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Cherayil BJ. Particle dynamics in viscoelastic media: Effects of non-thermal white noise on barrier crossing rates. J Chem Phys 2021; 155:244903. [PMID: 34972363 DOI: 10.1063/5.0071206] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
The growing interest in the dynamics of self-driven particle motion has brought increased attention to the effects of non-thermal noise on condensed phase diffusion. Thanks to data recently collected by Ferrer et al. on activated dynamics in the presence of memory [Phys. Rev. Lett. 126, 108001 (2021)], some of these effects can now be characterized quantitatively. In the present paper, the data collected by Ferrer et al. are used to calculate the extent to which non-thermal white noise alters the time taken by single micron-sized silica particles in a viscoelastic medium to cross the barrier separating the two wells of an optically created bistable potential. The calculation-based on a generalized version of Kramers's flux-over-population approach-indicates that the added noise causes the barrier crossing rate (compared to the noise-free case) to first increase as a function of the noise strength and then to plateau to a constant value. The precise degree of rate enhancement may depend on how the data from the experiments conducted by Ferrer et al. are used in the flux-over-population approach. As claimed by Ferrer et al., this approach predicts barrier crossing times for the original silica-fluid system that agree almost perfectly with their experimental counterparts. However, this near-perfect agreement between theory and experiment is only achieved if the theoretical crossing times are obtained from the most probable values of a crossing time distribution constructed from the distributions of various parameters in Kramers's rate expression. If the mean values of these parameters are used in the expression instead, as would be commonly done, the theoretical crossing times are found to be as much as 1.5 times higher than the experimental values. However, these times turn out to be consistent with an alternative model of viscoelastic barrier crossing based on a mean first passage time formalism, which also uses mean parameter values in its rate expression. The rate enhancements predicted for barrier crossing under non-thermal noise are based on these mean parameter values and are open to experimental verification.
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Affiliation(s)
- Binny J Cherayil
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, Karnataka, India
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Bullerjahn JT, Sturm S, Kroy K. Non-Markov bond model for dynamic force spectroscopy. J Chem Phys 2020; 152:064104. [PMID: 32061238 DOI: 10.1063/1.5134742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Single-molecule force spectroscopy data are conventionally analyzed using a schematic model, wherein a molecular bond is represented as a virtual particle diffusing in a one-dimensional free-energy landscape. However, this simple and efficient approach is unable to account for the "anomalous" bond-breaking kinetics increasingly observed in force spectroscopy experiments and simulations, e.g., in the form of non-exponential distributions of bond lifetimes under constant load. Here, we show that such characteristic traits arise naturally in a rigorous extension of the one-dimensional theory that accounts for the transient dynamics of a generic set of coupled degrees of freedom. These "hidden modes" affect the reaction dynamics in various ways, depending on their relaxation spectrum and the loading protocol, giving rise, in particular, to apparent static and dynamic disorder. In two complementary asymptotic limits, we are able to find exact analytical expressions for pertinent experimental observables, such as the mean rupture force and the rupture-force distribution. Intriguingly, our asymptotic results become unconditionally exact at high loading rates, thus providing us with a microscopically consistent theory of rapid force spectroscopy that avoids the usual Markov assumption.
