crystallization, the self-assembly of complexes is a fundamental form of biomolecular organization. While the number of methods for creating synthetic complexes is growing rapidly, most require empirical tuning of assembly conditions and/or produce low yields. We use coarse-grained simulations of the assembly kinetics of complexes to identify generic limitations on yields that arise because of the many simultaneous interactions allowed between the components and intermediates of a complex. Efficient assembly occurs when nucleation is fast and growth pathways are few, i.e. when there is an assembly "funnel". For typical complexes, an assembly funnel occurs in a narrow window of conditions whose location is highly complex specific. However, by redesigning the components this window can be drastically broadened, so that complexes can form quickly across many conditions. The generality of this approach suggests assembly funnel design as a foundational strategy for robust biomolecular complex synthesis.

Suppression and enhancement of transcriptional noise by DNA looping

DNA looping has been observed to enhance and suppress transcriptional noise but it is uncertain which of these two opposite effects is to be expected for given conditions. Here, we derive analytical expressions for the main quantifiers of transcriptional noise in terms of the molecular parameters and elucidate the role of DNA looping. Our results rationalize paradoxical experimental observations and provide the first quantitative explanation of landmark individual-cell measurements at the single molecule level on the classical lac operon genetic system [Choi, L. Cai, K. Frieda, and X. S. Xie, Science 322, 442 (2008)].

Systems biophysics of gene expression

Gene expression is a process central to any form of life. It involves multiple temporal and functional scales that extend from specific protein-DNA interactions to the coordinated regulation of multiple genes in response to intracellular and extracellular changes. This diversity in scales poses fundamental challenges to the use of traditional approaches to fully understand even the simplest gene expression systems. Recent advances in computational systems biophysics have provided promising avenues to reliably integrate the molecular detail of biophysical process into the system behavior. Here, we review recent advances in the description of gene regulation as a system of biophysical processes that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. There is now basic mechanistic understanding on how promoters controlled by multiple, local and distal, DNA binding sites for transcription factors can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including precision and flexibility of the transcriptional responses.

Reliable prediction of complex phenotypes from a modular design in free energy space: an extensive exploration of the lac operon

The basic methodology for designing, altering, and constructing biological systems is increasingly relying on well-established engineering principles to move forward from trial and error approaches to reliably predicting the system behavior from the properties of the components and their interactions. The inherent complexity of even the simplest biological systems, however, often precludes achieving such predictive power. A prototypical example is the lac operon, one of the best-characterized genetic systems, which still poses serious challenges for understanding the results of combining its parts into novel setups. The reason is the pervasive complex hierarchy of events involved in gene regulation that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. Here, we integrate such complexity into a few-parameter model to accurately predict gene expression from a few simple rules to connect the parts. The model accurately reproduces the observed transcriptional activity of the lac operon over a 10,000-fold range for 21 different operator setups, different repressor concentrations, and tetrameric and dimeric forms of the repressor. Incorporation of the calibrated model into more complex scenarios accurately captures the induction curves for key operator configurations and the temporal evolution of the β-galactosidase activity of cell populations.

Machines vs. ensembles: effective MAPK signaling through heterogeneous sets of protein complexes

Despite the importance of intracellular signaling networks, there is currently no consensus regarding the fundamental nature of the protein complexes such networks employ. One prominent view involves stable signaling machines with well-defined quaternary structures. The combinatorial complexity of signaling networks has led to an opposing perspective, namely that signaling proceeds via heterogeneous pleiomorphic ensembles of transient complexes. Since many hypotheses regarding network function rely on how we conceptualize signaling complexes, resolving this issue is a central problem in systems biology. Unfortunately, direct experimental characterization of these complexes has proven technologically difficult, while combinatorial complexity has prevented traditional modeling methods from approaching this question. Here we employ rule-based modeling, a technique that overcomes these limitations, to construct a model of the yeast pheromone signaling network. We found that this model exhibits significant ensemble character while generating reliable responses that match experimental observations. To contrast the ensemble behavior, we constructed a model that employs hierarchical assembly pathways to produce scaffold-based signaling machines. We found that this machine model could not replicate the experimentally observed combinatorial inhibition that arises when the scaffold is overexpressed. This finding provides evidence against the hierarchical assembly of machines in the pheromone signaling network and suggests that machines and ensembles may serve distinct purposes in vivo. In some cases, e.g. core enzymatic activities like protein synthesis and degradation, machines assembled via hierarchical energy landscapes may provide functional stability for the cell. In other cases, such as signaling, ensembles may represent a form of weak linkage, facilitating variation and plasticity in network evolution. The capacity of ensembles to signal effectively will ultimately shape how we conceptualize the function, evolution and engineering of signaling networks.

