Mechanisms of Protein Search for Targets on DNA: Theoretical Insights

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.

Skipping events impose repeated binding attempts: profound kinetic implications of protein-DNA conformational changes

The kinetics of protein-DNA recognition, along with its thermodynamic properties, including affinity and specificity, play a central role in shaping biological function. Protein-DNA recognition kinetics are characterized by two key elements: the time taken to locate the target site amid various nonspecific alternatives; and the kinetics involved in the recognition process, which may necessitate overcoming an energetic barrier. In this study, we developed a coarse-grained (CG) model to investigate interactions between a transcription factor called the sex-determining region Y (SRY) protein and DNA, in order to probe how DNA conformational changes affect SRY-DNA recognition and binding kinetics. We find that, not only does a requirement for such a conformational DNA transition correspond to a higher energetic barrier for binding and therefore slower kinetics, it may further impede the recognition kinetics by increasing unsuccessful binding events (skipping events) where the protein partially binds its DNA target site but fails to form the specific protein-DNA complex. Such skipping events impose the need for additional cycles protein search of nonspecific DNA sites, thus significantly extending the overall recognition time. Our results highlight a trade-off between the speed with which the protein scans nonspecific DNA and the rate at which the protein recognizes its specific target site. Finally, we examine molecular approaches potentially adopted by natural systems to enhance protein-DNA recognition despite its intrinsically slow kinetics.

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.

Why Are Nucleosome Breathing Dynamics Asymmetric?

In eukaryotic cells, DNA is bound to nucleosomes, but DNA segments occasionally unbind in the process known as nucleosome breathing. Although DNA can unwrap simultaneously from both ends of the nucleosome (symmetric breathing), experiments indicate that DNA prefers to dissociate from only one end (asymmetric breathing). However, the molecular origin of the asymmetry is not understood. We developed a new theoretical approach that gives microscopic explanations of asymmetric breathing. It is based on a stochastic description that leads to a comprehensive evaluation of dynamics by using effective free-energy landscapes. It is shown that asymmetric breathing follows the kinetically preferred pathways. In addition, it is also found that asymmetric breathing leads to a faster target search by transcription factors. Theoretical predictions, supported by computer simulations, agree with experiments. It is proposed that nature utilizes the symmetry of nucleosome breathing to achieve a better dynamic accessibility of chromatin for more efficient genetic regulation.

Stochastic nucleosome disassembly mediated by remodelers and histone fragmentation

We construct and analyze monomeric and multimeric models of the stochastic disassembly of a single nucleosome. Our monomeric model predicts the time needed for a number of histone-DNA contacts to spontaneously break, leading to dissociation of a non-fragmented histone from DNA. The dissociation process can be facilitated by DNA binding proteins or processing molecular motors that compete with histones for histone-DNA contact sites. Eigenvalue analysis of the corresponding master equation allows us to evaluate histone detachment times under both spontaneous detachment and protein-facilitated processes. We find that competitive DNA binding of remodeling proteins can significantly reduce the typical detachment time but only if these remodelers have DNA-binding affinities comparable to those of histone-DNA contact sites. In the presence of processive motors, the histone detachment rate is shown to be proportional to the product of the histone single-bond dissociation constant and the speed of motor protein procession. Our simple intact-histone model is then extended to allow for multimeric nucleosome kinetics that reveal additional pathways of disassembly. In addition to a dependence of complete disassembly times on subunit-DNA contact energies, we show how histone subunit concentrations in bulk solutions can mediate the disassembly process by rescuing partially disassembled nucleosomes. Moreover, our kinetic model predicts that remodeler binding can also bias certain pathways of nucleosome disassembly, with higher remodeler binding rates favoring intact-histone detachment.

