Real sequence effects on the search dynamics of transcription factors on DNA

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.

Dynamic and facilitated binding of topoisomerase accelerates topological relaxation

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.

Influence of Nonspecific Interactions between Proteins and In Vivo Cytoplasmic Crowders in Facilitated Diffusion of Proteins: Theoretical Insights

The binding of proteins to their respective specific sites on the DNA through facilitated diffusion serves as the initial step of various important biological processes. While this search process has been thoroughly investigated via in vitro studies, the cellular environment is complex and may interfere with the protein's search dynamics. The cytosol is heavily crowded, which can potentially modify the search by nonspecifically interacting with the protein that has been mostly overlooked. In this work, we probe the target search dynamics in the presence of explicit crowding agents that have an affinity toward the protein. We theoretically investigate the role of such protein-crowder associations in the target search process using a discrete-state stochastic framework that allows for the analytical description of dynamic properties. It is found that stronger nonspecific associations between the crowder and proteins can accelerate the facilitated diffusion of proteins in comparison with a purely inert, rather weakly interacting cellular environment. This effect depends on how strong these associations are, the spatial positions of the target with respect to the crowders, and the size of the crowded region. Our theoretical results are also tested with Monte Carlo computer simulations. Our predictions are in qualitative agreement with existing experimental observations and computational studies.

Search and Localization Dynamics of the CRISPR-Cas9 System

The CRISPR-Cas9 system acts as the prokaryotic immune system and has important applications in gene editing. The protein Cas9 is one of its crucial components. The role of Cas9 is to search for specific target sequences on the DNA and cleave them. In this Letter, we introduce a model of facilitated diffusion for Cas9 and fit its parameters to single-molecule experiments. Our model confirms that Cas9 search for targets by sliding, but shows that its sliding length is rather short. We then investigate how Cas9 explores a long stretch of DNA containing randomly placed targets. We solve this problem by mapping it into the theory of Anderson localization in condensed matter physics. Our theoretical approach rationalizes experimental evidence on the distribution of Cas9 molecules along the DNA.

Diffusion of DNA-Binding Species in the Nucleus: A Transient Anomalous Subdiffusion Model

Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies. Working forward, the observed distribution leads to transient anomalous subdiffusion, in which diffusion is anomalous at short times and normal at long times, here only mildly anomalous. Monte Carlo simulations are used to characterize the time-dependent diffusion coefficient D(t) in terms of the anomalous exponent α, the crossover time tcross, and the limits D(0) and D(∞) and to relate these quantities to the escape time distribution. The simplest interpretations identify the escape time as the actual binding time to DNA or the period of one-dimensional diffusion on DNA in the standard model combining one-dimensional and three-dimensional search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. 1) The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. 2) Non-target DNA sites have a significant effect on search kinetics. False positives in bioinformatic searches of the genome are potentially rate-determining in vivo. For simple binding, the search would be speeded if false-positive sequences were eliminated from the genome. 3) Both binding and obstruction affect diffusion. Obstruction ought to be measured directly, using as the primary probe the DNA-binding species with the binding site inactivated and eGFP as a calibration standard among laboratories and cell types. 4) Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. 5) The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP.

The effect of obstacles in multi-site protein target search with DNA looping

Many fundamental biological processes are regulated by protein-DNA complexes called synaptosomes, which possess multiple interaction sites. Despite the critical importance of synaptosomes, the mechanisms of their formation are not well understood. Because of the multisite nature of participating proteins, it is widely believed that their search for specific sites on DNA involves the formation and breaking of DNA loops and sliding in the looped configurations. In reality, DNA in live cells is densely covered by other biological molecules that might interfere with the formation of synaptosomes. In this work, we developed a theoretical approach to evaluate the role of obstacles in the target search of multisite proteins when the formation of DNA loops and the sliding in looped configurations are possible. Our theoretical method is based on analysis of a discrete-state stochastic model that uses a master equations approach and extensive computer simulations. It is found that the obstacle slows down the search dynamics in the system when DNA loops are long-lived, but the effect is minimal for short-lived DNA loops. In addition, the relative positions of the target and the obstacle strongly influence the target search kinetics. Furthermore, the presence of the obstacle might increase the noise in the system. These observations are discussed using physical-chemical arguments. Our theoretical approach clarifies the molecular mechanisms of formation of protein-DNA complexes with multiple interactions sites.

