Spatial effects on the speed and reliability of protein-DNA search

Role of Shape Deformation of DNA-Binding Sites in Regulating the Efficiency and Specificity in Their Recognition by DNA-Binding Proteins

Accurate transcription of genetic information is crucial, involving precise recognition of the binding motifs by DNA-binding proteins. While some proteins rely on short-range hydrophobic and hydrogen bonding interactions at binding sites, others employ a DNA shape readout mechanism for specific recognition. In this mechanism, variations in DNA shape at the binding motif resulted from either inherent flexibility or binding of proteins at adjacent sites are sensed and capitalized by the searching proteins to locate them specifically. Through extensive computer simulations, we investigate both scenarios to uncover the underlying mechanism and origin of specificity in the DNA shape readout mechanism. Our findings reveal that deformation in shape at the binding motif creates an entropy funnel, allowing information about altered shapes to manifest as fluctuations in minor groove widths. This signal enhances the efficiency of nonspecific search of nearby proteins by directing their movement toward the binding site, primarily driven by a gain in entropy. We propose this as a generic mechanism for DNA shape readout, where specificity arises from the alignment between the molecular frustration of the searching protein and the ruggedness of the entropic funnel governed by molecular features of the protein and arrangement of the DNA bases at the binding site, respectively.

Probing the modulation in facilitated diffusion guided by DNA-protein interactions in target search processes

Many fundamental biophysical processes involving gene regulation and gene editing rely, at the molecular level, on an intricate methodology of searching and locating the precise target base pair sequence on the genome by specific binding proteins. A unique mechanism, known as 'facilitated diffusion', which is a combination of 1D sliding along with 3D movement, is considered to be the key step for such events. This also explains the relatively much shorter timescale of the target searching process, compared to other diffusion-controlled biophysical processes. In this work, we aim to probe the modulation of target search dynamics of a protein moiety by estimating the rate of the target search process, and the statistics of the search rounds and timescales accomplished by the 1D and 3D motions, based on first passage time (FPT) calculations. This is studied with its characteristics getting influenced by various given conditions such as, when the DNA is rigid or flexible, and when the target is placed at different locations on the DNA. The current theoretical framework includes a Brownian dynamics simulation setup adopting a straightforward coarse-grained model for a diffusing protein on DNA. Moreover, this theoretical analysis provides insights into the complex target search dynamics by highlighting the significance of the chain dynamics in the mechanistic details of the facilitated diffusion process.

Protein-DNA recognition mechanisms and specificity

The accumulated knowledge about the structure of protein-DNA complexes allowed us to understand the mechanisms of protein-DNA recognition and searching for a specific site on DNA. Obviously, the mechanism of specific DNA recognition by a protein must satisfy two requirements. First, the probability of incorrect binding should be very small. Second, the time to find the "correct" binding site should not be too long. If we assume that protein recognition of a precise site on DNA occurs at some distance from DNA and calculate global minima, we can avoid local minima at short distances. The only long-range interaction is the interaction of charges. The location of charges on DNA in three-dimensional space depends on the local conformation of DNA and thus reflects the DNA sequence and sets the spatial pattern for recognition. Various factors such as counter ion concentration, ionic strength, and pH can affect protein recognition of DNA. Nowadays, the theory of long-range interactions makes it possible to calculate the best mutual spatial arrangement of protein and DNA molecules by charged groups and avoid misplaced binding.

The molecular grammar of protein disorder guiding genome-binding locations

Intrinsically disordered regions (IDRs) direct transcription factors (TFs) towards selected genomic occurrences of their binding motif, as exemplified by budding yeast's Msn2. However, the sequence basis of IDR-directed TF binding selectivity remains unknown. To reveal this sequence grammar, we analyze the genomic localizations of >100 designed IDR mutants, each carrying up to 122 mutations within this 567-AA region. Our data points at multivalent interactions, carried by hydrophobic-mostly aliphatic-residues dispersed within a disordered environment and independent of linear sequence motifs, as the key determinants of Msn2 genomic localization. The implications of our results for the mechanistic basis of IDR-based TF binding preferences are discussed.

Complementary strategies for directing in vivo transcription factor binding through DNA binding domains and intrinsically disordered regions

DNA binding domains (DBDs) of transcription factors (TFs) recognize DNA sequence motifs that are highly abundant in genomes. Within cells, TFs bind a subset of motif-containing sites as directed by either their DBDs or DBD-external (nonDBD) sequences. To define the relative roles of DBDs and nonDBDs in directing binding preferences, we compared the genome-wide binding of 48 (∼30%) budding yeast TFs with their DBD-only, nonDBD-truncated, and nonDBD-only mutants. With a few exceptions, binding locations differed between DBDs and TFs, resulting from the cumulative action of multiple determinants mapped mostly to disordered nonDBD regions. Furthermore, TFs' preferences for promoters of the fuzzy nucleosome architecture were lost in DBD-only mutants, whose binding spread across promoters, implicating nonDBDs' preferences in this hallmark of budding yeast regulatory design. We conclude that DBDs and nonDBDs employ complementary DNA-targeting strategies, whose balance defines TF binding specificity along genomes.

Theoretical insights into the full description of DNA target search by subdiffusing proteins

DNA binding proteins (DBPs) diffuse in the cytoplasm to recognise and bind with their respective target sites on the DNA to initiate several biologically important processes. The first passage time distributions (FPTDs) of DBPs are useful in quantifying the timescales of the most-probable search paths in addition to the mean value of the distribution which, strikingly, are decades of order apart in time. However, extremely crowded in vivo conditions or the viscoelasticity of the cellular medium among other factors causes biomolecules to exhibit anomalous diffusion which is usually overlooked in most theoretical studies. We have obtained approximate analytical expressions of a general FPTD and the two characteristic timescales that are valid for any single subdiffusing protein searching for its target in vivo. Our results can be applied to single-particle tracking experiments of target search.

