Effects of macromolecular crowding and DNA looping on gene regulation kinetics

Unexpected effects of disorder on current fluctuations in the symmetric simple exclusion process

We explore how the disorder impacts the current fluctuations in the symmetric simple exclusion process (SSEP) within a heterogeneous environment. First, we analyze the SSEP with a defect site under the periodic boundary conditions. We derive the exact expression for the second moment of the current and observe deviations from that of the homogeneous system. Notably, the second moment of the current shows asymmetric density dependence around a density of 1/2 and surpassing that of the homogeneous system in the low-density region. Furthermore, based on the finding from the SSEP with a defect site, we present an approximate derivation of the second moment of the current in the SSEP on a quenched random energy landscape using a partial-mean-field approach. The second moment of the current is heavily influenced by the energy landscape, revealing unique effects arising from the interplay between the heterogeneous environment and the many-body system. Our findings provide valuable insights that can be applied to control current fluctuations in systems involving the interactions of many particles, such as biological transport.

How to scan naked DNA using promiscuous recognition and no clamping: a model for pioneer transcription factors

Most DNA scanning proteins uniquely recognize their cognate sequence motif and slide on DNA assisted by some sort of clamping interface. The pioneer transcription factors that control cell fate in eukaryotes must forgo both elements to gain access to DNA in naked and chromatin forms; thus, whether or how these factors scan naked DNA is unknown. Here, we use single-molecule techniques to investigate naked DNA scanning by the Engrailed homeodomain (enHD) as paradigm of highly promiscuous recognition and open DNA binding interface. We find that enHD scans naked DNA quite effectively, and about 200000-fold faster than expected for a continuous promiscuous slide. To do so, enHD scans about 675 bp of DNA in 100 ms and then redeploys stochastically to another location 530 bp afar in just 10 ms. During the scanning phase enHD alternates between slow- and medium-paced modes every 3 and 40 ms, respectively. We also find that enHD binds nucleosomes and does so with enhanced affinity relative to naked DNA. Our results demonstrate that pioneer-like transcription factors can in principle do both, target nucleosomes and scan active DNA efficiently. The hybrid scanning mechanism used by enHD appears particularly well suited for the highly complex genomic signals of eukaryotic cells.

Memory effects of transcription regulator-DNA interactions in bacteria

Memory effect refers to the phenomenon where past events influence a system's current and future states or behaviors. In biology, memory effects often arise from intra- or intermolecular interactions, leading to temporally correlated behaviors. Single-molecule studies have shown that enzymes and DNA-binding proteins can exhibit time-correlated behaviors of their activity. While memory effects are well documented and studied in vitro, no such examples exist in cells to our knowledge. Combining single-molecule tracking (SMT) and single-cell protein quantitation, we find in living Escherichia coli cells distinct temporal correlations in the binding/unbinding events on DNA by MerR- and Fur-family metalloregulators, manifesting as memory effects with timescales of ~1 s. These memory effects persist irrespective of the type of the metalloregulators or their metallation states. Moreover, these temporal correlations of metalloregulator-DNA interactions are associated with spatial confinements of the metalloregulators near their DNA binding sites, suggesting microdomains of ~100 nm in size that possibly result from the spatial organizations of the bacterial chromosome without the involvement of membranes. These microdomains likely facilitate repeated binding events, enhancing regulator-DNA contact frequency and potentially gene regulation efficiency. These findings provide unique insights into the spatiotemporal dynamics of protein-DNA interactions in bacterial cells, introducing the concept of microdomains as a crucial player in memory effect-driven gene regulation.

Uphill Drift in the Absence of Current in Single-File Diffusion

Single-file diffusion is a paradigmatic model for the transport of Brownian colloidal particles in narrow one-dimensional channels, such as those found in certain porous media, where the particles cannot cross each other. We consider a system where a different external uniform potential is present to the right and left of an origin. For example, this is the case when two channels meeting at the origin have different radii. In equilibrium, the chemical potential of the particles are equal, the density is thus lower in the region with the higher potential, and by definition there is no net current in the system. Remarkably, a single-file tracer particle initially located at the origin, with position denoted by Y(t), exhibits an average uphill drift toward the region of highest potential. This drift has the late time behavior ⟨Y(t)⟩=Ct^{1/4}, where the prefactor C depends on the initial particle arrangement. This surprising result is shown analytically by computing the first two moments of Y(t) through a simple and physically illuminating method, and also via extensive numerical simulations.