Structural Basis of Enhanced Facilitated Diffusion of DNA-Binding Protein in Crowded Cellular Milieu

Although the fast association between DNA-binding proteins (DBPs) and DNA is explained by a facilitated diffusion mechanism, in which DBPs adopt a weighted combination of three-dimensional diffusion and one-dimensional (1D) sliding and hopping modes of transportation, the role of cellular environment that contains many nonspecifically interacting proteins and other biomolecules is mostly overlooked. By performing large-scale computational simulations with an appropriately tuned model of protein and DNA in the presence of nonspecifically interacting bulk and DNA-bound crowders (genomic crowders), we demonstrate the structural basis of the enhanced facilitated diffusion of DBPs inside a crowded cellular milieu through, to our knowledge, novel 1D scanning mechanisms. In this one-dimensional scanning mode, the protein can float along the DNA under the influence of nonspecific interactions of bulk crowder molecules. The search mode is distinctly different compared to usual 1D sliding and hopping dynamics in which protein diffusion is regulated by the DNA electrostatics. In contrast, the presence of genomic crowders expedites the target search process by transporting the protein over DNA segments through the formation of a transient protein-crowder bridged complex. By analyzing the ruggedness of the associated potential energy landscape, we underpin the molecular origin of the kinetic advantages of these search modes and show that they successfully explain the experimentally observed acceleration of facilitated diffusion of DBPs by molecular crowding agents and crowder-concentration-dependent enzymatic activity of transcription factors. Our findings provide crucial insights into gene regulation kinetics inside the crowded cellular milieu.

Energetic funnel facilitates facilitated diffusion

Transcription factors (TFs) are able to associate to their binding sites on DNA faster than the physical limit posed by diffusion. Such high association rates can be achieved by alternating between three-dimensional diffusion and one-dimensional sliding along the DNA chain, a mechanism-dubbed facilitated diffusion. By studying a collection of TF binding sites of Escherichia coli from the RegulonDB database and of Bacillus subtilis from DBTBS, we reveal a funnel in the binding energy landscape around the target sequences. We show that such a funnel is linked to the presence of gradients of AT in the base composition of the DNA region around the binding sites. An extensive computational study of the stochastic sliding process along the energetic landscapes obtained from the database shows that the funnel can significantly enhance the probability of TFs to find their target sequences when sliding in their proximity. We demonstrate that this enhancement leads to a speed-up of the association process.

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.

Molecular search with conformational change: One-dimensional discrete-state stochastic model

Molecular search phenomena are observed in a variety of chemical and biological systems. During the search, the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic modes. To understand the mechanisms of molecular search with alternating dynamics, we investigate the search dynamics with stochastic transitions between two conformations in a one-dimensional discrete-state stochastic model. It is explicitly analyzed using the first-passage time probability method to obtain a full dynamic description of the search process. A general dynamic phase diagram is developed. It is found that there are several dynamic regimes in the molecular search with conformational transitions, and they are determined by the relative values of the relevant length scales in the system. Theoretical predictions are fully supported by Monte Carlo computer simulations.

Mechanisms of Protein Search for Targets on DNA: Theoretical Insights

Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years, only recently microscopic aspects of these processes became more clear. In this work, we present a review on current theoretical understanding of the molecular mechanisms of the protein target search. A comprehensive discrete-state stochastic method to explain the dynamics of the protein search phenomena is introduced and explained. Our theoretical approach utilizes a first-passage analysis and it takes into account the most relevant physical-chemical processes. It is able to describe many fascinating features of the protein search, including unusually high effective association rates, high selectivity and specificity, and the robustness in the presence of crowders and sequence heterogeneity.

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.

Persistent Sinai-type diffusion in Gaussian random potentials with decaying spatial correlations

Logarithmic or Sinai-type subdiffusion is usually associated with random force disorder and nonstationary potential fluctuations whose root-mean-squared amplitude grows with distance. We show here that extremely persistent, macroscopic logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems. Combining results from extensive simulations with a scaling approach we elucidate the physical mechanism of this unusual subdiffusion. In particular, we explain why with growing temperature and/or time a first crossover occurs to standard, power-law subdiffusion, with a time-dependent power-law exponent, and then a second crossover occurs to normal diffusion with a disorder-renormalized diffusion coefficient. Interestingly, the initial, nominally ultraslow diffusion turns out to be much faster than the universal de Gennes-Bässler-Zwanzig limit of the renormalized normal diffusion, which realistically cannot be attained at sufficiently low temperatures and/or for strong disorder. The ultraslow diffusion is also shown to be nonergodic and it displays a local bias phenomenon. Our simple scaling theory not only explains our numerical findings but qualitatively also has a predictive character.

