How gene order is influenced by the biophysics of transcription regulation

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.

Transcription Factors behind MYB98 Regulation: What Does the Discovery of SaeM Suggest?

MYB98 is master regulator of the molecular network involved in pollen tube attraction. Until recently, it was unclear how this gene exhibits exclusively synergid cell-specific expression in ovule. Our recent study has established that a 16-bp-long SaeM element is crucial for its synergid cell-specific expression in ovule, and an 84-bp-long fragment harboring SaeM is sufficient to drive the process. In this study, we have developed a workflow to predict functional roles of potential transcription factors (TFs) putatively binding to the promoter region, taking MYB98 promoter as a test subject. After sequential assessment of co-expression pattern, network analysis, and potential master regulator identification, we have proposed a multi-TF model for MYB98 regulation. Our study suggests that ANL2, GT-1, and their respective homologs could be direct regulators of MYB98 and indicates that TCP15, TCP16, FRS9, and HB34 are likely master regulators of the majority of the TFs involved in its regulation. Comprehensive studies in the future are expected to offer more insights into such propositions. Developed workflow can be used while designing similar regulome-related studies for any other species and genes.

A genetic circuit on a single DNA molecule as an autonomous dissipative nanodevice

Realizing genetic circuits on single DNA molecules as self-encoded dissipative nanodevices is a major step toward miniaturization of autonomous biological systems. A circuit operating on a single DNA implies that genetically encoded proteins localize during coupled transcription-translation to DNA, but a single-molecule measurement demonstrating this has remained a challenge. Here, we use a genetically encoded fluorescent reporter system with improved temporal resolution and observe the synthesis of individual proteins tethered to a DNA molecule by transient complexes of RNA polymerase, messenger RNA, and ribosome. Against expectations in dilute cell-free conditions where equilibrium considerations favor dispersion, these nascent proteins linger long enough to regulate cascaded reactions on the same DNA. We rationally design a pulsatile genetic circuit by encoding an activator and repressor in feedback on the same DNA molecule. Driven by the local synthesis of only several proteins per hour and gene, the circuit dynamics exhibit enhanced variability between individual DNA molecules, and fluctuations with a broad power spectrum. Our results demonstrate that co-expressional localization, as a nonequilibrium process, facilitates single-DNA genetic circuits as dissipative nanodevices, with implications for nanobiotechnology applications and artificial cell design.

The Operon as a Conundrum of Gene Dynamics and Biochemical Constraints: What We Have Learned from Histidine Biosynthesis

Operons represent one of the leading strategies of gene organization in prokaryotes, having a crucial influence on the regulation of gene expression and on bacterial chromosome organization. However, there is no consensus yet on why, how, and when operons are formed and conserved, and many different theories have been proposed. Histidine biosynthesis is a highly studied metabolic pathway, and many of the models suggested to explain operons origin and evolution can be applied to the histidine pathway, making this route an attractive model for the study of operon evolution. Indeed, the organization of his genes in operons can be due to a progressive clustering of biosynthetic genes during evolution, coupled with a horizontal transfer of these gene clusters. The necessity of physical interactions among the His enzymes could also have had a role in favoring gene closeness, of particular importance in extreme environmental conditions. In addition, the presence in this pathway of paralogous genes, heterodimeric enzymes and complex regulatory networks also support other operon evolution hypotheses. It is possible that histidine biosynthesis, and in general all bacterial operons, may result from a mixture of several models, being shaped by different forces and mechanisms during evolution.

Toward Memory in a DNA Brush: Site-Specific Recombination Responsive to Polymer Density, Orientation, and Conformation

Site-specific recombination is a cellular process for the integration, inversion, and excision of DNA segments that could be tailored for memory transactions in artificial cells. Here, we demonstrate the compartmentalization of cascaded gene expression reactions in a DNA brush, starting from the cell-free synthesis of a unidirectional recombinase that exchanges information between two DNA molecules, leading to gene expression turn-on/turn-off. We show that recombination yield in the DNA brush was responsive to gene composition, density, and orientation, with kinetics faster than in a homogeneous dilute bulk solution reaction. Recombination yield scaled with a power law greater than 1 with respect to the fraction of recombining DNA polymers in a dense brush. The exponent approached either 1 or 2, depending on the intermolecular distance in the brush and the position of the recombination site along the DNA contour length, suggesting that a restricted-reach effect between the recombination sites governs the recombination yield. We further demonstrate the ability to encode the DNA recombinase in the same DNA brush with its substrate constructs, enabling multiple spatially resolved orthogonal recombination transactions within a common reaction volume. Our results highlight the DNA brush as a favorable compartment to study DNA recombination, with unique properties for encoding autonomous memory transactions in DNA-based artificial cells.

