1
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Gounaris G, Katifori E. Braess's Paradox Analog in Physical Networks of Optimal Exploration. PHYSICAL REVIEW LETTERS 2024; 133:067401. [PMID: 39178443 DOI: 10.1103/physrevlett.133.067401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Revised: 01/31/2024] [Accepted: 07/02/2024] [Indexed: 08/25/2024]
Abstract
In stochastic exploration of geometrically embedded graphs, intuition suggests that providing a shortcut between a pair of nodes reduces the mean first passage time of the entire graph. Counterintuitively, we find a Braess's paradox analog. For regular diffusion, shortcuts can worsen the overall search efficiency of the network, although they bridge topologically distant nodes. We propose an optimization scheme under which each edge adapts its conductivity to minimize the graph's search time. The optimization reveals a relationship between the structure and diffusion exponent and a crossover from dense to sparse graphs as the exponent increases.
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2
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Fuentenebro Navas D, Steens JA, de Lannoy C, Noordijk B, Pfeffer M, de Ridder D, H.J. Staals R, Schmid S. Nanopores Reveal the Stoichiometry of Single Oligoadenylates Produced by Type III CRISPR-Cas. ACS NANO 2024; 18:16505-16515. [PMID: 38875527 PMCID: PMC11223493 DOI: 10.1021/acsnano.3c11769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Revised: 05/27/2024] [Accepted: 06/05/2024] [Indexed: 06/16/2024]
Abstract
Cyclic oligoadenylates (cOAs) are small second messenger molecules produced by the type III CRISPR-Cas system as part of the prokaryotic immune response. The role of cOAs is to allosterically activate downstream effector proteins that induce dormancy or cell death, and thus abort viral spread through the population. Interestingly, different type III systems have been reported to utilize different cOA stoichiometries (with 3 to 6 adenylate monophosphates). However, so far, their characterization has only been possible in bulk and with sophisticated equipment, while a portable assay with single-molecule resolution has been lacking. Here, we demonstrate the label-free detection of single cOA molecules using a simple protein nanopore assay. It sensitively identifies the stoichiometry of individual cOA molecules and their mixtures from synthetic and enzymatic origin. To achieve this, we trained a convolutional neural network (CNN) and validated it with a series of experiments on mono- and polydisperse cOA samples. Ultimately, we determined the stoichiometric composition of cOAs produced enzymatically by the CRISPR type III-A and III-B variants of Thermus thermophilus and confirmed the results by liquid chromatography-mass spectroscopy (LC-MS). Interestingly, both variants produce cOAs of nearly identical composition (within experimental uncertainties), and we discuss the biological implications of this finding. The presented nanopore-CNN workflow with single cOA resolution can be adapted to many other signaling molecules (including eukaryotic ones), and it may be integrated into portable handheld devices with potential point-of-care applications.
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Affiliation(s)
- David Fuentenebro Navas
- Laboratory
of Biophysics, Wageningen University and
Research, Stippeneng 4, 6708WE Wageningen, The Netherlands
| | - Jurre A. Steens
- Laboratory
of Microbiology, Wageningen University and
Research, Stippeneng
4, 6708WE Wageningen, The Netherlands
| | - Carlos de Lannoy
- Bioinformatics
Group, Wageningen University and Research, Droevendaalsesteeg 1, 6708PB Wageningen, The Netherlands
- Department
of Bionanoscience, Delft University of Technology, Van der Maasweg 9, 2629HZ Delft, The Netherlands
| | - Ben Noordijk
- Bioinformatics
Group, Wageningen University and Research, Droevendaalsesteeg 1, 6708PB Wageningen, The Netherlands
| | - Michael Pfeffer
- Department
of Chemistry, University of Basel, Mattenstrasse 22, 4058 Basel, Switzerland
| | - Dick de Ridder
- Bioinformatics
Group, Wageningen University and Research, Droevendaalsesteeg 1, 6708PB Wageningen, The Netherlands
| | - Raymond H.J. Staals
- Laboratory
of Microbiology, Wageningen University and
Research, Stippeneng
4, 6708WE Wageningen, The Netherlands
| | - Sonja Schmid
- Laboratory
of Biophysics, Wageningen University and
Research, Stippeneng 4, 6708WE Wageningen, The Netherlands
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3
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Ertel B, Seifert U. Estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions. Phys Rev E 2024; 109:054109. [PMID: 38907510 DOI: 10.1103/physreve.109.054109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 03/25/2024] [Indexed: 06/24/2024]
Abstract
A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic bound, we derive an operationally accessible entropy estimator for this observation scenario. We illustrate the operational relevance and the quality of this entropy estimator with a numerical analysis of various representative examples.