Field theory of enzyme-substrate systems with restricted long-range interactions

Enzyme-substrate kinetics form the basis of many biomolecular processes. The interplay between substrate binding and substrate geometry can give rise to long-range interactions between enzyme binding events. Here we study a general model of enzyme-substrate kinetics with restricted long-range interactions described by an exponent -γ. We employ a coherent-state path integral and renormalization group approach to calculate the first moment and two-point correlation function of the enzyme-binding profile. We show that starting from an empty substrate the average occupancy follows a power law with an exponent 1/(1-γ) over time. The correlation function decays algebraically with two distinct spatial regimes characterized by exponents -γ on short distances and -(2/3)(2-γ) on long distances. The crossover between both regimes scales inversely with the average substrate occupancy. Our work allows associating experimental measurements of bound enzyme locations with their binding kinetics and the spatial conformation of the substrate.

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.

Attractive crowding effect on passive and active polymer looping kinetics

Loop formation in complex environments is crucially important to many biological processes in life. In the present work, we adopt three-dimensional Langevin dynamics simulations to investigate passive and active polymer looping kinetics in crowded media featuring polymer-crowder attraction. We find polymers undergo a remarkable coil-globule-coil transition, highlighted by a marked change in the Flory scaling exponent of the gyration radius. Meanwhile, looping time as a function of the crowder's volume fraction demonstrates an apparent non-monotonic alteration. A small number of crowders induce a compact structure, which largely facilitates the looping process. While a large number of crowders heavily impede end-to-end diffusion, looping kinetics is greatly inhibited. For a self-propelled chain, we find that the attractive crowding triggers an unusual activity effect on looping kinetics. Once a globular state is formed, activity takes an effort to open the chain from the compact structure, leading to an unexpected activity-induced inhibition of looping. If the chain maintains a coil state, the dominant role of activity is to enhance diffusivity and, thus, speed up looping kinetics. The novel conformational change and looping kinetics of both passive and active polymers in the presence of attractive crowding highlight a rather distinct scenario that has no analogy in a repulsive crowding counterpart. The underlying mechanism enriches our understanding of the crucial role of attractive interactions in modulating polymer structure and dynamics.

Dynamic 1D search and processive nucleosome translocations by RSC and ISW2 chromatin remodelers

Eukaryotic gene expression is linked to chromatin structure and nucleosome positioning by ATP-dependent chromatin remodelers that establish and maintain nucleosome-depleted regions (NDRs) near transcription start sites. Conserved yeast RSC and ISW2 remodelers exert antagonistic effects on nucleosomes flanking NDRs, but the temporal dynamics of remodeler search, engagement, and directional nucleosome mobilization for promoter accessibility are unknown. Using optical tweezers and two-color single-particle imaging, we investigated the Brownian diffusion of RSC and ISW2 on free DNA and sparse nucleosome arrays. RSC and ISW2 rapidly scan DNA by one-dimensional hopping and sliding, respectively, with dynamic collisions between remodelers followed by recoil or apparent co-diffusion. Static nucleosomes block remodeler diffusion resulting in remodeler recoil or sequestration. Remarkably, both RSC and ISW2 use ATP hydrolysis to translocate mono-nucleosomes processively at ~30 bp/s on extended linear DNA under tension. Processivity and opposing push-pull directionalities of nucleosome translocation shown by RSC and ISW2 shape the distinctive landscape of promoter chromatin.