Theoretical insights into the full description of DNA target search by subdiffusing proteins

DNA binding proteins (DBPs) diffuse in the cytoplasm to recognise and bind with their respective target sites on the DNA to initiate several biologically important processes. The first passage time distributions (FPTDs) of DBPs are useful in quantifying the timescales of the most-probable search paths in addition to the mean value of the distribution which, strikingly, are decades of order apart in time. However, extremely crowded in vivo conditions or the viscoelasticity of the cellular medium among other factors causes biomolecules to exhibit anomalous diffusion which is usually overlooked in most theoretical studies. We have obtained approximate analytical expressions of a general FPTD and the two characteristic timescales that are valid for any single subdiffusing protein searching for its target in vivo. Our results can be applied to single-particle tracking experiments of target search.

First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.

Standardization of regulatory nodes for engineering heterologous gene expression: a feasibility study

The potential of LacI/Ptrc , XylS/Pm , AlkS/PalkB , CprK/PDB3 and ChnR/PchnB regulatory nodes, recruited from both Gram-negative and Gram-positive bacteria, as the source of parts for formatting expression cargoes following the Standard European Vector Architecture (SEVA) has been examined. The five expression devices, which cover most known regulatory configurations in bacteria were assembled within exactly the same plasmid backbone and bearing the different functional segments arrayed in an invariable DNA scaffold. Their performance was then analysed in an Escherichia coli strain of reference through the readout of a fluorescence reporter gene that contained strictly identical translation signal elements. This approach allowed us to describe and compare the cognate expression systems with quantitative detail. The constructs under scrutiny diverged considerably in their capacity, expression noise, inducibility and ON/OFF ratios. Inspection of such a variance exposed the different constraints that rule the optimal arrangement of functional DNA segments in each case. The data highlighted also the ease of standardizing inducer-responsive devices subject to transcriptional activation as compared to counterparts based on repressors. The study resulted in a defined collection of formatted expression cargoes lacking any cross talk while offering a panoply of choices to potential users and help interoperability of the specific constructs.

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.

The economy of chromosomal distances in bacterial gene regulation

In the transcriptional regulatory network (TRN) of a bacterium, the nodes are genes and a directed edge represents the action of a transcription factor (TF), encoded by the source gene, on the target gene. It is a condensed representation of a large number of biological observations and facts. Nonrandom features of the network are structural evidence of requirements for a reliable systemic function. For the bacterium Escherichia coli we here investigate the (Euclidean) distances covered by the edges in the TRN when its nodes are embedded in the real space of the circular chromosome. Our work is motivated by 'wiring economy' research in Computational Neuroscience and starts from two contradictory hypotheses: (1) TFs are predominantly employed for long-distance regulation, while local regulation is exerted by chromosomal structure, locally coordinated by the action of structural proteins. Hence long distances should often occur. (2) A large distance between the regulator gene and its target requires a higher expression level of the regulator gene due to longer reaching times and ensuing increased degradation (proteolysis) of the TF and hence will be evolutionarily reduced. Our analysis supports the latter hypothesis.

Dynamics of Proteins and Macromolecular Machines in Escherichia coli

Proteins are major contributors to the composition and the functions in the cell. They often assemble into larger structures, macromolecular machines, to carry out intricate essential functions. Although huge progress in understanding how macromolecular machines function has been made by reconstituting them in vitro, the role of the intracellular environment is still emerging. The development of fluorescence microscopy techniques in the last 2 decades has allowed us to obtain an increased understanding of proteins and macromolecular machines in cells. Here, we describe how proteins move by diffusion, how they search for their targets, and how they are affected by the intracellular environment. We also describe how proteins assemble into macromolecular machines and provide examples of how frequent subunit turnover is used for them to function and to respond to changes in the intracellular conditions. This review emphasizes the constant movement of molecules in cells, the stochastic nature of reactions, and the dynamic nature of macromolecular machines.

