Publications by authors named "Anatoly B Kolomeisky"

143 Publications

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

J Chem Phys 2021 May;154(20):204104

Department of Chemistry, Rice University, Houston, Texas 77005, USA.

Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and provide a clear physical picture. Recent theoretical studies made a surprising discovery that in complex systems, the symmetry of molecular forward/backward transition times with respect to local bias in the dynamics may be broken and it may take longer to go downhill than uphill. The physical origins of these phenomena remain not fully understood. Here, we explore in more detail the microscopic features of the symmetry breaking in the forward/backward transition times by analyzing exactly solvable discrete-state stochastic models. In particular, we consider a specific case of two random walkers on a four-site periodic lattice as the way to represent the general systems with multiple pathways. It is found that the asymmetry in transition times depends on several factors that include the degree of deviation from equilibrium, the particle crowding, and methods of measurements of dynamic properties. Our theoretical analysis suggests that the asymmetry in transition times can be explored experimentally for determining the important microscopic features of natural processes by quantitatively measuring the local deviations from equilibrium and the degrees of crowding.
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http://dx.doi.org/10.1063/5.0053634DOI Listing
May 2021

Temporal order of mutations influences cancer initiation dynamics.

Phys Biol 2021 Jul 2;18(5). Epub 2021 Jul 2.

Department of Chemistry, Rice University, Houston, Texas, United States of America.

Cancer is a set of genetic diseases that are driven by mutations. It was recently discovered that the temporal order of genetic mutations affects the cancer evolution and even the nature of the decease itself. The mechanistic origin of these observations, however, remain not well understood. Here we present a theoretical model for cancer initiation dynamics that allows us to quantify the impact of the temporal order of mutations. In our approach, the cancer initiation process is viewed as a set of stochastic transitions between discrete states defined by the different numbers of mutated cells. Using a first-passage analysis, probabilities and times before the cancer initiation are explicitly evaluated for two alternative sequences of two mutations. It is found that the probability of cancer initiation is determined only by the first mutation, while the dynamics depends on both mutations. In addition, it is shown that the acquisition of a mutation with higher fitness before mutation with lower fitness increases the probability of the tumor formation but delays the cancer initiation. Theoretical results are explained using effective free-energy landscapes.
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http://dx.doi.org/10.1088/1478-3975/ac0b7eDOI Listing
July 2021

DNA Looping Mediated by Site-Specific SfiI-DNA Interactions.

J Phys Chem B 2021 05 29;125(18):4645-4653. Epub 2021 Apr 29.

Department of Pharmaceutical Sciences, College of Pharmacy, University of Nebraska Medical Center, 986025 Nebraska Medical Center, Omaha, Nebraska 68198-6025, United States.

Interactions between distant DNA segments play important roles in various biological processes, such as DNA recombination. Certain restriction enzymes create DNA loops when two sites are held together and then cleave the DNA. DNA looping is important during DNA synapsis. Here we investigated the mechanisms of DNA looping by restriction enzyme SfiI by measuring the properties of the system at various temperatures. Different sized loop complexes, mediated by SfiI-DNA interactions, were visualized with AFM. The experimental results revealed that small loops are more favorable compared to other loop sizes at all temperatures. Our theoretical model found that entropic cost dominates at all conditions, which explains the preference for short loops. Furthermore, specific loop sizes were predicted as favorable from an energetic point of view. These predictions were tested by experiments with transiently assembled SfiI loops on a substrate with a single SfiI site.
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http://dx.doi.org/10.1021/acs.jpcb.1c00763DOI Listing
May 2021

Long-Range Supercoiling-Mediated RNA Polymerase Cooperation in Transcription.

J Phys Chem B 2021 05 29;125(18):4692-4700. Epub 2021 Apr 29.

Department of Chemistry, Rice University, Houston, Texas 77005, United States.

It is widely believed that DNA supercoiling plays an important role in the regulation of transcriptional dynamics. Recent studies show that it could affect transcription not only through the buildup and relaxation of torsional strain on DNA strands but also via effective long-range supercoiling-mediated interactions between RNA polymerase (RNAP) molecules. Here, we present a theoretical study that quantitatively analyzes the effect of long-range RNAP cooperation in transcription dynamics. Our minimal chemical-kinetic model assumes that one or two RNAP molecules can simultaneously participate in the transcription, and it takes into account their binding to and dissociation from DNA. It also explicitly accounts for competition between the supercoiling buildup that reduces the RNA elongation speed and gyrase binding that rescues the RNA synthesis. The full analytical solution of the model accompanied by Monte Carlo computer simulations predicts that the system should exhibit transcriptional bursting dynamics, in agreement with experimental observations. The analysis also revealed that when there are two polymerases participating in the elongation rather than one, the transcription process becomes much more efficient since the level of stochastic noise decreases while more RNA transcripts are produced. Our theoretical investigation clarifies molecular aspects of the supercoiling-mediated RNAP cooperativity during transcription.
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http://dx.doi.org/10.1021/acs.jpcb.1c01859DOI Listing
May 2021

Charge-Free, Stabilizing Amide-π Interactions Can Be Used to Control Collagen Triple-Helix Self-Assembly.

