Effects of macromolecular crowding on intracellular diffusion from a single particle perspective

Biophysical Reviews' "Meet the Editors Series": a profile of Damien Hall

This piece introduces Damien Hall, Chief Editor of the Biophysical Reviews journal since 2019. Currently working as an Assistant Professor at Kanazawa University, the author describes his association with the journal along with some parts of his family history and academic journey.

HSAFM-MIREBA - Methodology for Inferring REsolution in biological applications

Due to a lack of requirement for any direct labelling of the target molecule, high speed atomic force microscopy (HS-AFM) is a potentially powerful procedure for the assessment of biological processes involving macromolecules. When the sample is static the AFM device can be purposefully setup to recover high-resolution information about the feature in question. However, when the feature to be studied moves an appreciable amount during the course of the measurement, the obtained image will be blurred. Encountering such blurred observations prompts the experimenter to sacrifice higher resolution images for higher scanning speeds by tuning available experimental parameters (such as the scanned image area, the image pixel size, the resonance frequency of the cantilever and/or the diameter of the AFM tip). The present work describes a software tool, HSAFM-MIREBA (High Speed Atomic Force Microscopy - Methodology for Inferring REsolution in Biological Applications) that allows for pre-experimental optimization of such parameters through iterative rounds of simulation of both the dynamic surface process and the HS-AFM measurement (based on the particular set of governing parameters). A representative set of five dynamic biological processes that describe a range of diffusive and directed motions (which can themselves be tuned by altering characteristic governing parameter sets) are provided.

MIL-CELL: a tool for multi-scale simulation of yeast replication and prion transmission

The single-celled baker's yeast, Saccharomyces cerevisiae, can sustain a number of amyloid-based prions, the three most prominent examples being [URE3], [PSI+], and [PIN+]. In the laboratory, haploid S. cerevisiae cells of a single mating type can acquire an amyloid prion in one of two ways (i) spontaneous nucleation of the prion within the yeast cell, and (ii) receipt via mother-to-daughter transmission during the cell division cycle. Similarly, prions can be lost due to (i) dissolution of the prion amyloid by its breakage into non-amyloid monomeric units, or (ii) preferential donation/retention of prions between the mother and daughter during cell division. Here we present a computational tool (Monitoring Induction and Loss of prions in Cells; MIL-CELL) for modelling these four general processes using a multiscale approach describing both spatial and kinetic aspects of the yeast life cycle and the amyloid-prion behavior. We describe the workings of the model, assumptions upon which it is based and some interesting simulation results pertaining to the wave-like spread of the epigenetic prion elements through the yeast population. MIL-CELL is provided as a stand-alone GUI executable program for free download with the paper. MIL-CELL is equipped with a relational database allowing all simulated properties to be searched, collated and graphed. Its ability to incorporate variation in heritable properties means MIL-CELL is also capable of simulating loss of the isogenic nature of a cell population over time. The capability to monitor both chronological and reproductive age also makes MIL-CELL potentially useful in studies of cell aging.

Brownian Motion in Optical Tweezers, a Comparison between MD Simulations and Experimental Data in the Ballistic Regime

The four most popular water models in molecular dynamics were studied in large-scale simulations of Brownian motion of colloidal particles in optical tweezers and then compared with experimental measurements in the same time scale. We present the most direct comparison of colloidal polystyrene particle diffusion in molecular dynamics simulations and experimental data on the same time scales in the ballistic regime. The four most popular water models, all of which take into account electrostatic interactions, are tested and compared based on yielded results and resources required. Three different conditions were simulated: a freely moving particle and one in a potential force field with two different strengths based on 1 pN/nm and 10 pN/nm. In all cases, the diameter of the colloidal particle was 50 nm. The acquired data were compared with experimental measurements performed using optical tweezers with position capture rates as high as 125 MHz. The experiments were performed in pure water on polystyrene particles with a 1 μm diameter in special microchannel cells.

A fortunate period of overlap with Prof. Haruki Nakamura

The author recounts a period of overlap with Prof. Haruki Nakamura that stretched from 2007 till the present day. Starting as a short-term research fellow in his laboratory, the author has also been a coauthor, academic colleague, and joint journal editorial board member of Prof. Nakamura.

Diffusive dynamics of charged nanoparticles in convex lens-induced confinement

Transport through heterogeneous confined geometries is encountered in many processes and applications such as filtration, drug delivery, and enhanced oil recovery. We have used differential dynamic microscopy (DDM) and particle tracking to investigate dynamics of 36 nm negatively-charged polystyrene particles in convex lens-induced confinement (CLiC). The confinement gap height was controlled from 0.085 μm to 3.6 mm by sandwiching the aqueous particle solution between a glass coverslip and a convex lens using a homemade sample holder. With an inverted fluorescence microscope, sequences of micrographs were taken at various radial positions and gap heights for five particle concentrations (i.e. φ = 0.5 × 10^-5, 1 × 10^-5, 5 × 10^-5, 10 × 10^-5, 50 × 10^-5) and ionic strengths ranging from 10^-3 to 150 mM. The resulting image structure functions were fitted with a simple exponential model to extract the ensemble-averaged diffusive dynamics. It was found that particle diffusion was more hindered as a function of increased confinement. In addition, the ensemble-averaged diffusion coefficient was found to depend on the bulk concentration, and the concentration dependence increased as a function of confinement. Increasing particle and salt concentration led to confinement-dependent adsorption onto the geometry surface. Overall, we show that CLiC devices are simple and effective and can be used to study dynamics in continuous confinement from sub 100 nm to 100's of μm. These findings could lead to better understanding of separations and interactions in confining devices.