Intracellular signaling networks are central to a cell's ability to adapt to its environment. Developing the capacity to effectively manipulate such networks would have a wide range of applications, from cancer therapy to synthetic biology. This requires a thorough understanding of the mechanisms of signal transduction, particularly the kinds of protein complexes that are formed during transmission of extracellular information to the nucleus. Traditionally, signaling complexes have been largely perceived (albeit often implicitly) as machine-like structures. However, the number of molecular complexes that could theoretically be formed by complex signaling networks is astronomically large. This has led to the pleiomorphic ensemble hypothesis, which posits that diverse and rapidly changing sets of transient protein complexes can transmit and process information. Our goal was to use computational approaches, specifically rule-based modeling, to test these hypotheses. We constructed a model of the prototypical yeast mating pathway and found significant ensemble-like behavior. Our results thus demonstrated that ensembles can in fact transmit extracellular signals with minimal noise. Additionally, a comparison of this model with one tailored to generate machine-like complexes displayed notable phenotypic differences, revealing potential advantages for ensemble-like signaling. Our demonstration that ensembles can function effectively will have a significant impact on how we conceptualize signaling and other processes inside cells.

Complex dynamics of transcription regulation

Transcription is a tightly regulated cellular function which can be triggered by endogenous (intrinsic) or exogenous (extrinsic) signals. The development of novel techniques to examine the dynamic behavior of transcription factors and the analysis of transcriptional activity at the single cell level with increased temporal resolution has revealed unexpected elements of stochasticity and dynamics of this process. Emerging research reveals a complex picture, wherein a wide range of time scales and temporal transcription patterns overlap to generate transcriptional programs. The challenge now is to develop a perspective that can guide us to common underlying mechanisms, and consolidate these findings. Here we review the recent literature on temporal dynamics and stochastic gene regulation patterns governed by intrinsic or extrinsic signals, utilizing the glucocorticoid receptor (GR)-mediated transcriptional model to illustrate commonality of these emerging concepts. This article is part of a Special Issue entitled: Chromatin in time and space.

The physics of protein-DNA interaction networks in the control of gene expression

Protein-DNA interaction networks play a central role in many fundamental cellular processes. In gene regulation, physical interactions and reactions among the molecular components together with the physical properties of DNA control how genes are turned on and off. A key player in all these processes is the inherent flexibility of DNA, which provides an avenue for long-range interactions between distal DNA elements through DNA looping. Such versatility enables multiple interactions and results in additional complexity that is remarkably difficult to address with traditional approaches. This topical review considers recent advances in statistical physics methods to study the assembly of protein-DNA complexes with loops, their effects in the control of gene expression, and their explicit application to the prototypical lac operon genetic system of the E. coli bacterium. In the last decade, it has been shown that the underlying physical properties of DNA looping can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including the balance between robustness and sensitivity of the induction process. These physical properties are largely dependent on the free energy of DNA looping, which accounts for DNA bending and twisting effects. These new physical methods have also been used in reverse to uncover the actual in vivo free energy of looping double-stranded DNA in living cells, which was not possible with existing experimental techniques. The results obtained for DNA looping by the lac repressor inside the E. coli bacterium showed a more malleable DNA than expected as a result of the interplay of the simultaneous presence of two distinct conformations of looped DNA.