Transcription factors perform a 2-step search of the nucleus

Transcription factors regulate gene expression by binding to regulatory DNA and recruiting regulatory protein complexes. The DNA-binding and protein-binding functions of transcription factors are traditionally described as independent functions performed by modular protein domains. Here, I argue that genome binding can be a 2-part process with both DNA-binding and protein-binding steps, enabling transcription factors to perform a 2-step search of the nucleus to find their appropriate binding sites in a eukaryotic genome. I support this hypothesis with new and old results in the literature, discuss how this hypothesis parsimoniously resolves outstanding problems, and present testable predictions.

The economy of chromosomal distances in bacterial gene regulation

In the transcriptional regulatory network (TRN) of a bacterium, the nodes are genes and a directed edge represents the action of a transcription factor (TF), encoded by the source gene, on the target gene. It is a condensed representation of a large number of biological observations and facts. Nonrandom features of the network are structural evidence of requirements for a reliable systemic function. For the bacterium Escherichia coli we here investigate the (Euclidean) distances covered by the edges in the TRN when its nodes are embedded in the real space of the circular chromosome. Our work is motivated by 'wiring economy' research in Computational Neuroscience and starts from two contradictory hypotheses: (1) TFs are predominantly employed for long-distance regulation, while local regulation is exerted by chromosomal structure, locally coordinated by the action of structural proteins. Hence long distances should often occur. (2) A large distance between the regulator gene and its target requires a higher expression level of the regulator gene due to longer reaching times and ensuing increased degradation (proteolysis) of the TF and hence will be evolutionarily reduced. Our analysis supports the latter hypothesis.

DNA Looping and DNA Conformational Fluctuations Can Accelerate Protein Target Search

Protein searching and binding to specific sites on DNA is a fundamentally important process that marks the beginning of all major cellular transformations. While the dynamics of protein-DNA interactions in in vitro settings is well investigated, the situation is much more complex for in vivo conditions because the DNA molecules in live cells are packed into chromosomal structures where they are undergoing strong dynamic and conformational fluctuations. In this work, we present a theoretical investigation on the role of DNA looping and DNA conformational fluctuations in the protein target search. It is based on a discrete-state stochastic analysis that allows for explicit calculations of dynamic properties, which is also supplemented by Monte Carlo computer simulations. It is found that for stronger nonspecific interactions between DNA and proteins the search occurs faster on the DNA looped conformation in comparison with the unlooped conformation, and the fastest search is observed when the loop is formed near the target site. It is also shown that DNA fluctuations between the looped and unlooped conformations influence the search dynamics, and this depends on the magnitude of conformational transition rates and on which conformation is more energetically stable. Physical-chemical arguments explaining these observations are presented. Our theoretical study suggests that the geometry and conformational changes in DNA are additional factors that might efficiently control the gene regulation processes.

Discrete-state stochastic kinetic models for target DNA search by proteins: Theory and experimental applications

To perform their functions, transcription factors and DNA-repair/modifying enzymes randomly search DNA in order to locate their specific targets on DNA. Discrete-state stochastic kinetic models have been developed to explain how the efficiency of the search process is influenced by the molecular properties of proteins and DNA as well as by other factors such as molecular crowding. These theoretical models not only offer explanations on the relation of microscopic processes to macroscopic behavior of proteins, but also facilitate the analysis and interpretation of experimental data. In this review article, we provide an overview on discrete-state stochastic kinetic models and explain how these models can be applied to experimental investigations using stopped-flow, single-molecule, nuclear magnetic resonance (NMR), and other biophysical and biochemical methods.

Speed-Specificity Trade-Offs in the Transcription Factors Search for Their Genomic Binding Sites

Transcription factors (TFs) regulate gene expression by binding DNA sequences recognized by their DNA-binding domains (DBDs). DBD-recognized motifs are short and highly abundant in genomes. The ability of TFs to bind a specific subset of motif-containing sites, and to do so rapidly upon activation, is fundamental for gene expression in all eukaryotes. Despite extensive interest, our understanding of the TF-target search process is fragmented; although binding specificity and detection speed are two facets of this same process, trade-offs between them are rarely addressed. In this opinion article, we discuss potential speed-specificity trade-offs in the context of existing models. We further discuss the recently described 'distributed specificity' paradigm, suggesting that intrinsically disordered regions (IDRs) promote specificity while reducing the TF-target search time.

A lattice model on the rate of in vivo site-specific DNA-protein interactions

We develop a lattice model of site-specific DNA-protein interactions under in vivo conditions where DNA is modelled as a self-avoiding random walk that is embedded in a cubic lattice box resembling the living cell. The protein molecule searches for its cognate site on DNA via a combination of three dimensional (3D) and one dimensional (1D) random walks. Hopping and intersegmental transfers occur depending on the conformational state of DNA. Results show that the search acceleration ratio (= search time in pure 3D route/search time in 3D and 1D routes) asymptotically increases towards a limiting value as the dilution factor of DNA (= volume of the cell/the volume of DNA) tends towards infinity. When the dilution ratio is low, then hopping and intersegmental transfers significantly enhance the search efficiency over pure sliding. At high dilution ratio, hopping does not enhance the search efficiency much since under such situation DNA will be in a relaxed conformation that favors only sliding. In the absence of hopping and intersegmental transfers, there exists an optimum sliding time at which the search acceleration ratio attains a maximum in line with the current theoretical results. However, existence of such optimum sliding length disappears in the presence of hopping. When the DNA is confined in a small volume inside the cell resembling a natural cell system, then there exists an optimum dilution and compression ratios (= total cell volume/volume in which DNA is confined) at which the search acceleration factor attains a maximum especially in the presence of hopping and intersegmental transfers. These optimum values are consistent with the values observed in the Escherichia coli cell system. In the absence of confinement of DNA, position of the specific binding site on the genomic DNA significantly influences the search acceleration. However, such position dependent changes in the search acceleration ratio will be nullified in the presence of hopping and intersegmental transfers especially when the DNA is confined in a small volume that is embedded in an outer cell.