Dynamic 1D Search and Processive Nucleosome Translocations by RSC and ISW2 Chromatin Remodelers

Eukaryotic gene expression is linked to chromatin structure and nucleosome positioning by ATP-dependent chromatin remodelers that establish and maintain nucleosome-depleted regions (NDRs) near transcription start-sites. Conserved yeast RSC and ISW2 remodelers exert antagonistic effects on nucleosomes flanking NDRs, but the temporal dynamics of remodeler search, engagement and directional nucleosome mobilization for promoter accessibility are unknown. Using optical tweezers and 2-color single-particle imaging, we investigated the Brownian diffusion of RSC and ISW2 on free DNA and sparse nucleosome arrays. RSC and ISW2 rapidly scan DNA by one-dimensional hopping and sliding respectively, with dynamic collisions between remodelers followed by recoil or apparent co-diffusion. Static nucleosomes block remodeler diffusion resulting in remodeler recoil or sequestration. Remarkably, both RSC and ISW2 use ATP hydrolysis to translocate mono-nucleosomes processively at ~30 bp/sec on extended linear DNA under tension. Processivity and opposing push-pull directionalities of nucleosome translocation shown by RSC and ISW2 shape the distinctive landscape of promoter chromatin.

Single-file diffusion in spatially inhomogeneous systems

We study the effect of spatially varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Noninteracting particles in such a system exhibit normal diffusion at late times, which is characterized by an effective diffusion constant D_{eff}. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially homogeneous system with constant diffusivity D_{eff}. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.

Large deviations of a tracer position in the dense and the dilute limits of single-file diffusion

We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large deviation functions for an initial step density profile with the fluctuating (annealed) and the fixed (quenched) initial conditions. These hydrodynamic results are applicable for a general single-file system and they agree with recent exact results obtained by microscopic solutions for specific model systems.

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.

Crowding-induced polymer trapping in a channel

In this work, we report an intriguing phenomenon: crowding-induced polymer trapping in a channel. Using Langevin dynamics simulations and analytical calculations, we find that for a polymer confined in a channel, crowding particles can push a polymer into the channel corner through inducing an effective polymer-corner attraction due to the depletion effect. This phenomenon is referred to as polymer trapping. The occurrence of polymer trapping requires a minimum volume fraction of crowders, ϕ^{*}, which scales as ϕ^{*}∼(a_{c}/L_{p})^{1/3} for a_{c}≫a_{m} and ϕ^{*}∼(a_{c}/L_{p})^{1/3}(a_{c}/a_{m})^{1/2} for a_{c}≪a_{m}, where a_{c} is the crowder diameter, a_{m} is the monomer diameter, and L_{p} is the polymer persistence length. For DNA, ϕ^{*} is estimated to be around 0.25 for crowders with a_{c}=2nm. We find that ϕ^{*} also strongly depends on the shape of the channel cross section, and ϕ^{*} is much smaller for a triangle channel than a square channel. The polymer trapping leads to a nearly fully stretched polymer conformation along a channel corner, which may have practical applications, such as full stretching of DNA for the nanochannel-based genome mapping technology.

Polymer looping kinetics in active heterogeneous environments

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

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.

The dynamics of the nuclear environment and their impact on gene function

In the last decades, it has become increasingly clear how the modulation of spatial organization of chromatin over time and through the cell cycle is closely connected to gene function regulation. Different physicochemical stimuli contribute to the realization of specific transcriptional programs and finally to a specific cellular phenotype. In this review, we aim to describe the current knowledge about the dynamics regulating the movements and the interactions of molecules within the nucleus and their impact on gene functions. In particular, taking into account that these forces exert their effect in a nuclear environment characterized by a high concentration of molecules, we will discuss the role of proteins and structures that regulate these movements and transduce physicochemical signals acting on the cell to the nucleus.

Mechanistic model for production of recombinant adeno-associated virus via triple transfection of HEK293 cells

Manufacturing of recombinant adeno-associated virus (rAAV) viral vectors remains challenging, with low yields and low full:empty capsid ratios in the harvest. To elucidate the dynamics of recombinant viral production, we develop a mechanistic model for the synthesis of rAAV viral vectors by triple plasmid transfection based on the underlying biological processes derived from wild-type AAV. The model covers major steps starting from exogenous DNA delivery to the reaction cascade that forms viral proteins and DNA, which subsequently result in filled capsids, and the complex functions of the Rep protein as a regulator of the packaging plasmid gene expression and a catalyst for viral DNA packaging. We estimate kinetic parameters using dynamic data from literature and in-house triple transient transfection experiments. Model predictions of productivity changes as a result of the varied input plasmid ratio are benchmarked against transfection data from the literature. Sensitivity analysis suggests that (1) the poorly coordinated timeline of capsid synthesis and viral DNA replication results in a low ratio of full virions in harvest, and (2) repressive function of the Rep protein could be impeding capsid production at a later phase. The analyses from the mathematical model provide testable hypotheses for evaluation and reveal potential process bottlenecks that can be investigated.