Biomacromolecules 2021 05 21;22(5):2137-2147. Epub 2021 Apr 21.

There is a noted lack of understood, controllable interactions for directing the organization of collagen triple helices. While the field has had success using charge-pair interactions and cation-π interactions in helix design, these alone are not adequate for achieving the degree of specificity desirable for these supramolecular structures. Furthermore, because of the reliance on electrostatic interactions, designed heterotrimeric systems have been heavily charged, a property undesirable in some applications. Amide-π interactions are a comparatively understudied class of charge-free interactions, which could potentially be harnessed for triple-helix design. Herein, we propose, validate, and utilize pairwise amino acid amide-π interactions in collagen triple-helix design. Glutamine-phenylalanine pairs, when arranged in an axial geometry, are found to exhibit a moderately stabilizing effect, while in the lateral geometry, this pair is destabilizing. Together this allows glutamine-phenylalanine pairs to effectively set the register of triple helices. In contrast, interactions between asparagine and phenylalanine appear to have little effect on triple-helical stability. After deconvoluting the contributions of these amino acids to triple-helix stability, we demonstrate these new glutamine-phenylalanine interactions in the successful design of a heterotrimeric triple helix. The results of all of these analyses are used to update our collagen triple-helix thermal stability prediction algorithm, Scoring function for Collagen Emulating Peptides' Temperature of Transition (SCEPTTr).
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http://dx.doi.org/10.1021/acs.biomac.1c00234DOI Listing
May 2021

Theoretical Analysis Reveals the Cost and Benefit of Proofreading in Coronavirus Genome Replication.

J Phys Chem Lett 2021 Mar 10;12(10):2691-2698. Epub 2021 Mar 10.

Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.

Severe acute respiratory syndrome coronaviruses have unusually large RNA genomes replicated by a multiprotein complex containing an RNA-dependent RNA polymerase (RdRp). Exonuclease activity enables the RdRp complex to remove wrongly incorporated bases via proofreading, a process not utilized by other RNA viruses. However, it is unclear why the RdRp complex needs proofreading and what the associated trade-offs are. Here we investigate the interplay among the accuracy, speed, and energetic cost of proofreading in the RdRp complex using a kinetic model and bioinformatics analysis. We find that proofreading nearly optimizes the rate of functional virus production. However, we find that further optimization would lead to a significant increase in the proofreading cost. Unexpected importance of the cost minimization is further supported by other global analyses. We speculate that cost optimization could help avoid cell defense responses. Thus, proofreading is essential for the production of functional viruses, but its rate is limited by energy costs.
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http://dx.doi.org/10.1021/acs.jpclett.1c00190DOI Listing
March 2021

Mesoscopic protein-rich clusters host the nucleation of mutant p53 amyloid fibrils.

Proc Natl Acad Sci U S A 2021 Mar;118(10)

William A. Brookshire Department of Chemical and Biomolecular Engineering, University of Houston, Houston, TX 77204;

The protein p53 is a crucial tumor suppressor, often called "the guardian of the genome"; however, mutations transform p53 into a powerful cancer promoter. The oncogenic capacity of mutant p53 has been ascribed to enhanced propensity to fibrillize and recruit other cancer fighting proteins in the fibrils, yet the pathways of fibril nucleation and growth remain obscure. Here, we combine immunofluorescence three-dimensional confocal microscopy of human breast cancer cells with light scattering and transmission electron microscopy of solutions of the purified protein and molecular simulations to illuminate the mechanisms of phase transformations across multiple length scales, from cellular to molecular. We report that the p53 mutant R248Q (R, arginine; Q, glutamine) forms, both in cancer cells and in solutions, a condensate with unique properties, mesoscopic protein-rich clusters. The clusters dramatically diverge from other protein condensates. The cluster sizes are decoupled from the total cluster population volume and independent of the p53 concentration and the solution concentration at equilibrium with the clusters varies. We demonstrate that the clusters carry out a crucial biological function: they host and facilitate the nucleation of amyloid fibrils. We demonstrate that the p53 clusters are driven by structural destabilization of the core domain and not by interactions of its extensive unstructured region, in contradistinction to the dense liquids typical of disordered and partially disordered proteins. Two-step nucleation of mutant p53 amyloids suggests means to control fibrillization and the associated pathologies through modifying the cluster characteristics. Our findings exemplify interactions between distinct protein phases that activate complex physicochemical mechanisms operating in biological systems.
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http://dx.doi.org/10.1073/pnas.2015618118DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7958401PMC
March 2021

DNA Looping and DNA Conformational Fluctuations Can Accelerate Protein Target Search.