Combinatorial complexity and compositional drift in protein interaction networks

The assembly of molecular machines and transient signaling complexes does not typically occur under circumstances in which the appropriate proteins are isolated from all others present in the cell. Rather, assembly must proceed in the context of large-scale protein-protein interaction (PPI) networks that are characterized both by conflict and combinatorial complexity. Conflict refers to the fact that protein interfaces can often bind many different partners in a mutually exclusive way, while combinatorial complexity refers to the explosion in the number of distinct complexes that can be formed by a network of binding possibilities. Using computational models, we explore the consequences of these characteristics for the global dynamics of a PPI network based on highly curated yeast two-hybrid data. The limited molecular context represented in this data-type translates formally into an assumption of independent binding sites for each protein. The challenge of avoiding the explicit enumeration of the astronomically many possibilities for complex formation is met by a rule-based approach to kinetic modeling. Despite imposing global biophysical constraints, we find that initially identical simulations rapidly diverge in the space of molecular possibilities, eventually sampling disjoint sets of large complexes. We refer to this phenomenon as "compositional drift". Since interaction data in PPI networks lack detailed information about geometric and biological constraints, our study does not represent a quantitative description of cellular dynamics. Rather, our work brings to light a fundamental problem (the control of compositional drift) that must be solved by mechanisms of assembly in the context of large networks. In cases where drift is not (or cannot be) completely controlled by the cell, this phenomenon could constitute a novel source of phenotypic heterogeneity in cell populations.

Optimizing ring assembly reveals the strength of weak interactions

Most cellular processes rely on large multiprotein complexes that must assemble into a well-defined quaternary structure in order to function. A number of prominent examples, including the 20S core particle of the proteasome and the AAA+ family of ATPases, contain ring-like structures. Developing an understanding of the complex assembly pathways employed by ring-like structures requires a characterization of the problems these pathways have had to overcome as they evolved. In this work, we use computational models to uncover one such problem: a deadlocked plateau in the assembly dynamics. When the molecular interactions between subunits are too strong, this plateau leads to significant delays in assembly and a reduction in steady-state yield. Conversely, if the interactions are too weak, assembly delays are caused by the instability of crucial intermediates. Intermediate affinities thus maximize the efficiency of assembly for homomeric ring-like structures. In the case of heteromeric rings, we find that rings including at least one weak interaction can assemble efficiently and robustly. Estimation of affinities from solved structures of ring-like complexes indicates that heteromeric rings tend to contain a weak interaction, confirming our prediction. In addition to providing an evolutionary rationale for structural features of rings, our work forms the basis for understanding the complex assembly pathways of stacked rings like the proteasome and suggests principles that would aid in the design of synthetic ring-like structures that self-assemble efficiently.

Control of gene expression by modulated self-assembly

Numerous transcription factors self-assemble into different order oligomeric species in a way that is actively regulated by the cell. Until now, no general functional role has been identified for this widespread process. Here, we capture the effects of modulated self-assembly in gene expression with a novel quantitative framework. We show that this mechanism provides precision and flexibility, two seemingly antagonistic properties, to the sensing of diverse cellular signals by systems that share common elements present in transcription factors like p53, NF-κB, STATs, Oct and RXR. Applied to the nuclear hormone receptor RXR, this framework accurately reproduces a broad range of classical, previously unexplained, sets of gene expression data and corroborates the existence of a precise functional regime with flexible properties that can be controlled both at a genome-wide scale and at the individual promoter level.

MicroRNAs and the Operon paper

The "Operon paper" by F. Jacob and J. Monod started 50 years of research into understanding how the expression of genes is regulated on a molecular level. Ten years ago, microRNAs (miRNAs) emerged as major regulators of eukaryotic gene expression. Here, I will review the basic principles of gene regulation by miRNAs and how these principles can be linked to insights from the Operon paper. A lot of what is understood about miRNAs required a combination of computational and experimental methods. I will discuss some examples that illustrate the power of this approach.