Argonaute bypasses cellular obstacles without hindrance during target search

Argonaute (Ago) proteins are key players in both gene regulation (eukaryotes) and host defense (prokaryotes). Acting on single-stranded nucleic-acid substrates, Ago relies on base pairing between a small nucleic-acid guide and its complementary target sequences for specificity. To efficiently scan nucleic-acid chains for targets, Ago diffuses laterally along the substrate and must bypass secondary structures as well as protein barriers. Using single-molecule FRET in conjunction with kinetic modelling, we reveal that target scanning is mediated through loose protein-nucleic acid interactions, allowing Ago to slide short distances over secondary structures, as well as to bypass protein barriers via intersegmental transfer. Our combined single-molecule experiment and kinetic modelling approach may serve as a platform to dissect search processes and study the effect of sequence on search kinetics for other nucleic acid-guided proteins.

A Model for the Spatiotemporal Design of Gene Regulatory Circuits †

Mathematical modeling assists the design of synthetic regulatory networks by providing a detailed mechanistic understanding of biological systems. Models that can predict the performance of a design are fundamental for synthetic biology since they minimize iterations along the design-build-test lifecycle. Such predictability depends crucially on what assumptions (i.e., biological simplifications) the model considers. Here, we challenge a common assumption when it comes to the modeling of bacterial-based gene regulation: considering negligible the effects of intracellular physical space. It is commonly assumed that molecules, such as transcription factors (TF), are homogeneously distributed inside a cell, so there is no need to model their diffusion. We describe a mathematical model that accounts for molecular diffusion and show how simulations of network performance are decisively affected by the distance between its components. Specifically, the model focuses on the search by a TF for its target promoter. The combination of local searches, via one-dimensional sliding along the chromosome, and global searches, via three-dimensional diffusion through the cytoplasm, determine TF-promoter interplay. Previous experimental results with engineered bacteria in which the distance between TF source and target was minimized or enlarged were successfully reproduced by the spatially resolved model we introduce here. This suggests that the spatial specification of the circuit alone can be exploited as a design parameter in synthetic biology to select programmable output levels.

Quantifying the two-state facilitated diffusion model of protein-DNA interactions

The current report extends the facilitated diffusion model to account for conflict between the search and recognition binding modes adopted by DNA-binding proteins (DBPs) as they search DNA and subsequently recognize and bind to their specific binding site. The speed of the search dynamics is governed by the energetic ruggedness of the protein-DNA landscape, whereas the rate for the recognition process is mostly dictated by the free energy barrier for the transition between the DBP's search and recognition binding modes. We show that these two modes are negatively coupled, such that fast 1D sliding and rapid target site recognition probabilities are unlikely to coexist. Thus, a tradeoff occurs between optimizing the timescales for finding and binding the target site. We find that these two kinetic properties can be balanced to produce a fast timescale for the total target search and recognition process by optimizing frustration. Quantification of the facilitated diffusion model by including a frustration term enables it to explain several experimental observations concerning search and recognition speeds. The extended model captures experimental estimate of the energetic ruggedness of the protein-DNA landscape and predicts how various molecular properties of protein-DNA binding affect recognition kinetics. Particularly, point mutations may change the frustration and so affect protein association with DNA, thus providing a means to modulate protein-DNA affinity by manipulating the protein's association or dissociation reactions.

Theory of Site-Specific DNA-Protein Interactions in the Presence of Nucleosome Roadblocks

We show that nucleosomes exert a maximal amount of hindrance to the one-dimensional diffusion of transcription factors (TFs) when they are present between TFs and their cognate sites on DNA. The effective one-dimensional diffusion coefficient of TFs (χ_TF) decreases with a rise in the free-energy barrier (μ_NU) of the sliding of nucleosomes as χ_TF∝exp(-μ_NU). The average time (η_L) required by TFs to slide over L sites on DNA increases with μ_NU as η_L∝exp(μ_NU). When TFs move close to nucleosomes, then they exhibit typical subdiffusion. Nucleosomes can enhance the search dynamics of TFs when TFs are present between nucleosomes and TF binding sites. These results suggest that nucleosome-depleted regions around the cognate sites of TFs are mandatory for efficient site-specific binding of TFs. Remarkably, the genome-wide in vivo positioning pattern of TFs shows a maximum at their specific binding sites where the occupancy of nucleosomes shows a minimum. This could be a consequence of an increasing level of breathing dynamics of nucleosome cores and decreasing levels of fluctuations in the DNA binding domains of TFs as they move across TF binding sites. The dynamics of TFs becomes slow as they approach their cognate sites so that TFs form a tight site-specific complex, whereas the dynamics of nucleosomes becomes rapid so that they quickly pass through the cognate sites of TFs. Several in vivo data sets on the genome-wide positioning pattern of nucleosomes and TFs agree well with our arguments. The retarding effects of nucleosomes can be minimized when the degree of condensation of DNA is such that it can permit a jump size associated with the dynamics of TFs beyond ∼160-180 bp.