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Affiliation(s)
- Benjamin Ertel
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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4
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Kumar V, Pal A, Shpielberg O. Emerging universality classes in thermally assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach. J Chem Phys 2024; 160:134107. [PMID: 38563303 DOI: 10.1063/5.0195570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Accepted: 03/01/2024] [Indexed: 04/04/2024] Open
Abstract
Thermal activation of a particle from a deep potential trap follows the Arrhenius law. Recently, this result has been generalized for interacting diffusive particles in the trap, revealing two universality classes-the Arrhenius class and the excluded volume class. The result was demonstrated with the aid of numerical analysis. Here, we present a perturbative hydrodynamic approach to analytically validate the existence and range of validity for the two universality classes.
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Affiliation(s)
- Vishwajeet Kumar
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Ohad Shpielberg
- Department of Mathematics and Physics, University of Haifa at Oranim, Kiryat Tivon 3600600, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Abba Khoushy Ave. 199, Haifa 3498838, Israel
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5
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Kumar V, Pal A, Shpielberg O. Arrhenius law for interacting diffusive systems. Phys Rev E 2024; 109:L032101. [PMID: 38632768 DOI: 10.1103/physreve.109.l032101] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 02/08/2024] [Indexed: 04/19/2024]
Abstract
Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory-a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.
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Affiliation(s)
- Vishwajeet Kumar
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Ohad Shpielberg
- Department of Mathematics and Physics, University of Haifa at Oranim, Kiryat Tivon 3600600, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Abba Khoushy Avenue 199, Haifa 3498838, Israel
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6
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Woods EJ, Wales DJ. Analysis and interpretation of first passage time distributions featuring rare events. Phys Chem Chem Phys 2024; 26:1640-1657. [PMID: 38059562 DOI: 10.1039/d3cp04199a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/08/2023]
Abstract
In this contribution we consider theory and associated computational tools to treat the kinetics associated with competing pathways on multifunnel energy landscapes. Multifunnel landscapes are associated with molecular switches and multifunctional materials, and are expected to exhibit multiple relaxation time scales and associated thermodynamic signatures in the heat capacity. Our focus here is on the first passage time distribution, which is encoded in a kinetic transition network containing all the locally stable states and the pathways between them. This network can be renormalised to reduce the dimensionality, while exactly conserving the mean first passage time and approximately conserving the full distribution. The structure of the reduced network can be visualised using disconnectivity graphs. We show how features in the first passage time distribution can be associated with specific kinetic traps, and how the appearance of competing relaxation time scales depends on the starting conditions. The theory is tested for two model landscapes and applied to an atomic cluster and a disordered peptide. Our most important contribution is probably the reconstruction of the full distribution for long time scales, where numerical problems prevent direct calculations. Here we combine accurate treatment of the mean first passage time with the reliable part of the distribution corresponding to faster time scales. Hence we now have a fundamental understanding of both thermodynamic and kinetic signatures of multifunnel landscapes.
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Affiliation(s)
- Esmae J Woods
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
| | - David J Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
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7
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Bebon R, Godec A. Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime. PHYSICAL REVIEW LETTERS 2023; 131:237101. [PMID: 38134782 DOI: 10.1103/physrevlett.131.237101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Revised: 10/18/2023] [Accepted: 10/31/2023] [Indexed: 12/24/2023]
Abstract
We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.
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Affiliation(s)
- Rick Bebon
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
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8
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Gerry M, Segal D. Random walks on modular chains: Detecting structure through statistics. Phys Rev E 2023; 108:024135. [PMID: 37723810 DOI: 10.1103/physreve.108.024135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Accepted: 08/04/2023] [Indexed: 09/20/2023]
Abstract
We study kinetic transport through one-dimensional modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it depends only on global, structural-averaged properties. However, by examining high-order cumulants characterizing the kinetics, we reveal information on the degree of inhomogeneity of blocks and the size of repeating units in the network. Specifically, in unbiased diffusion, the kurtosis is the first transport coefficient that exposes structural information, whereas in biased chains, the diffusion coefficient already reveals structural motifs. Nevertheless, this latter dependence is weak, and it disappears at both low and high biasing. Our study demonstrates that high-order moments of the population distribution over sites provide information about the network structure that is not captured by the first moment (mean velocity) alone. These results are useful towards deciphering mechanisms and determining architectures underlying long-range charge transport in biomolecules and biological and chemical reaction networks.
