Description of nonspecific DNA-protein interaction and facilitated diffusion with a dynamical model

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

Impact of Self-Association on the Architectural Properties of Bacterial Nucleoid Proteins

The chromosomal DNA of bacteria is folded into a compact body called the nucleoid, which is composed essentially of DNA (∼80%), RNA (∼10%), and a number of different proteins (∼10%). These nucleoid proteins act as regulators of gene expression and influence the organization of the nucleoid by bridging, bending, or wrapping the DNA. These so-called architectural properties of nucleoid proteins are still poorly understood. For example, the reason why certain proteins compact the DNA coil in certain environments but make the DNA more rigid instead in other environments is the subject of ongoing debates. Here, we address the question of the impact of the self-association of nucleoid proteins on their architectural properties and try to determine whether differences in self-association are sufficient to induce large changes in the organization of the DNA coil. More specifically, we developed two coarse-grained models of proteins, which interact identically with the DNA but self-associate differently by forming either clusters or filaments in the absence of the DNA. We showed through Brownian dynamics simulations that self-association of the proteins dramatically increases their ability to shape the DNA coil. Moreover, we observed that cluster-forming proteins significantly compact the DNA coil (similar to the DNA-bridging mode of H-NS proteins), whereas filament-forming proteins significantly increase the stiffness of the DNA chain instead (similar to the DNA-stiffening mode of H-NS proteins). This work consequently suggests that the knowledge of the DNA-binding properties of the proteins is in itself not sufficient to understand their architectural properties. Rather, their self-association properties must also be investigated in detail because they might actually drive the formation of different DNA-protein complexes.

Requirements for DNA-Bridging Proteins to Act as Topological Barriers of the Bacterial Genome

Bacterial genomes have been shown to be partitioned into several-kilobase-long chromosomal domains that are topologically independent from each other, meaning that change of DNA superhelicity in one domain does not propagate to neighbors. Both in vivo and in vitro experiments have been performed to question the nature of the topological barriers at play, leading to several predictions on possible molecular actors. Here, we address the question of topological barriers using polymer models of supercoiled DNA chains that are constrained such as to mimic the action of predicted molecular actors. More specifically, we determine under which conditions DNA-bridging proteins may act as topological barriers. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. As a result, we find that DNA-bridging proteins must exert rather strong constraints on their binding sites; they must block the diffusion of the excess of twist through the two binding sites on the DNA molecule and, simultaneously, prevent the rotation of one DNA segment relative to the other one. Importantly, not all DNA-bridging proteins satisfy this second condition. For example, single bridges formed by proteins that bind DNA nonspecifically, like H-NS dimers, are expected to fail with this respect. Our findings might also explain, in the case of specific DNA-bridging proteins like LacI, why multiple bridges are required to create stable independent topological domains. Strikingly, when the relative rotation of the DNA segments is not prevented, relaxation results in complex intrication of the two domains. Moreover, although the value of the torsional stress in each domain may vary, their differential is preserved. Our work also predicts that nucleoid-associated proteins known to wrap DNA must form higher protein-DNA complexes to efficiently work as topological barriers.

Bacterial Nucleoid: Interplay of DNA Demixing and Supercoiling

This work addresses the question of the interplay of DNA demixing and supercoiling in bacterial cells. Demixing of DNA from other globular macromolecules results from the overall repulsion between all components of the system and leads to the formation of the nucleoid, which is the region of the cell that contains the genomic DNA in a rather compact form. Supercoiling describes the coiling of the axis of the DNA double helix to accommodate the torsional stress injected in the molecule by topoisomerases. Supercoiling is able to induce some compaction of the bacterial DNA, although to a lesser extent than demixing. In this work, we investigate the interplay of these two mechanisms with the goal of determining whether the total compaction ratio of the DNA is the mere sum or some more complex function of the compaction ratios due to each mechanism. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. This work reveals that there actually exist different regimes, depending on the crowder volume ratio and the DNA superhelical density. In particular, a regime in which the effects of DNA demixing and supercoiling on the compaction of the DNA coil simply add up is shown to exist up to moderate values of the superhelical density. In contrast, the mean radius of the DNA coil no longer decreases above this threshold and may even increase again for sufficiently large crowder concentrations. Finally, the model predicts that the DNA coil may depart from the spherical geometry very close to the jamming threshold as a trade-off between the need to minimize both the bending energy of the stiff plectonemes and the volume of the DNA coil to accommodate demixing.