Facilitated Diffusion Mechanisms in DNA Base Excision Repair and Transcriptional Activation

Preservation of the coding potential of the genome and highly regulated gene expression over the life span of a human are two fundamental requirements of life. These processes require the action of repair enzymes or transcription factors that efficiently recognize specific sites of DNA damage or transcriptional regulation within a restricted time frame of the cell cycle or metabolism. A failure of these systems to act results in accumulated mutations, metabolic dysfunction, and disease. Despite the multifactorial complexity of cellular DNA repair and transcriptional regulation, both processes share a fundamental physical requirement that the proteins must rapidly diffuse to their specific DNA-binding sites that are embedded within the context of a vastly greater number of nonspecific DNA-binding sites. Superimposed on the needle-in-the-haystack problem is the complex nature of the cellular environment, which contains such high concentrations of macromolecules that the time frame for diffusion is expected to be severely extended as compared to dilute solution. Here we critically review the mechanisms for how these proteins solve the needle-in-the-haystack problem and how the effects of cellular macromolecular crowding can enhance facilitated diffusion processes. We restrict the review to human proteins that use stochastic, thermally driven site-recognition mechanisms, and we specifically exclude systems involving energy cofactors or circular DNA clamps. Our scope includes ensemble and single-molecule studies of the past decade or so, with an emphasis on connecting experimental observations to biological function.

Protein motion in the nucleus: from anomalous diffusion to weak interactions

Understanding how transcription factors (TFs) regulate mammalian gene expression in space and time is a central topic in biology. To activate a gene, a TF has first to diffuse in the available space of the nucleus until it reaches a target DNA sequence or protein (target site). This eventually results in the recruitment of the whole transcriptional machinery. All these processes take place in the mammalian nucleoplasm, a highly organized and dynamic environment, in which some complexes transiently assemble and break apart, whereas others appear more stable. This diversity of dynamic behaviors arises from the number of biomolecules that make up the nucleoplasm and their pairwise interactions. Indeed, interactions energies that span several orders of magnitude, from covalent bounds to transient and dynamic interactions, can shape nuclear landscapes. Thus, the nuclear environment determines how frequently and how fast a TF contacts its target site, and it indirectly regulates gene expression. How exactly transient interactions are involved in the regulation of TF diffusion is unclear, but are reflected by live cell imaging techniques, including single-particle tracking (SPT). Overall, the macroscopic result of these microscopic interactions is almost always anomalous diffusion, a phenomenon widely studied and modeled. Here, we review the connections between the anomalous diffusion of a TF observed by SPT and the microscopic organization of the nucleus, including recently described topologically associated domains and dynamic phase-separated compartments. We propose that anomalous diffusion found in SPT data result from weak and transient interactions with dynamic nuclear substructures, and that SPT data analysis would benefit from a better description of such structures.

Acceleration of bursty multiprotein target search kinetics on DNA by colocalisation

Proteins are capable of locating specific targets on DNA by employing a facilitated diffusion process with intermittent 1D and 3D search steps. We here uncover the implications of colocalisation of protein production and DNA binding sites via computer simulations.

The Role of Chromatin Density in Cell Population Heterogeneity during Stem Cell Differentiation

We incorporate three-dimensional (3D) conformation of chromosome (Hi-C) and single-cell RNA sequencing data together with discrete stochastic simulation, to explore the role of chromatin reorganization in determining gene expression heterogeneity during development. While previous research has emphasized the importance of chromatin architecture on activation and suppression of certain regulatory genes and gene networks, our study demonstrates how chromatin remodeling can dictate gene expression distribution by folding into distinct topological domains. We hypothesize that the local DNA density during differentiation accentuate transcriptional bursting due to the crowding effect of chromatin. This phenomenon yields a heterogeneous cell population, thereby increasing the potential of differentiation of the stem cells.

Macromolecular Crowding Regulates the Gene Expression Profile by Limiting Diffusion

We seek to elucidate the role of macromolecular crowding in transcription and translation. It is well known that stochasticity in gene expression can lead to differential gene expression and heterogeneity in a cell population. Recent experimental observations by Tan et al. have improved our understanding of the functional role of macromolecular crowding. It can be inferred from their observations that macromolecular crowding can lead to robustness in gene expression, resulting in a more homogeneous cell population. We introduce a spatial stochastic model to provide insight into this process. Our results show that macromolecular crowding reduces noise (as measured by the kurtosis of the mRNA distribution) in a cell population by limiting the diffusion of transcription factors (i.e. removing the unstable intermediate states), and that crowding by large molecules reduces noise more efficiently than crowding by small molecules. Finally, our simulation results provide evidence that the local variation in chromatin density as well as the total volume exclusion of the chromatin in the nucleus can induce a homogenous cell population.

The cellular nucleus is packed with macromolecules such as DNAs and proteins, which leaves limited space for other molecules to move around. Recent experimental results by C. Tan et al. have shown that macromolecular crowding can regulate gene expression, resulting in a more homogenous cell population. We introduce a computational model to uncover the mechanism by which macromolecular crowding functions. Our results suggest that macromolecular crowding limits the diffusion of the transcription factors and attenuates the transcriptional bursting, which leads to a more homogenous cell population. Regulation of gene expression noise by macromolecules depends on the size of the crowders, i.e. larger macromolecules can reduce the noise more effectively than smaller macromolecules. We also demonstrate that local variation of chromatin density can affect the noise of gene expression. This shows the importance of the chromatin structure in gene expression regulation.

Theory on the mechanism of site-specific DNA-protein interactions in the presence of traps

The speed of site-specific binding of transcription factor (TFs) proteins with genomic DNA seems to be strongly retarded by the randomly occurring sequence traps. Traps are those DNA sequences sharing significant similarity with the original specific binding sites (SBSs). It is an intriguing question how the naturally occurring TFs and their SBSs are designed to manage the retarding effects of such randomly occurring traps. We develop a simple random walk model on the site-specific binding of TFs with genomic DNA in the presence of sequence traps. Our dynamical model predicts that (a) the retarding effects of traps will be minimum when the traps are arranged around the SBS such that there is a negative correlation between the binding strength of TFs with traps and the distance of traps from the SBS and (b) the retarding effects of sequence traps can be appeased by the condensed conformational state of DNA. Our computational analysis results on the distribution of sequence traps around the putative binding sites of various TFs in mouse and human genome clearly agree well the theoretical predictions. We propose that the distribution of traps can be used as an additional metric to efficiently identify the SBSs of TFs on genomic DNA.