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Affiliation(s)
- Jakob Tómas Bullerjahn
- Universität Leipzig, Institut für Theoretische Physik, Postfach 100 920, 04009 Leipzig, Germany
| | - Sebastian Sturm
- Universität Leipzig, Institut für Theoretische Physik, Postfach 100 920, 04009 Leipzig, Germany
| | - Klaus Kroy
- Universität Leipzig, Institut für Theoretische Physik, Postfach 100 920, 04009 Leipzig, Germany
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Newby JM, Seim I, Lysy M, Ling Y, Huckaby J, Lai SK, Forest MG. Technological strategies to estimate and control diffusive passage times through the mucus barrier in mucosal drug delivery. Adv Drug Deliv Rev 2018; 124:64-81. [PMID: 29246855 PMCID: PMC5809312 DOI: 10.1016/j.addr.2017.12.002] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2017] [Revised: 12/05/2017] [Accepted: 12/06/2017] [Indexed: 01/05/2023]
Abstract
In mucosal drug delivery, two design goals are desirable: 1) insure drug passage through the mucosal barrier to the epithelium prior to drug removal from the respective organ via mucus clearance; and 2) design carrier particles to achieve a prescribed arrival time and drug uptake schedule at the epithelium. Both goals are achievable if one can control "one-sided" diffusive passage times of drug carrier particles: from deposition at the mucus interface, through the mucosal barrier, to the epithelium. The passage time distribution must be, with high confidence, shorter than the timescales of mucus clearance to maximize drug uptake. For 100nm and smaller drug-loaded nanoparticulates, as well as pure drug powders or drug solutions, diffusion is normal (i.e., Brownian) and rapid, easily passing through the mucosal barrier prior to clearance. Major challenges in quantitative control over mucosal drug delivery lie with larger drug-loaded nanoparticulates that are comparable to or larger than the pores within the mucus gel network, for which diffusion is not simple Brownian motion and typically much less rapid; in these scenarios, a timescale competition ensues between particle passage through the mucus barrier and mucus clearance from the organ. In the lung, as a primary example, coordinated cilia and air drag continuously transport mucus toward the trachea, where mucus and trapped cargo are swallowed into the digestive tract. Mucus clearance times in lung airways range from minutes to hours or significantly longer depending on deposition in the upper, middle, lower airways and on lung health, giving a wide time window for drug-loaded particle design to achieve controlled delivery to the epithelium. We review the physical and chemical factors (of both particles and mucus) that dictate particle diffusion in mucus, and the technological strategies (theoretical and experimental) required to achieve the design goals. First we describe an idealized scenario - a homogeneous viscous fluid of uniform depth with a particle undergoing passive normal diffusion - where the theory of Brownian motion affords the ability to rigorously specify particle size distributions to meet a prescribed, one-sided, diffusive passage time distribution. Furthermore, we describe how the theory of Brownian motion provides the scaling of one-sided diffusive passage times with respect to mucus viscosity and layer depth, and under reasonable caveats, one can also prescribe passage time scaling due to heterogeneity in viscosity and layer depth. Small-molecule drugs and muco-inert, drug-loaded carrier particles 100nm and smaller fall into this class of rigorously controllable passage times for drug delivery. Second we describe the prevalent scenarios in which drug-loaded carrier particles in mucus violate simple Brownian motion, instead exhibiting anomalous sub-diffusion, for which all theoretical control over diffusive passage times is lost, and experiments are prohibitive if not impossible to measure one-sided passage times. We then discuss strategies to overcome these roadblocks, requiring new particle-tracking experiments and emerging advances in theory and computation of anomalous, sub-diffusive processes that are necessary to predict and control one-sided particle passage times from deposition at the mucosal interface to epithelial uptake. We highlight progress to date, remaining hurdles, and prospects for achieving the two design goals for 200nm and larger, drug-loaded, non-dissolving, nanoparticulates.
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Affiliation(s)
- Jay M Newby
- Department of Mathematics and Applied Physical Sciences, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States
| | - Ian Seim
- Department of Mathematics and Applied Physical Sciences, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States
| | - Martin Lysy
- Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, United States
| | - Yun Ling
- Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, United States
| | - Justin Huckaby
- Division of Pharmacoengineering and Molecular Pharmaceutics, Eshelman School of Pharmacy, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States
| | - Samuel K Lai
- Division of Pharmacoengineering and Molecular Pharmaceutics, Eshelman School of Pharmacy, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States; UNC-NCSU Joint Department of Biomedical Engineering, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States; Department of Microbiology and Immunology, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States
| | - M Gregory Forest
- Department of Mathematics and Applied Physical Sciences, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States; UNC-NCSU Joint Department of Biomedical Engineering, University of North Carolina-Chapel Hill, Chapel Hill, NC 27599, United States.
