Inferring diffusion in single live cells at the single molecule level

The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single molecule and single cell level can add significant insight into understanding molecular architectures of diffusing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence (TIRF) with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell membrane under relatively physiological conditions compared to competing single molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the molecular level due to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles, however, this generally requires more data points than is typical for single FP tracks due to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes (BARD) to discriminate multiple complex modes probabilistically. It is a computational approach which biologists can use to understand single molecule features in live cells.Comment: combined ms (1-37 pages, 8 figures) and SI (38-55, 3 figures

On Bioelectric Algorithms

Cellular bioelectricity describes the biological phenomenon in which cells in living tissue generate and maintain patterns of voltage gradients across their membranes induced by differing concentrations of charged ions. A growing body of research suggests that bioelectric patterns represent an ancient system that plays a key role in guiding many important developmental processes including tissue regeneration, tumor suppression, and embryogenesis. This paper applies techniques from distributed algorithm theory to help better understand how cells work together to form these patterns. To do so, we present the cellular bioelectric model (CBM), a new computational model that captures the primary capabilities and constraints of bioelectric interactions between cells and their environment. We use this model to investigate several important topics from the relevant biology research literature. We begin with symmetry breaking, analyzing a simple cell definition that when combined in single hop or multihop topologies, efficiently solves leader election and the maximal independent set problem, respectively - indicating that these classical symmetry breaking tasks are well-matched to bioelectric mechanisms. We then turn our attention to the information processing ability of bioelectric cells, exploring upper and lower bounds for approximate solutions to threshold and majority detection, and then proving that these systems are in fact Turing complete - resolving an open question about the computational power of bioelectric interactions

Experimentally-calibrated population of models predicts and explains inter-subject variability in cardiac cellular\ud electrophysiology

Cellular and ionic causes of variability in the electrophysiological activity of hearts from individuals of the same species are unknown. However, improved understanding of this variability is key to enable prediction of the response of specific hearts to disease and therapies. Limitations of current mathematical modeling and experimental techniques hamper our ability to provide insight into variability. Here we describe a methodology to unravel the ionic determinants of inter-subject variability exhibited in experimental recordings, based on the construction and calibration of populations of models. We illustrate the methodology through its application to rabbit Purkinje preparations, due to their importance in arrhythmias and safety pharmacology assessment. We consider a set of equations describing the biophysical processes underlying rabbit Purkinje electrophysiology and we construct a population of over 10,000 models by randomly assigning specific parameter values corresponding to ionic current conductances and kinetics. We calibrate the model population by closely comparing simulation output and experimental recordings at three pacing frequencies. We show that 213 of the 10,000 candidate models are fully consistent with the experimental dataset. Ionic properties in the 213 models cover a wide range of values, including differences up to ±100% in several conductances. Partial correlation analysis shows that particular combinations of ionic properties determine the precise shape, amplitude and rate dependence of specific action potentials. Finally, we demonstrate that the population of models calibrated using data obtained under physiological conditions quantitatively predicts the action potential duration prolongation caused by exposure to four concentrations of the potassium channel blocker dofetilide

Exploring emergent properties in cellular homeostasis using OnGuard to model K+ and other ion transport in guard cells

It is widely recognized that the nature and characteristics of transport across eukaryotic membranes are so complex as to defy intuitive understanding. In these circumstances, quantitative mathematical modeling is an essential tool, both to integrate detailed knowledge of individual transporters and to extract the properties emergent from their interactions. As the first, fully integrated and quantitative modeling environment for the study of ion transport dynamics in a plant cell, OnGuard offers a unique tool for exploring homeostatic properties emerging from the interactions of ion transport, both at the plasma membrane and tonoplast in the guard cell. OnGuard has already yielded detail sufficient to guide phenotypic and mutational studies, and it represents a key step toward ‘reverse engineering’ of stomatal guard cell physiology, based on rational design and testing in simulation, to improve water use efficiency and carbon assimilation. Its construction from the HoTSig libraries enables translation of the software to other cell types, including growing root hairs and pollen. The problems inherent to transport are nonetheless challenging, and are compounded for those unfamiliar with conceptual ‘mindset’ of the modeler. Here we set out guidelines for the use of OnGuard and outline a standardized approach that will enable users to advance quickly to its application both in the classroom and laboratory. We also highlight the uncanny and emergent property of OnGuard models to reproduce the ‘communication’ evident between the plasma membrane and tonoplast of the guard cell

Cellular Automata Applications in Shortest Path Problem

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 201

Linearized models of calcium dynamics: formal equivalence to the cable equation

The dynamics of calcium and other diffusible second messengers play an important role in intracellular signaling. We show here the conditions under which nonlinear equations governing the diffusion, extrusion, and buffering of calcium can be linearized. Because the resulting partial differential equation is formally identical to the one-dimensional cable equation, quantities analogous to the input resistance, space constant, and time constant--familiar from the study of passive electrical propagation--can be defined. Using simulated calcium dynamics in an infinite cable and in a dendritic spine as examples, we bound the errors due to the linearization, and show that parameter uncertainty is so large that most nonlinearities can usually b

In Memoriam, Solomon Marcus

This book commemorates Solomon Marcus’s fifth death anniversary with a selection of articles in mathematics, theoretical computer science, and physics written by authors who work in Marcus’s research fields, some of whom have been influenced by his results and/or have collaborated with him

Numerical P Systems with Thresholds

Numerical P systems are a class of P systems inspired both from the structure of living cells and from economics. In this work, a control of using evolution programs is introduced into numerical P systems: a threshold is considered and a program can be applied only when the values of the variables involved in the production function of the program are greater than/equal to (lower-threshold) or smaller than/equal to (upper-threshold) the threshold. The computational power of numerical P systems with lower-threshold or upper-threshold is investigated. It is proved that numerical P systems with a lower-threshold, with one membrane and linear production functions, working both in the all-parallel mode and in the one-parallel mode are universal. The result is also extended to numerical P systems with an upperthreshold, by proving the equivalence of the numerical P systems with lower- and upper-thresholds

A practical approach to fixed-site-carrier facilitated transport modeling for the separation of propylene/propane mixtures through silver-containing polymeric membranes

In this work, a new consistent mathematical model for the description of the olefin flux through Ag+-containing polymeric dense membranes is proposed. A fixed site carrier "hopping" parameter acting as an effective permeability for this specific transport phenomenon is defined and calculated for the first time. This study reports a simple and versatile approach that can be incorporated into future models to simulate the more complex mobile/fixed hybrid mechanism acting in composite membranes. Furthermore, in order to validate the model, the proof of concept has been carried out with PVDF-HFP/AgBF4 facilitated transport membranes. The experimental analysis has been performed by the continuous flow permeation method through flat membranes containing increasing silver loads, from 17 to 38% w/w at olefin partial pressures ranging from 0.5 to 1.5 bar and temperatures of 293 and 303 K. These membranes showed a promising performance, reaching values of propylene permeability up to 1800 Barrer and very high propylene/propane selectivities. The reported model constitutes a very useful tool for process optimisation and scale-up.Financial support from the Spanish Ministry of Science under the projects CTQ2015-66078-R and CTQ2016-75158-R (MINECO, Spain-FEDER 2014–2020) is gratefully acknowledged. Raúl Zarca also thanks the Universidad de Cantabria for a postgraduate fellowship