Preferential Localization of the Bacterial Nucleoid

Prokaryotes do not make use of a nucleus membrane to segregate their genetic material from the cytoplasm, so that their nucleoid is potentially free to explore the whole volume of the cell. Nonetheless, high resolution images of bacteria with very compact nucleoids show that such spherical nucleoids are invariably positioned at the center of mononucleoid cells. The present work aims to determine whether such preferential localization results from generic (entropic) interactions between the nucleoid and the cell membrane or instead requires some specific mechanism, like the tethering of DNA at mid-cell or periodic fluctuations of the concentration gradient of given chemical species. To this end, we performed numerical simulations using a coarse-grained model based on the assumption that the formation of the nucleoid results from a segregative phase separation mechanism driven by the de-mixing of the DNA and non-binding globular macromolecules. These simulations show that the abrupt compaction of the DNA coil, which takes place at large crowder density, close to the jamming threshold, is accompanied by the re-localization of the DNA coil close to the regions of the bounding wall with the largest curvature, like the hemispherical caps of rod-like cells, as if the DNA coil were suddenly acquiring the localization properties of a solid sphere. This work therefore supports the hypothesis that the localization of compact nucleoids at regular cell positions involves either some anchoring of the DNA to the cell membrane or some dynamical localization mechanism.

A segregative phase separation scenario of the formation of the bacterial nucleoid

The mechanism responsible for the compaction of the genomic DNA of bacteria inside a structure called the nucleoid is a longstanding but still lively debated question. Most puzzling is the fact that the nucleoid occupies only a small fraction of the cell, although it is not separated from the rest of the cytoplasm by any membrane and would occupy a volume about a thousand times larger outside the cell. Here, by performing numerical simulations using coarse-grained models, we elaborate on the conjecture that the formation of the nucleoid may result from a segregative phase separation mechanism driven by the demixing of the DNA coil and non-binding globular macromolecules present in the cytoplasm, presumably functional ribosomes. Simulations performed with crowders having a spherical, dumbbell or octahedral geometry highlight the sensitive dependence of the level of DNA compaction on the dissymmetry of DNA/DNA, DNA/crowder, and crowder/crowder repulsive interactions, thereby supporting the segregative phase separation scenario. Simulations also consistently predict a much stronger DNA compaction close to the jamming threshold. Moreover, simulations performed with crowders of different sizes suggest that the final density distribution of each species results from the competition between thermodynamic forces and steric hindrance, so that bigger crowders are expelled selectively from the nucleoid only at moderate total crowder concentrations. This work leads to several predictions, which may eventually be tested experimentally.

Role of Salt Valency in the Switch of H-NS Proteins between DNA-Bridging and DNA-Stiffening Modes

This work investigates the interactions of H-NS proteins and bacterial genomic DNA through computer simulations performed with a coarse-grained model. The model was developed specifically to study the switch of H-NS proteins from the DNA-stiffening to the DNA-bridging mode, which has been observed repeatedly upon addition of multivalent cations to the buffer but is still not understood. Unraveling the corresponding mechanism is all the more crucial, as the regulation properties of H-NS proteins, as well as other nucleoid proteins, are linked to their DNA-binding properties. The simulations reported here support a mechanism, according to which the primary role of multivalent cations consists in decreasing the strength of H-NS/DNA interactions compared to H-NS/H-NS interactions, with the latter ones becoming energetically favored with respect to the former ones above a certain threshold of the effective valency of the cations of the buffer. Below the threshold, H-NS dimers form filaments, which stretch along the DNA molecule but are quite inefficient in bridging genomically distant DNA sites (DNA-stiffening mode). In contrast, just above the threshold, H-NS dimers form three-dimensional clusters, which are able to connect DNA sites that are distant from the genomic point of view (DNA-bridging mode). The model provides clear rationales for the experimental observations that the switch between the two modes is a threshold effect and that the ability of H-NS dimers to form higher order oligomers is crucial for their bridging capabilities.

