Theoretical estimates of exposure timescales of protein binding sites on DNA regulated by nucleosome kinetics

Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime

We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

Bubble Relaxation Dynamics in Homopolymer DNA Sequences

Understanding the inherent timescales of large bubbles in DNA is critical to a thorough comprehension of its physicochemical characteristics, as well as their potential role on helix opening and biological function. In this work, we employ the coarse-grained Peyrard-Bishop-Dauxois model of DNA to study relaxation dynamics of large bubbles in homopolymer DNA, using simulations up to the microsecond time scale. By studying energy autocorrelation functions of relatively large bubbles inserted into thermalised DNA molecules, we extract characteristic relaxation times from the equilibration process for both adenine-thymine (AT) and guanine-cytosine (GC) homopolymers. Bubbles of different amplitudes and widths are investigated through extensive statistics and appropriate fittings of their relaxation. Characteristic relaxation times increase with bubble amplitude and width. We show that, within the model, relaxation times are two orders of magnitude longer in GC sequences than in AT sequences. Overall, our results confirm that large bubbles leave a lasting impact on the molecule's dynamics, for times between 0.5-500 ns depending on the homopolymer type and bubble shape, thus clearly affecting long-time evolutions of the molecule.

Exact Distribution of Threshold Crossing Times for Protein Concentrations: Implication for Biological Timekeeping

Stochastic protein accumulation up to some concentration threshold sets the timing of many cellular physiological processes. Here we obtain the exact distribution of first threshold crossing times of protein concentration, in either Laplace or time domain, and its associated cumulants: mean, variance, and skewness. The distribution is asymmetric, and its skewness nonmonotonically varies with the threshold. We study lysis times of E. coli cells for holin gene mutants of bacteriophage-λ and find a good match with theory. Mutants requiring higher holin thresholds show more skewed lysis time distributions as predicted. The theory also predicts a linear relationship between infection delay time and host doubling time for lytic viruses, that has recently been experimentally observed.

Computational analysis of GAL pathway pinpoints mechanisms underlying natural variation

Quantitative traits are measurable phenotypes that show continuous variation over a wide phenotypic range. Enormous effort has recently been put into determining the genetic influences on a variety of quantitative traits with mixed success. We identified a quantitative trait in a tractable model system, the GAL pathway in yeast, which controls the uptake and metabolism of the sugar galactose. GAL pathway activation depends both on galactose concentration and on the concentrations of competing, preferred sugars such as glucose. Natural yeast isolates show substantial variation in the behavior of the pathway. All studied yeast strains exhibit bimodal responses relative to external galactose concentration, i.e. a set of galactose concentrations existed at which both GAL-induced and GAL-repressed subpopulations were observed. However, these concentrations differed in different strains. We built a mechanistic model of the GAL pathway and identified parameters that are plausible candidates for capturing the phenotypic features of a set of strains including standard lab strains, natural variants, and mutants. In silico perturbation of these parameters identified variation in the intracellular galactose sensor, Gal3p, the negative feedback node within the GAL regulatory network, Gal80p, and the hexose transporters, HXT, as the main sources of the bimodal range variation. We were able to switch the phenotype of individual yeast strains in silico by tuning parameters related to these three elements. Determining the basis for these behavioral differences may give insight into how the GAL pathway processes information, and into the evolution of nutrient metabolism preferences in different strains. More generally, our method of identifying the key parameters that explain phenotypic variation in this system should be generally applicable to other quantitative traits.

Microbes adopt elaborate strategies for the preferred uptake and use of nutrients to cope with complex and fluctuating environments. As a result, yeast strains originating from different ecological niches show significant variation in the way they induce genes in the galactose metabolism (GAL) pathway in response to nutrient signals. To identify the mechanistic sources of this variation, we built a mathematical model to simulate the dynamics of the galactose metabolic regulation network, and studied how parameters with different biological implications contributed to the natural variation. We found that variations in the behavior of the galactose sensor Gal3p, the negative feedback node Gal80p, and the hexose transporters HXT were critical elements in the GAL pathway response. Tuning single parameters in silico was sufficient to achieve phenotype switching between different yeast strains. Our computational approach should be generally useful to help pinpoint the genetic and molecular bases of natural variation in other systems.

Capture of a diffusive prey by multiple predators in confined space

The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some detail, a systematic study in confined space is still lacking. In this paper, we study the first passage times for this problem in one, two, and three dimensions. Due to confinement, the survival probability of the target takes a form ∼e^{-t/τ} at large times t. The characteristic capture timescale τ associated with the rare capture events are rather challenging to measure. We use a computational algorithm that allows us to estimate τ with high accuracy. We study in detail the behavior of τ as a function of the system parameters, namely, the number of searchers N, the relative diffusivity r of the target with respect to the searcher, and the system size. We find that τ deviates from the ∼1/N scaling seen in the case of a static target, and this deviation varies continuously with r and the spatial dimensions.