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Affiliation(s)
- Matthew Gerry
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Dvira Segal
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
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9
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Contreras-Vergara O, Sánchez-Salas N, Valencia-Ortega G, Jiménez-Aquino JI. Carnot, Stirling, and Ericsson stochastic heat engines: Efficiency at maximum power. Phys Rev E 2023; 108:014123. [PMID: 37583186 DOI: 10.1103/physreve.108.014123] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Accepted: 06/26/2023] [Indexed: 08/17/2023]
Abstract
This work uses the low-dissipation strategy to obtain efficiency at maximum power from a stochastic heat engine performing Carnot-, Stirling- and Ericsson-like cycles at finite time. The heat engine consists of a colloidal particle trapped by optical tweezers, in contact with two thermal baths at different temperatures, namely hot (T_{h}) and cold (T_{c}). The particle dynamics is characterized by a Langevin equation with time-dependent control parameters bounded to a harmonic potential trap. In a low-dissipation approach, the equilibrium properties of the system are required, which in our case, can be calculated through a statelike equation for the mean value 〈x^{2}〉_{eq} coming from a macroscopic expression associated with the Langevin equation.
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Affiliation(s)
- O Contreras-Vergara
- Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. 9 UP Zacatenco, CP 07738, CDMX, México
| | - N Sánchez-Salas
- Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. 9 UP Zacatenco, CP 07738, CDMX, México
| | - G Valencia-Ortega
- División de Matemáticas e Ingeniería, Facultad de Estudios Superiores Acatlán, Universidad Nacional Autónoma de México, Av. Alcanfores y San Juan Totoltepec, Santa Cruz Acatlán, Naucalpan de Juárez, 53150, Estado de México, México
| | - J I Jiménez-Aquino
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, C.P. 09340, CDMX, México
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10
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Luo J, Guan T, Chen G, Yu Z, Zhai H, Yan C, Luo H. SLHSD: hybrid scaffolding method based on short and long reads. Brief Bioinform 2023; 24:7152317. [PMID: 37141142 DOI: 10.1093/bib/bbad169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2022] [Revised: 01/08/2023] [Accepted: 04/12/2023] [Indexed: 05/05/2023] Open
Abstract
In genome assembly, scaffolding can obtain more complete and continuous scaffolds. Current scaffolding methods usually adopt one type of read to construct a scaffold graph and then orient and order contigs. However, scaffolding with the strengths of two or more types of reads seems to be a better solution to some tricky problems. Combining the advantages of different types of data is significant for scaffolding. Here, a hybrid scaffolding method (SLHSD) is present that simultaneously leverages the precision of short reads and the length advantage of long reads. Building an optimal scaffold graph is an important foundation for getting scaffolds. SLHSD uses a new algorithm that combines long and short read alignment information to determine whether to add an edge and how to calculate the edge weight in a scaffold graph. In addition, SLHSD develops a strategy to ensure that edges with high confidence can be added to the graph with priority. Then, a linear programming model is used to detect and remove remaining false edges in the graph. We compared SLHSD with other scaffolding methods on five datasets. Experimental results show that SLHSD outperforms other methods. The open-source code of SLHSD is available at https://github.com/luojunwei/SLHSD.
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Affiliation(s)
- Junwei Luo
- School of Software, Henan Polytechnic University, Jiaozuo 454003, China
| | - Ting Guan
- School of Software, Henan Polytechnic University, Jiaozuo 454003, China
| | - Guolin Chen
- School of Software, Henan Polytechnic University, Jiaozuo 454003, China
| | - Zhonghua Yu
- School of Software, Henan Polytechnic University, Jiaozuo 454003, China
| | - Haixia Zhai
- School of Software, Henan Polytechnic University, Jiaozuo 454003, China
| | - Chaokun Yan
- School of Computer and Information Engineering, Henan University, Kaifeng 475001, China
| | - Huimin Luo
- School of Computer and Information Engineering, Henan University, Kaifeng 475001, China
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11
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Song K, Makarov DE, Vouga E. The effect of time resolution on the observed first passage times in diffusive dynamics. J Chem Phys 2023; 158:111101. [PMID: 36948823 DOI: 10.1063/5.0142166] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2023] Open
Abstract
Single-molecule and single-particle tracking experiments are typically unable to resolve fine details of thermal motion at short timescales where trajectories are continuous. We show that, when a diffusive trajectory xt is sampled at finite time intervals δt, the resulting error in measuring the first passage time to a given domain can exceed the time resolution of the measurement by more than an order of magnitude. Such surprisingly large errors originate from the fact that the trajectory may enter and exit the domain while being unobserved, thereby lengthening the apparent first passage time by an amount that is larger than δt. Such systematic errors are particularly important in single-molecule studies of barrier crossing dynamics. We show that the correct first passage times, as well as other properties of the trajectories such as splitting probabilities, can be recovered via a stochastic algorithm that reintroduces unobserved first passage events probabilistically.