Hill function-based models of transcriptional switches: impact of specific, nonspecific, functional and nonfunctional binding

We explore minimalist models of transcription in which we take into account that a cis-regulatory sequence is embedded in, and interacts with, a complex genome. The classical Hill equation is the simplest way to represent a transcriptional response. However, it may overlook the fact that a transcription factor (TF) establishes specific and nonspecific nonfunctional interactions with chromatin. Classical papers have shown that nonfunctional binding (not leading to transcription) may influence gene expression. We examine how the presence of additional binding sites for a TF, besides those on the gene(s) of interest, affect the shape and parameters of the transcriptional response. We consider two conditions: at equilibrium and at steady-state. In many cases the TF level is determined by the position of the cell within a spatial or temporal gradient. We show that such gradients can be adjusted by evolutionary selection to compensate for the alteration of the gene transcription response by the presence of nonfunctional binding sites. Finally, we analyse how the transcriptional response is affected by a decrease in TF concentration, as in cases of haploinsufficiency. We show that the nonlinearity of the transcriptional response as a function of [TF] exacerbates the effect of a decrease in the latter, at least for weakly expressed TFs. Although decades of work on TFs have led to the impression that almost everything is known about the control of gene expression, we show that even the simplest models of transcription control have not delivered all their secrets yet.

Method for the analysis of contribution of sliding and hopping to a facilitated diffusion of DNA-binding protein: Application to in vivo data

DNA-binding protein searches for its target, a specific site on DNA, by means of diffusion. The search process consists of many recurrent steps of one-dimensional diffusion (sliding) along the DNA chain and three-dimensional diffusion (hopping) after dissociation of a protein from the DNA chain. Here we propose a computational method that allows extracting the contribution of sliding and hopping to the search process in vivo from the measurements of the kinetics of the target search by the lac repressor in Escherichia coli [P. Hammar et al., Science 336, 1595 (2012)]. The method combines lattice Monte Carlo simulations with the Brownian excursion theory and includes explicitly steric constraints for hopping due to the helical structure of DNA. The simulation results including all experimental data reveal that the in vivo target search is dominated by sliding. The short-range hopping to the same base pair interrupts one-dimensional sliding while long-range hopping does not contribute significantly to the kinetics of the search of the target in vivo.

An integrated model of transcription factor diffusion shows the importance of intersegmental transfer and quaternary protein structure for target site finding

We present a computational model of transcription factor motion that explains both the observed rapid target finding of transcription factors, and how this motion influences protein and genome structure. Using the Smoldyn software, we modelled transcription factor motion arising from a combination of unrestricted 3D diffusion in the nucleoplasm, sliding along the DNA filament, and transferring directly between filament sections by intersegmental transfer. This presents a fine-grain picture of the way in which transcription factors find their targets two orders of magnitude faster than 3D diffusion alone allows. Eukaryotic genomes contain sections of nucleosome free regions (NFRs) around the promoters; our model shows that the presence and size of these NFRs can be explained as their acting as antennas on which transcription factors slide to reach their targets. Additionally, our model shows that intersegmental transfer may have shaped the quaternary structure of transcription factors: sequence specific DNA binding proteins are unusually enriched in dimers and tetramers, perhaps because these allow intersegmental transfer, which accelerates target site finding. Finally, our model shows that a ‘hopping’ motion can emerge from 3D diffusion on small scales. This explains the apparently long sliding lengths that have been observed for some DNA binding proteins observed in vitro. Together, these results suggest that transcription factor diffusion dynamics help drive the evolution of protein and genome structure.

Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting

Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.

Facilitated diffusion buffers noise in gene expression

Transcription factors perform facilitated diffusion [three-dimensional (3D) diffusion in the cytosol and 1D diffusion on the DNA] when binding to their target sites to regulate gene expression. Here, we investigated the influence of this binding mechanism on the noise in gene expression. Our results showed that, for biologically relevant parameters, the binding process can be represented by a two-state Markov model and that the accelerated target finding due to facilitated diffusion leads to a reduction in both the mRNA and the protein noise.

Physical constraints determine the logic of bacterial promoter architectures

Site-specific transcription factors (TFs) bind to their target sites on the DNA, where they regulate the rate at which genes are transcribed. Bacterial TFs undergo facilitated diffusion (a combination of 3D diffusion around and 1D random walk on the DNA) when searching for their target sites. Using computer simulations of this search process, we show that the organization of the binding sites, in conjunction with TF copy number and binding site affinity, plays an important role in determining not only the steady state of promoter occupancy, but also the order at which TFs bind. These effects can be captured by facilitated diffusion-based models, but not by standard thermodynamics. We show that the spacing of binding sites encodes complex logic, which can be derived from combinations of three basic building blocks: switches, barriers and clusters, whose response alone and in higher orders of organization we characterize in detail. Effective promoter organizations are commonly found in the E. coli genome and are highly conserved between strains. This will allow studies of gene regulation at a previously unprecedented level of detail, where our framework can create testable hypothesis of promoter logic.

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.

Fungal genes in context: genome architecture reflects regulatory complexity and function

Gene context determines gene expression, with local chromosomal environment most influential. Comparative genomic analysis is often limited in scope to conserved or divergent gene and protein families, and fungi are well suited to this approach with low functional redundancy and relatively streamlined genomes. We show here that one aspect of gene context, the amount of potential upstream regulatory sequence maintained through evolution, is highly predictive of both molecular function and biological process in diverse fungi. Orthologs with large upstream intergenic regions (UIRs) are strongly enriched in information processing functions, such as signal transduction and sequence-specific DNA binding, and, in the genus Aspergillus, include the majority of experimentally studied, high-level developmental and metabolic transcriptional regulators. Many uncharacterized genes are also present in this class and, by implication, may be of similar importance. Large intergenic regions also share two novel sequence characteristics, currently of unknown significance: they are enriched for plus-strand polypyrimidine tracts and an information-rich, putative regulatory motif that was present in the last common ancestor of the Pezizomycotina. Systematic consideration of gene UIR in comparative genomics, particularly for poorly characterized species, could help reveal organisms’ regulatory priorities.