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, promoter architecture, defined by the number, strength and regulatory role of the operators that control transcription, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect variability in gene expression in a systematic rather than case-by-case fashion. In this article we make such a systematic investigation, based on a microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcriptional output from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can be used to test kinetic models of gene regulation. The emphasis of the discussion is on prokaryotic gene regulation, but our analysis can be extended to eukaryotic cells as well.

Accurate prediction of gene expression by integration of DNA sequence statistics with detailed modeling of transcription regulation

Gene regulation involves a hierarchy of events that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. The effects of DNA sequence on these processes have typically been studied based either on its quantitative connection with single-domain binding free energies or on empirical rules that combine different DNA motifs to predict gene expression trends on a genomic scale. The middle-point approach that quantitatively bridges these two extremes, however, remains largely unexplored. Here, we provide an integrated approach to accurately predict gene expression from statistical sequence information in combination with detailed biophysical modeling of transcription regulation by multidomain binding on multiple DNA sites. For the regulation of the prototypical lac operon, this approach predicts within 0.3-fold accuracy transcriptional activity over a 10,000-fold range from DNA sequence statistics for different intracellular conditions.

Scalable rule-based modelling of allosteric proteins and biochemical networks

Much of the complexity of biochemical networks comes from the information-processing abilities of allosteric proteins, be they receptors, ion-channels, signalling molecules or transcription factors. An allosteric protein can be uniquely regulated by each combination of input molecules that it binds. This “regulatory complexity” causes a combinatorial increase in the number of parameters required to fit experimental data as the number of protein interactions increases. It therefore challenges the creation, updating, and re-use of biochemical models. Here, we propose a rule-based modelling framework that exploits the intrinsic modularity of protein structure to address regulatory complexity. Rather than treating proteins as “black boxes”, we model their hierarchical structure and, as conformational changes, internal dynamics. By modelling the regulation of allosteric proteins through these conformational changes, we often decrease the number of parameters required to fit data, and so reduce over-fitting and improve the predictive power of a model. Our method is thermodynamically grounded, imposes detailed balance, and also includes molecular cross-talk and the background activity of enzymes. We use our Allosteric Network Compiler to examine how allostery can facilitate macromolecular assembly and how competitive ligands can change the observed cooperativity of an allosteric protein. We also develop a parsimonious model of G protein-coupled receptors that explains functional selectivity and can predict the rank order of potency of agonists acting through a receptor. Our methodology should provide a basis for scalable, modular and executable modelling of biochemical networks in systems and synthetic biology.

The complexity of biochemical networks challenges our ability to create quantitative and predictive models of cellular responses to extracellular changes. In these networks, the regulation of allosteric receptors and proteins by multiple drugs or endogenous ligands introduces “regulatory complexity” because a large number of parameters is required to describe such interactions. Protein interactions also give rise to “combinatorial complexity” by generating large numbers of protein complexes and covalent modification states. To address these twin problems, we propose a modelling framework that combines a modular description of protein structure and function with a rule-based description of protein interactions. We define the input-output function of an allosteric protein through its thermodynamic properties and structural components. We show that our “biomolecule-centric” methodology, in contrast to ad hoc approaches that emphasize the regulatory logic of interactions, can reduce the number of parameters required to model experimental observations. We also demonstrate how the application of our framework gives insights into the assembly of macromolecular complexes and increases the predictive power of a standard model of G protein-coupled receptors. These benefits are possible in many systems, given the ubiquity of allostery in biochemical networks. Our research delineates a fundamental relationship between allostery, modularity, and complexity in biochemical networks.

Exact equilibrium-state solution of an intracellular complex formation model: kA↔P reaction in a small volume

A generic model of complex formation in small volumes was studied under the assumption of perfect mixing. Particles A react in clusters, and each reaction converts k A particles into a P particle. The back reaction is also allowed. The equilibrium state of the model is solved exactly. Fluctuations in product particle number are reduced by increasing the degree of cooperativity k. Three qualitatively distinct reactant fluctuation characteristics emerge.