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Affiliation(s)
- Kevin Song
- Department of Computer Science, University of Texas at Austin, Austin, Texas 78712, USA
| | - Dmitrii E Makarov
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - Etienne Vouga
- Department of Computer Science, University of Texas at Austin, Austin, Texas 78712, USA
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12
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Abstract
Multifunctional systems, such as molecular switches, exhibit multifunnel energy landscapes associated with the alternative functional states. In this contribution the multifunnel organization is decoded from dynamical signatures in the first passage time distribution between reactants and products. Characteristic relaxation rates are revealed by analyzing the kinetics as a function of the observation time scale, which scans the underlying distribution. Extracting the corresponding dynamical signatures provides direct insight into the organization of the molecular energy landscape, which will facilitate a rational design of target functionality. Examples are illustrated for multifunnel landscapes in biomolecular systems and an atomic cluster.
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13
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Knowles SF, Fletcher M, Mc Hugh J, Earle M, Keyser UF, Thorneywork AL. Observing capture with a colloidal model membrane channel. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:344001. [PMID: 35679844 DOI: 10.1088/1361-648x/ac7764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 06/09/2022] [Indexed: 06/15/2023]
Abstract
We use video microscopy to study the full capture process for colloidal particles transported through microfluidic channels by a pressure-driven flow. In particular, we obtain trajectories for particles as they move from the bulk into confinement, using these to map in detail the spatial velocity and concentration fields for a range of different flow velocities. Importantly, by changing the height profiles of our microfluidic devices, we consider systems for which flow profiles in the channel are the same, but flow fields in the reservoir differ with respect to the quasi-2D monolayer of particles. We find that velocity fields and profiles show qualitative agreement with numerical computations of pressure-driven fluid flow through the systems in the absence of particles, implying that in the regimes studied here particle-particle interactions do not strongly perturb the flow. Analysis of the particle flux through the channel indicates that changing the reservoir geometry leads to a change between long-range attraction of the particles to the pore and diffusion-to-capture-like behaviour, with concentration fields that show qualitative changes based on device geometry. Our results not only provide insight into design considerations for microfluidic devices, but also a foundation for experimental elucidation of the concept of a capture radius. This long standing problem plays a key role in transport models for biological channels and nanopore sensors.
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Affiliation(s)
- Stuart F Knowles
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Marcus Fletcher
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Jeffrey Mc Hugh
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Max Earle
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Ulrich F Keyser
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Alice L Thorneywork
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
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14
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Rijal K, Prasad A, Singh A, Das D. Exact Distribution of Threshold Crossing Times for Protein Concentrations: Implication for Biological Timekeeping. PHYSICAL REVIEW LETTERS 2022; 128:048101. [PMID: 35148123 DOI: 10.1103/physrevlett.128.048101] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2021] [Accepted: 01/03/2022] [Indexed: 06/14/2023]
Abstract
Stochastic protein accumulation up to some concentration threshold sets the timing of many cellular physiological processes. Here we obtain the exact distribution of first threshold crossing times of protein concentration, in either Laplace or time domain, and its associated cumulants: mean, variance, and skewness. The distribution is asymmetric, and its skewness nonmonotonically varies with the threshold. We study lysis times of E. coli cells for holin gene mutants of bacteriophage-λ and find a good match with theory. Mutants requiring higher holin thresholds show more skewed lysis time distributions as predicted. The theory also predicts a linear relationship between infection delay time and host doubling time for lytic viruses, that has recently been experimentally observed.
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Affiliation(s)
- Krishna Rijal
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Ashok Prasad
- Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Abhyudai Singh
- Departments of Electrical and Computer Engineering, Biomedical Engineering and Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA
| | - Dibyendu Das
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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15
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Zunke C, Bewerunge J, Platten F, Egelhaaf SU, Godec A. First-passage statistics of colloids on fractals: Theory and experimental realization. SCIENCE ADVANCES 2022; 8:eabk0627. [PMID: 35061533 PMCID: PMC8782457 DOI: 10.1126/sciadv.abk0627] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Accepted: 11/29/2021] [Indexed: 05/30/2023]
Abstract
In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.