Stochastic nucleosome disassembly mediated by remodelers and histone fragmentation

We construct and analyze monomeric and multimeric models of the stochastic disassembly of a single nucleosome. Our monomeric model predicts the time needed for a number of histone-DNA contacts to spontaneously break, leading to dissociation of a non-fragmented histone from DNA. The dissociation process can be facilitated by DNA binding proteins or processing molecular motors that compete with histones for histone-DNA contact sites. Eigenvalue analysis of the corresponding master equation allows us to evaluate histone detachment times under both spontaneous detachment and protein-facilitated processes. We find that competitive DNA binding of remodeling proteins can significantly reduce the typical detachment time but only if these remodelers have DNA-binding affinities comparable to those of histone-DNA contact sites. In the presence of processive motors, the histone detachment rate is shown to be proportional to the product of the histone single-bond dissociation constant and the speed of motor protein procession. Our simple intact-histone model is then extended to allow for multimeric nucleosome kinetics that reveal additional pathways of disassembly. In addition to a dependence of complete disassembly times on subunit-DNA contact energies, we show how histone subunit concentrations in bulk solution can mediate the disassembly process by rescuing partially disassembled nucleosomes. Moreover, our kinetic model predicts that remodeler binding can also bias certain pathways of nucleosome disassembly, with higher remodeler binding rates favoring intact-histone detachment.

Role of Nucleosome Sliding in the Protein Target Search for Covered DNA Sites

Associations of transcription factors (TFs) with specific sites on DNA initiate major cellular processes. But DNA in eukaryotic cells is covered by nucleosomes which prevent TFs from binding. However, nucleosome structures on DNA are not static and exhibit breathing and sliding. We develop a theoretical framework to investigate the effect of nucleosome sliding on a protein target search. By analysis of a discrete-state stochastic model of nucleosome sliding, search dynamics are explicitly evaluated. It is found that for long sliding lengths the target search dynamics are faster for normal TFs that cannot enter the nucleosomal DNA. But for more realistic short sliding lengths, the so-called pioneer TFs, which can invade nucleosomal DNA, locate specific sites faster. It is also suggested that nucleosome breathing, which is a faster process, has a stronger effect on protein search dynamics than that of nucleosome sliding. Theoretical arguments to explain these observations are presented.

smFRET Detection of Cis and Trans DNA Interactions by the BfiI Restriction Endonuclease

Protein-DNA interactions are fundamental to many biological processes. Proteins must find their target site on a DNA molecule to perform their function, and mechanisms for target search differ across proteins. Especially challenging phenomena to monitor and understand are transient binding events that occur across two DNA target sites, whether occurring in cis or trans. Type IIS restriction endonucleases rely on such interactions. They play a crucial role in safeguarding bacteria against foreign DNA, including viral genetic material. BfiI, a type IIS restriction endonuclease, acts upon a specific asymmetric sequence, 5-ACTGGG-3, and precisely cuts both upper and lower DNA strands at fixed locations downstream of this sequence. Here, we present two single-molecule Förster resonance energy-transfer-based assays to study such interactions in a BfiI-DNA system. The first assay focuses on DNA looping, detecting both "Phi"- and "U"-shaped DNA looping events. The second assay only allows in trans BfiI-target DNA interactions, improving the specificity and reducing the limits on observation time. With total internal reflection fluorescence microscopy, we directly observe on- and off-target binding events and characterize BfiI binding events. Our results show that BfiI binds longer to target sites and that BfiI rarely changes conformations during binding. This newly developed assay could be employed for other DNA-interacting proteins that bind two targets and for the dsDNA substrate BfiI-PAINT, a useful strategy for DNA stretch assays and other super-resolution fluorescence microscopy studies.

How Do Nucleosome Dynamics Regulate Protein Search on DNA?

Nearly three-fourths of all eukaryotic DNA is occupied by nucleosomes, protein-DNA complexes comprising octameric histone core proteins and ∼150 base pairs of DNA. In addition to acting as a DNA compaction vehicle, the dynamics of nucleosomes regulate the DNA site accessibility for the nonhistone proteins, thereby controlling regulatory processes involved in determining the cell identity and cell fate. Here, we propose an analytical framework to analyze the role of nucleosome dynamics on the target search process of transcription factors through a simple discrete-state stochastic description of the search process. By considering the experimentally determined kinetic rates associated with protein and nucleosome dynamics as the only inputs, we estimate the target search time of a protein via first-passage probability calculations separately during nucleosome breathing and sliding dynamics. Although both the nucleosome dynamics permit transient access to the DNA sites that are otherwise occluded by the histone proteins, our result suggests substantial differences between the protein search mechanism on a nucleosome performing breathing and sliding dynamics. Furthermore, we identify the molecular factors that influence the search efficiency and demonstrate how these factors together portray a highly dynamic landscape of gene regulation. Our analytical results are validated using extensive Monte Carlo simulations.