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Ai BQ, He YF, Zhong WR. Transport in periodic potentials induced by fractional Gaussian noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061102. [PMID: 21230639 DOI: 10.1103/physreve.82.061102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2010] [Revised: 10/02/2010] [Indexed: 05/30/2023]
Abstract
Directed transport of overdamped Brownian particles driven by fractional Gaussian noises is investigated in asymmetrically periodic potentials. By using Langevin dynamics simulations, we find that rectified currents occur in the absence of any external driving forces. Unlike white Gaussian noises, fractional Gaussian noises can break thermodynamical equilibrium and induce directed transport. Remarkably, the average velocity for persistent fractional noise is opposite to that for antipersistent fractional noise. The velocity increases monotonically with Hurst exponent for the persistent case, whereas there exists an optimal value of Hurst exponent at which the velocity takes its maximal value for the antipersistent case.
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Affiliation(s)
- Bao-quan Ai
- Laboratory of Quantum Information Technology, ICMP and SPTE, South China Normal University, 510006 Guangzhou, China
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Min W, Jiang L, Xie X. Complex Kinetics of Fluctuating Enzymes: Phase Diagram Characterization of a Minimal Kinetic Scheme. Chem Asian J 2010; 5:1129-38. [DOI: 10.1002/asia.200900627] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chakrabarti R, Sebastian KL. A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space. J Chem Phys 2009; 131:224504. [PMID: 20001054 DOI: 10.1063/1.3269613] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.
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Affiliation(s)
- Rajarshi Chakrabarti
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.
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Chaudhury S, Chatterjee D, Cherayil BJ. The dynamics of single enzyme reactions: A reconsideration of Kramers' model for colored noise processes. J Chem Phys 2008; 129:075104. [DOI: 10.1063/1.2969767] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chaudhury S, Cherayil BJ. A Model of Anomalous Chain Translocation Dynamics. J Phys Chem B 2008; 112:15973-9. [DOI: 10.1021/jp7108362] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Srabanti Chaudhury
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore-560012, India
| | - Binny J. Cherayil
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore-560012, India
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Min W, Xie XS, Bagchi B. Two-dimensional reaction free energy surfaces of catalytic reaction: effects of protein conformational dynamics on enzyme catalysis. J Phys Chem B 2007; 112:454-66. [PMID: 18085768 DOI: 10.1021/jp076533c] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We introduce a two-dimensional (2D) multisurface reaction free energy description of the catalytic cycle that explicitly connects the recently observed multi-time-scale conformational dynamics as well as dispersed enzymatic kinetics to the classical Michaelis-Menten equation. A slow conformational motion on a collective enzyme coordinate Q facilitates the catalytic reaction along the intrinsic reaction coordinate X, providing a dynamic realization of Pauling's well-known idea of transition-state stabilization. The catalytic cycle is modeled as transitions between multiple displaced harmonic wells in the XQ space representing different states of the cycle, which is constructed according to the free energy driving force of the cycle. Subsequent to substrate association with the enzyme, the enzyme-substrate complex under strain exhibits a nonequilibrium relaxation toward a new conformation that lowers the activation energy of the reaction, as first proposed by Haldane. The chemical reaction in X is thus enslaved to the down hill slow motion on the Q surface. One consequence of the present theory is that, in spite of the existence of dispersive kinetics, the Michaelis-Menten expression of the catalysis rate remains valid under certain conditions, as observed in recent single-molecule experiments. This dynamic theory builds the relationship between the protein conformational dynamics and the enzymatic reaction kinetics and offers a unified description of enzyme fluctuation-assisted catalysis.
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Affiliation(s)
- Wei Min
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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Abstract
This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the FPT distributions out of those states must be describable by a simple exponential law. The observation of non-exponential first-passage time distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system.
