Intracellular facilitated diffusion: searchers, crowders, and blockers

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.

Single-Molecule Fluorescence Microscopy in Sensory Cilia of Living Caenorhabditis elegans

Intracellular transport of organelles and biomolecules is vital for several cellular processes. Single-molecule fluorescence microscopy can illuminate molecular aspects of the dynamics of individual biomolecules that remain unresolved in ensemble experiments. For example, studying single-molecule trajectories of moving biomolecules can reveal motility properties such as velocity, diffusivity, location and duration of pauses, etc. We use single-molecule imaging to study the dynamics of microtubule-based motor proteins and their cargo in the primary cilia of living C. elegans. To this end, we employ standard fluorescent proteins, an epi-illuminated, widefield fluorescence microscope, and primarily open-source software. This chapter describes the setup we use, the preparation of samples, a protocol for single-molecule imaging in primary cilia of C. elegans, and data analysis.

Interplay between stochastic enzyme activity and microtubule stability drives detyrosination enrichment on microtubule subsets

Microtubules in cells consist of functionally diverse subpopulations carrying distinct post-translational modifications (PTMs). Akin to the histone code, the tubulin code regulates a myriad of microtubule functions, ranging from intracellular transport to chromosome segregation. However, how individual PTMs only occur on subsets of microtubules to contribute to microtubule specialization is not well understood. In particular, microtubule detyrosination, the removal of the C-terminal tyrosine on α-tubulin subunits, marks the stable population of microtubules and modifies how microtubules interact with other microtubule-associated proteins to regulate a wide range of cellular processes. Previously, we found that in certain cell types, only ∼30% of microtubules are highly enriched with the detyrosination mark and that detyrosination spans most of the length of a microtubule, often adjacent to a completely tyrosinated microtubule. How the activity of a cytosolic detyrosinase, vasohibin (VASH), leads to only a small subpopulation of highly detyrosinated microtubules is unclear. Here, using quantitative super-resolution microscopy, we visualized nascent microtubule detyrosination events in cells consisting of 1-3 detyrosinated α-tubulin subunits after nocodazole washout. Microtubule detyrosination accumulates slowly and in a dispersed pattern across the microtubule length. By visualizing single molecules of VASH in live cells, we found that VASH engages with microtubules stochastically on a short timescale, suggesting limited removal of tyrosine per interaction, consistent with the super-resolution results. Combining these quantitative imaging results with simulations incorporating parameters from our experiments, we provide evidence for a stochastic model for cells to establish a subset of detyrosinated microtubules via a detyrosination-stabilization feedback mechanism.

Importin alpha family NAAT/IBB domain: Functions of a pleiotropic long chameleon sequence

Nuclear transport is essential for eukaryotic cell survival and regulates the movement of functional molecules in and out of the nucleus via the nuclear pore. Transport is facilitated by protein-protein interactions between cargo and transport receptors, which contribute to the expression and regulation of downstream genetic information. This chapter focuses on the molecular basis of the multifunctional nature of the importin α family, the representative transport receptors that bring proteins into the nucleus. Importin α performs multiple functions during the nuclear transport cycle through interactions with multiple molecules by a single domain called the IBB domain. This domain is a long chameleon sequence, which can change its conformation and binding mode depending on the interaction partners. By considering the evolutionarily conserved biochemical/physicochemical propensities of the amino acids constituting the functional complex interfaces, together with their structural properties, the mechanisms of switching between multiple complexes formed via IBB and the regulation of downstream functions are examined in detail. The mechanism of regulation by IBB indicates that the time has come for a paradigm shift in the way we view the molecular mechanisms by which proteins regulate downstream functions through their interactions with other molecules.

Structure and Dynamics of dsDNA in Cell-like Environments

Deoxyribonucleic acid (DNA) is a fundamental biomolecule for correct cellular functioning and regulation of biological processes. DNA's structure is dynamic and has the ability to adopt a variety of structural conformations in addition to its most widely known double-stranded DNA (dsDNA) helix structure. Stability and structural dynamics of dsDNA play an important role in molecular biology. In vivo, DNA molecules are folded in a tightly confined space, such as a cell chamber or a channel, and are highly dense in solution; their conformational properties are restricted, which affects their thermodynamics and mechanical properties. There are also many technical medical purposes for which DNA is placed in a confined space, such as gene therapy, DNA encapsulation, DNA mapping, etc. Physiological conditions and the nature of confined spaces have a significant influence on the opening or denaturation of DNA base pairs. In this review, we summarize the progress of research on the stability and dynamics of dsDNA in cell-like environments and discuss current challenges and future directions. We include studies on various thermal and mechanical properties of dsDNA in ionic solutions, molecular crowded environments, and confined spaces. By providing a better understanding of melting and unzipping of dsDNA in different environments, this review provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA/RNA nanostructures.