Nucleosome Breathing Facilitates the Search for Hidden DNA Sites by Pioneer Transcription Factors

Transfer of genetic information starts with transcription factors (TFs) binding to specific sites on DNA. But in living cells, DNA is mostly covered by nucleosomes. There are proteins, known as pioneer TFs, that can efficiently reach the DNA sites hidden by nucleosomes, although the underlying mechanisms are not understood. Using the recently proposed idea of interaction-compensation mechanism, we develop a stochastic model for the target search on DNA with nucleosome breathing. It is found that nucleosome breathing can significantly accelerate the search by pioneer TFs in comparison to situations without breathing. We argue that this is the result of the interaction-compensation mechanism that allows proteins to enter the inner nucleosome region through the outer DNA segment. It is suggested that nature optimized pioneer TFs to take advantage of nucleosome breathing. The presented theoretical picture provides a possible microscopic explanation for the successful invasion of nucleosome-buried genes.

Repetitive DNA symmetry elements negatively regulate gene expression in embryonic stem cells

Transcription factor (TF) binding to genomic DNA elements constitutes one of the key mechanisms that regulates gene expression program in cells. Both consensus and nonconsensus DNA sequence elements influence the recognition specificity of TFs. Based on the analysis of experimentally determined c-Myc binding preferences to genomic DNA, here we statistically predict that certain repetitive, nonconsensus DNA symmetry elements can relatively reduce TF-DNA binding preferences. This is in contrast to a different set of repetitive, nonconsensus symmetry elements that can increase the strength of TF-DNA binding. Using c-Myc enhancer reporter system containing consensus motif flanked by nonconsensus sequences in embryonic stem cells, we directly demonstrate that the enrichment in such negatively regulating repetitive symmetry elements is sufficient to reduce the gene expression level compared with native genomic sequences. Negatively regulating repetitive symmetry elements around consensus c-Myc motif and DNA sequences containing consensus c-Myc motif flanked by entirely randomized sequences show similar expression baseline. A possible explanation for this observation is that rather than complete repression, negatively regulating repetitive symmetry elements play a regulatory role in fine-tuning the reduction of gene expression, most probably by binding TFs other than c-Myc.

How Pioneer Transcription Factors Search for Target Sites on Nucleosomal DNA

All major biological processes start after protein molecules known as transcription factors detect specific regulatory sequences on DNA and initiate genetic expression by associating to them. But in eukaryotic cells, much of the DNA is covered by nucleosomes and other chromatin structures, preventing transcription factors from binding to their targets. At the same time, experimental studies show that there are several classes of proteins, called "pioneer transcription factors", that are able to reach the targets on nucleosomal DNA; however, the underlying microscopic mechanisms remain not well understood. We propose a new theoretical approach that might explain how pioneer transcription factors can find their targets. It is argued that pioneer transcription factors might weaken the interactions between the DNA and nucleosome by substituting them with similar interactions between transcription factors and DNA. Using this idea, we develop a discrete-state stochastic model that allows for exact calculations of target search dynamics on nucleosomal DNA using first-passage probabilities approach. It is found that the target search on nuclesomal DNA for pioneer transcription factors might be significantly accelerated while the search is slower on naked DNA in comparison with normal transcription factors. Our theoretical predictions are supported by Monte Carlo computer simulations, and they also agree with available experimental observations.