Comparative study of polymer looping kinetics in passive and active environments

Intra-chain looping in complex environments is significant in advancing our understanding of biological processes in life. We adopt Langevin dynamics simulations to perform a comparative study of polymer looping kinetics in passive and active environments. From the analysis of looping quantities, including looping-unlooping times and looping probabilities, we unraveled the intriguing effects of active crowder size, activity and crowding. Firstly, we figured out the phase diagram involving a novel facilitation-inhibition transition in the parameter space of active crowder size and active force, and the two-fold roles of activity are clarified. In particular, we find that active particles of a size comparable to the polymer monomer are most favorable for facilitated looping, while those with a similar size to the polymer gyration radius impede the looping most seriously. Secondly, the underlying looping mechanisms in different active crowder size regimes are rationalized by the interplay among diffusion, polymer conformational change and the free-energy barrier. For small active crowders, activity significantly promotes end-to-end distance diffusion, which dominantly facilitates both looping and unlooping processes. In the case of moderate active crowders, the polymer chain suffers from prominent swelling, and thus inevitable inhibited looping will occur. For large active crowders, activity induces a counterintuitive non-cage effect on the looping kinetics, through yielding a higher effective temperature and larger unlooping free-energy barrier. This is in sharp contrast to the caging phenomena observed in passive media. Lastly, the volume-fraction dependence of the looping quantities in an active bath demonstrates dramatic discrepancies from that in a passive bath, which highlights the contrasting effects of activity and crowding.

Diffusion of confined fluids in microporous zeolites and clay materials

Fluids exhibit remarkable variation in their structural and dynamic properties when they are confined at the nanoscopic scale. Various factors, including geometric restriction, the size and shape of the guest molecules, the topology of the host, and guest-host interactions, are responsible for the alterations in these properties. Due to their porous structures, aluminosilicates provide a suitable host system for studying the diffusion of sorbates in confinement. Zeolites and clays are two classes of the aluminosilicate family, comprising very ordered porous or layered structures. Zeolitic materials are important due to their high catalytic activity and molecular sieving properties. Guest molecules adsorbed by zeolites display many interesting features including unidimensional diffusion, non-isotropic rotation, preferred orientation and levitation effects, depending on the guest and host characteristics. These are useful for the separation of hydrocarbons which commonly exist as mixtures in nature. Similarly, clay materials have found application in catalysis, desalination, enhanced oil recovery, and isolation barriers used in radioactive waste disposal. It has been shown that the bonding interactions, level of hydration, interlayer spacing, and number of charge-balancing cations are the important factors that determine the nature of diffusion of water molecules in clays. Here, we present a review of the current status of the diffusion mechanisms of various adsorbed species in different microporous zeolites and clays, as investigated using quasielastic neutron scattering and classical molecular dynamics simulation techniques. It is impossible to write an exhaustive review of the subject matter, as it has been explored over several decades and involves many research topics. However, an effort is made to cover the relevant issues specific to the dynamics of different molecules in microporous zeolites and clay materials and to highlight a variety of interesting features that are important for both practical applications and fundamental aspects.

Transient non-specific DNA binding dominates the target search of bacterial DNA-binding proteins

Despite their diverse biochemical characteristics and functions, all DNA-binding proteins share the ability to accurately locate their target sites among the vast excess of non-target DNA. Toward identifying universal mechanisms of the target search, we used single-molecule tracking of 11 diverse DNA-binding proteins in living Escherichia coli. The mobility of these proteins during the target search was dictated by DNA interactions rather than by their molecular weights. By generating cells devoid of all chromosomal DNA, we discovered that the nucleoid is not a physical barrier for protein diffusion but significantly slows the motion of DNA-binding proteins through frequent short-lived DNA interactions. The representative DNA-binding proteins (irrespective of their size, concentration, or function) spend the majority (58%–99%) of their search time bound to DNA and occupy as much as ∼30% of the chromosomal DNA at any time. Chromosome crowding likely has important implications for the function of all DNA-binding proteins.

