scholarly journals PPDiffuse: A Quantitative Prediction Tool for Diffusion of Charged Polymers in a Nanopore

2020 ◽  
Vol 125 ◽  
Author(s):  
David P. Hoogerheide
Keyword(s):  
Single Molecule ◽  
Rational Design ◽  
First Passage Time ◽  
Ionic Current ◽  
Passage Time ◽  
Quantitative Prediction ◽  
Analyte Molecule ◽  
Wide Range ◽  
Electrochemical Electrodes ◽  
Set Up

Nanopore-based sensing of charged biopolymers is a powerful single-molecule method. In aconventional nanopore experiment, a single biological (proteinaceous) or solid-state nanopore perforates a thin membrane that is wetted by, and electrically isolates, two opposing reservoirs of electrolyte solution. A potential is applied across the membrane via external electronics coupled to the electrolyte reservoirs with electrochemical electrodes, actuating the system. The electric field set up by the applied potential in the nanopore and its immediate environment plays two roles: supporting an ionic current through the nanopore, which reports on the properties of the pore and its contents; and acting on analyte molecules to attract them to, and drive them into, the nanopore. The presence of a large biopolymer in the pore modulates the ionic current 𝐼(𝑡). The duration of the ionic current modulation corresponds to the length of time the polymer spends in the pore from capture to its ultimate escape, either by retraction to the reservoir from which it was captured, or by translocation to the opposite reservoir . The probabilities of retraction or translocation, or splitting probabilities, and the corresponding distributions of escape times (𝑡esc), are particularly sensitive to the size and charge of the analyte molecule and have been the focus of much theoretical, computational, and experimental effort. An underlying physical framework in which the distribution of escape times is modeled as a first-passage time from a one-dimensional potential is quantitatively predictive for a wide range of experiments. The complexity of this potential for the general case, however, requires calculations to guide experimental design that can be tedious to implement. PPDiffuse is intended to remove this burden from the nanopore research community and enable convenient, rational design of nanopore experiments with complex substrates such as polypeptides.

Hitting-Time Densities of a Two-Dimensional Markov Process

1992 ◽  
Vol 6 (4) ◽  
pp. 561-580
Author(s):  
C. H. Hesse
Keyword(s):  
Global Analysis ◽  
First Passage Time ◽  
Type Equation ◽  
Passage Time ◽  
Two Dimensional ◽  
First Passage ◽  
Wide Range ◽  
The Laplace Transform ◽  
Mean And Variance

This paper deals with the two-dimensional stochastic process (X(t), V(t)) where dX(t) = V(t)dt, V(t) = W(t) + ν for some constant ν and W(t) is a one-dimensional Wiener process with zero mean and variance parameter σ2= 1. We are interested in the first-passage time of (X(t), V(t)) to the plane X = 0 for a process starting from (X(0) = −x, V(0) = ν) with x > 0. The partial differential equation for the Laplace transform of the first-passage time density is transformed into a Schrödinger-type equation and, using methods of global analysis, such as the method of dominant balance, an approximation to the first-passage density is obtained. In a series of simulations, the quality of this approximation is checked. Over a wide range of x and ν it is found to perform well, globally in t. Some applications are mentioned.

Relating cellular signaling timescales to single-molecule kinetics: A first-passage time analysis of Ras activation by SOS

2021 ◽  
Vol 118 (45) ◽  
pp. e2103598118
Author(s):  
William Y. C. Huang ◽  
Steven Alvarez ◽  
Yasushi Kondo ◽  
John Kuriyan ◽  
Jay T. Groves
Keyword(s):  
Single Molecule ◽  
Cellular Signaling ◽  
First Passage Time ◽  
Passage Time ◽  
Nucleotide Exchange ◽  
Time Analysis ◽  
First Passage ◽  
Nucleotide Exchange Factor ◽  
Ras Activation ◽  
Son Of Sevenless

