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Ophir Flomenbom

Publications and source records attributed to Ophir Flomenbom.

17 recordsLinked to original sources
arXiv2022

Single file dynamics in soft materials

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-section comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a \emph{single file}, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural-shaped channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membrane, just to mention a few examples. Albeit introduced in '65, over the last decade the classical notion of SF dynamics has been generalized to account through a more realistic modeling of, among others, particles properties, file geometry, particle-particle and channel-particles interactions, thus paving the way to remarkable applications in, for example, the technology of bio-integrated nanodevices. We then provide a comprehensive review of the recent advances in the theory of SF dynamics and the ensuing experimental realisations.

cond-mat.soft↗
arXiv2013

Solving single molecules: filtering noisy discrete data made of photons and other type of observables

In numerous systems in biophysics and related fields, scientists measure (with very smart methods) individual molecules (e.g. biopolymers (proteins, DNA, RNA, etc), nano - crystals, ion channels), aiming at finding a model from the data. But the noise is not solved accurately in not so few cases and this may lead to misleading models. Here, we solve the noise. We consider two state photon trajectories from any on off kinetic scheme (KS): the process emitting photons with a rate γon when it is in the on state, and emitting with a rate γoff when it is in the off state. We develop a filter that removes the noise resulting in clean data also in cases where binning fails. The filter is a numerical algorithm with various new statistical treatments. It is based on a new general likelihood function developed here, with observable dependent form. The filter can solve the noise, in the detectable region of the rate space: that is, we also find a region where the data is "too" noisy. Consistency tests will find the region's type from the data. If the data is ruled "too noisy", binning obviously fails, and one should apply simpler methods on the raw data and realizing that the extracted information is partial. We show that not applying the filter while cleaning results in erroneous rates. This filter (with minor adjustments) can solve the noise in any discrete state trajectories, yet extensions are needed in "tackling" the noise from other data, e.g. continuous data and FRET data. The filter developed here is complementary with our previous projects in this field, where we have solved clean two state data with the development of reduced dimensions forms (RDFs): only the combined procedures enabling building the most accurate model from noisy trajectories from single molecules

q-bio.SC↗
arXiv2011

Fairness in society

Models that explain the economical and political realities of nowadays societies should help all the world's citizens. Yet, the last four years showed that the current models are missing. Here we develop a dynamical society-deciders model showing that the long lasting economical stress can be solved when increasing fairness in nations. fairness is computed for each nation using indicators from economy and politics. Rather than austerity versus spending, the dynamical model suggests that solving crises in western societies is possible with regulations that reduce the stability of the deciders, while shifting wealth in the direction of the people. This shall increase the dynamics among socio-economic classes, further increasing fairness.

physics.soc-ph↗
arXiv2011

Dynamics of heterogeneous hard spheres in a file

Normal dynamics in a quasi-one-dimensional channel of length L (\to\infty) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W D^(-γ), for small D, where 0\leqγ<1. The initial spheres' density ρ is non-uniform and scales with the distance (from the origin) l as, ρ l^(-a), 0\leqa\leq1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, ~t^(1-γ)/(2c-γ), where c=1/(1+a). The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.

cond-mat.soft↗
arXiv2011

Clustering in anomalous files of independent particles

The dynamics of classical hard particles in a quasi one-dimensional channel were studied since the 1960s and used for explaining processes in chemistry, physics and biology and in applications. Here we show that in a previously un-described file made of anomalous, independent, particles (with jumping times taken from, ψ_α (t) t^(-1-α), 0<α<1), particles form clusters. At steady state, the percentage of particles in clusters is about, \surd(1-α^3), only for anomalous α, characterizing the criticality of a phase transition. The asymptotic mean square displacement per particle in the file is about, log^2(t). We show numerically that this exciting phenomenon of a phase transition is very stable, and relate it with the mysterious phenomenon of rafts in biological membranes, and with regulation of biological channels.

cond-mat.soft↗
arXiv2010

Making it possible: constructing a reliable mechanism from a finite trajectory

Deducing an underlying multi-substate on-off kinetic scheme (KS) from the statistical properties of a two-state trajectory is the aim from many experiments in biophysics and chemistry, such as, ion channel recordings, enzymatic activity and structural dynamics of bio-molecules. Doing so is almost always impossible, as the mapping of a KS into a two-state trajectory leads to the loss of information about the KS (almost always). Here, we present the optimal way to solve this problem. It is based on unique forms of reduced dimensions (RD). RD forms are on-off networks with connections only between substates of different states, where the connections can have multi-exponential waiting time probability density functions (WT-PDFs). A RD form has the simplest toplogy that can reproduce a given data. In theory, only a single RD form can be constructed from the full data (hence its uniqueness), still this task is not easy when dealing with finite data. For doing so, a toolbox made of known statistical methods in data analysis and new statistical methods and numerical algorithms develped for this problem is presented. Our toolbox is self-contained: it builds a mechanism based only on the information it extracts from the data. The implementation of the toolbox on the data is fast. The toolbox is automated and is available for academic research upon electronic request.