J Phys Chem B 2021 02 11;125(7):1727-1734. Epub 2021 Feb 11.

Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States.

Protein searching and binding to specific sites on DNA is a fundamentally important process that marks the beginning of all major cellular transformations. While the dynamics of protein-DNA interactions in settings is well investigated, the situation is much more complex for conditions because the DNA molecules in live cells are packed into chromosomal structures where they are undergoing strong dynamic and conformational fluctuations. In this work, we present a theoretical investigation on the role of DNA looping and DNA conformational fluctuations in the protein target search. It is based on a discrete-state stochastic analysis that allows for explicit calculations of dynamic properties, which is also supplemented by Monte Carlo computer simulations. It is found that for stronger nonspecific interactions between DNA and proteins the search occurs faster on the DNA looped conformation in comparison with the unlooped conformation, and the fastest search is observed when the loop is formed near the target site. It is also shown that DNA fluctuations between the looped and unlooped conformations influence the search dynamics, and this depends on the magnitude of conformational transition rates and on which conformation is more energetically stable. Physical-chemical arguments explaining these observations are presented. Our theoretical study suggests that the geometry and conformational changes in DNA are additional factors that might efficiently control the gene regulation processes.
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http://dx.doi.org/10.1021/acs.jpcb.0c09599DOI Listing
February 2021

Discrete-state stochastic kinetic models for target DNA search by proteins: Theory and experimental applications.

Biophys Chem 2021 02 10;269:106521. Epub 2020 Dec 10.

Department of Chemistry, Department of Chemical and Biomolecular Engineering, Department of Physics and Astronomy and Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA.

To perform their functions, transcription factors and DNA-repair/modifying enzymes randomly search DNA in order to locate their specific targets on DNA. Discrete-state stochastic kinetic models have been developed to explain how the efficiency of the search process is influenced by the molecular properties of proteins and DNA as well as by other factors such as molecular crowding. These theoretical models not only offer explanations on the relation of microscopic processes to macroscopic behavior of proteins, but also facilitate the analysis and interpretation of experimental data. In this review article, we provide an overview on discrete-state stochastic kinetic models and explain how these models can be applied to experimental investigations using stopped-flow, single-molecule, nuclear magnetic resonance (NMR), and other biophysical and biochemical methods.
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http://dx.doi.org/10.1016/j.bpc.2020.106521DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7855466PMC
February 2021

Asymmetry of forward/backward transition times as a non-equilibrium measure of complexity of microscopic mechanisms.

J Chem Phys 2020 Sep;153(12):124103

Department of Chemistry, Rice University, Houston, Texas 77005, USA.

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http://dx.doi.org/10.1063/5.0021840DOI Listing
September 2020

Stochastic Mechanisms of Cell-Size Regulation in Bacteria.

J Phys Chem Lett 2020 Oct 1;11(20):8777-8782. Epub 2020 Oct 1.

Department of Chemistry, Rice University, Houston, Texas 77251, United States.

How bacteria are able to maintain their sizes remains an open question. It is believed that cells have narrow distributions of sizes as a consequence of a homeostasis that allows bacteria to function at the optimal conditions. Several phenomenological approaches to explain these observations have been presented, but the microscopic origins of the cell-size regulation are still not understood. Here, we propose a new stochastic approach to investigate the molecular mechanisms of maintaining the cell sizes in bacteria. It is argued that the cell-size regulation is a result of coupling of two stochastic processes, cell growth and division, which eliminates the need for introducing the thresholds. Dynamic properties of the system are explicitly evaluated, and it is shown that the model is consistent with the experimentally supported adder principle of the cell-size regulation. In addition, theoretical predictions agree with experimental observations on bacteria. Theoretical analysis clarifies some important features of bacterial cell growth.
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http://dx.doi.org/10.1021/acs.jpclett.0c02627DOI Listing
October 2020

Do We Understand the Mechanisms Used by Biological Systems to Correct Their Errors?