Stochastic Kinetic Treatment of Protein Aggregation and the Effects of Macromolecular Crowding

Investigation of protein self-assembly processes is important for understanding the growth processes of functional proteins as well as disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so high that they cast doubt on the validity of the deterministic rate-equation approach. Furthermore, the protein environments inside cells are often crowded with other macromolecules, with volume fractions of the crowders as high as 40%. We have developed a stochastic kinetic framework using Gillespie's algorithm for general systems undergoing particle self-assembly, including particularly protein aggregation at the cellular level. The effects of macromolecular crowding are investigated using models built on scaled-particle and transition-state theories. The stochastic kinetic method can be formulated to provide information on the dominating aggregation mechanisms in a method called reaction frequency (or propensity) analysis. This method reveals that the change of scaling laws related to the lag time can be directly related to the change in the frequencies of reaction mechanisms. Further examination of the time evolution of the fibril mass and length quantities unveils that maximal fluctuations occur in the periods of rapid fibril growth and the fluctuations of both quantities can be sensitive functions of rate constants. The presence of crowders often amplifies the roles of primary and secondary nucleation and causes shifting in the relative importance of elongation, shrinking, fragmentation, and coagulation of linear aggregates. We also show a dual effect of changing volume on the halftime of aggregation for ApoC2 which is reduced in the presence of crowders. A comparison of the results of stochastic simulations with those of rate equations gives us information on the convergence relation between them and how the roles of reaction mechanisms change as the system volume is varied.

Quasi-robust control of biochemical reaction networks via stochastic morphing

One of the main objectives of synthetic biology is the development of molecular controllers that can manipulate the dynamics of a given biochemical network that is at most partially known. When integrated into smaller compartments, such as living or synthetic cells, controllers have to be calibrated to factor in the intrinsic noise. In this context, biochemical controllers put forward in the literature have focused on manipulating the mean (first moment) and reducing the variance (second moment) of the target molecular species. However, many critical biochemical processes are realized via higher-order moments, particularly the number and configuration of the probability distribution modes (maxima). To bridge the gap, we put forward the stochastic morpher controller that can, under suitable timescale separations, morph the probability distribution of the target molecular species into a predefined form. The morphing can be performed at a lower-resolution, allowing one to achieve desired multi-modality/multi-stability, and at a higher-resolution, allowing one to achieve arbitrary probability distributions. Properties of the controller, such as robustness and convergence, are rigorously established, and demonstrated on various examples. Also proposed is a blueprint for an experimental implementation of stochastic morpher.

Towards Conformation-Sensitive Inhibition of Gyrase: Implications of Mechanistic Insight for the Identification and Improvement of Inhibitors

Gyrase is a bacterial type IIA topoisomerase that catalyzes negative supercoiling of DNA. The enzyme is essential in bacteria and is a validated drug target in the treatment of bacterial infections. Inhibition of gyrase activity is achieved by competitive inhibitors that interfere with ATP- or DNA-binding, or by gyrase poisons that stabilize cleavage complexes of gyrase covalently bound to the DNA, leading to double-strand breaks and cell death. Many of the current inhibitors suffer from severe side effects, while others rapidly lose their antibiotic activity due to resistance mutations, generating an unmet medical need for novel, improved gyrase inhibitors. DNA supercoiling by gyrase is associated with a series of nucleotide- and DNA-induced conformational changes, yet the full potential of interfering with these conformational changes as a strategy to identify novel, improved gyrase inhibitors has not been explored so far. This review highlights recent insights into the mechanism of DNA supercoiling by gyrase and illustrates the implications for the identification and development of conformation-sensitive and allosteric inhibitors.

Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

We study the experimentally measured ciprofloxacin antibiotic diffusion through a gel-like artificial sputum medium (ASM) mimicking physiological conditions typical for a cystic fibrosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. To quantify the antibiotic diffusion dynamics we employ a phenomenological model using a subdiffusion-absorption equation with a fractional time derivative. This effective equation describes molecular diffusion in a medium structured akin Thompson's plumpudding model; here the 'pudding' background represents the ASM and the 'plums' represent the bacterial biofilm. The pudding is a subdiffusion barrier for antibiotic molecules that can affect bacteria found in plums. For the experimental study we use an interferometric method to determine the time evolution of the amount of antibiotic that has diffused through the biofilm. The theoretical model shows that this function is qualitatively different depending on whether or not absorption of the antibiotic in the biofilm occurs. We show that the process can be divided into three successive stages: (1) only antibiotic subdiffusion with constant biofilm parameters, (2) subdiffusion and absorption of antibiotic molecules with variable biofilm transport parameters, (3) subdiffusion and absorption in the medium but the biofilm parameters are constant again. Stage 2 is interpreted as the appearance of an intensive defence build-up of bacteria against the action of the antibiotic, and in the stage 3 it is likely that the bacteria have been inactivated. Times at which stages change are determined from the experimentally obtained temporal evolution of the amount of antibiotic that has diffused through the ASM with bacteria. Our analysis shows good agreement between experimental and theoretical results and is consistent with the biologically expected biofilm response. We show that an experimental method to study the temporal evolution of the amount of a substance that has diffused through a biofilm is useful in studying the processes occurring in a biofilm. We also show that the complicated biological process of antibiotic diffusion in a biofilm can be described by a fractional subdiffusion-absorption equation with subdiffusion and absorption parameters that change over time.

From deterministic to fuzzy decision-making in artificial cells

Building autonomous artificial cells capable of homeostasis requires regulatory networks to gather information and make decisions that take time and cost energy. Decisions based on few molecules may be inaccurate but are cheap and fast. Realizing decision-making with a few molecules in artificial cells has remained a challenge. Here, we show decision-making by a bistable gene network in artificial cells with constant protein turnover. Reducing the number of gene copies from 10⁵ to about 10 per cell revealed a transition from deterministic and slow decision-making to a fuzzy and rapid regime dominated by small-number fluctuations. Gene regulation was observed at lower DNA and protein concentrations than necessary in equilibrium, suggesting rate enhancement by co-expressional localization. The high-copy regime was characterized by a sharp transition and hysteresis, whereas the low-copy limit showed strong fluctuations, state switching, and cellular individuality across the decision-making point. Our results demonstrate information processing with low-power consumption inside artificial cells.

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

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

Modeling the dynamics of phospholipids in the fluid phase of liposomes

We present the derivation of a new model to describe neutron spin echo spectroscopy and quasi-elastic neutron scattering data on liposomes. We compare the new model with existing approaches and benchmark it with experimental data. The analysis indicates the importance of including all major contributions in the modeling of the intermediate scattering function. Simultaneous analysis of the experimental data on lipids with full contrast and tail contrast matched samples reveals highly confined lipid tail motion. A comparison of their dynamics demonstrates the statistical independence of tail-motion and height-height correlation of the membrane. A more detailed analysis indicates that the lipid tail relaxation is confined to a potential with cylindrical symmetry, in addition to the undulation and diffusive motion of the liposome. Despite substantial differences in the chemistry of the fatty acid tails, the observation indicates a universal behavior. The analysis of partially deuterated systems confirms the strong contribution of the lipid tail to the intermediate scattering function. Within the time range from 5 to 100 ns, the intermediate scattering function can be described by the height-height correlation function. The existence of the fast-localized tail motion and the contribution of slow translational diffusion of liposomes determine the intermediate scattering function for t < 5 ns and t > 100 ns, respectively. Taking into account the limited time window lowers the bending moduli by a factor of 1.3 (DOPC) to 2 (DMPC) compared to the full range.

Job Opening for Nucleosome Mechanic: Flexibility Required

The nucleus has been studied for well over 100 years, and chromatin has been the intense focus of experiments for decades. In this review, we focus on an understudied aspect of chromatin biology, namely the chromatin fiber polymer’s mechanical properties. In recent years, innovative work deploying interdisciplinary approaches including computational modeling, in vitro manipulations of purified and native chromatin have resulted in deep mechanistic insights into how the mechanics of chromatin might contribute to its function. The picture that emerges is one of a nucleus that is shaped as much by external forces pressing down upon it, as internal forces pushing outwards from the chromatin. These properties may have evolved to afford the cell a dynamic and reversible force-induced communication highway which allows rapid coordination between external cues and internal genomic function.

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.