q-bio.QM↗
arXiv2010

Renewal-anomalous-heterogeneous files

Renewal-anomalous-heterogeneous files are solved. A simple file is made of Brownian hard spheres that diffuse stochastically in an effective 1D channel. Generally, Brownian files are heterogeneous: the spheres' diffusion coefficients are distributed and the initial spheres' density is non-uniform. In renewal-anomalous files, the distribution of waiting times for individual jumps is exponential as in Brownian files, yet obeys: ψ_α (t)~t^(-1-α), 0<α<1. The file is renewal as all the particles attempt to jump at the same time. It is shown that the mean square displacement (MSD) in a renewal-anomalous-heterogeneous file, , obeys, ~[ _{nrml}]^α, where _{nrml} is the MSD in the corresponding Brownian file. This scaling is an outcome of an exact relation (derived here) connecting probability density functions of Brownian files and renewal-anomalous files. It is also shown that non-renewal-anomalous files are slower than the corresponding renewal ones.

cond-mat.soft↗
arXiv2008

The rule for a subdiffusive particle in an extremely diverse environment

The dynamics of a subdiffusive continuous time random walker in an inhomogeneous environment is analyzed. In each microscopic jump, a random time is drawn from a waiting time probability density function (WT-PDF) that decays as a power law: phi(t;k)~k/(1+kt)^(1+beta), 0 beta;, mu=beta, but when 1-gamma<beta, mu=1-gamma. The transition in the scaling of psi(t) reflects the competition between two different mechanisms for subdiffusion: subdiffusion due to the heavily tailed phi(t;k) for microscopic jumps, and subdiffusion due to the collective effect of an environment made of many slow local regions. These two different mechanisms for subdiffusion are not additive, and compete each other. The reported transition is dimension independent, and disappears when the power beta is also distributed, in the range, 0<bate<1. Simulations exemplified the transition, and implications are discussed.

cond-mat.soft↗
arXiv2007

Unique mechanisms from finite two-state trajectories

Single molecule data made of on and off events are ubiquitous. Famous examples include enzyme turnover, probed via fluorescence, and opening and closing of ion-channel, probed via the flux of ions. The data reflects the dynamics in the underlying multi-substate on-off kinetic scheme (KS) of the process, but the determination of the underlying KS is difficult, and sometimes even impossible, due to the loss of information in the mapping of the mutli-dimensional KS onto two dimensions. A way to deal with this problem considers canonical (unique) forms. (Unique canonical form is constructed from an infinitely long trajectory, but many KSs.) Here we introduce canonical forms of reduced dimensions that can handle any KS (i.e. also KSs with symmetry and irreversible transitions). We give the mapping of KSs into reduced dimensions forms, which is based on topology of KSs, and the tools for extracting the reduced dimensions form from finite data. The canonical forms of reduced dimensions constitute a powerful tool in discriminating between KSs.

q-bio.QM↗
arXiv2007

Utilizing the information content in two-state trajectories

The signal from many single molecule experiments monitoring molecular processes, such as enzyme turnover via fluorescence and opening and closing of ion channel via the flux of ions, consists of a time series of stochastic on and off (or open and closed) periods, termed a two-state trajectory. This signal reflects the dynamics in the underlying multi-substate on-off kinetic scheme (KS) of the process. The determination of the underlying KS is difficult and sometimes even impossible due to the loss of information in the mapping of the mutli dimensional KS onto two dimensions. Here we introduce a new procedure that efficiently and optimally relates the signal to all equivalent underlying KSs. This procedure partitions the space of KSs into canonical (unique) forms that can handle any KS, and obtains the topology and other details of the canonical form from the data without the need for fitting. Also established are relationships between the data and the topology of the canonical form to the on-off connectivity of a KS. The suggested canonical forms constitute a powerful tool in discriminating between KSs. Based on our approach, the upper bound on the information content in two state trajectories is determined.

q-bio.QM↗
arXiv2007

Closed-form solutions for continuous time random walks on finite chains

Continuous time random walks (CTRW) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions are also the Laplace space solutions of the generalized master equation (GME). Moreover, based on our counting technique, we introduce the adaptor function for expressing higher order propagators (joint PDFs of time-position variables) for CTRWs in terms of Green's functions. Using the derived formulae, an escape problem from a biased chain is considered.