•

Protein motion was compared between unperturbed cells and DNA-free cells

•

Protein mobility was dictated by DNA interactions rather than molecular weight

•

The nucleoid is not a physical barrier for protein diffusion

•

The proteins studied spend most (58%–99%) of their search time bound to DNA

Dynamics of chromosomal target search by a membrane-integrated one-component receptor

Membrane proteins account for about one third of the cellular proteome, but it is still unclear how dynamic they are and how they establish functional contacts with cytoplasmic interaction partners. Here, we consider a membrane-integrated one-component receptor that also acts as a transcriptional activator, and analyze how it kinetically locates its specific binding site on the genome. We focus on the case of CadC, the pH receptor of the acid stress response Cad system in E. coli. CadC is a prime example of a one-component signaling protein that directly binds to its cognate target site on the chromosome to regulate transcription. We combined fluorescence microscopy experiments, mathematical analysis, and kinetic Monte Carlo simulations to probe this target search process. Using fluorescently labeled CadC, we measured the time from activation of the receptor until successful binding to the DNA in single cells, exploiting that stable receptor-DNA complexes are visible as fluorescent spots. Our experimental data indicate that CadC is highly mobile in the membrane and finds its target by a 2D diffusion and capture mechanism. DNA mobility is constrained due to the overall chromosome organization, but a labeled DNA locus in the vicinity of the target site appears sufficiently mobile to randomly come close to the membrane. Relocation of the DNA target site to a distant position on the chromosome had almost no effect on the mean search time, which was between four and five minutes in either case. However, a mutant strain with two binding sites displayed a mean search time that was reduced by about a factor of two. This behavior is consistent with simulations of a coarse-grained lattice model for the coupled dynamics of DNA within a cell volume and proteins on its surface. The model also rationalizes the experimentally determined distribution of search times. Overall our findings reveal that DNA target search does not present a much bigger kinetic challenge for membrane-integrated proteins than for cytoplasmic proteins. More generally, diffusion and capture mechanisms may be sufficient for bacterial membrane proteins to establish functional contacts with cytoplasmic targets.

Adaptation to changing environments is vital to bacteria and is enabled by sophisticated signal transduction systems. While signal transduction by two-component systems is well studied, the signal transduction of membrane-integrated one-component systems, where one protein performs both sensing and response regulation, are insufficiently understood. How can a membrane-integrated protein bind to specific sites on the genome to regulate transcription? Here, we study the kinetics of this process, which involves both protein diffusion within the membrane and conformational fluctuations of the genomic DNA. A well-suited model system for this question is CadC, the signaling protein of the E. coli Cad system involved in pH stress response. Fluorescently labeled CadC forms visible spots in single cells upon stable DNA-binding, marking the end of the protein-DNA search process. Moreover, the start of the search is triggered by a medium shift exposing cells to pH stress. We probe the underlying mechanism by varying the number and position of DNA target sites. We combine these experiments with mathematical analysis and kinetic Monte Carlo simulations of lattice models for the search process. Our results suggest that CadC diffusion in the membrane is pivotal for this search, while the DNA target site is just mobile enough to reach the membrane.

Single-file diffusion in a bi-stable potential: Signatures of memory in the barrier-crossing of a tagged-particle

We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model, we analyze tagged-particle diffusion in a single file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the "confining" (all background particles in front of the tagged-particle) and "pushing" (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behaviors. Notably and somewhat unexpectedly, at a fixed particle number, we find that the higher the barrier, the stronger the memory effects are. The fact that the external potential alters the memory is important more generally and should be taken into account in applications of generalized Langevin equations. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.