Guided nuclear exploration increases CTCF target search efficiency

The enormous size of mammalian genomes means that for a DNA-binding protein, the number of non-specific, off-target sites vastly exceeds the number of specific, cognate sites. How mammalian DNA-binding proteins overcome this challenge to efficiently locate their target sites is not known. Here through live-cell single-molecule tracking, we show that CCCTC-binding factor, CTCF, is repeatedly trapped in small zones that likely correspond to CTCF clusters, in a manner that is largely dependent on an internal RNA-binding region (RBR_i). We develop a new theoretical model, Anisotropic Diffusion through transient Trapping in Zones (ADTZ), to explain CTCF dynamics. Functionally, transient RBR_i-mediated trapping increases the efficiency of CTCF target search by ~2.5 fold. Overall, our results suggest a “guided” mechanism where CTCF clusters concentrate diffusing CTCF proteins near cognate binding sites, thus increasing the local ON-rate. We suggest that local guiding may allow DNA-binding proteins to more efficiently locate their target sites.

Survival and confinement under quenched disorder

We study the survival and confinement of random walkers under quenched disorder characterized by spatially-varying waiting times and decay rates. Spatial heterogeneity and segregation lead to a dynamic coupling between transport and reaction, resulting in history-dependent dynamics exhibiting long survivals and confinement. The survival probability decays as a power law, in contrast to the classical exponential law for decay at a homogeneous rate. The mean squared displacement shows dimension-dependent subdiffusive growth followed by localization, with stronger confinement in higher dimensions.

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.

A Model for the Spatiotemporal Design of Gene Regulatory Circuits †

Mathematical modeling assists the design of synthetic regulatory networks by providing a detailed mechanistic understanding of biological systems. Models that can predict the performance of a design are fundamental for synthetic biology since they minimize iterations along the design-build-test lifecycle. Such predictability depends crucially on what assumptions (i.e., biological simplifications) the model considers. Here, we challenge a common assumption when it comes to the modeling of bacterial-based gene regulation: considering negligible the effects of intracellular physical space. It is commonly assumed that molecules, such as transcription factors (TF), are homogeneously distributed inside a cell, so there is no need to model their diffusion. We describe a mathematical model that accounts for molecular diffusion and show how simulations of network performance are decisively affected by the distance between its components. Specifically, the model focuses on the search by a TF for its target promoter. The combination of local searches, via one-dimensional sliding along the chromosome, and global searches, via three-dimensional diffusion through the cytoplasm, determine TF-promoter interplay. Previous experimental results with engineered bacteria in which the distance between TF source and target was minimized or enlarged were successfully reproduced by the spatially resolved model we introduce here. This suggests that the spatial specification of the circuit alone can be exploited as a design parameter in synthetic biology to select programmable output levels.

Burst statistics in an early biofilm quorum sensing model: the role of spatial colony-growth heterogeneity

Quorum-sensing bacteria in a growing colony of cells send out signalling molecules (so-called “autoinducers”) and themselves sense the autoinducer concentration in their vicinity. Once—due to increased local cell density inside a “cluster” of the growing colony—the concentration of autoinducers exceeds a threshold value, cells in this clusters get “induced” into a communal, multi-cell biofilm-forming mode in a cluster-wide burst event. We analyse quantitatively the influence of spatial disorder, the local heterogeneity of the spatial distribution of cells in the colony, and additional physical parameters such as the autoinducer signal range on the induction dynamics of the cell colony. Spatial inhomogeneity with higher local cell concentrations in clusters leads to earlier but more localised induction events, while homogeneous distributions lead to comparatively delayed but more concerted induction of the cell colony, and, thus, a behaviour close to the mean-field dynamics. We quantify the induction dynamics with quantifiers such as the time series of induction events and burst sizes, the grouping into induction families, and the mean autoinducer concentration levels. Consequences for different scenarios of biofilm growth are discussed, providing possible cues for biofilm control in both health care and biotechnology.

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.

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.