Quantitative influence of macromolecular crowding on gene regulation kinetics

We introduce macromolecular crowding quantitatively into the model for kinetics of gene regulation in Escherichia coli. We analyse and compute the specific-site searching time for 180 known transcription factors (TFs) regulating 1300 operons. The time is between 160 s (e.g. for SoxS M_w = 12.91 kDa) and 1550 s (e.g. for PepA₆ of M_w = 329.28 kDa). Diffusion coefficients for one-dimensional sliding are between for large proteins up to for small monomers or dimers. Three-dimensional diffusion coefficients in the cytoplasm are 2 orders of magnitude larger than 1D sliding coefficients, nevertheless the sliding enhances the binding rates of TF to specific sites by 1–2 orders of magnitude. The latter effect is due to ubiquitous non-specific binding. We compare the model to experimental data for LacI repressor and find that non-specific binding of the protein to DNA is activation- and not diffusion-limited. We show that the target location rate by LacI repressor is optimized with respect to microscopic rate constant for association to non-specific sites on DNA. We analyse the effect of oligomerization of TFs and DNA looping effects on searching kinetics. We show that optimal searching strategy depends on TF abundance.

The effects of transcription factor competition on gene regulation

Transcription factor (TF) molecules translocate by facilitated diffusion (a combination of 3D diffusion around and 1D random walk on the DNA). Despite the attention this mechanism received in the last 40 years, only a few studies investigated the influence of the cellular environment on the facilitated diffusion mechanism and, in particular, the influence of "other" DNA binding proteins competing with the TF molecules for DNA space. Molecular crowding on the DNA is likely to influence the association rate of TFs to their target site and the steady state occupancy of those sites, but it is still not clear how it influences the search in a genome-wide context, when the model includes biologically relevant parameters (such as: TF abundance, TF affinity for DNA and TF dynamics on the DNA). We performed stochastic simulations of TFs performing the facilitated diffusion mechanism, and considered various abundances of cognate and non-cognate TFs. We show that, for both obstacles that move on the DNA and obstacles that are fixed on the DNA, changes in search time are not statistically significant in case of biologically relevant crowding levels on the DNA. In the case of non-cognate proteins that slide on the DNA, molecular crowding on the DNA always leads to statistically significant lower levels of occupancy, which may confer a general mechanism to control gene activity levels globally. When the "other" molecules are immobile on the DNA, we found a completely different behavior, namely: the occupancy of the target site is always increased by higher molecular crowding on the DNA. Finally, we show that crowding on the DNA may increase transcriptional noise through increased variability of the occupancy time of the target sites.

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.

Distance matters: the impact of gene proximity in bacterial gene regulation

Following recent discoveries of colocalization of downstream-regulating genes in living cells, the impact of the spatial distance between such genes on the kinetics of gene product formation is increasingly recognized. We here show from analytical and numerical analysis that the distance between a transcription factor (TF) gene and its target gene drastically affects the speed and reliability of transcriptional regulation in bacterial cells. For an explicit model system, we develop a general theory for the interactions between a TF and a transcription unit. The observed variations in regulation efficiency are linked to the magnitude of the variation of the TF concentration peaks as a function of the binding site distance from the signal source. Our results support the role of rapid binding site search for gene colocalization and emphasize the role of local concentration differences.

How do proteins locate specific targets in DNA?

Many aspects of biology depend on the ability of DNA-binding proteins to locate specific binding sites within the genome. Interest in this target search problem has been reinvigorated through the recent development of microscopy-based technologies capable of tracking individual proteins in real-time as they search for binding sites. In this review we discuss how two different proteins, lac repressor and RNA polymerase, have solved the target search problem through seemingly different mechanisms, with an emphasis on how recent in vitro single-molecule studies have influenced our understanding of these reactions.

Promoter sequence determines the relationship between expression level and noise

A single transcription factor can activate or repress expression by three different mechanisms: one that increases cell-to-cell variability in target gene expression (noise) and two that decrease noise.

The ability of cells to accurately control gene expression levels in response to extracellular cues is limited by the inherently stochastic nature of transcriptional regulation. A change in transcription factor (TF) activity results in changes in the expression of its targets, but the way in which cell-to-cell variability in expression (noise) changes as a function of TF activity, and whether targets of the same TF behave similarly, is not known. Here, we measure expression and noise as a function of TF activity for 16 native targets of the transcription factor Zap1 that are regulated by it through diverse mechanisms. For most activated and repressed Zap1 targets, noise decreases as expression increases. Kinetic modeling suggests that this is due to two distinct Zap1-mediated mechanisms that both change the frequency of transcriptional bursts. Notably, we found that another mechanism of repression by Zap1, which is encoded in the promoter DNA, likely decreases the size of transcriptional bursts, producing a unique transcriptional state characterized by low expression and low noise. In addition, we find that further reduction in noise is achieved when a single TF both activates and represses a single target gene. Our results suggest a global principle whereby at low TF concentrations, the dominant source of differences in expression between promoters stems from differences in burst frequency, whereas at high TF concentrations differences in burst size dominate. Taken together, we show that the precise amount by which noise changes with expression is specific to the regulatory mechanism of transcription and translation that acts at each gene.