Precise sequencing of single protected-DNA fragment molecules for profiling of protein distribution and assembly on DNA

Multiple DNA-interacting protein molecules are often dynamically distributed and/or assembled along a DNA molecule to adapt to their intricate functions temporally. However, analytical technology for measuring such binding behaviours is still missing. Here, we demonstrate the unique capacity of a supernuclease for a highly efficient cutting of the unprotected-DNA segments and with complete preservation of the protein-occluded DNA segments at near single-nucleotide resolution. By exploring this high-resolution cutting, an unprecedented assay that allows a precise sequencing of single protected-DNA fragment molecules (SPDFMS) was developed. As relevant applications, relevant information was gained on the respective distribution/assembly patterns and coordinated displacement of single-stranded DNA-binding protein and recombinase RecA, two model proteins, on DNA. Benefiting from this assay, we also for the first time provide direct measurement of the length of single RecA nucleofilaments, showing the predominant stoichiometry of 5-7 RecA monomers per RecA nucleofilament under physiologically relevant conditions. This innovative assay appears as a promising analytical tool for studying diverse protein-DNA interactions implicated in DNA replication, transcription, recombination, repair, and gene editing.

The Accidental Ally: Nucleosome Barriers Can Accelerate Cohesin-Mediated Loop Formation in Chromatin

An important question in the context of the three-dimensional organization of chromosomes is the mechanism of formation of large loops between distant basepairs. Recent experiments suggest that the formation of loops might be mediated by loop extrusion factor proteins such as cohesin. Experiments on cohesin have shown that cohesins walk diffusively on the DNA and that nucleosomes act as obstacles to the diffusion, lowering the permeability and hence reducing the effective diffusion constant. An estimation of the times required to form the loops of typical sizes seen in Hi-C experiments using these low-effective-diffusion constants leads to times that are unphysically large. The puzzle then is the following: how does a cohesin molecule diffusing on the DNA backbone achieve speeds necessary to form the large loops seen in experiments? We propose a simple answer to this puzzle and show that although at low densities, nucleosomes act as barriers to cohesin diffusion, beyond a certain concentration they can reduce loop formation times because of a subtle interplay between the nucleosome size and the mean linker length. This effect is further enhanced on considering stochastic binding kinetics of nucleosomes on the DNA backbone and leads to predictions of lower loop formation times than might be expected from a naive obstacle picture of nucleosomes.

Protein hourglass: Exact first passage time distributions for protein thresholds

Protein thresholds have been shown to act as an ancient timekeeping device, such as in the time to lysis of Escherichia coli infected with bacteriophage λ. The time taken for protein levels to reach a particular threshold for the first time is defined as the first passage time (FPT) of the protein synthesis system, which is a stochastic quantity. The first few moments of the distribution of first passage times were known earlier, but an analytical expression for the full distribution was not available. In this work, we derive an analytical expression for the first passage times for a long-lived protein. This expression allows us to calculate the full distribution not only for cases of no self-regulation, but also for both positive and negative self-regulation of the threshold protein. We show that the shape of the distribution matches previous experimental data on λ-phage lysis time distributions. We also provide analytical expressions for the FPT distribution with non-zero degradation in Laplace space. Furthermore, we study the noise in the precision of the first passage times described by coefficient of variation (CV) of the distribution as a function of the protein threshold value. We show that under conditions of positive self-regulation, the CV declines monotonically with increasing protein threshold, while under conditions of linear negative self-regulation, there is an optimal protein threshold that minimizes the noise in the first passage times.

Nucleosome positioning and chromatin organization

In our cells, DNA is folded and packed with the help of many proteins into chromatin whose basic unit is a nucleosome-DNA wrapped around octamer of histone proteins. The chain of nucleosomes is further folded and arranged into many layers and has a dynamic organization. How does the complex chromatin organization emerge from interactions among DNA, histones, and non-histone proteins have been a question of great interest. Here we review recent literature that investigated how nucleosome positioning and nucleosome-mediated interactions drive chromatin organization. Unlike our earlier understanding, chromatin is organized into 3D domains of various sizes having irregularly organized nucleosomes. These domains emerge due to heterogeneous nucleosome positioning and diverse inter-nucleosome interactions that vary in space and time.

First passage of an active particle in the presence of passive crowders

We experimentally study the stochastic transport of a self-propelled camphor boat, driven by Marangoni forces, through a crowd of passive paper discs floating on water. We analyze the statistics of the first passage times of the active particle to travel from the center of a circular container to its boundary. While the mean times rise monotonically as a function of the covered area fraction φ of the passive paper discs, their fluctuations show a non-monotonic behavior - being higher at low and high value of φ compared to intermediate values. The reason is traced to an interplay of two distinct sources of fluctuations - one intrinsic to the dynamics, while the other due to the crowding.

Transcription in Living Cells: Molecular Mechanisms of Bursting

Transcription in several organisms from certain bacteria to humans has been observed to be stochastic in nature: toggling between active and inactive states. Periods of active nascent RNA synthesis known as bursts represent individual gene activation events in which multiple polymerases are initiated. Therefore, bursting is the single locus illustration of both gene activation and repression. Although transcriptional bursting was originally observed decades ago, only recently have technological advances enabled the field to begin elucidating gene regulation at the single-locus level. In this review, we focus on how biochemical, genomic, and single-cell data describe the regulatory steps of transcriptional bursts.