Son of Sevenless (SOS) is a Ras guanine nucleotide exchange factor (GEF) that plays a central role in numerous cellular signaling pathways. Like many other signaling molecules, SOS is autoinhibited in the cytosol and activates only after recruitment to the membrane. The mean activation time of individual SOS molecules has recently been measured to be ∼60 s, which is unexpectedly long and seemingly contradictory with cellular signaling timescales, which have been measured to be as fast as several seconds. Here, we rectify this discrepancy using a first-passage time analysis to reconstruct the effective signaling timescale of multiple SOS molecules from their single-molecule activation kinetics. Along with corresponding experimental measurements, this analysis reveals how the functional response time, comprised of many slowly activating molecules, can become substantially faster than the average molecular kinetics. This consequence stems from the enzymatic processivity of SOS in a highly out-of-equilibrium reaction cycle during receptor triggering. Ultimately, rare, early activation events dominate the macroscopic reaction dynamics.

A stochastic theoretical approach to study the size-dependent catalytic activity of a metal nanoparticle at the single molecule level

2017 ◽  
Vol 19 (13) ◽  
pp. 8889-8895 ◽  
Author(s):  
Divya Singh ◽  
Srabanti Chaudhury
Keyword(s):  
Catalytic Activity ◽  
Single Molecule ◽  
Time Distribution ◽  
First Passage Time ◽  
Theoretical Method ◽  
Passage Time ◽  
Metal Nanoparticle ◽  
First Passage ◽  
Single Molecule Level ◽  
Size Dependent

We present a theoretical method based on the first passage time distribution formalism to study the size-dependent catalytic activity of metal nanoparticle at the single molecule level.

scholarly journals First passage time study of DNA strand displacement

2020 ◽  
Author(s):  
D. W. Bo Broadwater ◽  
Alexander W. Cook ◽  
Harold D. Kim
Keyword(s):  
Single Molecule ◽  
First Passage Time ◽  
Resonance Energy ◽  
Passage Time ◽  
Single Step ◽  
Strand Displacement ◽  
First Passage ◽  
Dna Strand Displacement ◽  
Dna Strand ◽  
Kinetics Of

AbstractDNA strand displacement, where a single-stranded nucleic acid invades a DNA duplex, is pervasive in genomic processes and DNA engineering applications. The kinetics of strand displacement have been studied in bulk; however, the kinetics of the underlying strand exchange were obfuscated by a slow bimolecular association step. Here, we use a novel single-molecule Fluorescence Resonance Energy Transfer (smFRET) approach termed the “fission” assay to obtain the full distribution of first passage times of unimolecular strand displacement. At a frame time of 4.4 ms, the first passage time distribution for a 14-nt displacement domain exhibited a nearly monotonic decay with little delay. Among the eight different sequences we tested, the mean displacement time was on average 35 ms and varied by up to a factor of 13. The measured displacement kinetics also varied between complementary invaders and between RNA and DNA invaders of the same base sequence except for T→U substitution. However, displacement times were largely insensitive to the monovalent salt concentration in the range of 0.25 M to 1 M. Using a one-dimensional random walk model, we infer that the single-step displacement time is in the range of ∼30 µs to ∼300 µs depending on the base identity. The framework presented here is broadly applicable to the kinetic analysis of multistep processes investigated at the single-molecule level.

scholarly journals Double-barrier first-passage times of jump-diffusion processes

2013 ◽  
Vol 19 (2) ◽  
pp. 107-141
Author(s):  
Lexuri Fernández ◽  
Peter Hieber ◽  
Matthias Scherer
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Asset Price ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
Passage Time ◽  
First Passage ◽  
Double Barrier ◽  
Jump Diffusion Processes ◽  
Wide Range

Abstract. Required in a wide range of applications in, e.g., finance, engineering, and physics, first-passage time problems have attracted considerable interest over the past decades. Since analytical solutions often do not exist, one strand of research focuses on fast and accurate numerical techniques. In this paper, we present an efficient and unbiased Monte-Carlo simulation to obtain double-barrier first-passage time probabilities of a jump-diffusion process with arbitrary jump size distribution; extending single-barrier results by [Journal of Derivatives 10 (2002), 43–54]. In mathematical finance, the double-barrier first-passage time is required to price exotic derivatives, for example corridor bonus certificates, (step) double barrier options, or digital first-touch options, that depend on whether or not the underlying asset price exceeds certain threshold levels. Furthermore, it is relevant in structural credit risk models if one considers two exit events, e.g., default and early repayment.

Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics

2020 ◽  
Vol 49 (1) ◽  
pp. 69-85 ◽  
Author(s):  
Ron Elber
Keyword(s):  
Protein Translocation ◽  
First Passage Time ◽  
Passage Time ◽  
Phospholipid Membrane ◽  
Molecular Processes ◽  
Time Dynamics ◽  
Wide Range ◽  
Long Time ◽  
The Mean ◽  
Kinetics Of

Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.

Influence of Solution pH on DNA Translocation Velocity Through Alumina Nanopores

2016 ◽  
Author(s):  
Haojie Yang ◽  
Zaoqi Duan ◽  
Wei Si ◽  
Kun Li ◽  
Yunfei Chen
Keyword(s):  
Time Distribution ◽  
Ph Value ◽  
First Passage Time ◽  
Diffusion Constant ◽  
Ionic Current ◽  
Passage Time ◽  
Dna Translocation ◽  
Solution Ph ◽  
First Passage ◽  
Dna Molecule

Nanopores, which are promising as single-molecule sensing devices with low cost and high throughput, have offered significant insights into the research fields of static and dynamic molecular activities, properties, or interactions. In particular, due to its inherent sensitivity, high throughput, amplification-free sample preparation, nanopore will be potentially used in DNA sequencing. Nanopore-based sequencing is based on Coulter Counters, by measuring the distinct current reductions from individual DNA bases with different sizes as they are translocating through a nanopore. The sub-molecular details of an individual molecule can be gathered via recording modulations in the ionic current when a molecule passes through the nanopore under a bias voltage applied across the pore by two Ag/AgCl electrodes. The current blockage and dwell time obtained when the dsDNA translocates through nanopore are accumulated into scatter plots. Ionic current trace recorded at 1000 mv as 48kbp dsDNA translocate through 20 nm thickness with 35 nm alumina nanopore. Here, we apply Schrödinger’s first-passage-time distribution formula to study the distribution of DNA translocation time through alumina nanopores. The first-passage-time distribution is solved with the production of Fokker-Plank equation. Two useful parameters yielded the experimental results are analyzed: the diffusion constant of DNA inside the nanopore and the drift velocity of DNA translocation. By changing the pH value from 5.2 to 10.8 of the electrolyte solution, we notice that the drift velocity of DNA translocation and the diffusion constant of DNA inside the nanopore are extremely close to almost as 34 nm/μs. By changing the pH value of the electrolyte solution, we find that the surface charge density of the wall and the charge of the DNA molecule can be turned, which will result in different DNA molecule capture behaviors. The capture rate is about 17 s−1; the DNA molecule translocates through nanopore when the solution pH is 10.8; and 20 s−1 as the solution pH is 5.2. Theoretical modelling has also been conducted to analyze the experimental results. Hopefully, these findings will shed light on the transport properties of DNA in nanopores, which are relevant to future nanopore applications.