Bacterial Vivisection: How Fluorescence-Based Imaging Techniques Shed a Light on the Inner Workings of Bacteria

The rise in fluorescence-based imaging techniques over the past 3 decades has improved the ability of researchers to scrutinize live cell biology at increased spatial and temporal resolution. In microbiology, these real-time vivisections structurally changed the view on the bacterial cell away from the "watery bag of enzymes" paradigm toward the perspective that these organisms are as complex as their eukaryotic counterparts. Capitalizing on the enormous potential of (time-lapse) fluorescence microscopy and the ever-extending pallet of corresponding probes, initial breakthroughs were made in unraveling the localization of proteins and monitoring real-time gene expression. However, later it became clear that the potential of this technique extends much further, paving the way for a focus-shift from observing single events within bacterial cells or populations to obtaining a more global picture at the intra- and intercellular level. In this review, we outline the current state of the art in fluorescence-based vivisection of bacteria and provide an overview of important case studies to exemplify how to use or combine different strategies to gain detailed information on the cell's physiology. The manuscript therefore consists of two separate (but interconnected) parts that can be read and consulted individually. The first part focuses on the fluorescent probe pallet and provides a perspective on modern methodologies for microscopy using these tools. The second section of the review takes the reader on a tour through the bacterial cell from cytoplasm to outer shell, describing strategies and methods to highlight architectural features and overall dynamics within cells.

Diffusion toward non-overlapping partially reactive spherical traps: Fresh insights onto classic problems

Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation of variables for solving boundary value problems of the associated modified Helmholtz equation. In particular, we derive a semi-analytical solution for the Green function that is the key ingredient to determine various diffusion-reaction characteristics such as the survival probability, the first-passage time distribution, and the reaction rate. We also present modifications of the method to determine numerically or asymptotically the eigenvalues and eigenfunctions of the Laplace operator and the Dirichlet-to-Neumann operator in such perforated domains. Some potential applications in chemical physics and biophysics are discussed, including diffusion-controlled reactions for mortal particles.

Non-monotonic dependence of polymer chain dynamics on active crowder size

Configuration dynamics of flexible polymer chains is of ubiquitous importance in many biological processes. Here, we investigate a polymer chain immersed in a bath of size-changed active particles in two dimensional space using Langevin dynamics simulations. Particular attention is paid to how the radius of gyration R_g of the polymer chain depends on the size σ_c of active crowders. We find that R_g shows nontrivial non-monotonic dependence on σ_c: The chain first swells upon increasing σ_c, reaching a fully expanded state with maximum R_g, and then, R_g decreases until the chain collapses to a compact coil state if the crowder is large enough. Interestingly, the chain may oscillate between a collapse state and a stretched state at moderate crowder size. Analysis shows that it is the competition between two effects of active particles, one stretching the chain from inside due to persistence motion and the other compressing the chain from outside, that leads to the non-monotonic dependence. Besides, the diffusion of the polymer chain also shows nontrivial non-monotonic dependence on σ_c. Our results demonstrate the important interplay between particle activity and size associated with polymer configurations in active crowding environments.

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.

Argonaute bypasses cellular obstacles without hindrance during target search

Argonaute (Ago) proteins are key players in both gene regulation (eukaryotes) and host defense (prokaryotes). Acting on single-stranded nucleic-acid substrates, Ago relies on base pairing between a small nucleic-acid guide and its complementary target sequences for specificity. To efficiently scan nucleic-acid chains for targets, Ago diffuses laterally along the substrate and must bypass secondary structures as well as protein barriers. Using single-molecule FRET in conjunction with kinetic modelling, we reveal that target scanning is mediated through loose protein-nucleic acid interactions, allowing Ago to slide short distances over secondary structures, as well as to bypass protein barriers via intersegmental transfer. Our combined single-molecule experiment and kinetic modelling approach may serve as a platform to dissect search processes and study the effect of sequence on search kinetics for other nucleic acid-guided proteins.

Facilitated diffusion of Argonaute-mediated target search

Argonaute (Ago) proteins are of key importance in many cellular processes. In eukaryotes, Ago can induce translational repression followed by deadenylation and degradation of mRNA molecules through base pairing of microRNAs (miRNAs) with a complementary target on a mRNA sequence. In bacteria, Ago eliminates foreign DNA through base pairing of siDNA (small interfering DNA) with a target on a DNA sequence. Effective targeting activities of Ago require fast recognition of the cognate target sequence among numerous off-target sites. Other target search proteins such as transcription factors (TFs) are known to rely on facilitated diffusion for this goal, but it is undetermined to what extent these small nucleic acid-guided proteins utilize this mechanism. Here, we review recent single-molecule studies on Ago target search. We discuss the consequences of the recent findings on the search mechanism. Furthermore, we discuss the open standing research questions that need to be addressed for a complete picture of facilitated target search by small nucleic acids.