Surface-facilitated trapping by active sites: From catalysts to viruses

Trapping by active sites on surfaces plays important roles in various chemical and biological processes, including catalysis, enzymatic reactions, and viral entry into host cells. However, the mechanisms of these processes remain not well understood, mostly because the existing theoretical descriptions are not fully accounting for the role of the surfaces. Here, we present a theoretical investigation on the dynamics of surface-assisted trapping by specific active sites. In our model, a diffusing particle can occasionally reversibly bind to the surface and diffuse on it before reaching the final target site. An approximate theoretical framework is developed, and its predictions are tested by Brownian dynamics computer simulations. It is found that the surface diffusion can be crucial in mediating trapping by active sites. Our theoretical predictions work reasonably well as long as the area of the active site is much smaller than the overall surface area. Potential applications of our approach are discussed.

Kinetic Analysis of the Interaction of Nicking Endonuclease BspD6I with DNA

Nicking endonucleases (NEs) are enzymes that incise only one strand of the duplex to produce a DNA molecule that is 'nicked' rather than cleaved in two. Since these precision tools are used in genetic engineering and genome editing, information about their mechanism of action at all stages of DNA recognition and phosphodiester bond hydrolysis is essential. For the first time, fast kinetics of the Nt.BspD6I interaction with DNA were studied by the stopped-flow technique, and changes of optical characteristics were registered for the enzyme or DNA molecules. The role of divalent metal cations was estimated at all steps of Nt.BspD6I-DNA complex formation. It was demonstrated that divalent metal ions are not required for the formation of a non-specific complex of the protein with DNA. Nt.BspD6I bound five-fold more efficiently to its recognition site in DNA than to a random DNA. DNA bending was confirmed during the specific binding of Nt.BspD6I to a substrate. The optimal size of Nt.BspD6I's binding site in DNA as determined in this work should be taken into account in methods of detection of nucleic acid sequences and/or even various base modifications by means of NEs.

Revealing atomic-scale molecular diffusion of a plant-transcription factor WRKY domain protein along DNA

In transcription factors’ search for target genes, one-dimensional diffusion of the protein along DNA is essential. Experimentally, it remains challenging to resolve the individual diffusional steps of protein on DNA. Here, we report mainly all-atom equilibrium simulations of a WRKY domain protein in association with and diffusion along DNA. We demonstrate a complete stepping cycle of the protein for one base pair on DNA within microseconds, along with stochastic motions. Processive protein diffusions on DNA have been further sampled in a coarse-grained model. We have also found preferential DNA-strand association of the domain protein, which becomes most prominent at specific DNA binding, and it can be common for small-domain proteins to balance movements on the DNA with the sequence recognition.

Transcription factor (TF) target search on genome is highly essential for gene expression and regulation. High-resolution determination of TF diffusion along DNA remains technically challenging. Here, we constructed a TF model system using the plant WRKY domain protein in complex with DNA from crystallography and demonstrated microsecond diffusion dynamics of WRKY on DNA by employing all-atom molecular-dynamics (MD) simulations. Notably, we found that WRKY preferentially binds to one strand of DNA with significant energetic bias compared with the other, or nonpreferred strand. The preferential DNA-strand binding becomes most prominent in the static process, from nonspecific to specific DNA binding, but less distinct during diffusive movements of the domain protein on the DNA. Remarkably, without employing acceleration forces or bias, we captured a complete one-base-pair stepping cycle of the protein tracking along major groove of DNA with a homogeneous poly-adenosine sequence, as individual hydrogen bonds break and reform at the protein–DNA binding interface. Further DNA-groove tracking motions of the protein forward or backward, with occasional sliding as well as strand crossing to minor groove of DNA, were also captured. The processive diffusion of WRKY along DNA has been further sampled via coarse-grained MD simulations. The study thus provides structural dynamics details on diffusion of a small TF domain protein, suggests how the protein approaches a specific recognition site on DNA, and supports further high-precision experimental detection. The stochastic movements revealed in the TF diffusion also provide general clues about how other protein walkers step and slide along DNA.