J Phys Chem B 2020 10 21;124(42):9289-9296. Epub 2020 Sep 21.

Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.

Most cellular processes involved in biological information processing display a surprisingly low error rate despite the stochasticity of the underlying biochemical reactions and the presence of competing chemical species. Such high fidelity is the result of nonequilibrium kinetic proofreading mechanisms, i.e., the existence of dissipative pathways for correcting the reactions that went in the wrong direction. While proofreading was often studied from the perspective of error minimization, a number of recent studies have demonstrated that the underlying mechanisms need to consider the interplay of other characteristic properties such as speed, energy dissipation, and noise reduction. Here, we present current views and new insights on the mechanisms of error-correction phenomena and various trade-off scenarios in the optimization of the functionality of biological systems. Existing challenges and future directions are also discussed.
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http://dx.doi.org/10.1021/acs.jpcb.0c06180DOI Listing
October 2020

Dye Quenching of Carbon Nanotube Fluorescence Reveals Structure-Selective Coating Coverage.

ACS Nano 2020 09 1;14(9):12148-12158. Epub 2020 Sep 1.

Department of Chemistry and the Smalley-Curl Institute, Rice University, Houston, Texas 77005, United States.

Many properties and applications of single-wall carbon nanotubes (SWCNTs) depend strongly on the coatings that allow their suspension in aqueous media. We report that SWCNT fluorescence is quenched by reversible physisorption of dye molecules such as methylene blue, and that measurements of that quenching can be used to infer structure-specific exposures of the nanotube surface to the surrounding solution. SWCNTs suspended in single-stranded DNA oligomers show quenching dependent on the combination of nanotube structure and ssDNA base sequence. Several sequences are found to give notably high or low surface coverages for specific SWCNT species. These effects seem correlated with the selective recognitions used for DNA-based structural sorting of nanotubes. One notable example is that dye quenching of fluorescence from SWCNTs coated with the (ATT) base sequence is far stronger for one (7,5) enantiomer than for the other, showing that coating coverage is associated with the coating affinity difference reported previously for this system. Equilibrium modeling of quenching data has been used to extract parameters for comparative complexation constants and accessible surface areas. Further insights are obtained from molecular dynamics simulations, which give estimated contact areas between ssDNA and SWCNTs that correlate with experimentally inferred surface exposures and account for the enantiomeric discrimination of (ATT).
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http://dx.doi.org/10.1021/acsnano.0c05720DOI Listing
September 2020

Single C-to-T substitution using engineered APOBEC3G-nCas9 base editors with minimum genome- and transcriptome-wide off-target effects.

Sci Adv 2020 Jul 15;6(29):eaba1773. Epub 2020 Jul 15.

Department of Bioengineering, Rice University, Houston, TX 77030, USA.

Cytosine base editors (CBEs) enable efficient cytidine-to-thymidine (C-to-T) substitutions at targeted loci without double-stranded breaks. However, current CBEs edit all Cs within their activity windows, generating undesired bystander mutations. In the most challenging circumstance, when a bystander C is adjacent to the targeted C, existing base editors fail to discriminate them and edit both Cs. To improve the precision of CBE, we identified and engineered the human APOBEC3G (A3G) deaminase; when fused to the Cas9 nickase, the resulting A3G-BEs exhibit selective editing of the second C in the 5'-CC-3' motif in human cells. Our A3G-BEs could install a single disease-associated C-to-T substitution with high precision. The percentage of perfectly modified alleles is more than 6000-fold for disease correction and more than 600-fold for disease modeling compared with BE4max. On the basis of the two-cell embryo injection method and RNA sequencing analysis, our A3G-BEs showed minimum genome- and transcriptome-wide off-target effects, achieving high targeting fidelity.
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http://dx.doi.org/10.1126/sciadv.aba1773DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7439359PMC
July 2020

Relaxation Times of Ligand-Receptor Complex Formation Control T Cell Activation.

Biophys J 2020 07 9;119(1):182-189. Epub 2020 Jun 9.