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.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

eGFRD in all dimensions

Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present "eGFRD2," a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions.

DNA size in confined environments

For short DNA molecules in crowded environments, we evaluate macroscopic parameters such as the average end-to-end distance and the twist conformation by tuning the strength of the site specific confinement driven by the crowders.

Understanding chain looping kinetics in polymer solutions: crowding effects of microviscosity and collapse

A theoretical framework based on a generalized Langevin equation with fractional Gaussian noise is presented to describe the looping kinetics of chains in polymer solutions. Particular attention is paid to quantitatively revealing crowding effects on the loop formation rate in terms of microviscosity and collapse. By the aid of empirical relations for these two crowding associated physical quantities, we explicitly investigate the relationship between the looping rate and polymer concentration, the degree of polymerization, and system parameters. According to our analysis, the dependence of the looping rate on the crowder volume fraction exhibits three typical regimes: monotonic decreasing, a non-monotonic trend and monotonic increasing. We reveal that these non-trivial behaviors can be attributed to the competition between the two opposing factors of viscosity-associated inhibition and collapse-induced facilitation of loop formation. We apply our theory to analyze the kinetics of single-stranded DNA hairpin base pairing in polyethylene glycol solutions. The theoretical results can reproduce the experimental data on the closing rate of hairpins quantitatively to a certain degree with reasonable fitting parameters. The unexpected increase of the closing rate upon the addition of increasing amounts of polymer is well rationalised. Such good agreements clearly demonstrate the validity of our theory, appropriately addressing the very role of crowding effects in the relevant kinetics.

Anomalously slow transport in single-file diffusion with slow binding kinetics

We computationally study the effects of binding kinetics to the channel wall, leading to transient immobility, on the diffusive transport of particles within narrow channels, that exhibit single-file diffusion (SFD). We find that slow binding kinetics leads to an anomalously slow diffusive transport. Remarkably, the scaled diffusivity D[over ̂] characterizing transport exhibits scaling collapse with respect to the occupation fraction p of sites along the channel. We present a simple "cage-physics" picture that captures the characteristic occupation fraction p_{scale} and the asymptotic 1/p^{2} behavior for p/p_{scale}≳1. We confirm that subdiffusive behavior of tracer particles is controlled by the same D[over ̂] as particle transport.

Topology-dependent density optima for efficient simultaneous network exploration

A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimize this process: How many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimized at a searcher density that is well predicted by the spectral gap. Furthermore, we find that nonequilibrium processes, realized through the addition of bias, can support significantly increased density optima. Our results suggest alternative hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.

Crowding, Entropic Forces, and Confinement: Crucial Factors for Structures and Functions in the Cell Nucleus

The view of the cell nucleus as a crowded system of colloid particles and that chromosomes are giant self-avoiding polymers is stimulating rapid advances in our understanding of its structure and activities, thanks to concepts and experimental methods from colloid, polymer, soft matter, and nano sciences and to increased computational power for simulating macromolecules and polymers. This review summarizes current understanding of some characteristics of the molecular environment in the nucleus, of how intranuclear compartments are formed, and of how the genome is highly but precisely compacted, and underlines the crucial, subtle, and sometimes unintuitive effects on structures and reactions of entropic forces caused by the high concentration of macromolecules in the nucleus.

Crowding Induces Entropically-Driven Changes to DNA Dynamics That Depend on Crowder Structure and Ionic Conditions

Macromolecular crowding plays a principal role in a wide range of biological processes including gene expression, chromosomal compaction, and viral infection. However, the impact that crowding has on the dynamics of nucleic acids remains a topic of debate. To address this problem, we use single-molecule fluorescence microscopy and custom particle-tracking algorithms to investigate the impact of varying macromolecular crowding conditions on the transport and conformational dynamics of large DNA molecules. Specifically, we measure the mean-squared center-of-mass displacements, as well as the conformational size, shape, and fluctuations, of individual 115 kbp DNA molecules diffusing through various in vitro solutions of crowding polymers. We determine the role of crowder structure and concentration, as well as ionic conditions, on the diffusion and configurational dynamics of DNA. We find that branched, compact crowders (10 kDa PEG, 420 kDa Ficoll) drive DNA to compact, whereas linear, flexible crowders (10, 500 kDa dextran) cause DNA to elongate. Interestingly, the extent to which DNA mobility is reduced by increasing crowder concentrations appears largely insensitive to crowder structure (branched vs. linear), despite the highly different configurations DNA assumes in each case. We also characterize the role of ionic conditions on crowding-induced DNA dynamics. We show that both DNA diffusion and conformational size exhibit an emergent non-monotonic dependence on salt concentration that is not seen in the absence of crowders.