Crowding breaks the forward/backward symmetry of transition times in biased random walks

Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and provide a clear physical picture. Recent theoretical studies made a surprising discovery that in complex systems, the symmetry of molecular forward/backward transition times with respect to local bias in the dynamics may be broken and it may take longer to go downhill than uphill. The physical origins of these phenomena remain not fully understood. Here, we explore in more detail the microscopic features of the symmetry breaking in the forward/backward transition times by analyzing exactly solvable discrete-state stochastic models. In particular, we consider a specific case of two random walkers on a four-site periodic lattice as the way to represent the general systems with multiple pathways. It is found that the asymmetry in transition times depends on several factors that include the degree of deviation from equilibrium, the particle crowding, and methods of measurements of dynamic properties. Our theoretical analysis suggests that the asymmetry in transition times can be explored experimentally for determining the important microscopic features of natural processes by quantitatively measuring the local deviations from equilibrium and the degrees of crowding.

On the Role of Magnesium Ions in the DNA-Scissoring Activity of the Restriction Endonuclease ApaI: Stochastic Kinetics from a Single Molecule to Mesoscopic Paradigm

Biochemical reactions occurring inside cells have significant stochastic signatures due to the low copy number of reacting species. Kinetics of DNA cleavage by restriction endonucleases are no exception as established by single-molecule experiments. Here, we propose a simple reaction scheme to understand the role of the cofactor magnesium ion in the action of the endonuclease ApaI. The methodology is based on the waiting time distribution of cleavage product formation that enables us to determine the corresponding rate both analytically and numerically. The theory is developed at the single-molecule level and then generalized to the biologically relevant case of a population of DNA-endonuclease complexes present inside a cell. The theoretical rate versus cofactor concentration curve is matched with relevant single-molecule experimental data that reveals positive cooperativity of cofactor binding and provides a reliable estimate of model parameters. Furthermore, a parameter range is identified where the dispersion of the waiting time, measured using the coefficient of variation, is significantly lower than the Poisson limit and becomes minimum at the in vivo magnesium ion concentration level. Such low dispersion can play a role in the robust DNA-scissoring activity of ApaI under in vivo conditions.

What Are the Molecular Requirements for Protein Sliding along DNA?

DNA-binding proteins rely on linear diffusion along the longitudinal DNA axis, supported by their nonspecific electrostatic affinity for DNA, to search for their target recognition sites. One may therefore expect that the ability to engage in linear diffusion along DNA is universal to all DNA-binding proteins, with the detailed biophysical characteristics of that diffusion differing between proteins depending on their structures and functions. One key question is whether the linear diffusion mechanism is defined by translation coupled with rotation, a mechanism that is often termed sliding. We conduct coarse-grained and atomistic molecular dynamics simulations to investigate the minimal requirements for protein sliding along DNA. We show that coupling, while widespread, is not universal. DNA-binding proteins that slide along DNA transition to uncoupled translation–rotation (i.e., hopping) at higher salt concentrations. Furthermore, and consistently with experimental reports, we find that the sliding mechanism is the less dominant mechanism for some DNA-binding proteins, even at low salt concentrations. In particular, the toroidal PCNA protein is shown to follow the hopping rather than the sliding mechanism.

Effects of isolated nonspecific binders upon the search for specific targets: Absolute rates versus competition between the targets

Many biological processes involve macromolecules searching for their specific targets that are surrounded by other objects, and binding to these objects affects the target search. Acceleration of the target search by nonspecific binders was observed experimentally and analyzed theoretically, for example, for DNA-binding proteins. According to existing theories this acceleration requires continuous transfer between the nonspecific binders and the specific target. In contrast, our analysis predicts that (i) nonspecific binders could accelerate the search without continuous transfer to the specific target provided that the searching particle is capable of sliding along the binder; (ii) in some cases such binders could decelerate the target search, but provide an advantage in competition with the "binder-free" target; (iii) nonbinding objects decelerate the target search. We also show that although the target search in the presence of binders could be considered as diffusion in inhomogeneous media, in the general case it cannot be described by the effective diffusion coefficient.

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.