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.

Importin α2 association with chromatin: Direct DNA binding via a novel DNA-binding domain

The nuclear transport of proteins is important for facilitating appropriate nuclear functions. The importin α family proteins play key roles in nuclear transport as transport receptors for copious nuclear proteins. Additionally, these proteins possess other functions, including chromatin association and gene regulation. However, these nontransport functions of importin α are not yet fully understood, especially their molecular-level mechanisms and consequences for functioning with chromatin. Here, we report the novel molecular characteristics of importin α binding to diverse DNA sequences in chromatin. We newly identified and characterized a DNA-binding domain-the Nucleic Acid Associating Trolley pole domain (NAAT domain)-in the N-terminal region of importin α within the conventional importin β binding (IBB) domain that is necessary for nuclear transport of cargo proteins. Furthermore, we found that the DNA binding of importin α synergistically coupled the recruitment of its cargo protein to DNA. This is the first study to delineate the interaction between importin α and chromatin DNA via the NAAT domain, indicating the bifunctionality of the importin α N-terminal region for nuclear transport and chromatin association.

Polymer brush-induced depletion interactions and clustering of membrane proteins

We investigate the effect of mobile polymer brushes on proteins embedded in biological membranes by employing both Asakura-Oosawa type of theoretical model and coarse-grained molecular dynamics simulations. The brush polymer-induced depletion attraction between proteins changes non-monotonically with the size of brush. The depletion interaction, which is determined by the ratio of the protein size to the grafting distance between brush polymers, increases linearly with the brush size as long as the polymer brush height is shorter than the protein size. When the brush height exceeds the protein size, however, the depletion attraction among proteins is slightly reduced. We also explore the possibility of the brush polymer-induced assembly of a large protein cluster, which can be related to one of many molecular mechanisms underlying recent experimental observations of integrin nanocluster formation and signaling.

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.

Nonequilibrium Strategy for Fast Target Search on the Genome

Vital biological processes such as genome repair require fast and efficient binding of selected proteins to specific target sites on DNA. Here we propose an active target search mechanism based on "chromophoresis," the dynamics of DNA-binding proteins up or down gradients in the density of epigenetic marks, or colors (biochemical tags on the genome). We focus on a set of proteins that deposit marks from which they are repelled-a case which is only encountered away from thermodynamic equilibrium. For suitable ranges of kinetic parameter values, chromophoretic proteins can perform undirectional motion and are optimally redistributed along the genome. Importantly, they can also locally unravel a region of the genome which is collapsed due to self-interactions and "dive" deep into its core, for a striking enhancement of the efficiency of target search on such an inaccessible substrate. We discuss the potential relevance of chromophoresis for DNA repair.

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.

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.

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.

Disparity in anomalous diffusion of proteins searching for their target DNA sites in a crowded medium is controlled by the size, shape and mobility of macromolecular crowders

Using extensive computer simulations, we analyzed the role of physical properties of molecular crowding agents such as size, shape and mobility in the target search dynamics of DNA binding proteins. Our main result is that the sub-diffusive dynamics of a protein inside a crowded medium strongly depends on the crowder properties and also on the protein's mode of diffusion. For instance, while scanning the DNA one-dimensionally, the protein dynamics does not vary with the change in crowder properties. Conversely, the diffusion exponent varies non-monotonically during 3D diffusion and is maximally affected when the crowders match the protein physically. The investigation shows that the effect stems from the ruggedness of the associated potential energy landscape, which is regulated by the protein-crowder and DNA-crowder interactions. Our findings have broad significance in understanding the target search dynamics of proteins on DNA in crowded cellular milieu and selecting appropriate crowding agents when designing in vitro experiments.