In response to environmental changes, cells regulate the activity of transcription factors (TFs), which in turn change the expression of dozens of downstream target genes by binding to their promoters. The response of each target gene is determined by the interplay between TF concentration and the context in which TF binding sites occur in each target promoter. To examine the relationship between promoter sequence, mechanism of regulation, and response to TF activity, we measured expression of 16 target genes of a single TF in response to changes in TF concentration in single cells. We found that different native promoters that are all targets of the same TF exhibit diverse responses to changing TF levels in terms of both gene expression level and cell-to-cell variability (noise) in expression. Using computational modeling and mutations of specific promoter elements, we show that the molecular mechanisms of regulation can be inferred by measuring how noise changes with expression. These results show that a single TF can regulate transcription through multiple mechanisms, resulting in similar changes in mean expression but vastly different changes in cell-to-cell variability.

In vivo facilitated diffusion model

Under dilute in vitro conditions transcription factors rapidly locate their target sequence on DNA by using the facilitated diffusion mechanism. However, whether this strategy of alternating between three-dimensional bulk diffusion and one-dimensional sliding along the DNA contour is still beneficial in the crowded interior of cells is highly disputed. Here we use a simple model for the bacterial genome inside the cell and present a semi-analytical model for the in vivo target search of transcription factors within the facilitated diffusion framework. Without having to resort to extensive simulations we determine the mean search time of a lac repressor in a living E. coli cell by including parameters deduced from experimental measurements. The results agree very well with experimental findings, and thus the facilitated diffusion picture emerges as a quantitative approach to gene regulation in living bacteria cells. Furthermore we see that the search time is not very sensitive to the parameters characterizing the DNA configuration and that the cell seems to operate very close to optimal conditions for target localization. Local searches as implied by the colocalization mechanism are only found to mildly accelerate the mean search time within our model.

The promoter-search mechanism of Escherichia coli RNA polymerase is dominated by three-dimensional diffusion

Gene expression, DNA replication and genome maintenance are all initiated by proteins that must recognize specific targets from among a vast excess of nonspecific DNA. For example, to initiate transcription, Escherichia coli RNA polymerase (RNAP) must locate promoter sequences, which compose <2% of the bacterial genome. This search problem remains one of the least understood aspects of gene expression, largely owing to the transient nature of search intermediates. Here we visualize RNAP in real time as it searches for promoters, and we develop a theoretical framework for analyzing target searches at the submicroscopic scale on the basis of single-molecule target-association rates. We demonstrate that, contrary to long-held assumptions, the promoter search is dominated by three-dimensional diffusion at both the microscopic and submicroscopic scales in vitro, which has direct implications for understanding how promoters are located within physiological settings.

Coordinated induction of multi-gene pathways in Saccharomyces cerevisiae

Bacterial operons are nature’s tool for regulating and coordinating multi-gene expression in prokaryotes. They are also a gene architecture commonly used in the biosynthesis of many pharmaceutically important compounds and industrially useful chemicals. Despite being an important eukaryotic production host, Saccharomyces cerevisiae has never had such gene architecture. Here, we report the development of a system to assemble and regulate a multi-gene pathway in S. cerevisiae. Full pathways can be constructed using pre-made parts from a plasmid toolbox. Subsequently, through the use of a yeast strain containing a stably integrated gene switch, the assembled pathway can be regulated using a readily available and inexpensive compound—estradiol—with extremely high sensitivity (10 nM). To demonstrate the use of the system, we assembled the five-gene zeaxanthin biosynthetic pathway in a single step and showed the ligand-dependent coordinated expression of all five genes as well as the tightly regulated production of zeaxanthin. Compared with a previously reported constitutive zeaxanthin pathway, our inducible pathway was shown to have 50-fold higher production level.

Computational models for large-scale simulations of facilitated diffusion

The binding of site-specific transcription factors to their genomic target sites is a key step in gene regulation. While the genome is huge, transcription factors belong to the least abundant protein classes in the cell. It is therefore fascinating how short the time frame is that they require to home in on their target sites. The underlying search mechanism is called facilitated diffusion and assumes a combination of three-dimensional diffusion in the space around the DNA combined with one-dimensional random walk on it. In this review, we present the current understanding of the facilitated diffusion mechanism and identify questions that lack a clear or detailed answer. One way to investigate these questions is through stochastic simulation and, in this manuscript, we support the idea that such simulations are able to address them. Finally, we review which biological parameters need to be included in such computational models in order to obtain a detailed representation of the actual process.

Massively parallel measurements of molecular interaction kinetics on a microfluidic platform

Quantitative biology requires quantitative data. No high-throughput technologies exist capable of obtaining several hundred independent kinetic binding measurements in a single experiment. We present an integrated microfluidic device (k-MITOMI) for the simultaneous kinetic characterization of 768 biomolecular interactions. We applied k-MITOMI to the kinetic analysis of transcription factor (TF)-DNA interactions, measuring the detailed kinetic landscapes of the mouse TF Zif268, and the yeast TFs Tye7p, Yox1p, and Tbf1p. We demonstrated the integrated nature of k-MITOMI by expressing, purifying, and characterizing 27 additional yeast transcription factors in parallel on a single device. Overall, we obtained 2,388 association and dissociation curves of 223 unique molecular interactions with equilibrium dissociation constants ranging from 2 × 10(-6) M to 2 × 10(-9) M, and dissociation rate constants of approximately 6 s(-1) to 8.5 × 10(-3) s(-1). Association rate constants were uniform across 3 TF families, ranging from 3.7 × 10(6) M(-1) s(-1) to 9.6 × 10(7) M(-1) s(-1), and are well below the diffusion limit. We expect that k-MITOMI will contribute to our quantitative understanding of biological systems and accelerate the development and characterization of engineered systems.

System size reduction in stochastic simulations of the facilitated diffusion mechanism

Background

Site-specific Transcription Factors (TFs) are proteins that bind to specific sites on the DNA and control the activity of a target gene by enhancing or decreasing the rate at which the gene is transcribed by RNA polymerase. The process by which TF molecules locate their target sites is a key component of transcriptional regulation. Therefore it is essential to gain insight into the mechanisms by which TFs search for the target sites.