Protein-DNA target search relies on quantum walk

Protein-DNA interactions play a fundamental role in all life systems. A critical issue of such interactions is given by the strategy of protein search for specific targets on DNA. The mechanisms by which the protein are able to find relatively small cognate sequences, typically 15-20 base pairs (bps) for repressors, and 4-6 bps for restriction enzymes among the millions of bp of non-specific chromosomal DNA have hardly engaged researchers for decades. Recent experimental studies have generated new insights on the basic processes of protein-DNA interactions evidencing the underlying complex dynamic phenomena involved, which combine three-dimensional and one-dimensional motion along the DNA chain. It has been demonstrated that protein molecules have an extraordinary ability to find the target very quickly on the DNA chain, in some cases, with two orders of magnitude faster than the diffusion limit. This unique property of protein-DNA search mechanism is known as facilitated diffusion. Several theoretical mechanisms have been suggested to describe the origin of facilitated diffusion. However, none of such models currently has the ability to fully describe the protein search strategy. In this paper, we suggest that the ability of proteins to identify consensus sequences on DNA is based on the entanglement of π-π electrons between DNA nucleotides and protein amino acids. The π-π entanglement is based on Quantum Walk (QW), through Coin-position entanglement (CPE). First, the protein identifies a dimer belonging to the consensus sequence, and localize a π on such dimer, hence, the other π electron scans the DNA chain until the sequence is identified. Focusing on the example of recognition of consensus sequences of EcoRV or EcoRI, we will describe the quantum features of QW on protein-DNA complexes during the search strategy, such as walker quadratic spreading on a coherent superposition of different vertices and environment-supported long-time survival probability of the walker. We will employ both discrete- or continuous-time versions of QW. Biased and unbiased classical Random Walk (CRW) have been used for a long time to describe the Protein-DNA search strategy. QW, the quantum version of CRW, has been widely studied for its applications in quantum information applications. In our biological application, the walker (the protein) resides at a vertex in a graph (the DNA structural topology). Differently to CRW, where the walker moves randomly, the quantum walker can hop along the edges in the graph to reach other vertices entering coherently a superposition across different vertices spreading quadratically faster than CRW analogous evidencing the typical speed up features of the QW. When applied to a protein-DNA target search problem, QW gives the possibility to achieve the experimental diffusional motion of proteins over diffusion classical limits experienced along DNA chains exploiting quantum features such as CPE and long-time survival probability supported by the environment. In turn, we come to the conclusion that, under quantum picture, the protein search strategy does not distinguish between one-dimensional (1D) and three-dimensional (3D) cases.

Inchworm stepping of Myc-Max heterodimer protein diffusion along DNA

Oncogenic protein Myc serves as a transcription factor to control cell metabolisms. Myc dimerizes via leucine zipper with its associated partner protein Max to form a heterodimer structure, which then binds target DNA sequences to regulate gene transcription. The regulation depends on Myc-Max binding to DNA and searching for target sequences via diffusional motions along DNA. Here, we conduct structure-based molecular dynamics (MD) simulations to investigate the diffusion dynamics of the Myc-Max heterodimer along DNA. We found that the heterodimer protein slides on the DNA in a rotation-uncoupled manner in coarse-grained simulations, as its two helical DNA binding basic regions (BRs) alternate between open and closed conformations via inchworm stepping motions. In such motions, the two BRs of the heterodimer step across the DNA strand one by one, with step sizes reaching about half of a DNA helical pitch length. Atomic MD simulations of the Myc-Max heterodimer in complex with DNA have also been conducted. Hydrogen bond interactions are revealed between the two BRs and two complementary DNA strands, respectively. In the non-specific DNA binding, the BR from Myc shows an onset of stepping on one association DNA strand and starts detaching from the other strand. Overall, our simulation studies suggest that the inchworm stepping motions of the Myc-Max heterodimer can be achieved during the protein diffusion along DNA.

Effect of DNA Conformation on the Protein Search for Targets on DNA: A Theoretical Perspective

Protein-DNA interactions are important for all biological processes and involve the process of proteins searching for and recognizing specific binding sites on the DNA. Many aspects of the mechanism of the protein search for targets on DNA are not well understood. One important problem is the effect of DNA conformation on the protein search dynamics. Using a theoretical method based on a discrete-state stochastic approach, we obtained an analytical description of the dynamic properties. We investigated a system with two DNA conformers. It was found that the average search time on one DNA conformer via 1D or 3D motions depended on the dynamics of the search process on the other DNA conformer.