Intersegmental transfer of proteins between DNA regions in the presence of crowding

Intersegmental transfer that involves direct relocation of a DNA-binding protein from one nonspecific DNA site to another was previously shown to contribute to speeding up the identification of the DNA target site. This mechanism is promoted when the protein is composed of at least two domains that have different DNA binding affinities and thus show a degree of mobility. In this study, we investigate the effect of particle crowding on the ability of a multi-domain protein to perform intersegmental transfer. We show that although crowding conditions often favor 1D diffusion of proteins along DNA over 3D diffusion, relocation of one of the tethered domains to initiate intersegmental transfer is possible even under crowding conditions. The tendency to perform intersegmental transfer by a multi-domain protein under crowding conditions is much higher for larger crowding particles than smaller ones and can be even greater than under no-crowding conditions. We report that the asymmetry of the two domains is even magnified by the crowders. The observations that crowding supports intersegmental transfer serve as another example that in vivo complexity does not necessarily slow down DNA search kinetics by proteins.

Role of Macromolecular Crowding on the Intracellular Diffusion of DNA Binding Proteins

Recent experiments suggest that cellular crowding facilitates the target search dynamics of proteins on DNA, the mechanism of which is not yet known. By using large scale computer simulations, we show that two competing factors, namely the width of the depletion layer that separates the crowder cloud from the DNA molecule and the degree of protein-crowder crosstalk, act in harmony to affect the target search dynamics of proteins. The impacts vary from nonspecific to specific target search regime. During a nonspecific search, dynamics of a protein is only minimally affected, whereas, a significantly different behaviour is observed when the protein starts forming a specific protein-DNA complex. We also find that the severity of impacts largely depends upon physiological crowder concentration and deviation from it leads to attenuation in the binding kinetics. Based on extensive kinetic study and binding energy landscape analysis, we further present a comprehensive molecular description of the search process that allows us to interpret the experimental findings.

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.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

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.

Facilitated diffusion in the presence of obstacles on the DNA

Biological functions of DNA depend on the sequence-specific binding of DNA-binding proteins to their corresponding binding sites. Binding of these proteins to their binding sites occurs through a facilitated diffusion process that combines three-dimensional diffusion in the cytoplasm with one-dimensional diffusion (sliding) along the DNA. In this work, we use a lattice model of facilitated diffusion to study how the dynamics of binding of a protein to a specific site (e.g., binding of an RNA polymerase to a promoter or of a transcription factor to its operator site) is affected by the presence of other proteins bound to the DNA, which act as 'obstacles' in the sliding process. Different types of these obstacles with different dynamics are implemented. While all types impair facilitated diffusion, the extent of the hindrance depends on the type of obstacle. As a consequence of hindrance by obstacles, more excursions into the cytoplasm are required for optimal target binding compared to the case without obstacles.

DNA melting in the presence of molecular crowders

We study the opening of double stranded DNA (dsDNA) in the presence of molecular crowders using the Peyrard–Bishop–Dauxois (PBD) model.

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.

Rad4 recognition-at-a-distance: Physical basis of conformation-specific anomalous diffusion of DNA repair proteins

Since Robert Brown's first observations of random walks by pollen particles suspended in solution, the concept of diffusion has been subject to countless theoretical and experimental studies in diverse fields from finance and social sciences, to physics and biology. Diffusive transport of macromolecules in cells is intimately linked to essential cellular functions including nutrient uptake, signal transduction, gene expression, as well as DNA replication and repair. Advancement in experimental techniques has allowed precise measurements of these diffusion processes. Mathematical and physical descriptions and computer simulations have been applied to model complicated biological systems in which anomalous diffusion, in addition to simple Brownian motion, was observed. The purpose of this review is to provide an overview of the major physical models of anomalous diffusion and corresponding experimental evidence on the target search problem faced by DNA-binding proteins, with an emphasis on DNA repair proteins and the role of anomalous diffusion in DNA target recognition.

Dynamic DNA binding licenses a repair factor to bypass roadblocks in search of DNA lesions

DNA-binding proteins search for specific targets via facilitated diffusion along a crowded genome. However, little is known about how crowded DNA modulates facilitated diffusion and target recognition. Here we use DNA curtains and single-molecule fluorescence imaging to investigate how Msh2-Msh3, a eukaryotic mismatch repair complex, navigates on crowded DNA. Msh2-Msh3 hops over nucleosomes and other protein roadblocks, but maintains sufficient contact with DNA to recognize a single lesion. In contrast, Msh2-Msh6 slides without hopping and is largely blocked by protein roadblocks. Remarkably, the Msh3-specific mispair-binding domain (MBD) licences a chimeric Msh2-Msh6(3MBD) to bypass nucleosomes. Our studies contrast how Msh2-Msh3 and Msh2-Msh6 navigate on a crowded genome and suggest how Msh2-Msh3 locates DNA lesions outside of replication-coupled repair. These results also provide insights into how DNA repair factors search for DNA lesions in the context of chromatin.