Quantitative Prediction of Impact Forces In Elastomers

1999 ◽  
Vol 121 (3) ◽  
pp. 294-304 ◽  
Author(s):  
Suresh Goyal ◽  
Ronald G. Larson ◽  
Charles J. Aloisio
Keyword(s):  
Rational Design ◽  
Quantitative Prediction ◽  
Impact Surface ◽  
Impact Forces ◽  
Wide Range ◽  
Elastomeric Materials ◽  
Drop Tests ◽  
Linear Viscoelastic ◽  
Viscoelastic Characteristics ◽  
The Impact

We measure the impact forces and deflections resulting from drop tests of a mass with a flat impact surface onto flat pads of various elastomeric materials, and show that the forces can be predicted quantitatively with no adjustable parameters by using a theory whose only inputs are the linear viscoelastic characteristics of the materials, measured in small-amplitude oscillatory deformations. The theory, which models the elastomer as a nonlinear neo-Hookean material, is accurate for several elastomeric solids including polyurethanes, polynorbomene, and poly-vinyl-chlorides (PVCs), over a wide range of impact velocities, masses, temperatures and pad thicknesses. Some steps are taken to extend the model to surfaces which are not flat. The application in mind is the rational design of elastomeric components in impact-tolerant portable electronic equipment.

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

2018 ◽  
Vol 20 (24) ◽  
pp. 16393-16401 ◽  
Author(s):  
Denis S. Grebenkov ◽  
Ralf Metzler ◽  
Gleb Oshanin
Keyword(s):  
Single Molecule ◽  
First Passage Time ◽  
Quantitative Description ◽  
Threshold Value ◽  
Mathematical Concept ◽  
Passage Time ◽  
Molecule Reaction ◽  
Cylindrical Annulus ◽  
The Moment ◽  
First Time

The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. We present a robust explicit approach for obtaining the full distribution of FPT to a partially reactive target in a cylindrical-annulus domain.

Synchronization of Motor Proteins Coupled Through a Shared Load

2006 ◽  
Author(s):  
Adam G. Hendricks ◽  
Bogdan I. Epureanu ◽  
Edgar Meyho¨fer
Keyword(s):  
Single Molecule ◽  
Stochastic Dynamics ◽  
First Passage Time ◽  
Mechanistic Model ◽  
Thermal Fluctuations ◽  
Transient Dynamics ◽  
Time Varying ◽  
Nano Scale ◽  
Wide Range

Kinesin-1 is a processive molecular motor that converts the energy from adenosine triphosphate (ATP) hydrolysis and thermal fluctuations into motion along microtubules. This motion can be interpreted as a result of ATP-fueled nonlinear nonsmooth oscillations of coupled motor domains which interact with a microtubule to transport a cargo. This class of nano-scale motors transport cargoes for distances of several micrometers in cells. This transport can also be achieved in vitro, opening the possibility of developing robust and extremely versatile nano-scale actuators or sensors based on the machinery used by biological systems. These devices could be used in a range of nano-scale applications such as drug delivery and lab-on-a-chip. However, to design such systems, a quantitative, in-depth understanding of molecular motors is essential. Single-molecule techniques have allowed the experimental characterization of kinesin-1 in vitro at a range of loads and ATP concentrations. Existing models of kinesin movement are stochastic in nature and are not well suited to describing transient dynamics. However, kinesin-1 is expected to undergo transient dynamics when external perturbations (e.g. interaction with other kinesin molecules) cause the load to vary in time. It is thought that in the cell, several kinesin motors work cooperatively to transport a common load. Thus, a transient description is integral to capturing kinesin behavior. This paper presents a mechanistic model that describes, deterministically, the average motion of kinesin-1. The structure of the kinesin-1 molecule is approximated with a simplified geometry, explicitly describing the coupling between its two heads. The diffusion is modeled using a novel approach based on the mean first-passage time, where the potential in which the free head diffuses is time varying and updated at each instant during the motion. The mechanistic model is able to predict existing force-velocity data over a wide range of ATP concentrations (including the interval 1μM to 10 mM). More importantly, the model provides a transient description, allowing predictions of kinesin-1 pulling time-varying loads and coordinated transport involving several kinesin-1 molecules. The deterministic approach is validated by comparing results to experiments and Monte Carlo simulations of the stochastic dynamics. Furthermore, using this model, the synchronization of several kinesin-1 molecules transporting a common load is investigated. Novel methods to characterize synchronization, tailored to the particularities of these nonsmooth systems, are presented.

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