High Free-Energy Barrier of 1D Diffusion Along DNA by Architectural DNA-Binding Proteins

Architectural DNA-binding proteins function to regulate diverse DNA reactions and have the defining property of significantly changing DNA conformation. Although the 1D movement along DNA by other types of DNA-binding proteins has been visualized, the mobility of architectural DNA-binding proteins on DNA remains unknown. Here, we applied single-molecule fluorescence imaging on arrays of extended DNA molecules to probe the binding dynamics of three structurally distinct architectural DNA-binding proteins: Nhp6A, HU, and Fis. Each of these proteins was observed to move along DNA, and the salt concentration independence of the 1D diffusion implies sliding with continuous contact to DNA. Nhp6A and HU exhibit a single sliding mode, whereas Fis exhibits two sliding modes. Based on comparison of the diffusion coefficients and sizes of many DNA binding proteins, the architectural proteins are categorized into a new group distinguished by an unusually high free-energy barrier for 1D diffusion. The higher free-energy barrier for 1D diffusion by architectural proteins can be attributed to the large DNA conformational changes that accompany binding and impede rotation-coupled movement along the DNA grooves.

Coarse-Grained Model of the Demixing of DNA and Non-Binding Globular Macromolecules

The volume occupied by the unconstrained genomic DNA of prokaryotes in saline solutions is thousand times larger than the cell. Moreover, it is not separated from the rest of the cell by a membrane. Nevertheless, it occupies only a small fraction of the cell called the nucleoid. The mechanisms leading to such compaction are the matter of ongoing debates. The present work aims at exploring a newly proposed mechanism, according to which the formation of the nucleoid would result from the demixing of the DNA and nonbinding globular macromolecules of the cytoplasm, like ribosomes. To this end, a coarse-grained model of prokaryotic cells was developed, and demixing was analyzed as a function of the size and number of crowders. The model suggests that compaction of the DNA is actually governed by the volume occupancy ratio of the crowders and remains weak almost up to the jamming critical density. Strong compaction is however observed just before jamming, suggesting that crowding and electrostatic repulsion work synergetically in this limit. Finally, simulations performed with crowders with different sizes indicate that the DNA and the largest crowders demix preferentially. Together with the recent observation of the gradual compaction of long DNA molecules upon increase of the concentration of bovine serum albumin proteins and silica nanoparticles, this work supports the demixing mechanism as a key player for the formation of the nucleoid.

Streptavidin-coated gold nanoparticles: critical role of oligonucleotides on stability and fractal aggregation

Gold nanoparticles (AuNPs) exhibit unique properties that can be modulated through a tailored surface functionalization, enabling their targeted use in biochemical sensing and medical diagnostics. In particular, streptavidin-modified AuNPs are increasingly used for biosensing purposes. We report here a study of AuNPs surface-functionalized with streptavidin-biotinylated oligonucleotide, focussing on the role played by the oligonucleotide probes in the stabilization/destabilization of the functionalized nanoparticle dispersion. The behaviour of the modified AuNP dispersion as a consequence of the competitive displacement of the biotinylated oligonucleotide has been investigated and the critical role of displaced oligonucletides in triggering the quasi one-dimensional aggregation of nanoparticles is demonstrated for the first time. The thorough understanding of the fundamental properties of bioconjugated AuNPs is of great importance for the design of highly sensitive and reliable functionalized AuNP-based assays.

Theory of bimolecular reactions in a solution with linear traps: Application to the problem of target search on DNA

One-dimensional sliding along DNA as a means to accelerate protein target search is a well-known phenomenon occurring in various biological systems. Using a biomimetic approach, we have recently demonstrated the practical use of DNA-sliding peptides to speed up bimolecular reactions more than an order of magnitude by allowing the reactants to associate not only in the solution by three-dimensional (3D) diffusion, but also on DNA via one-dimensional (1D) diffusion [A. Turkin et al., Chem. Sci. (2015)]. Here we present a mean-field kinetic model of a bimolecular reaction in a solution with linear extended sinks (e.g., DNA) that can intermittently trap molecules present in a solution. The model consists of chemical rate equations for mean concentrations of reacting species. Our model demonstrates that addition of linear traps to the solution can significantly accelerate reactant association. We show that at optimum concentrations of linear traps the 1D reaction pathway dominates in the kinetics of the bimolecular reaction; i.e., these 1D traps function as an assembly line of the reaction product. Moreover, we show that the association reaction on linear sinks between trapped reactants exhibits a nonclassical third-order behavior. Predictions of the model agree well with our experimental observations. Our model provides a general description of bimolecular reactions that are controlled by a combined 3D+1D mechanism and can be used to quantitatively describe both naturally occurring as well as biomimetic biochemical systems that reduce the dimensionality of search.