Department of Chemistry, Rice University, Houston, Texas; Center for Theoretical Biological Physics, Rice University, Houston, Texas; Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas; Department of Physics and Astronomy, Rice University, Houston, Texas. Electronic address:

One of the most important functions of immune T cells is to recognize the presence of the pathogen-derived ligands and to quickly respond to them while at the same time not responding to its own ligands. This is known as absolute discrimination, and it is one of the most challenging phenomena to explain. The effectiveness of pathogen detection by T cell receptor is limited by chemical similarity of foreign and self-peptides and very low concentrations of foreign ligands. We propose a new mechanism of how absolute discrimination by T cells might function. It is suggested that the decision to activate or not to activate the immune response is controlled by the time to reach the stationary concentration of the T-cell-receptor-ligand-activated complex, which transfers the signal to downstream cellular biochemical networks. Our theoretical method models T cell receptor phosphorylation events as a sequence of stochastic transitions between discrete biochemical states, and this allows us to explicitly describe the dynamical properties of the system. It is found that the proposed criterion on the relaxation times is able to explain available experimental observations. In addition, we suggest that the level of stochastic noise might be an additional factor in the activation mechanisms. Furthermore, our theoretical approach explicitly analyzes the relationships between speed, sensitivity, and specificity of T cell functioning, which are the main characteristics of the process. Thus, it clarifies the molecular picture of T cell activation in immune response.
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http://dx.doi.org/10.1016/j.bpj.2020.06.002DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7335936PMC
July 2020

Direct detection of molecular intermediates from first-passage times.

Sci Adv 2020 May 1;6(18):eaaz4642. Epub 2020 May 1.

Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK.

All natural phenomena are governed by energy landscapes. However, the direct measurement of this fundamental quantity remains challenging, particularly in complex systems involving intermediate states. Here, we uncover key details of the energy landscapes that underpin a range of experimental systems through quantitative analysis of first-passage time distributions. By combined study of colloidal dynamics in confinement, transport through a biological pore, and the folding kinetics of DNA hairpins, we demonstrate conclusively how a short-time, power-law regime of the first-passage time distribution reflects the number of intermediate states associated with each of these processes, despite their differing length scales, time scales, and interactions. We thereby establish a powerful method for investigating the underlying mechanisms of complex molecular processes.
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http://dx.doi.org/10.1126/sciadv.aaz4642DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7195145PMC
May 2020

Biased Random Walk in Crowded Environment: Breaking Uphill/Downhill Symmetry of Transition Times.

J Phys Chem Lett 2020 Jun 27;11(11):4530-4535. Epub 2020 May 27.

Department of Chemistry, Rice University, Houston, Texas 77005, United States.

Various natural processes can be analyzed using the concept of random walks. For a single random walker, the mean waiting times for uphill and downhill transitions between neighboring sites are equal. Here we investigate the uphill/downhill symmetry of waiting times for transitions of a tracer in crowded environment using exactly solvable one-dimensional stochastic models. It is found that, unexpectedly, the time to move in the direction of the bias (downhill) is always longer than the time to move against the bias (uphill). The degree of asymmetry depends on the particle density, the strength of the bias, and the size of the system. The microscopic origin of the symmetry breaking is discussed.
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http://dx.doi.org/10.1021/acs.jpclett.0c01113DOI Listing
June 2020

Trade-Offs between Speed, Accuracy, and Dissipation in tRNA Aminoacylation.

J Phys Chem Lett 2020 May 6;11(10):4001-4007. Epub 2020 May 6.

Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.

Living systems maintain a high fidelity in information processing through kinetic proofreading, a mechanism for preferentially removing incorrect substrates at the cost of energy dissipation and slower speed. Proofreading mechanisms must balance their demand for higher speed, fewer errors, and lower dissipation, but it is unclear how rates of individual reaction steps are evolutionarily tuned to balance these needs, especially when multiple proofreading mechanisms are present. Here, using a discrete-state stochastic model, we analyze the optimization strategies in isoleucyl-tRNA synthetase. Surprisingly, this enzyme adopts an economic proofreading strategy and improves speed and dissipation as long as the error is tolerable. Through global parameter sampling, we reveal a fundamental dissipation-error relation that bounds the enzyme's optimal performance and explains the importance of the post-transfer editing mechanism. The proximity of native system parameters to this bound demonstrates the importance of energy dissipation as an evolutionary force affecting fitness.
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http://dx.doi.org/10.1021/acs.jpclett.0c01073DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7890467PMC
May 2020

Kinetic control of stationary flux ratios for a wide range of biochemical processes.

Proc Natl Acad Sci U S A 2020 04 7;117(16):8884-8889. Epub 2020 Apr 7.