Searching target sites on DNA by proteins: Role of DNA dynamics under confinement

DNA-binding proteins (DBPs) rapidly search and specifically bind to their target sites on genomic DNA in order to trigger many cellular regulatory processes. It has been suggested that the facilitation of search dynamics is achieved by combining 3D diffusion with one-dimensional sliding and hopping dynamics of interacting proteins. Although, recent studies have advanced the knowledge of molecular determinants that affect one-dimensional search efficiency, the role of DNA molecule is poorly understood. In this study, by using coarse-grained simulations, we propose that dynamics of DNA molecule and its degree of confinement due to cellular crowding concertedly regulate its groove geometry and modulate the inter-communication with DBPs. Under weak confinement, DNA dynamics promotes many short, rotation-decoupled sliding events interspersed by hopping dynamics. While this results in faster 1D diffusion, associated probability of missing targets by jumping over them increases. In contrast, strong confinement favours rotation-coupled sliding to locate targets but lacks structural flexibility to achieve desired specificity. By testing under physiological crowding, our study provides a plausible mechanism on how DNA molecule may help in maintaining an optimal balance between fast hopping and rotation-coupled sliding dynamics, to locate target sites rapidly and form specific complexes precisely.

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

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

The robustness of proofreading to crowding-induced pseudo-processivity in the MAPK pathway

Double phosphorylation of protein kinases is a common feature of signaling cascades. This motif may reduce cross-talk between signaling pathways because the second phosphorylation site allows for proofreading, especially when phosphorylation is distributive rather than processive. Recent studies suggest that phosphorylation can be pseudo-processive in the crowded cellular environment, since rebinding after the first phosphorylation is enhanced by slow diffusion. Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding increases and pseudo-processive behavior becomes possible. However, this loss of specificity with increased rebinding is typically also observed if two distinct enzyme species are required for phosphorylation, i.e., when the system is necessarily distributive. Thus the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself. We also show that proofreading can remain effective when the intended signaling pathway exhibits high levels of rebinding-induced pseudo-processivity, unlike other proposed advantages of the dual phosphorylation motif.

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.

Signal focusing through active transport

The accuracy of molecular signaling in biological cells and novel diagnostic devices is ultimately limited by the counting noise floor imposed by the thermal diffusion. Motivated by the fact that messenger RNA and vesicle-engulfed signaling molecules transiently bind to molecular motors and are actively transported in biological cells, we show here that the random active delivery of signaling particles to within a typical diffusion distance to the receptor generically reduces the correlation time of the counting noise. Considering a variety of signaling particle sizes from mRNA to vesicles and cell sizes from prokaryotic to eukaryotic cells, we show that the conditions for active focusing-faster and more precise signaling-are indeed compatible with observations in living cells. Our results improve the understanding of molecular cellular signaling and novel diagnostic devices.

Optimization and universality of Brownian search in a basic model of quenched heterogeneous media

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.

A simple model for DNA bridging proteins and bacterial or human genomes: bridging-induced attraction and genome compaction

We present computer simulations of the phase behaviour of an ensemble of proteins interacting with a polymer, mimicking non-specific binding to a piece of bacterial DNA or eukaryotic chromatin. The proteins can simultaneously bind to the polymer in two or more places to create protein bridges. Despite the lack of any explicit interaction between the proteins or between DNA segments, our simulations confirm previous results showing that when the protein-polymer interaction is sufficiently strong, the proteins come together to form clusters. Furthermore, a sufficiently large concentration of bridging proteins leads to the compaction of the swollen polymer into a globular phase. Here we characterise both the formation of protein clusters and the polymer collapse as a function of protein concentration, protein-polymer affinity and fibre flexibility.