Equilibration of complexes of DNA and H-NS proteins on charged surfaces: a coarse-grained model point of view

The Histone-like Nucleoid Structuring protein (H-NS) is a nucleoid-associated protein, which is involved in both gene regulation and DNA compaction. Although it is a key player in genome organization by forming bridges between DNA duplexes, the precise structure of complexes of DNA and H-NS proteins is still not well understood. In particular, it is not clear whether the structure of DNA/H-NS complexes in the living cell is similar to that of complexes deposited on mica surfaces, which may be observed by AFM microscopy. A coarse-grained model, which helps getting more insight into this question, is described and analyzed in the present paper. This model is able of describing both the bridging of bacterial DNA by H-NS in the bulk and the deposition and equilibration of the complex on a charged surface. Simulations performed with the model reveal that a slight attraction between DNA and the charged surface is sufficient to let DNA/H-NS complexes reorganize from 3D coils to planar plasmids bridged by H-NS proteins similar to those observed by AFM microscopy. They furthermore highlight the antagonistic effects of the interactions between DNA and the surface. Indeed, increasing these interactions slows down the equilibration of naked plasmids on the surface but, on the other hand, enables a faster equilibration of DNA/H-NS complexes. Based on the distribution of the lifetimes of H-NS bridges and the time evolution of the number of trans-binding protein dimers during equilibration of the complexes on the surface, it is argued that the decrease of the equilibration time of the complex upon increase of the interaction strength between DNA and the surface is ascribable to the associated decrease of the probability to form new bridges between DNA and the proteins.

Compaction of bacterial genomic DNA: clarifying the concepts

The unconstrained genomic DNA of bacteria forms a coil, whose volume exceeds 1000 times the volume of the cell. Since prokaryotes lack a membrane-bound nucleus, in sharp contrast with eukaryotes, the DNA may consequently be expected to occupy the whole available volume when constrained to fit in the cell. Still, it has been known for more than half a century that the DNA is localized in a well-defined region of the cell, called the nucleoid, which occupies only 15% to 25% of the total volume. Although this problem has focused the attention of many scientists in recent decades, there is still no certainty concerning the mechanism that enables such a dramatic compaction. The goal of this Topical Review is to take stock of our knowledge on this question by listing all possible compaction mechanisms with the proclaimed desire to clarify the physical principles they are based upon and discuss them in the light of experimental results and the results of simulations based on coarse-grained models. In particular, the fundamental differences between ψ-condensation and segregative phase separation and between the condensation by small and long polycations are highlighted. This review suggests that the importance of certain mechanisms, like supercoiling and the architectural properties of DNA-bridging and DNA-bending nucleoid proteins, may have been overestimated, whereas other mechanisms, like segregative phase separation and the self-association of nucleoid proteins, as well as the possible role of the synergy of two or more mechanisms, may conversely deserve more attention.

Molecular crowding effect on dynamics of DNA-binding proteins search for their targets

DNA-binding proteins locate and bind their target sequences positioned on DNA in crowded environments, but the molecular crowding effect on this search process is not clear. Using analytical techniques and Langevin dynamics simulations in two dimensions (2D), we find that the essential physics for facilitated diffusion in 2D search and 3D search is the same. We observe that the average search times have minima at the same optimal nonspecific binding energy for the cases with and without the crowding particle. Moreover, the molecular crowding increases the search time by increasing the average search rounds and the one-dimensional (1D) sliding time of a round, but almost not changing the average 2D diffusion time of a round. In addition, the fraction of 1D sliding time out of the total search time increases with increasing the concentration of crowders. For 2D diffusion, the molecular crowding decreases the jumping length and narrows its distribution due to the cage effect from crowders. These results shed light on the role of facilitated diffusion in DNA targeting kinetics in living cells.

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

Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs.

Conformational and mechanical changes of DNA upon transcription factor binding detected by a QCM and transmission line model

A novel quartz crystal microbalance (QCM) analytical method is developed based on the transmission line model (TLM) algorithm to analyze the binding of transcription factors (TFs) to immobilized DNA oligoduplexes. The method is used to characterize the mechanical properties of biological films through the estimation of the film dynamic shear moduli, G and G, and the film thickness. Using the Saccharomyces cerevisiae transcription factor Haa1 (Haa1DBD) as a biological model two sensors were prepared by immobilizing DNA oligoduplexes, one containing the Haa1 recognition element (HRE(wt)) and another with a random sequence (HRE(neg)) used as a negative control. The immobilization of DNA oligoduplexes was followed in real time and we show that DNA strands initially adsorb with low or non-tilting, laying flat close to the surface, which then lift-off the surface leading to final film tilting angles of 62.9° and 46.7° for HRE(wt) and HRE(neg), respectively. Furthermore we show that the binding of Haa1DBD to HRE(wt) leads to a more ordered and compact film, and forces a 31.7° bending of the immobilized HRE(wt) oligoduplex. This work demonstrates the suitability of the QCM to monitor the specific binding of TFs to immobilized DNA sequences and provides an analytical methodology to study protein-DNA biophysics and kinetics.

Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems

Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne-Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne-Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead-shell molecular models, using either the analytical Rotne-Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies.

A model of H-NS mediated compaction of bacterial DNA

The histone-like nucleoid structuring protein (H-NS) is a nucleoid-associated protein, which is involved in both gene regulation and DNA compaction. H-NS can bind to DNA in two different ways: in trans, by binding to two separate DNA duplexes, or in cis, by binding to different sites on the same duplex. Based on scanning force microscopy imaging and optical trap-driven unzipping assays, it has recently been suggested that DNA compaction may result from the antagonistic effects of H-NS binding to DNA in trans and cis configurations. To get more insight into the compaction mechanism, we constructed a coarse-grained model description of the compaction of bacterial DNA by H-NS. These simulations highlight the fact that DNA compaction indeed results from the subtle equilibrium between several competing factors, which include the deformation dynamics of the plasmid and the several binding modes of protein dimers to DNA, i.e., dangling configurations, cis- and trans-binding. In particular, the degree of compaction is extremely sensitive to the difference in binding energies of the cis and trans configurations. Our simulations also point out that the conformations of the DNA-protein complexes are significantly different in bulk and in planar conditions, suggesting that conformations observed on mica surfaces may differ significantly from those that prevail in living cells.

Intracellular facilitated diffusion: searchers, crowders, and blockers

In bacteria, regulatory proteins search for a specific DNA-binding target via "facilitated diffusion": a series of rounds of three-dimensional diffusion in the cytoplasm, and one-dimensional (1D) linear diffusion along the DNA contour. Using large scale Brownian dynamics simulations we find that each of these steps is affected differently by crowding proteins, which can either be bound to the DNA acting as a road block to the 1D diffusion, or freely diffusing in the cytoplasm. Macromolecular crowding can strongly affect mechanistic features such as the balance between three-dimensional and 1D diffusion, but leads to surprising robustness of the total search time.

Effect of DNA conformation on facilitated diffusion

Within a living cell, site-specific DNA-binding proteins need to search the whole genome to find a target of ~10-20 bp. That they find the target, and do so quickly, is vital for the correct functioning of the DNA, and of the cell as a whole. The current understanding is that this search is performed via facilitated diffusion, i.e. by combining three-dimensional bulk diffusion within the cytoplasm or nucleoplasm, with one-dimensional diffusion along the DNA backbone, to which the protein binds non-specifically. After reviewing the standard theory of facilitated diffusion, we discuss in the present article the still rather rare direct computer simulations of this process, focusing on the three-dimensional part of the search, and the effect of DNA looping and the general DNA conformation on its efficiency. We close by highlighting some open questions in this field.

Proteins searching for their target on DNA by one-dimensional diffusion: overcoming the "speed-stability" paradox

The sequence dependence of DNA-protein interactions that allows proteins to find the correct reaction site also slows down the 1D diffusion of the protein along the DNA molecule, leading to the so-called "speed-stability paradox," wherein fast diffusion along the DNA molecule is seemingly incompatible with stable targeting of the reaction site. Here, we develop diffusion-reaction models that use discrete and continuous Gaussian random 1D diffusion landscapes with or without a high-energy cut-off, and two-state models with a transition to and from a "searching" mode in which the protein diffuses rapidly without recognizing the target. We show the conditions under which such considerations lead to a predicted speed-up of the targeting process, and under which the presence of a "searching" mode in a two-state model is nearly equivalent to the existence of a high-energy cut-off in a one-state model. We also determine the conditions under which the search is either diffusion-limited or reaction-limited, and develop quantitative expressions for the rate of successful targeting as a function of the site-specific reaction rate, the roughness of the DNA-protein interaction potential, and the presence of a "searching" mode. In general, we find that a rough landscape is compatible with a fast search if the highest energy barriers can be avoided by "hopping" or by the protein transitioning to a lower-energy "searching" mode. We validate these predictions with the results of Brownian dynamics, kinetic Metropolis, and kinetic Monte Carlo simulations of the diffusion and targeting process, and apply these concepts to the case of T7 RNA polymerase searching for its target site on T7 DNA.