Transcription factor target site search and gene regulation in a background of unspecific binding sites

Response time and transcription level are vital parameters of gene regulation. They depend on how fast transcription factors (TFs) find and how efficient they occupy their specific target sites. It is well known that target site search is accelerated by TF binding to and sliding along unspecific DNA and that unspecific associations alter the occupation frequency of a gene. However, whether target site search time and occupation frequency can be optimized simultaneously is mostly unclear. We developed a transparent and intuitively accessible state-based formalism to calculate search times to target sites on and occupation frequencies of promoters of arbitrary state structure. Our formalism is based on dissociation rate constants experimentally accessible in live cell experiments. To demonstrate our approach, we consider promoters activated by a single TF, by two coactivators or in the presence of a competitive inhibitor. We find that target site search time and promoter occupancy differentially vary with the unspecific dissociation rate constant. Both parameters can be harmonized by adjusting the specific dissociation rate constant of the TF. However, while measured DNA residence times of various eukaryotic TFs correspond to a fast search time, the occupation frequencies of target sites are generally low. Cells might tolerate low target site occupancies as they enable timely gene regulation in response to a changing environment.

Theoretical principles of transcription factor traffic on folded chromatin

All organisms regulate transcription of their genes. To understand this process, a complete understanding of how transcription factors find their targets in cellular nuclei is essential. The DNA sequence and other variables are known to influence this binding, but the distribution of transcription factor binding patterns remains mostly unexplained in metazoan genomes. Here, we investigate the role of chromosome conformation in the trajectories of transcription factors. Using molecular dynamics simulations, we uncover the principles of their diffusion on chromatin. Chromosome contacts play a conflicting role: at low density they enhance transcription factor traffic, but at high density they lower it by volume exclusion. Consistently, we observe that in human cells, highly occupied targets, where protein binding is promiscuous, are found at sites engaged in chromosome loops within uncompacted chromatin. In summary, we provide a framework for understanding the search trajectories of transcription factors, highlighting the key contribution of genome conformation.

How transcription factors find their targets in vivo is still poorly understood. Here the authors use molecular dynamics simulations to investigate how transcription factors diffuse on chromatin, providing a theoretical framework for understanding the key role of genome conformation in this process.

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.

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.

Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius

Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

How to switch the motor on: RNA polymerase initiation steps at the single-molecule level

RNA polymerase (RNAP) is the central motor of gene expression since it governs the process of transcription. In prokaryotes, this holoenzyme is formed by the RNAP core and a sigma factor. After approaching and binding the specific promoter site on the DNA, the holoenzyme-promoter complex undergoes several conformational transitions that allow unwinding and opening of the DNA duplex. Once the first DNA basepairs (∼10 bp) are transcribed in an initial transcription process, the enzyme unbinds from the promoter and proceeds downstream along the DNA while continuously opening the helix and polymerizing the ribonucleotides in correspondence with the template DNA sequence. When the gene is transcribed into RNA, the process generally is terminated and RNAP unbinds from the DNA. The first step of transcription-initiation, is considered the rate-limiting step of the entire process. This review focuses on the single-molecule studies that try to reveal the key steps in the initiation phase of bacterial transcription. Such single-molecule studies have, for example, allowed real-time observations of the RNAP target search mechanism, a mechanism still under debate. Moreover, single-molecule studies using Förster Resonance Energy Transfer (FRET) revealed the conformational changes that the enzyme undergoes during initiation. Force-based techniques such as scanning force microscopy and magnetic tweezers allowed quantification of the energy that drives the RNAP translocation along DNA and its dynamics. In addition to these in vitro experiments, single particle tracking in vivo has provided a direct quantification of the relative populations in each phase of transcription and their locations within the cell.