Research in this area uses experimental and analytical approaches, but also stochastic simulations of the search process. Previous work based on stochastic simulations focussed only on short sequences, primarily for reasons of technical feasibility. Many of these studies had to disregard possible biases introduced by reducing a genome-wide system to a smaller subsystem. In particular, we identified crucial parameters that require adjustment, which were not adequately changed in these previous studies.

Results

We investigated several methods that adequately adapt the parameters of stochastic simulations of the facilitated diffusion, when the full sequence space is reduced to smaller regions of interest. We found two methods that scale the system accordingly: the copy number model and the association rate model. We systematically compared the results produced by simulations of the subsystem with respect to the original system. Our results confirmed that the copy number model is adequate only for high abundance TFs, while for low abundance TFs the association rate model is the only one that reproduces with high accuracy the results of the full system.

Conclusions

We propose a strategy to reduce the size of the system that adequately adapts important parameters to capture the behaviour of the full system. This enables correct simulations of a smaller sequence space (which can be as small as 100 Kbp) and, thus, provides independence from computationally intensive genome-wide simulations of the facilitated diffusion mechanism.

The bZIP dimer localizes at DNA full-sites where each basic region can alternately translocate and bind to subsites at the half-site

Crystal structures of the GCN4 bZIP (basic region/leucine zipper) with the AP-1 or CRE site show how each GCN4 basic region binds to a 4 bp cognate half-site as a single DNA target; however, this may not always fully describe how bZIP proteins interact with their target sites. Previously, we showed that the GCN4 basic region interacts with all 5 bp in half-site TTGCG (termed 5H-LR) and that 5H-LR comprises two 4 bp subsites, TTGC and TGCG, which individually are also target sites of the basic region. In this work, we explore how the basic region interacts with 5H-LR when the bZIP dimer localizes to full-sites. Using AMBER molecular modeling, we simulated GCN4 bZIP complexes with full-sites containing 5H-LR to investigate in silico the interface between the basic region and 5H-LR. We also performed in vitro investigation of bZIP-DNA interactions at a number of full-sites that contain 5H-LR versus either subsite: we analyzed results from DNase I footprinting and electrophoretic mobility shift assay (EMSA) and from EMSA titrations to quantify binding affinities. Our computational and experimental results together support a highly dynamic DNA-binding model: when a bZIP dimer localizes to its target full-site, the basic region can alternately recognize either subsite as a distinct target at 5H-LR and translocate between the subsites, potentially by sliding and hopping. This model provides added insights into how α-helical DNA-binding domains of transcription factors can localize to their gene regulatory sequences in vivo.

Mesoscopic model for free-energy-landscape analysis of DNA sequences

A mesoscopic model which allows us to identify and quantify the strength of binding sites in DNA sequences is proposed. The model is based on the Peyrard-Bishop-Dauxois model for the DNA chain coupled to a Brownian particle which explores the sequence interacting more importantly with open base pairs of the DNA chain. We apply the model to promoter sequences of different organisms. The free energy landscape obtained for these promoters shows a complex structure that is strongly connected to their biological behavior. The analysis method used is able to quantify free energy differences of sites within genome sequences.

A comprehensive computational model of facilitated diffusion in prokaryotes

MOTIVATION

Gene activity is mediated by site-specific transcription factors (TFs). Their binding to defined regions in the genome determines the rate at which their target genes are transcribed.

RESULTS

We present a comprehensive computational model of the search process of TF for their genomic target site(s). The computational model considers: the DNA sequence, various TF species and the interaction of the individual molecules with the DNA or between themselves. We also demonstrate a systematic approach how to parametrize the system using available experimental data.

GRiP: a computational tool to simulate transcription factor binding in prokaryotes

Motivation: Transcription factors (TFs) are proteins that regulate gene activity by binding to specific sites on the DNA. Understanding the way these molecules locate their target site is of great importance in understanding gene regulation. We developed a comprehensive computational model of this process and estimated the model parameters in (N.R.Zabet and B.Adryan, submitted for publication).

Results: GRiP (gene regulation in prokaryotes) is a highly versatile implementation of this model and simulates the search process in a computationally efficient way. This program aims to provide researchers in the field with a flexible and highly customizable simulation framework. Its features include representation of DNA sequence, TFs and the interaction between TFs and the DNA (facilitated diffusion mechanism), or between various TFs (cooperative behaviour). The software will record both information on the dynamics associated with the search process (locations of molecules) and also steady-state results (affinity landscape, occupancy-bias and collision hotspots).

Availability:http://logic.sysbiol.cam.ac.uk/grip, program and source code

Contact:n.r.zabet@gen.cam.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.

Intra-nuclear mobility and target search mechanisms of transcription factors: a single-molecule perspective on gene expression

Precise expression of specific genes in time and space is at the basis of cellular viability as well as correct development of organisms. Understanding the mechanisms of gene regulation is fundamental and still one of the great challenges for biology. Gene expression is regulated also by specific transcription factors that recognize and bind to specific DNA sequences. Transcription factors dynamics, and especially the way they sample the nucleoplasmic space during the search for their specific target in the genome, are a key aspect for regulation and it has been puzzling researchers for forty years. The scope of this review is to give a state-of-the-art perspective over the intra-nuclear mobility and the target search mechanisms of specific transcription factors at the molecular level. Going through the seminal biochemical experiments that have raised the first questions about target localization and the theoretical grounds concerning target search processes, we describe the most recent experimental achievements and current challenges in understanding transcription factors dynamics and interactions with DNA using in vitro assays as well as in live prokaryotic and eukaryotic cells. This article is part of a Special Issue entitled: Nuclear Transport and RNA Processing.