Facilitated diffusion on mobile DNA: configurational traps and sequence heterogeneity

We present Brownian dynamics simulations of the facilitated diffusion of a protein, modeled as a sphere with a binding site on its surface, along DNA, modeled as a semiflexible polymer. We consider both the effect of DNA organization in three dimensions and of sequence heterogeneity. We find that in a network of DNA loops, which are thought to be present in bacterial DNA, the search process is very sensitive to the spatial location of the target within such loops. Therefore, specific genes might be repressed or promoted by changing the local topology of the genome. On the other hand, sequence heterogeneity creates traps which normally slow down facilitated diffusion. When suitably positioned, though, these traps can, surprisingly, render the search process much more efficient.

Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states

Transcription factors (TFs) such as the lac repressor find their target sequence on DNA at remarkably high rates. In the established Berg-von Hippel model for this search process, the TF alternates between three-dimensional diffusion in the bulk solution and one-dimensional sliding along the DNA chain. To overcome the so-called speed-stability paradox, in similar models the TF was considered as being present in two conformations (search state and recognition state) between which it switches stochastically. Combining both the facilitated diffusion model and alternating states, we obtain a generalized model. We explicitly treat bulk excursions for rodlike chains arranged in parallel and consider a simplified model for coiled DNA. Compared to previously considered facilitated diffusion models, corresponding to limiting cases of our generalized model, we surprisingly find a reduced target search rate. Moreover, at optimal conditions there is no longer an equipartition between the time spent by the protein on and off the DNA chain.

Facilitated diffusion on confined DNA

In living cells, proteins combine three-dimensional bulk diffusion and one-dimensional sliding along the DNA to reach a target faster. This process is known as facilitated diffusion and we investigate its dynamics in the physiologically relevant case of confined DNA. The confining geometry and DNA elasticity are key parameters: We find that facilitated diffusion is most efficient inside an isotropic volume and on a flexible polymer. By considering the typical copy numbers of proteins in vivo, we show that the speedup due to sliding becomes insensitive to fine tuning of parameters, rendering facilitated diffusion a robust mechanism to speed up intracellular diffusion-limited reactions. The parameter range we focus on is relevant for in vitro systems and for facilitated diffusion on yeast chromatin.

Classes of fast and specific search mechanisms for proteins on DNA

Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.

Towards a molecular view of transcriptional control

The accumulation of experimental data over recent years has fueled theoretical work on how transcription factors (TFs) search for and recognise their DNA target sites, how they interact with one another, or with other DNA-binding proteins, and how they cope with the compaction of DNA within bacterial nucleoids or within eukaryotic chromatin. Many models have been built to study the kinetic, thermodynamic and mechanistic aspects of these questions. In some cases they have resulted in a relatively clear consensus view, but a number of questions remain controversial. We present an overview of recent work, with an emphasis on models that provide, or can inspire, a better understanding of transcriptional control at a detailed molecular level.

The binding process of a nonspecific enzyme with DNA

Protein-DNA recognition of a nonspecific complex is modeled to understand the nature of the transient encounter states. We consider the structural and energetic features and the role of water in the DNA grooves in the process of protein-DNA recognition. Here we have used the nuclease domain of colicin E7 (N-ColE7) from Escherichia coli in complex with a 12-bp DNA duplex as the model system to consider how a protein approaches, encounters, and associates with DNA. Multiscale simulation studies using Brownian dynamics and molecular-dynamics simulations were performed to provide the binding process on multiple length- and timescales. We define the encounter states and identified the spatial and orientational aspects. For the molecular length-scales, we used molecular-dynamics simulations. Several intermediate binding states were found, which have different positions and orientations of protein around DNA including major and minor groove orientations. The results show that the contact number and the hydrated interfacial area are measures that facilitate better understanding of sequence-independent protein-DNA binding landscapes and pathways.

Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide

In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts et al. [J. Chem. Phys. 126, 084901 (2007)], can be adapted to describe the thermal and mechanical denaturation of long DNA sequences by adjusting slightly the base pairing contribution. The adjusted model leads to (i) critical temperatures for long homogeneous sequences that are in good agreement with both experimental ones and those obtained from statistical models, (ii) a realistic step-like denaturation behaviour for long inhomogeneous sequences, and (iii) critical forces at ambient temperature of the order of 10 pN, close to measured values. The adjusted model furthermore supports the conclusion that the thermal denaturation of long homogeneous sequences corresponds to a first-order phase transition and yields a critical exponent for the critical force equal to σ = 0.70. This model is both geometrically and energetically realistic, in the sense that the helical structure and the grooves, where most proteins bind, are satisfactorily reproduced, while the energy and the force required to break a base pair lie in the expected range. It therefore represents a promising tool for studying the dynamics of DNA-protein specific interactions at an unprecedented detail level.

Theoretical and computational modeling of target-site search kinetics in vitro and in vivo

Access to genetically encoded data depends on the dynamics of DNA-binding proteins searching for specific target sites in the genome. This search process is thought to occur by facilitated diffusion-a combination of three-dimensional diffusion and one-dimensional sliding. Although facilitated diffusion is capable of significantly speeding up the search in vitro, the importance of this mechanism in vivo remains unclear. We use numeric simulations and analytical theory to model the target-search dynamics of DNA-binding proteins under a wide range of conditions. Our models reproduce experimental measurements of search-rate enhancement within bulk in vitro experiments, as well as the target search time for transcription factors measured in vivo. We find that facilitated diffusion can accelerate the search process only for a limited range of parameters and only under dilute DNA conditions. We address the role of DNA configuration and confinement, demonstrating that facilitated diffusion does not speed up the search on coiled versus straight DNA. Furthermore, we show that, under in vivo conditions, the search process becomes effectively diffusive and is independent of DNA configuration. We believe our results cast in a new light the role of facilitated diffusion in DNA targeting kinetics within the cell.

Diffusion in crowded biological environments: applications of Brownian dynamics

Biochemical reactions in living systems occur in complex, heterogeneous media with total concentrations of macromolecules in the range of 50 - 400 mgml. Molecular species occupy a significant fraction of the immersing medium, up to 40% of volume. Such complex and volume-occupied environments are generally termed 'crowded' and/or 'confined'. In crowded conditions non-specific interactions between macromolecules may hinder diffusion - a major process determining metabolism, transport, and signaling. Also, the crowded media can alter, both qualitatively and quantitatively, the reactions in vivo in comparison with their in vitro counterparts. This review focuses on recent developments in particle-based Brownian dynamics algorithms, their applications to model diffusive transport in crowded systems, and their abilities to reproduce and predict the behavior of macromolecules under in vivo conditions.

Protein sliding and hopping kinetics on DNA

Using Monte Carlo simulations, we deconvolved the sliding and hopping kinetics of GFP-LacI proteins on elongated DNA from their experimentally observed seconds-long diffusion trajectories. Our simulations suggest the following results: (i) in each diffusion trajectory, a protein makes on average hundreds of alternating slides and hops with a mean sliding time of several tens of milliseconds; (ii) sliding dominates the root-mean-square displacement of fast diffusion trajectories, whereas hopping dominates slow ones; (iii) flow and variations in salt concentration have limited effects on hopping kinetics, while in vivo DNA configuration is not expected to influence sliding kinetics; and (iv) the rate of occurrence for hops longer than 200 nm agrees with experimental data for EcoRV proteins.

Dynamic strategies for target-site search by DNA-binding proteins

Gene regulatory proteins find their target sites on DNA remarkably quickly; the experimental binding rate for lac repressor is orders-of-magnitude higher than predicted by free diffusion alone. It has been proposed that nonspecific binding aids the search by allowing proteins to slide and hop along DNA. We develop a reaction-diffusion theory of protein translocation that accounts for transport both on and off the strand and incorporates the physical conformation of DNA. For linear DNA modeled as a wormlike chain, the distribution of hops available to a protein exhibits long, power-law tails that make the long-time displacement along the strand superdiffusive. Our analysis predicts effective superdiffusion coefficients for given nonspecific binding and unbinding rate parameters. Translocation rate exhibits a maximum at intermediate values of the binding rate constant, while search efficiency is optimized at larger binding rate constant values. Thus, our theory predicts a region of values of the nonspecific binding and unbinding rate parameters that balance the protein translocation rate and the efficiency of the search. Published data for several proteins falls within this predicted region of parameter values.