DNA Internal Motion Likely Accelerates Protein Target Search in a Packed Nucleoid

Transcription factors must diffuse through densely packed and coiled DNA to find their binding sites. Using a coarse-grained model of DNA and lac repressor (LacI) in the Escherichia coli nucleoid, simulations were performed to examine how LacI diffuses in such a space. Despite the canonical picture of LacI diffusing rather freely, in reality the DNA is densely packed, is not rigid but highly mobile, and the dynamics of DNA dictates to a great extent the LacI motion. A possibly better picture of unbound LacI motion is that of gated diffusion, where DNA confines LacI in a cage, but LacI can move between cages when hindering DNA strands move out of the way. Three-dimensional diffusion constants for unbound LacI computed from simulations closely match those for unbound LacI in vivo reported in the literature. The internal motions of DNA appear to be governed by strong internal forces arising from being crowded into the small space of the nucleoid. A consequence of the DNA internal motion is that protein target search may be accelerated.

One-Dimensional Search Dynamics of Tumor Suppressor p53 Regulated by a Disordered C-Terminal Domain

Tumor suppressor p53 slides along DNA and finds its target sequence in drastically different and changing cellular conditions. To elucidate how p53 maintains efficient target search at different concentrations of divalent cations such as Ca²⁺ and Mg²⁺, we prepared two mutants of p53, each possessing one of its two DNA-binding domains, the CoreTet mutant having the structured core domain plus the tetramerization (Tet) domain, and the TetCT mutant having Tet plus the disordered C-terminal domain. We investigated their equilibrium and kinetic dissociation from DNA and search dynamics along DNA at various [Mg²⁺]. Although binding of CoreTet to DNA becomes markedly weaker at higher [Mg²⁺], binding of TetCT depends slightly on [Mg²⁺]. Single-molecule fluorescence measurements revealed that the one-dimensional diffusion of CoreTet along DNA consists of fast and slow search modes, the ratio of which depends strongly on [Mg²⁺]. In contrast, diffusion of TetCT consisted of only the fast mode. The disordered C-terminal domain can associate with DNA irrespective of [Mg²⁺], and can maintain an equilibrium balance of the two search modes and the p53 search distance. These results suggest that p53 modulates the quaternary structure of the complex between p53 and DNA under different [Mg²⁺] and that it maintains the target search along DNA.

On the Mechanism of Homology Search by RecA Protein Filaments

Genetic stability is a key factor in maintaining, survival, and reproduction of biological cells. It relies on many processes, but one of the most important is a homologous recombination, in which the repair of breaks in double-stranded DNA molecules is taking place with a help of several specific proteins. In bacteria, this task is accomplished by RecA proteins that are active as nucleoprotein filaments formed on single-stranded segments of DNA. A critical step in the homologous recombination is a search for a corresponding homologous region on DNA, which is called a homology search. Recent single-molecule experiments clarified some aspects of this process, but its molecular mechanisms remain not well understood. We developed a quantitative theoretical approach to analyze the homology search. It is based on a discrete-state stochastic model that takes into account the most relevant physical-chemical processes in the system. Using a method of first-passage processes, a full dynamic description of the homology search is presented. It is found that the search dynamics depends on the degree of extension of DNA molecules and on the size of RecA nucleoprotein filaments, in agreement with experimental single-molecule measurements of DNA pairing by RecA proteins. Our theoretical calculations, supported by extensive Monte Carlo computer simulations, provide a molecular description of the mechanisms of the homology search.

How nonspecifically DNA-binding proteins search for the target in crowded environments

We investigate how a tracer particle searches a target located in DNA modeled by a stiff chain in crowded environments using theoretical analysis and Langevin dynamics simulations. First, we show that the three-dimensional (3D) diffusion coefficient of the tracer only depends on the density of crowders ϕ, while its one-dimensional (1D) diffusion coefficient is affected by not only ϕ but also the nonspecific binding energy ε. With increasing ϕ and ε, no obvious change in the average 3D diffusion time is observed, while the average 1D sliding time apparently increases. We propose theoretically that the 1D sliding of the tracer along the chain could be well captured by the Kramers' law of escaping rather than the Arrhenius law, which is verified directly by the simulations. Finally, the average search time increases monotonously with an increase in ϕ while it has a minimum as a function of ε, which could be understood from the different behaviors of the average number of search rounds with the increasing ϕ or ε. These results provide a deeper understanding of the role of facilitated diffusion in target search of proteins on DNA in vivo.