Amplification of salt-induced polymer diffusiophoresis by increasing salting-out strength

The role of salting-out strength on (1) polymer diffusiophoresis from high to low salt concentration, and (2) salt osmotic diffusion from high to low polymer concentration was investigated. These two cross-diffusion phenomena were experimentally characterized by Rayleigh interferometry at 25 °C. Specifically, we report ternary diffusion coefficients for polyethylene glycol (molecular weight, 20 kg·mol(-1)) in aqueous solutions of several salts (NaCl, KCl, NH4Cl, CaCl2, and Na2SO4) as a function of salt concentration at low polymer concentration (0.5% w/w). We also measured polymer diffusion coefficients by dynamic light scattering in order to discuss the interpretation of these transport coefficients in the presence of cross-diffusion effects. Our cross-diffusion results, primarily those on salt osmotic diffusion, were utilized to extract N(w), the number of water molecules in thermodynamic excess around a macromolecule. This preferential-hydration parameter characterizes the salting-out strength of the employed salt. For chloride salts, changing cation has a small effect on N(w). However, replacing NaCl with Na2SO4 (i.e., changing anion) leads to a 3-fold increase in N(w), in agreement with cation and anion Hofmeister series. Theoretical arguments show that polymer diffusiophoresis is directly proportional to the difference N(w) - n(w), where n(w) is the number of water molecules transported by the migrating macromolecule. Interestingly, the experimental ratio, n(w)/N(w), was found to be approximately the same for all investigated salts. Thus, the magnitude of polymer diffusiophoresis is also proportional to salting-out strength as described by N(w). A basic hydrodynamic model was examined in order to gain physical insight on the role of n(w) in particle diffusiophoresis and explain the observed invariance of n(w)/N(w). Finally, we consider a steady-state diffusion problem to show that concentration gradients of strong salting-out agents such as Na2SO4 can produce large amplifications and depletions of macromolecule concentration. These effects may be exploited in self-assembly and adsorption processes.

Search by proteins for their DNA target site: 1. The effect of DNA conformation on protein sliding

The recognition of DNA-binding proteins (DBPs) to their specific site often precedes by a search technique in which proteins slide, hop along the DNA contour or perform inter-segment transfer and 3D diffusion to dissociate and re-associate to distant DNA sites. In this study, we demonstrated that the strength and nature of the non-specific electrostatic interactions, which govern the search dynamics of DBPs, are strongly correlated with the conformation of the DNA. We tuned two structural parameters, namely curvature and the extent of helical twisting in circular DNA. These two factors are mutually independent of each other and can modulate the electrostatic potential through changing the geometry of the circular DNA conformation. The search dynamics for DBPs on circular DNA is therefore markedly different compared with linear B-DNA. Our results suggest that, for a given DBP, the rotation-coupled sliding dynamics is precluded in highly curved DNA (as well as for over-twisted DNA) because of the large electrostatic energy barrier between the inside and outside of the DNA molecule. Under such circumstances, proteins prefer to hop in order to explore interior DNA sites. The change in the balance between sliding and hopping propensities as a function of DNA curvature or twisting may result in different search efficiency and speed.

Facilitated diffusion buffers noise in gene expression

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

Effect of particle size on salt-induced diffusiophoresis compared to Brownian mobility

For ternary polymer-salt-water systems at low polymer concentration (0.5%, w/w), we have experimentally investigated the effect of polymer size on polymer diffusiophoresis (i.e., polymer migration induced by a salt concentration gradient) and salt osmotic diffusion (i.e., salt migration induced by a polymer concentration gradient). Specifically, Rayleigh interferometry was employed to measure ternary diffusion coefficients for aqueous solutions of poly(ethylene glycol) (PEG) and KCl at 25 °C. Our investigation focused on four polymer molecular masses (from 10 to 100 kg mol(-1)) and two salt concentrations (0.25 and 0.50 M). To describe and examine our experimental results, we introduced a normalized diffusiophoresis coefficient as the ratio of polymer diffusiophoresis to polymer Brownian mobility. This coefficient was found to increase with polymer molecular mass, thereby demonstrating that the relative importance of polymer diffusiophoresis compared to its intrinsic Brownian mobility increases with particle size. The observed behavior was linked to preferential hydration (water thermodynamic excess) and hydration (bound water) of the macromolecule. The ratio of salt osmotic diffusion to binary salt-water diffusion approximately describes the nonuniform spatial distribution of salt along a static polymer concentration gradient at equilibrium. The significance of polymer diffusiophoresis, especially at high PEG molecular mass, was examined by considering a steady-state diffusion problem showing that salt concentration gradients can produce large enhancements and depletions of polymer concentration. This work is valuable for understanding and modeling the effect of salt concentration gradients on diffusion-based transport of polymers with applications to interfacial processes.

Physical constraints determine the logic of bacterial promoter architectures

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

The effects of transcription factor competition on gene regulation

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