Gene Expression Is Not Random: Scaling, Long-Range Cross-Dependence, and Fractal Characteristics of Gene Regulatory Networks

Gene expression is a vital process through which cells react to the environment and express functional behavior. Understanding the dynamics of gene expression could prove crucial in unraveling the physical complexities involved in this process. Specifically, understanding the coherent complex structure of transcriptional dynamics is the goal of numerous computational studies aiming to study and finally control cellular processes. Here, we report the scaling properties of gene expression time series in Escherichia coli and Saccharomyces cerevisiae. Unlike previous studies, which report the fractal and long-range dependency of DNA structure, we investigate the individual gene expression dynamics as well as the cross-dependency between them in the context of gene regulatory network. Our results demonstrate that the gene expression time series display fractal and long-range dependence characteristics. In addition, the dynamics between genes and linked transcription factors in gene regulatory networks are also fractal and long-range cross-correlated. The cross-correlation exponents in gene regulatory networks are not unique. The distribution of the cross-correlation exponents of gene regulatory networks for several types of cells can be interpreted as a measure of the complexity of their functional behavior.

Towards a full quantitative description of single-molecule reaction kinetics in biological cells

The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of instances when biomolecules in a biological cell reach their specific binding sites and trigger cellular regulation. Typically, the first-passage properties are given in terms of mean first-passage times. However, modern experiments now monitor single-molecular binding-processes in living cells and thus provide access to the full statistics of the underlying first-passage events, in particular, inherent cell-to-cell fluctuations. We here present a robust explicit approach for obtaining the distribution of FPTs to a small partially reactive target in cylindrical-annulus domains, which represent typical bacterial and neuronal cell shapes. We investigate various asymptotic behaviours of this FPT distribution and show that it is typically very broad in many biological situations, thus, the mean FPT can differ from the most probable FPT by orders of magnitude. The most probable FPT is shown to strongly depend only on the starting position within the geometry and to be almost independent of the target size and reactivity. These findings demonstrate the dramatic relevance of knowing the full distribution of FPTs and thus open new perspectives for a more reliable description of many intracellular processes initiated by the arrival of one or few biomolecules to a small, spatially localised region inside the cell.

Dynamics of Phospholipid Membranes beyond Thermal Undulations

We investigated the molecular dynamics of unilamellar liposomes by neutron spin echo spectroscopy. We report the first experimental evidence of a short-range motion at the length scale of the size of the headgroup of a lipid. The associated mean squared displacement shows a t^0.26 dependence in the pico- to nanosecond region that indicates another process beyond the predictions of the Zilman-Granek (ZG) model ( t^0.66) and translational diffusion ( t¹). A comparison with theory shows that the observed low exponent is associated with a non-Gaussian transient trapping of lipid molecules in a local area and supports the continuous time random walk model. The analysis of the mean squared displacement leads to the important conclusion that the friction at the interface between water and liposomes plays a minor role. Center of mass diffusion of liposomes and transient trapping of lipids define the range in which the ZG model can be applied to analyze membrane fluctuations.

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.

The dynamics of the monomeric restriction endonuclease BcnI during its interaction with DNA

Endonucleases that generate DNA double strand breaks often employ two independent subunits such that the active site from each subunit cuts either DNA strand. Restriction enzyme BcnI is a remarkable exception. It binds to the 5΄-CC/SGG-3΄ (where S = C or G, ‘/’ designates the cleavage position) target as a monomer forming an asymmetric complex, where a single catalytic center approaches the scissile phosphodiester bond in one of DNA strands. Bulk kinetic measurements have previously shown that the same BcnI molecule cuts both DNA strands at the target site without dissociation from the DNA. Here, we analyse the BcnI DNA binding and target recognition steps at the single molecule level. We find, using FRET, that BcnI adopts either ‘open’ or ‘closed’ conformation in solution. Next, we directly demonstrate that BcnI slides over long distances on DNA using 1D diffusion and show that sliding is accompanied by occasional jumping events, where the enzyme leaves the DNA and rebinds immediately at a distant site. Furthermore, we quantify the dynamics of the BcnI interactions with cognate and non-cognate DNA, and determine the preferred binding orientation of BcnI to the target site. These results provide new insights into the intricate dynamics of BcnI–DNA interactions.