On the spontaneous stochastic dynamics of a single gene: complexity of the molecular interplay at the promoter

BACKGROUND

Gene promoters can be in various epigenetic states and undergo interactions with many molecules in a highly transient, probabilistic and combinatorial way, resulting in a complex global dynamics as observed experimentally. However, models of stochastic gene expression commonly consider promoter activity as a two-state on/off system. We consider here a model of single-gene stochastic expression that can represent arbitrary prokaryotic or eukaryotic promoters, based on the combinatorial interplay between molecules and epigenetic factors, including energy-dependent remodeling and enzymatic activities.

RESULTS

We show that, considering the mere molecular interplay at the promoter, a single-gene can demonstrate an elaborate spontaneous stochastic activity (eg. multi-periodic multi-relaxation dynamics), similar to what is known to occur at the gene-network level. Characterizing this generic model with indicators of dynamic and steady-state properties (including power spectra and distributions), we reveal the potential activity of any promoter and its influence on gene expression. In particular, we can reproduce, based on biologically relevant mechanisms, the strongly periodic patterns of promoter occupancy by transcription factors (TF) and chromatin remodeling as observed experimentally on eukaryotic promoters. Moreover, we link several of its characteristics to properties of the underlying biochemical system. The model can also be used to identify behaviors of interest (eg. stochasticity induced by high TF concentration) on minimal systems and to test their relevance in larger and more realistic systems. We finally show that TF concentrations can regulate many aspects of the stochastic activity with a considerable flexibility and complexity.

CONCLUSIONS

This tight promoter-mediated control of stochasticity may constitute a powerful asset for the cell. Remarkably, a strongly periodic activity that demonstrates a complex TF concentration-dependent control is obtained when molecular interactions have typical characteristics observed on eukaryotic promoters (high mobility, functional redundancy, many alternate states/pathways). We also show that this regime results in a direct and indirect energetic cost. Finally, this model can constitute a framework for unifying various experimental approaches. Collectively, our results show that a gene - the basic building block of complex regulatory networks - can itself demonstrate a significantly complex behavior.

A computational study of lambda-lac mutants

We present a comprehensive, computational study of the properties of bacteriophage lambda mutants designed by Atsumi and Little (2006 Proc. Natl. Acad. Sci. 103 4558-63). These phages underwent a genetic reconstruction where Cro was replaced by a dimeric form of the Lac repressor. To clarify the theoretical characteristics of these mutants, we built a detailed thermodynamic model. The mutants all have a different genetic wiring than the wild-type lambda. One group lacks regulation of P(RM) by the lytic protein. These mutants only exhibit the lysogenic equilibrium, with no transiently active P(R). The other group lacks the negative feedback from CI. In this group, we identify a handful of bi-stable mutants, although the majority only exhibit the lysogenic equilibrium. The experimental identification of functional phages differs from our predictions. From a theoretical perspective, there is no reason why only 4 out of 900 mutants should be functional. The differences between theory and experiment can be explained in two ways. Either, the view of the lambda phage as a bi-stable system needs to be revised, or the mutants have in fact not undergone a modular replacement, as intended by Atsumi and Little, but constitute instead a wider systemic change.

Ab initio thermodynamic modeling of distal multisite transcription regulation

Transcription regulation typically involves the binding of proteins over long distances on multiple DNA sites that are brought close to each other by the formation of DNA loops. The inherent complexity of assembling regulatory complexes on looped DNA challenges the understanding of even the simplest genetic systems, including the prototypical lac operon. Here we implement a scalable approach based on thermodynamic molecular properties to model ab initio systems regulated through multiple DNA sites with looping. We show that this approach applied to the lac operon accurately predicts the system behavior for a wide range of cellular conditions, which include the transcription rate over five orders of magnitude as a function of the repressor concentration for wild type and all seven combinations of deletions of three operators, as well as the observed induction curves for cells with and without active catabolite activator protein. Our results provide new insights into the detailed functioning of the lac operon and reveal an efficient avenue to incorporate the required underlying molecular complexity into fully predictive models of gene regulation.