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Affiliation(s)
- David S Talaga
- Rutgers, The State University of New Jersey, Department of Chemistry and Chemical Biology, 610 Taylor Road, Piscataway, NJ 08854
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Goychuk I, Hänggi P. Anomalous escape governed by thermal 1/f noise. PHYSICAL REVIEW LETTERS 2007; 99:200601. [PMID: 18233128 DOI: 10.1103/physrevlett.99.200601] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2007] [Indexed: 05/07/2023]
Abstract
We present an analytic study for subdiffusive escape of overdamped particles out of a cusp-shaped parabolic potential well which are driven by thermal, fractional Gaussian noise with a 1/omega 1-alpha power spectrum. This long-standing challenge becomes mathematically tractable by use of a generalized Langevin dynamics via its corresponding non-Markovian, time-convolutionless master equation: We find that the escape is governed asymptotically by a power-law whose exponent depends exponentially on the ratio of barrier height and temperature. This result is in distinct contrast to a description with a corresponding subdiffusive fractional Fokker-Planck approach, thus providing experimentalists an amenable testbed to differentiate between the two escape scenarios.
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Affiliation(s)
- I Goychuk
- University of Augsburg, Institute of Physics, Universitätsstr. 1, D-86135 Augsburg, Germany
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Chaudhury S, Cherayil BJ. Modulation of electron transfer kinetics by protein conformational fluctuations during early-stage photosynthesis. J Chem Phys 2007; 127:145103. [DOI: 10.1063/1.2783845] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chaudhury S, Cherayil BJ. Dynamic disorder in single-molecule Michaelis-Menten kinetics: The reaction-diffusion formalism in the Wilemski-Fixman approximation. J Chem Phys 2007; 127:105103. [PMID: 17867782 DOI: 10.1063/1.2768059] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Single-molecule equations for the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] mechanism of enzyme action are analyzed within the Wilemski-Fixman [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)] approximation after the effects of dynamic disorder--modeled by the anomalous diffusion of a particle in a harmonic well--are incorporated into the catalytic step of the reaction. The solution of the Michaelis-Menten equations is used to calculate the distribution of waiting times between successive catalytic turnovers in the enzyme beta-galactosidase. The calculated distribution is found to agree qualitatively with experimental results on this enzyme obtained at four different substrate concentrations. The calculations are also consistent with measurements of correlations in the fluctuations of the fluorescent light emitted during the course of catalysis, and with measurements of the concentration dependence of the randomness parameter.
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Affiliation(s)
- Srabanti Chaudhury
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
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Chaudhury S, Kou SC, Cherayil BJ. Model of Fluorescence Intermittency in Single Enzymes. J Phys Chem B 2007; 111:2377-84. [PMID: 17288472 DOI: 10.1021/jp065737a] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The intermittent emission of fluorescent light from single enzymes, quantum dots, and other nanoscale systems is often characterized by statistical correlations in the emitted signal. A one-dimensional model of such correlations in enzymes, based on a model of protein conformational fluctuations developed by Kou and Xie (Phys. Rev. Lett. 2004, 93, 180603), is formulated in the present paper in terms of the dynamics of a particle moving stochastically between "on" and "off" states under the action of fractional Gaussian noise. The model yields predictions for the short and long time behavior of the following quantities: the time correlation function, C(t), of the fluctuations of the signal intensity, the distribution, f(t), of time intervals between intensity fluctuations, and the Mandel parameter, Q(t), describing the extent of bunching or anti-bunching in the signal. At short times, C(t) and f(t) are found to decay exponentially, while, at long times, they are found to decay as power laws, the exponents being functions solely of the nature of the temporal correlations in the noise. The results are in good qualitative agreement with results from single-molecule experiments on fluorescence intermittency in the enzyme cholesterol oxidase carried out by Xie and co-workers (Science 1998, 282, 1877). The Mandel parameter, Q(t), for this model is positive at short and long times, indicating super-Poisson statistics in these limits, consistent with bunching of the fluorescent signal.
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Affiliation(s)
- Srabanti Chaudhury
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
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