Kinetics of lipid-nanoparticle-mediated intracellular mRNA delivery and function

mRNA delivery into cells forms the basis for one of the new and promising ways to treat various diseases. Among suitable carriers, lipid nanoparticles (LNPs) with a size of about 100 nm are now often employed. Despite high current interest in this area, the understanding of the basic details of LNP-mediated mRNA delivery and function is limited. To clarify the kinetics of mRNA release from LNPs, the author uses three generic models implying (i) exponential, (ii) diffusion-controlled, and (iii) detachment-controlled kinetic regimes, respectively. Despite the distinct differences in these kinetics, the associated transient kinetics of mRNA translation to the corresponding protein and its degradation are shown to be not too sensitive to the details of the mRNA delivery by LNPs (or other nanocarriers). In addition, the author illustrates how this protein may temporarily influence the expression of one gene or a few equivalent genes. The analysis includes positive or negative regulation of the gene transcription via the attachment of the protein without or with positive or negative feedback in the gene expression. Stable, bistable, and oscillatory schemes have been scrutinized in this context.

Optimal Length of Conformational Transition Region in Protein Search for Targets on DNA

The starting point of many fundamental biological processes is associated with protein molecules finding and recognizing specific sites on DNA. However, despite a large number of experimental and theoretical studies on protein search for targets on DNA, many molecular aspects of underlying mechanisms are still not well understood. Experiments show that proteins bound to DNA can switch between slow recognition and fast search conformations. However, from a theoretical point of view, such conformational transitions should slow down the protein search for specific sites on DNA, in contrast to available experimental observations. In addition, experiments indicate that the nucleotide composition near the target site is more symmetrically homogeneous, leading to stronger effective interactions between proteins and DNA at these locations. However, as has been shown theoretically, this should also make the search less efficient, which is not observed. We propose a possible resolution of these problems by suggesting that conformational transitions occur only within a segment around the target where stronger interactions between proteins and DNA are observed. Two theoretical methods, based on continuum and discrete-state stochastic calculations, are developed, allowing us to obtain a comprehensive dynamic description for the protein search process in this system. The existence of an optimal length of the conformational transition zone with the shortest mean search time is predicted.

Genome composition and phylogeny of microbes predict their co-occurrence in the environment

The genomic information of microbes is a major determinant of their phenotypic properties, yet it is largely unknown to what extent ecological associations between different species can be explained by their genome composition. To bridge this gap, this study introduces two new genome-wide pairwise measures of microbe-microbe interaction. The first (genome content similarity index) quantifies similarity in genome composition between two microbes, while the second (microbe-microbe functional association index) summarizes the topology of a protein functional association network built for a given pair of microbes and quantifies the fraction of network edges crossing organismal boundaries. These new indices are then used to predict co-occurrence between reference genomes from two 16S-based ecological datasets, accounting for phylogenetic relatedness of the taxa. Phylogenetic relatedness was found to be a strong predictor of ecological associations between microbes which explains about 10% of variance in co-occurrence data, but genome composition was found to be a strong predictor as well, it explains up to 4% the variance in co-occurrence when all genomic-based indices are used in combination, even after accounting for evolutionary relationships between the species. On their own, the metrics proposed here explain a larger proportion of variance than previously reported more complex methods that rely on metabolic network comparisons. In summary, results of this study indicate that microbial genomes do indeed contain detectable signal of organismal ecology, and the methods described in the paper can be used to improve mechanistic understanding of microbe-microbe interactions.

It is still unknown to what extent ecological associations between microbes, as measured by co-occurrence of different taxa in 16S rRNA surveys, can be explained, or predicted, using composition and structure of microbial genomes alone. Here I introduce two new genome-wide, pairwise indices for quantifying the propensity of microbial species to interact with each other. The first measure quantifies similarity in genome composition between two microbes. The second measure summarizes the topology of a protein functional association network built for a given pair of microbes and quantifies the fraction of network edges crossing organismal boundaries. I then study the ability of two newly proposed and two previously reported indices to explain variation in microbial co-occurrence. All four measures are significantly correlated with co-occurrence of microbes even when accounting for evolutionary relationships between the species. One of the newly developed indices outperforms previously proposed ones and explains up to 3.5% of the variance in co-occurrence. In summary, the indices described here are able to detect ecological associations between species using only their genomic information; however, additional methods are needed to provide more reliable genomic tools for microbial ecology.