General transfer matrix formalism to calculate DNA-protein-drug binding in gene regulation: application to OR operator of phage lambda

The transfer matrix methodology is proposed as a systematic tool for the statistical-mechanical description of DNA-protein-drug binding involved in gene regulation. We show that a genetic system of several cis-regulatory modules is calculable using this method, considering explicitly the site-overlapping, competitive, cooperative binding of regulatory proteins, their multilayer assembly and DNA looping. In the methodological section, the matrix models are solved for the basic types of short- and long-range interactions between DNA-bound proteins, drugs and nucleosomes. We apply the matrix method to gene regulation at the O(R) operator of phage lambda. The transfer matrix formalism allowed the description of the lambda-switch at a single-nucleotide resolution, taking into account the effects of a range of inter-protein distances. Our calculations confirm previously established roles of the contact CI-Cro-RNAP interactions. Concerning long-range interactions, we show that while the DNA loop between the O(R) and O(L) operators is important at the lysogenic CI concentrations, the interference between the adjacent promoters P(R) and P(RM) becomes more important at small CI concentrations. A large change in the expression pattern may arise in this regime due to anticooperative interactions between DNA-bound RNA polymerases. The applicability of the matrix method to more complex systems is discussed.

Multilevel deconstruction of the In vivo behavior of looped DNA-protein complexes

Protein-DNA complexes with loops play a fundamental role in a wide variety of cellular processes, ranging from the regulation of DNA transcription to telomere maintenance. As ubiquitous as they are, their precise in vivo properties and their integration into the cellular function still remain largely unexplored. Here, we present a multilevel approach that efficiently connects in both directions molecular properties with cell physiology and use it to characterize the molecular properties of the looped DNA-lac repressor complex while functioning in vivo. The properties we uncover include the presence of two representative conformations of the complex, the stabilization of one conformation by DNA architectural proteins, and precise values of the underlying twisting elastic constants and bending free energies. Incorporation of all this molecular information into gene-regulation models reveals an unprecedented versatility of looped DNA-protein complexes at shaping the properties of gene expression.

A quantitative study of lambda-phage SWITCH and its components

We propose what we believe is a new model to quantitatively describe the lambda-phage SWITCH system. The model incorporates facilitated transfer mechanism of transcription factor, which can be simplified into a two-step reaction. We first sequentially obtain two indispensable parameters by fitting our model to experimental data of two simple systems, and then apply them to study the natural lambda-SWITCH system. By incorporating the facilitated transfer mechanism, we find that in RecA(-) host Escherichia coli, the wild-type lambda-lysogenic state is in a monostable regime rather than in a bistable regime. Furthermore, the model explains the weak role of Cro protein and probably sheds light on the evolution of lambda-Cro protein, which is known to be structurally distinct from the other Cros in lambdoid family members.

Multiprotein DNA looping

DNA looping plays a fundamental role in a wide variety of biological processes, providing the backbone for long range interactions on DNA. Here we develop the first model for DNA looping by an arbitrarily large number of proteins and solve it analytically in the case of identical binding. We uncover a switchlike transition between looped and unlooped phases and identify the key parameters that control this transition. Our results establish the basis for the quantitative understanding of fundamental cellular processes like DNA recombination, gene silencing, and telomere maintenance.

DNA looping: the consequences and its control

The formation of DNA loops by proteins and protein complexes is ubiquitous to many fundamental cellular processes, including transcription, recombination and replication. Recently, advances have been made in understanding the properties of DNA looping in its natural context and how they propagate to cellular behavior through gene regulation. The result of connecting the molecular properties of DNA looping with cellular physiology measurements indicates that looping of DNA in vivo is much more complex and easier than predicted from current models, and reveals a wealth of previously unappreciated details.