CRISPR-Cas9 Genome Interrogation: A Facilitated Subdiffusive Target Search Strategy

The functional application of RNA-guided CRISPR-associated Cas9 protein, a bacterial immune system-based protein complex, via which in vivo, highly specific, and well-regulated, gene-editing processes are being monitored at an unprecedented level, has led to remarkable progress in genetic engineering and technology. The complicated in vivo process of genome interrogation followed by gene editing by the Cas9 complex was recently reported by Knight et al. (Science, 2015, 350, 823-826) using an elegant single-particle tracking method, aided by the two-photon fluorescence correlation spectroscopic technique. In contrast to the usually observed fast target-searching and protein-binding events in biophysical systems, an interesting slow genome-interrogation process by the RNA-guided CRISPR-Cas9 system through a crowded chromatin environment of a mammalian cell has been revealed in Knight et al.'s study. Motivated by this experiment, in this paper, we provide a generalized theoretical framework to capture this particular target-searching mechanism of the CRISPR-Cas9 protein complex. We show that an analysis on the basis of 3D subdiffusion under a cylindrical volume, created by several nonspecific off-target interactions from the DNA strands, can capture the essential details of the process. Moreover, on the basis of this model, we quantify the dynamics of this process and estimate the survival probability, first passage time, and the intensity correlation function of the tagged proteins of the experiment. The results from our theoretical predictions are found to be consistent with the experimental observations, and hence, seem to provide a plausible microscopic picture of the process.

Target search on DNA by interacting molecules: First-passage approach

Gene regulation is one of the most important fundamental biological processes in living cells. It involves multiple protein molecules that locate specific sites on DNA and assemble gene initiation or gene repression multimolecular complexes. While the protein search dynamics for DNA targets has been intensively investigated, the role of intermolecular interactions during the genetic activation or repression remains not well quantified. Here, we present a simple one-dimensional model of target search for two interacting molecules that can reversibly form a dimer molecular complex, which also participates in the search process. In addition, the proteins have finite residence times on specific target sites, and the gene is activated or repressed when both proteins are simultaneously present at the target. The model is analyzed using first-passage analytical calculations and Monte Carlo computer simulations. It is shown that the search dynamics exhibit a complex behavior depending on the strength of intermolecular interactions and on the target residence times. We also found that the search time shows a nonmonotonic behavior as a function of the dissociation rate for the molecular complex. Physical-chemical arguments to explain these observations are presented. Our theoretical approach highlights the importance of molecular interactions in the complex process of gene activation/repression by multiple transcription factor proteins.

Influence of Oligonucleotide Grafting Density on Surface-Mediated DNA Transport and Hybridization

Adsorption of soluble DNA to surfaces decorated with complementary DNA plays an important role in many bionanotechnology applications, and previous studies have reported complex dependencies of the surface density of immobilized DNA on hybridization. While these effects have been speculatively ascribed to steric or electrostatic effects, the influence of surface-mediated molecular transport (i.e., intermittent "hopping diffusion") has not been fully appreciated. Here, single-molecule tracking and Förster resonance energy transfer (FRET) were employed to characterize the mobility and the hybridization efficiency of adsorbed ssDNA oligonucleotides ("target") at solid-liquid interfaces exhibiting surface-immobilized ssDNA ("probe") over a wide range of surface grafting densities. Two distinct regimes were observed, with qualitatively different transport and hybridization behaviors. At dilute grafting density, only 1-3% of target molecules were observed to associate with probes (i.e., to hybridize). Adsorbing target molecules often searched unsuccessfully and "flew", via desorption-mediated diffusion, to secondary locations before hybridizing. In contrast, at high probe grafting density, approximately 20% of target DNA hybridized to immobilized probes, and almost always in the vicinity of initial adsorption. Moreover, following a dehybridization event, target molecules rehybridized at high probe density, but rehybridization was infrequent in the dilute density regime. Interestingly, the intermittent interfacial transport of mobile target molecules was suppressed by the presence of immobilized probe DNA, presumably due to an increased probability of readsorption following each "hop". Together, these findings suggested that many salient effects of grafting density on surface-mediated DNA hybridization can be directly related to the mechanisms of surface-mediated intermittent diffusion.

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.