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.

First passage of a particle in a potential under stochastic resetting: A vanishing transition of optimal resetting rate

First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here, we study the interplay between these two strategies, for a diffusing particle in a one-dimensional trapping potential V(x), being randomly reset at a constant rate r. Stochastic resetting has been of great interest as it is known to provide an "optimal rate" (r_{*}) at which the mean first passage time is a minimum. On the other hand, an attractive potential also assists in the first capture process. Interestingly, we find that for a sufficiently strong external potential, the advantageous optimal resetting rate vanishes (i.e., r_{*}→0). We derive a condition for this optimal resetting rate vanishing transition, which is continuous. We study this problem for various functional forms of V(x), some analytically, and the rest numerically. We find that the optimal rate r_{*} vanishes with a deviation from the critical strength of the potential as a power law with an exponent β which appears to be universal.

A unified computational framework for modeling genome-wide nucleosome landscape

Nucleosomes form the fundamental building blocks of eukaryotic chromatin, and previous attempts to understand the principles governing their genome-wide distribution have spurred much interest and debate in biology. In particular, the precise role of DNA sequence in shaping local chromatin structure has been controversial. This paper rigorously quantifies the contribution of hitherto-debated sequence features-including G+C content, 10.5 bp periodicity, and poly(dA:dT) tracts-to three distinct aspects of genome-wide nucleosome landscape: occupancy, translational positioning and rotational positioning. Our computational framework simultaneously learns nucleosome number and nucleosome-positioning energy from genome-wide nucleosome maps. In contrast to other previous studies, our model can predict both in vitro and in vivo nucleosome maps in Saccharomyces cerevisiae. We find that although G+C content is the primary determinant of MNase-derived nucleosome occupancy, MNase digestion biases may substantially influence this GC dependence. By contrast, poly(dA:dT) tracts are seen to deter nucleosome formation, regardless of the experimental method used. We further show that the 10.5 bp nucleotide periodicity facilitates rotational but not translational positioning. Applying our method to in vivo nucleosome maps demonstrates that, for a subset of genes, the regularly-spaced nucleosome arrays observed around transcription start sites can be partially recapitulated by DNA sequence alone. Finally, in vivo nucleosome occupancy derived from MNase-seq experiments around transcription termination sites can be mostly explained by the genomic sequence. Implications of these results and potential extensions of the proposed computational framework are discussed.

Coupling of replisome movement with nucleosome dynamics can contribute to the parent-daughter information transfer

Positioning of nucleosomes along the genomic DNA is crucial for many cellular processes that include gene regulation and higher order packaging of chromatin. The question of how nucleosome-positioning information from a parent chromatin gets transferred to the daughter chromatin is highly intriguing. Accounting for experimentally known coupling between replisome movement and nucleosome dynamics, we propose a model that can obtain de novo nucleosome assembly similar to what is observed in recent experiments. Simulating nucleosome dynamics during replication, we argue that short pausing of the replication fork, associated with nucleosome disassembly, can be a event crucial for communicating nucleosome positioning information from parent to daughter. We show that the interplay of timescales between nucleosome disassembly (τ_p) at the replication fork and nucleosome sliding behind the fork (τ_s) can give rise to a rich ‘phase diagram’ having different inherited patterns of nucleosome organization. Our model predicts that only when τ_p ≥ τ_s the daughter chromatin can inherit nucleosome positioning of the parent.

Regulation of Sensing, Transportation, and Catabolism of Nitrogen Sources in Saccharomyces cerevisiae

Nitrogen is one of the most important essential nutrient sources for biogenic activities. Regulation of nitrogen metabolism in microorganisms is complicated and elaborate. For this review, the yeast Saccharomyces cerevisiae was chosen to demonstrate the regulatory mechanism of nitrogen metabolism because of its relative clear genetic background. Current opinions on the regulation processes of nitrogen metabolism in S. cerevisiae, including nitrogen sensing, transport, and catabolism, are systematically reviewed. Two major upstream signaling pathways, the Ssy1-Ptr3-Ssy5 sensor system and the target of rapamycin pathway, which are responsible for sensing extracellular and intracellular nitrogen, respectively, are discussed. The ubiquitination of nitrogen transporters, which is the most general and efficient means for controlling nitrogen transport, is also summarized. The following metabolic step, nitrogen catabolism, is demonstrated at two levels: the transcriptional regulation process related to GATA transcriptional factors and the translational regulation process related to the general amino acid control pathway. The interplay between nitrogen regulation and carbon regulation is also discussed. As a model system, understanding the meticulous process by which nitrogen metabolism is regulated in S. cerevisiae not only could facilitate research on global regulation mechanisms and yeast metabolic engineering but also could provide important insights and inspiration for future studies of other common microorganisms and higher eukaryotic cells.

A structural bioinformatics investigation on protein–DNA complexes delineates their modes of interaction

A non-redundant dataset of 629 protein–DNA complexes has been used to investigate on amino acid composition of protein-DNA interfaces. Structural proteins, transcription factors and DNA-related enzymes show specific patterns accounting for different modes of their interaction with DNA.

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.