Sequence heterogeneity accelerates protein search for targets on DNA

The process of protein search for specific binding sites on DNA is fundamentally important since it marks the beginning of all major biological processes. We present a theoretical investigation that probes the role of DNA sequence symmetry, heterogeneity, and chemical composition in the protein search dynamics. Using a discrete-state stochastic approach with a first-passage events analysis, which takes into account the most relevant physical-chemical processes, a full analytical description of the search dynamics is obtained. It is found that, contrary to existing views, the protein search is generally faster on DNA with more heterogeneous sequences. In addition, the search dynamics might be affected by the chemical composition near the target site. The physical origins of these phenomena are discussed. Our results suggest that biological processes might be effectively regulated by modifying chemical composition, symmetry, and heterogeneity of a genome.

Conformational selection underpins recognition of multiple DNA sequences by proteins and consequent functional actions

Recognition of multiple functional DNA sequences by a DNA-binding protein occurs widely in nature. The physico-chemical basis of this phenomenon is not well-understood. The E. coli gal repressor, a gene regulatory protein, binds two homologous but non-identical sixteen basepair sequences in the gal operon and interacts by protein-protein interaction to regulate gene expression. The two sites have nearly equal affinities for the Gal repressor. Spectroscopic studies of the Gal repressor bound to these two different DNA sequences detected significant conformational differences between them. Comprehensive single base-substitution and binding measurements were carried out on the two sequences to understand the nature of the two protein-DNA interfaces. Magnitudes of basepair-protein interaction energy show significant variation between homologous positions of the two DNA sequences. Magnitudes of variation are such that when summed over the whole sequence they largely cancel each other out, thus producing nearly equal net affinity. Modeling suggests significant alterations in the protein-DNA interface in the two complexes, which are consistent with conformational adaptation of the protein to different DNA sequences. The functional role of the two sequences was studied by substitution of one site by the other and vice versa. In both cases, substitution reduces repression in vivo. This suggests that naturally occurring DNA sequence variations play functional roles beyond merely acting as high-affinity anchoring points. We propose that two different pre-existing conformations in the conformational ensemble of the free protein are selected by two different DNA sequences for efficient sequence read-out and the conformational difference of the bound proteins leads to different functional roles.

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.

Protein search for multiple targets on DNA

Protein-DNA interactions are crucial for all biological processes. One of the most important fundamental aspects of these interactions is the process of protein searching and recognizing specific binding sites on DNA. A large number of experimental and theoretical investigations have been devoted to uncovering the molecular description of these phenomena, but many aspects of the mechanisms of protein search for the targets on DNA remain not well understood. One of the most intriguing problems is the role of multiple targets in protein search dynamics. Using a recently developed theoretical framework we analyze this question in detail. Our method is based on a discrete-state stochastic approach that takes into account most relevant physical-chemical processes and leads to fully analytical description of all dynamic properties. Specifically, systems with two and three targets have been explicitly investigated. It is found that multiple targets in most cases accelerate the search in comparison with a single target situation. However, the acceleration is not always proportional to the number of targets. Surprisingly, there are even situations when it takes longer to find one of the multiple targets in comparison with the single target. It depends on the spatial position of the targets, distances between them, average scanning lengths of protein molecules on DNA, and the total DNA lengths. Physical-chemical explanations of observed results are presented. Our predictions are compared with experimental observations as well as with results from a continuum theory for the protein search. Extensive Monte Carlo computer simulations fully support our theoretical calculations.

Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes

We investigate the diffusive and ergodic properties of massive and confined particles in a model disordered medium, in which the local diffusivity fluctuates in time while its mean has a power law dependence on the diffusion time.

Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation

Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.

Dynamics of the Protein Search for Targets on DNA in the Presence of Traps

Protein search for specific binding sites on DNA is a fundamental biological phenomenon associated with the beginning of most major biological processes. It is frequently found that proteins find and recognize their specific targets quickly and efficiently despite the complex nature of protein-DNA interactions in living cells. Although significant experimental and theoretical efforts were made in recent years, the mechanisms of these processes remain not well-clarified. We present a theoretical study of the protein target search dynamics in the presence of semispecific binding sites which are viewed as traps. Our theoretical approach employs a discrete-state stochastic method that accounts for the most important physical and chemical processes in the system. It also leads to a full analytical description for all dynamic properties of the protein search. It is found that the presence of traps can significantly modify the protein search dynamics. This effect depends on the spatial positions of the targets and traps, on distances between them, on the average sliding length of the protein along the DNA, and on the total length of DNA. Theoretical predictions are discussed using simple physical-chemical arguments, and they are also validated with extensive Monte Carlo computer simulations.