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Affiliation(s)
- Christoph Zunke
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Jörg Bewerunge
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Florian Platten
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
- Institute of Biological Information Processing, Biomacromolecular Systems and Processes (IBI-4), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Stefan U. Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
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16
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Berezhkovskii AM, Makarov DE. On distributions of barrier crossing times as observed in single-molecule studies of biomolecules. BIOPHYSICAL REPORTS 2021; 1:100029. [PMID: 36425456 PMCID: PMC9680812 DOI: 10.1016/j.bpr.2021.100029] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/15/2021] [Accepted: 10/19/2021] [Indexed: 06/16/2023]
Abstract
Single-molecule experiments that monitor time evolution of molecular observables in real time have expanded beyond measuring transition rates toward measuring distributions of times of various molecular events. Of particular interest is the first-passage time for making a transition from one molecular configuration ( a ) to another ( b ) and conditional first-passage times such as the transition path time, which is the first-passage time from a to b conditional upon not leaving the transition region intervening between a and b . Another experimentally accessible (but not yet studied experimentally) observable is the conditional exit time, i.e., the time to leave the transition region through a specified boundary. The distributions of such times contain a wealth of mechanistic information about the transitions in question. Here, we use the first and the second (and, if desired, higher) moments of these distributions to characterize their relative width for the model in which the experimental observable undergoes Brownian motion in a potential of mean force. We show that although the distributions of transition path times are always narrower than exponential (in that the ratio of the standard deviation to the distribution's mean is always less than 1), distributions of first-passage times and of conditional exit times can be either narrow or broad, in some cases displaying long power-law tails. The conditional exit time studied here provides a generalization of the transition path time that also allows one to characterize the temporal scales of failed barrier crossing attempts.
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Affiliation(s)
- Alexander M. Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland
| | - Dmitrii E. Makarov
- Department of Chemistry and Biochemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas
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17
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Shin J, Kolomeisky AB. Asymmetry of forward/backward transition times as a non-equilibrium measure of complexity of microscopic mechanisms. J Chem Phys 2021; 153:124103. [PMID: 33003756 DOI: 10.1063/5.0021840] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Jaeoh Shin
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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18
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Lapolla A, Godec A. Single-file diffusion in a bi-stable potential: Signatures of memory in the barrier-crossing of a tagged-particle. J Chem Phys 2020; 153:194104. [PMID: 33218229 DOI: 10.1063/5.0025785] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model, we analyze tagged-particle diffusion in a single file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the "confining" (all background particles in front of the tagged-particle) and "pushing" (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behaviors. Notably and somewhat unexpectedly, at a fixed particle number, we find that the higher the barrier, the stronger the memory effects are. The fact that the external potential alters the memory is important more generally and should be taken into account in applications of generalized Langevin equations. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.
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Affiliation(s)
- Alessio Lapolla
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
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Broad distributions of transition-path times are fingerprints of multidimensionality of the underlying free energy landscapes. Proc Natl Acad Sci U S A 2020; 117:27116-27123. [PMID: 33087575 DOI: 10.1073/pnas.2008307117] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Recent single-molecule experiments have observed transition paths, i.e., brief events where molecules (particularly biomolecules) are caught in the act of surmounting activation barriers. Such measurements offer unprecedented mechanistic insights into the dynamics of biomolecular folding and binding, molecular machines, and biological membrane channels. A key challenge to these studies is to infer the complex details of the multidimensional energy landscape traversed by the transition paths from inherently low-dimensional experimental signals. A common minimalist model attempting to do so is that of one-dimensional diffusion along a reaction coordinate, yet its validity has been called into question. Here, we show that the distribution of the transition path time, which is a common experimental observable, can be used to differentiate between the dynamics described by models of one-dimensional diffusion from the dynamics in which multidimensionality is essential. Specifically, we prove that the coefficient of variation obtained from this distribution cannot possibly exceed 1 for any one-dimensional diffusive model, no matter how rugged its underlying free energy landscape is: In other words, this distribution cannot be broader than the single-exponential one. Thus, a coefficient of variation exceeding 1 is a fingerprint of multidimensional dynamics. Analysis of transition paths in atomistic simulations of proteins shows that this coefficient often exceeds 1, signifying essential multidimensionality of those systems.
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