Center for Theoretical Biological Physics, Rice University, Houston, TX 77005;

One of the most intriguing features of biological systems is their ability to regulate the steady-state fluxes of the underlying biochemical reactions; however, the regulatory mechanisms and their physicochemical properties are not fully understood. Fundamentally, flux regulation can be explained with a chemical kinetic formalism describing the transitions between discrete states, with the reaction rates defined by an underlying free energy landscape. Which features of the energy landscape affect the flux distribution? Here we prove that the ratios of the steady-state fluxes of quasi-first-order biochemical processes are invariant to energy perturbations of the discrete states and are only affected by the energy barriers. In other words, the nonequilibrium flux distribution is under kinetic and not thermodynamic control. We illustrate the generality of this result for three biological processes. For the network describing protein folding along competing pathways, the probabilities of proceeding via these pathways are shown to be invariant to the stability of the intermediates or to the presence of additional misfolded states. For the network describing protein synthesis, the error rate and the energy expenditure per peptide bond is proven to be independent of the stability of the intermediate states. For molecular motors such as myosin-V, the ratio of forward to backward steps and the number of adenosine 5'-triphosphate (ATP) molecules hydrolyzed per step is demonstrated to be invariant to energy perturbations of the intermediate states. These findings place important constraints on the ability of mutations and drug perturbations to affect the steady-state flux distribution for a wide class of biological processes.
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http://dx.doi.org/10.1073/pnas.1920873117DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7183173PMC
April 2020

Theoretical Investigations of the Dynamics of Chemical Reactions on Nanocatalysts with Multiple Active Sites.

J Phys Chem Lett 2020 Mar 9;11(6):2330-2335. Epub 2020 Mar 9.

Department of Chemistry, Department of Chemical and Biomolecular Engineering, Department of Physics and Astronomy, and Center for Theoretical Biological Physics, Rice University, 6100 Main Street, Houston, Texas 77005, United States.

Recent synthetic advances led to the development of new catalytic particles with well-defined atomic structures and multiple active sites, which are called nanocatalysts. Experimental studies of processes at nanocatalysts uncovered a variety of surprising effects, but the molecular mechanisms of these phenomena remain not well understood. We propose a theoretical method to investigate the dynamics of chemical reactions on catalytic particles with multiple active sites. It is based on a discrete-state stochastic description that allows us to explicitly evaluate dynamic properties of the system. It is found that for independently occurring chemical reactions, the mean turnover times are inversely proportional to the number of active sites, showing no stochastic effects. However, the molecular details of reactions and the number of active sites influence the higher moments of reaction times. Our theoretical method provides a way to quantify the molecular mechanisms of processes at nanocatalysts.
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http://dx.doi.org/10.1021/acs.jpclett.0c00316DOI Listing
March 2020

A Mechanochemical Model of Transcriptional Bursting.

Biophys J 2020 03 28;118(5):1213-1220. Epub 2020 Jan 28.

Department of Chemistry, Rice University, Houston, Texas; Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas; Department of Physics, Rice University, Houston, Texas; Center for Theoretical Biological Physics, Rice University, Houston, Texas. Electronic address:

Populations of genetically identical cells generally show a large variability in cell phenotypes, which is typically associated with the stochastic nature of gene expression processes. It is widely believed that a significant source of such randomness is transcriptional bursting, which is when periods of active production of RNA molecules alternate with periods of RNA degradation. However, the molecular mechanisms of such strong fluctuations remain unclear. Recent studies suggest that DNA supercoiling, which happens during transcription, might be directly related to the bursting behavior. Stimulated by these observations, we developed a stochastic mechanochemical model of supercoiling-induced transcriptional bursting in which the RNA synthesis leads to the buildup of torsion in DNA. This slows down the RNA production until it is bound by the enzyme gyrase to DNA, which releases the stress and allows for the RNA synthesis to restart with the original rate. Using a thermodynamically consistent coupling between mechanical and chemical processes, the dynamic properties of transcription are explicitly evaluated. In addition, a first-passage method to evaluate the dynamics of transcription is developed. Theoretical analysis shows that transcriptional bursting is observed when both the supercoiling and the mechanical stress release due to gyrase are present in the system. It is also found that the overall RNA production rate is not constant and depends on the number of previously synthesized RNA molecules. A comparison with experimental data on bacteria allows us to evaluate the energetic cost of supercoiling during transcription. It is argued that the relatively weak mechanochemical coupling might allow transcription to be regulated most effectively.
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http://dx.doi.org/10.1016/j.bpj.2020.01.017DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7063482PMC
March 2020

The effect of obstacles in multi-site protein target search with DNA looping.

J Chem Phys 2020 Jan;152(2):025101

Department of Physics, Rice University, Houston, Texas 77005, USA.