The Role of DNA Looping in the Search for Specific Targets on DNA by Multisite Proteins

Many cellular processes involve simultaneous interactions between DNA and protein molecules at several locations. They are regulated and controlled by special protein-DNA complexes, which are known as synaptic complexes or synaptosomes. Because of the multisite nature of involved proteins, it was suggested that during the formation of synaptic complexes DNA loops might appear, but their role is unclear. We developed a theoretical model that allowed us to evaluate the effect of transient DNA loop formation. It is based on a discrete-state stochastic method that explicitly takes into account the free-energy contributions due to the appearance of DNA loops. The formation of the synaptic complexes is viewed as a search for a specific binding site on DNA by the protein molecule already bound to DNA at another location. It was found that the search might be optimized by varying the position of the target and the total length of DNA. Furthermore, the formation of transient DNA loops leads to faster dynamics if it is associated with favorable enthalpic contributions to nonspecific protein-DNA interactions. It is also shown that DNA looping might reduce stochastic noise in the system.

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

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

Sequence heterogeneity accelerates protein search for targets on DNA

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

Crowding on DNA in Protein Search for Targets

Proteins searching and recognizing specific sites on DNA is required for initiating all major biological processes. While the details of the protein search for targets on DNA in purified in vitro systems are reasonably well understood, the situation in real cells is much less clear. The presence of other types of molecules on DNA should prevent reaching the targets, but experiments show that, surprisingly, the molecular crowding on DNA influences the search dynamics much less than expected. We develop a theoretical method that allowed us to clarify the mechanisms of the protein search on DNA in the presence of crowding. It is found that the dimensionality of the search trajectories specifies whether the crowding will affect the target finding. For 3D search pathways it is minimal, while the strongest effect is for 1D search pathways when the crowding particle can block the search. In addition, for 1D search we determined that the critical parameter is a mobility of crowding agents: highly mobile molecules do not affect the search dynamics, while the slow particles can significantly slow down the process. Physical-chemical explanations of the observed phenomena are presented. Our theoretical predictions thus explain the experimental observations, and they are also supported by extensive numerical simulations.

Dichotomous noise models of gene switches

Molecular noise in gene regulatory networks has two intrinsic components, one part being due to fluctuations caused by the birth and death of protein or mRNA molecules which are often present in small numbers and the other part arising from gene state switching, a single molecule event. Stochastic dynamics of gene regulatory circuits appears to be largely responsible for bifurcations into a set of multi-attractor states that encode different cell phenotypes. The interplay of dichotomous single molecule gene noise with the nonlinear architecture of genetic networks generates rich and complex phenomena. In this paper, we elaborate on an approximate framework that leads to simple hybrid multi-scale schemes well suited for the quantitative exploration of the steady state properties of large-scale cellular genetic circuits. Through a path sum based analysis of trajectory statistics, we elucidate the connection of these hybrid schemes to the underlying master equation and provide a rigorous justification for using dichotomous noise based models to study genetic networks. Numerical simulations of circuit models reveal that the contribution of the genetic noise of single molecule origin to the total noise is significant for a wide range of kinetic regimes.

Protein search for multiple targets on DNA

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

Conserved Units of Co-Expression in Bacterial Genomes: An Evolutionary Insight into Transcriptional Regulation

Genome-wide measurements of transcriptional activity in bacteria indicate that the transcription of successive genes is strongly correlated beyond the scale of operons. Here, we analyze hundreds of bacterial genomes to identify supra-operonic segments of genes that are proximal in a large number of genomes. We show that these synteny segments correspond to genomic units of strong transcriptional co-expression. Structurally, the segments contain operons with specific relative orientations (co-directional or divergent) and nucleoid-associated proteins are found to bind at their boundaries. Functionally, operons inside a same segment are highly co-expressed even in the apparent absence of regulatory factors at their promoter regions. Remote operons along DNA can also be co-expressed if their corresponding segments share a transcriptional or sigma factor, without requiring these factors to bind directly to the promoters of the operons. As evidence that these results apply across the bacterial kingdom, we demonstrate them both in the Gram-negative bacterium Escherichia coli and in the Gram-positive bacterium Bacillus subtilis. The underlying process that we propose involves only RNA-polymerases and DNA: it implies that the transcription of an operon mechanically enhances the transcription of adjacent operons. In support of a primary role of this regulation by facilitated co-transcription, we show that the transcription en bloc of successive operons as a result of transcriptional read-through is strongly and specifically enhanced in synteny segments. Finally, our analysis indicates that facilitated co-transcription may be evolutionary primitive and may apply beyond bacteria.