cond-mat.soft↗
arXiv2007

Correctly validating results from single molecule data: the case of stretched exponential decay in the catalytic activity of single lipase B molecules

The question of how to validate and interpret correctly the waiting time probability density functions (WT-PDFs) from single molecule data is addressed. It is shown by simulation that when a stretched exponential WT-PDF, with a stretched exponent alfa and a time scale parameter tau, generates the off periods of a two-state trajectory, a reliable recovery of the input WT-PDF from the trajectory is obtained even when the bin size used to define the trajectory, dt, is much larger than the parameter tau. This holds true as long as the first moment of the WT-PDF is much larger than dt. Our results validate the results in an earlier study of the activity of single Lipase B molecules and disprove recent related critique.

q-bio.SC↗
arXiv2007

On the relationships between kinetic schemes and two-state single molecule trajectories

Trajectories of a signal that fluctuates between two states which originate from single molecule activities have become ubiquitous. Common examples are trajectories of ionic flux through individual membrane-channels, and of photon counts collected from diffusion, activity, and conformational changes of biopolymers. By analyzing the trajectory, one wishes to deduce the underlying mechanism, which is usually described by a multi-substate kinetic scheme. In previous works, we divided kinetic schemes that generate two-state trajectories into two types: reducible schemes and irreducible schemes. We showed that all the information in trajectories generated from reducible schemes is contained in the waiting time probability density functions (PDFs) of the two states. It follows that reducible schemes with the same waiting time PDFs are not distinguishable. In this work, we further characterize the topologies of kinetic schemes, now of irreducible schemes, and further study two-state trajectories from the two types of scheme. We suggest various methods for extracting information about the underlying kinetic scheme from the trajectory (e. g., calculate the binned successive waiting times PDF and analyze the ordered waiting times trajectory), and point out the advantages and disadvantages of each. We show that the binned successive waiting times PDF is not only more robust than other functions when analyzing finite trajectories, but contains, in most cases, more information about the underlying kinetic scheme than other functions in the limit of infinitely long trajectories. For some cases however, analyzing the ordered waiting times trajectory may supply unique information about the underlying kinetic scheme.

q-bio.QM↗
arXiv2005

What can one learn from two-state single molecule trajectories?

A time trajectory of an observable that fluctuates between two values (say, on and off), stemming from some unknown multi-substate kinetic scheme, is the output of many single molecule experiments. Here we show that when all successive waiting times along the trajectory are uncorrelated the on and the off waiting time probability density functions (PDFs) contain all the information. By relating the lack of correlation in the trajectory to the topology of kinetic schemes, we can immediately specify those kinetic schemes that are equally consistent with experiment, which means that it is impossible to differentiate between them by any sophisticated analyses of the trajectory. Correlated trajectories, however, contain additional information about the underlying kinetic scheme, and we consider the strategy that one should use to extract it. An example is given on correlations in the activity of individual lipase molecules.

q-bio.SC↗
arXiv2005

Uncorrelated two-state single molecule trajectories from reducible kinetic schemes

Trajectories of on-off events are the output of many single molecule experiments. Usually, one describes the underlying mechanism that generates the trajectory using a kinetic scheme, and by analyzing the trajectory aims at deducing this scheme. In a previous work [O. Flomenbom, J. Klafter, and A. Szabo, submitted (2004)], we showed that when successive events along a trajectory are uncorrelated, all the information in the trajectory is contained in two basic functions, which are the waiting time probability functions (PDFs) of the on state and of the off state. The kinetic schemes that lead to such uncorrelated trajectories were termed reducible. Here we discuss the reasons that lead to reducible schemes. In particular, the topology of reducible schemes is characterized and proven.

q-bio.SC↗
arXiv2004

Some New Aspects of Dendrimer Applications

Dendrimers are characterized by special features that make them promising candidates for many applications. Here we focus on two such applications: dendrimers as light harvesting antennae, and dendrimers as molecular amplifiers, which may serve as novel platforms for drug delivery. Both applications stem from the unique structure of dendrimers. We present a theoretical framework based on the master equation within which we describe these applications. The quantities of interest are the first passage time (FPT) probability density function (PDF), and its moments. We examine how the FPT PDF and its characteristics depend on the geometric and energetic structures of the dendrimeric system. In particular, we investigate the dependence of the FPT properties on the number of generations (dendrimer size), and the system bias. We present analytical expressions for the FPT PDF for very efficient dendrimeric antennae and for dendrimeric amplifiers. For these cases the mean first passage time scales linearly with the system length, and fluctuations around the mean first passage time are negligible for large systems. Relationships of the FPT to light harvesting process for other types of system-bias are discussed.

cond-mat.soft↗