Many fundamental biological processes are regulated by protein-DNA complexes called synaptosomes, which possess multiple interaction sites. Despite the critical importance of synaptosomes, the mechanisms of their formation are not well understood. Because of the multisite nature of participating proteins, it is widely believed that their search for specific sites on DNA involves the formation and breaking of DNA loops and sliding in the looped configurations. In reality, DNA in live cells is densely covered by other biological molecules that might interfere with the formation of synaptosomes. In this work, we developed a theoretical approach to evaluate the role of obstacles in the target search of multisite proteins when the formation of DNA loops and the sliding in looped configurations are possible. Our theoretical method is based on analysis of a discrete-state stochastic model that uses a master equations approach and extensive computer simulations. It is found that the obstacle slows down the search dynamics in the system when DNA loops are long-lived, but the effect is minimal for short-lived DNA loops. In addition, the relative positions of the target and the obstacle strongly influence the target search kinetics. Furthermore, the presence of the obstacle might increase the noise in the system. These observations are discussed using physical-chemical arguments. Our theoretical approach clarifies the molecular mechanisms of formation of protein-DNA complexes with multiple interactions sites.
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http://dx.doi.org/10.1063/1.5135917DOI Listing
January 2020

Molecular Model for the Surface-Catalyzed Protein Self-Assembly.

J Phys Chem B 2020 01 7;124(2):366-372. Epub 2020 Jan 7.

Department of Pharmaceutical Sciences, College of Pharmacy , University of Nebraska Medical Center , 986025 Nebraska Medical Center, Omaha , Nebraska 68198-6025 , United States.

The importance of cell surfaces in the self-assembly of proteins is widely accepted. One biologically significant event is the assembly of amyloidogenic proteins into aggregates, which leads to neurodegenerative disorders like Alzheimer's and Parkinson's diseases. The interaction of amyloidogenic proteins with cellular membranes appears to dramatically facilitate the aggregation process. Recent findings indicate that, in the presence of surfaces, aggregation occurs at physiologically low concentrations, suggesting that interaction with surfaces plays a critical role in the disease-prone aggregation process. However, the molecular mechanisms behind the on-surface aggregation process remain unclear. Here, we provide a theoretical model that offers a molecular explanation. According to this model, monomers transiently immobilized to surfaces increase the local monomer protein concentration and thus work as nuclei to dramatically accelerate the entire aggregation process. This physical-chemical theory was verified by experimental studies, using mica surfaces, to examine the aggregation kinetics of amyloidogenic α-synuclein protein and non-amyloidogenic cytosine deaminase APOBEC3G.
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http://dx.doi.org/10.1021/acs.jpcb.9b10052DOI Listing
January 2020

Elucidating the correlations between cancer initiation times and lifetime cancer risks.

Sci Rep 2019 12 12;9(1):18940. Epub 2019 Dec 12.

Department of Chemistry, Rice University, Houston, TX, United States.

Cancer is a genetic disease that results from accumulation of unfavorable mutations. As soon as genetic and epigenetic modifications associated with these mutations become strong enough, the uncontrolled tumor cell growth is initiated, eventually spreading through healthy tissues. Clarifying the dynamics of cancer initiation is thus critically important for understanding the molecular mechanisms of tumorigenesis. Here we present a new theoretical method to evaluate the dynamic processes associated with the cancer initiation. It is based on a discrete-state stochastic description of the formation of tumors as a fixation of cancerous mutations in tissues. Using a first-passage analysis the probabilities for the cancer to appear and the times before it happens, which are viewed as fixation probabilities and fixation times, respectively, are explicitly calculated. It is predicted that the slowest cancer initiation dynamics is observed for neutral mutations, while it is fast for both advantageous and, surprisingly, disadvantageous mutations. The method is applied for estimating the cancer initiation times from experimentally available lifetime cancer risks for different types of cancer. It is found that the higher probability of the cancer to occur does not necessary lead to the faster times of starting the cancer. Our theoretical analysis helps to clarify microscopic aspects of cancer initiation processes.
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http://dx.doi.org/10.1038/s41598-019-55300-wDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6908632PMC
December 2019

Role of Intrinsically Disordered Regions in Acceleration of Protein-Protein Association.

J Phys Chem B 2020 01 19;124(1):20-27. Epub 2019 Dec 19.

Although intrinsically disordered proteins and intrinsically disordered regions (IDRs) in folded proteins are not able to form stable structures, it is known that they play critically important roles in various biological processes. However, despite multiple studies, the molecular mechanisms of their functions remain not fully understood. In this work, we theoretically investigate the role of IDRs in acceleration of protein-protein association processes. Our hypothesis is that, in protein pairs with several independent binding sites, the association process goes faster if some of these binding sites are located on IDRs or connected by IDRs. To test this idea, we employed analytical modeling, numerical calculations, and Brownian dynamics computer simulations to calculate protein-protein association reaction rates for the ERK2-EtsΔ138 system, belonging to the RAS-RAF-MEK-ERK signaling pathway in living cells. It is found that putting a binding site on IDR accelerates the association process by a factor of 3 to 4. Possible molecular explanations for these observations are presented, and other systems that might use this mechanism are also mentioned.
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http://dx.doi.org/10.1021/acs.jpcb.9b08793DOI Listing
January 2020

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

J Chem Phys 2019 Sep;151(12):125101

Department of Chemistry, Rice University, Houston, Texas 77005, USA.

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.
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http://dx.doi.org/10.1063/1.5123988DOI Listing
September 2019

Theoretical Analysis of Run Length Distributions for Coupled Motor Proteins.

J Phys Chem B 2019 07 27;123(27):5805-5813. Epub 2019 Jun 27.

Motor proteins, also known as biological molecular motors, play important roles in various biological processes. In recent years, properties of single-motor proteins have been intensively investigated using multiple experimental and theoretical tools. However, in real cellular systems biological motors typically function in groups, but the mechanisms of their collective dynamics remain not well understood. Here we investigate theoretically distributions of run lengths for coupled motor proteins that move along linear tracks. Our approach utilizes a method of first-passage processes, which is supplemented by Monte Carlo computer simulations. Theoretical analysis allowed us to clarify several aspects of the cooperativity mechanisms for coupled biological molecular motors. It is found that the run length distribution for two motors, in contrast to single motors, is nonmonotonic. In addition, the transport efficiency of two-motor complexes might be strongly increased. We also argue that the degree of cooperativity is influenced by several characteristics of motor proteins such as the strength of intermolecular interactions, stall forces, dissociations constants, and the detachment forces. The application of our theoretical analysis for several motor proteins is also discussed.
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http://dx.doi.org/10.1021/acs.jpcb.9b04710DOI Listing
July 2019

Facilitation of DNA loop formation by protein-DNA non-specific interactions.

Soft Matter 2019 Jul 17;15(26):5255-5263. Epub 2019 Jun 17.

Department of Chemistry, Rice University, Houston, Texas 77005, USA. and Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA.

Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these systems remain not well understood. Existing theoretical studies focus only on specific interactions between protein and DNA molecules at target sequences. However, the electrostatic origin of primary protein-DNA interactions suggests that interactions of proteins with all DNA segments should be considered. Here we theoretically investigate the role of non-specific interactions between protein and DNA molecules on the dynamics of loop formation. Our approach is based on analyzing a discrete-state stochastic model via a method of first-passage probabilities supplemented by Monte Carlo computer simulations. It is found that depending on a protein sliding length during the non-specific binding event three different dynamic regimes of the DNA loop formation might be observed. In addition, the loop formation time might be optimized by varying the protein sliding length, the size of the DNA molecule, and the position of the specific target sequences on DNA. Our results demonstrate the importance of non-specific protein-DNA interactions in the dynamics of DNA loop formations.
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http://dx.doi.org/10.1039/c9sm00671kDOI Listing
July 2019

Trade-Offs between Error, Speed, Noise, and Energy Dissipation in Biological Processes with Proofreading.

J Phys Chem B 2019 06 23;123(22):4718-4725. Epub 2019 May 23.

High accuracy of major biological processes relies on the ability of the participating enzymatic molecules to preferentially select the correct substrate from a pool of chemically similar substrates by activating the so-called proofreading mechanisms. While the importance of such mechanisms is widely accepted, it is still unclear how evolution has optimized the biological systems with respect to certain characteristic properties. Here, using a discrete-state stochastic framework with a first-passage analysis, we theoretically investigate trade-offs between four characteristic properties of enzymatic systems, namely, error, speed, noise, and energy dissipation. Specifically, two fundamental biological processes are examined, i.e., DNA replication in the T7 bacteriophage and tRNA selection during protein translation in Escherichia coli. Notably, all of the characteristic properties cannot be completely optimized at the same time due to trade-offs between them. To understand the relative importance of the computed quantities to the enzymatic functionality, we introduce a new quantitative metric to rank the properties. The results demonstrate that the reaction speed is the principal characteristic property that evolution optimizes in both enzymatic systems and that the energy dissipation comes in second. In addition, the error and the noise are always ranked third and fourth, respectively, regardless of the system considered. Physicochemical arguments to explain these observations are presented.
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http://dx.doi.org/10.1021/acs.jpcb.9b03757DOI Listing
June 2019
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