Growth and Antifungal Resistance of the Pathogenic Yeast, Candida Albicans, in the Microgravity Environment of the International Space Station: An Aggregate of Multiple Flight Experiences

This report was designed to compare spaceflight-induced cellular and physiological adaptations of Candida albicans cultured in microgravity on the International Space Station across several payloads. C. albicans is a common opportunistic fungal pathogen responsible for a variety of superficial infections as well as systemic and more severe infections in humans. Cumulatively, the propensity of this organism to be widespread through the population, the ability to produce disease in immunocompromised individuals, and the tendency to respond to environmental stress with characteristics associated with increased virulence, require a better understanding of the yeast response to microgravity for spaceflight crew safety. As such, the responses of this yeast cultivated during several missions using two in-flight culture bioreactors were analyzed and compared herein. In general, C. albicans had a slightly shorter generation time and higher growth propensity in microgravity as compared to terrestrial controls. Rates of cell filamentation differed between bioreactors, but were low and not significantly different between flight and terrestrial controls. Viable cells were retrieved and cultured, resulting in a colony morphology that was similar between cells cultivated in flight and in terrestrial control conditions, and in contrast to that previously observed in a ground-based microgravity analog system. Of importance, yeast demonstrated an increased resistance when challenged during spaceflight with the antifungal agent, amphotericin B. Similar levels of resistance were not observed when challenged with the functionally disparate antifungal drug caspofungin. In aggregate, yeast cells cultivated in microgravity demonstrated a subset of characteristics associated with virulence. In addition, and beyond the value of the specific responses of C. albicans to microgravity, this report includes an analysis of biological reproducibility across flight opportunities, compares two spaceflight hardware systems, and includes a summary of general flight and payload timelines.

Crowd Control: Effects of Physical Crowding on Cargo Movement in Healthy and Diseased Neurons

High concentration of cytoskeletal filaments, organelles, and proteins along with the space constraints due to the axon's narrow geometry lead inevitably to intracellular physical crowding along the axon of a neuron. Local cargo movement is essential for maintaining steady cargo transport in the axon, and this may be impeded by physical crowding. Molecular motors that mediate active transport share movement mechanisms that allow them to bypass physical crowding present on microtubule tracks. Many neurodegenerative diseases, irrespective of how they are initiated, show increased physical crowding owing to the greater number of stalled organelles and structural changes associated with the cytoskeleton. Increased physical crowding may be a significant factor in slowing cargo transport to synapses, contributing to disease progression and culminating in the dying back of the neuronal process. This review explores the idea that physical crowding can impede cargo movement along the neuronal process. We examine the sources of physical crowding and strategies used by molecular motors that might enable cargo to circumvent physically crowded locations. Finally, we describe sub-cellular changes in neurodegenerative diseases that may alter physical crowding and discuss the implications of such changes on cargo movement.

On the nature of the optimal form of the holdase-type chaperone stress response

The holdase paradigm of chaperone action involves preferential binding by the chaperone to the unfolded protein state, thereby preventing it from either, associating with other unstable proteins (to form large dysfunctional aggregates), or being degraded by the proteolytic machinery of the cell/organism. In this paper, we examine the necessary physical constraints imposed upon the holdase chaperone response in a cell-like environment and use these limitations to comment on the likely nature of the optimal form of chaperone response in vivo.

Unified theoretical description of the kinetics of protein aggregation

Solution conditions chosen for the production of amyloid can also promote formation of significant extents of amorphous protein aggregate. In one interpretation, the amyloid and amorphous aggregation pathways are considered to be in competition with each other. An alternative conceptualization involves considering amorphous aggregation as an obligatory intermediate process of the amyloid formation pathway. Here, we review recently developed macroscopic-level theories of protein aggregation that unify these two competing models into a single paradigm. Key features of the unified model included (1) a description of the amorphous aggregate as a second liquid phase with the degree of liquid-like character determined by the mobility of the monomer within it, and (2) heterogeneous growth pathways based on nucleation, growth, and fragmentation of amyloid occurring within different phases and at their interfacial boundary. Limiting-case behaviors of the protein aggregation reaction, either singly involving amyloid or amorphous aggregate production, and mixed-case behaviors, involving competitive and/or facilitated growth of amorphous and amyloid species, are presented and reviewed in context. This review principally describes an approach developed by Hirota and Hall 2019 (Hirota, N. and Hall, D. 2019. Protein Aggregation Kinetics: A Unified Theoretical Description. Chapter 7 of 'Protein Solubility and Amorphous Aggregation: From Academic Research to Applications in Drug Discovery and Bioindustry' edited by Y. Kuroda and F. Arisaka. CMC Publishers). Sections of that work are translated from the original Japanese and republished here with the full permission of CMC Publishing Corporation.

A note of appreciation for Prof. Cristobal dos Remedios on behalf of Biophysical Reviews

Following the initial five-year tenure (2009-2014) of the founding Chief Editor, Dr. Jean Garnier, Prof. Cristobal dos Remedios (University of Sydney) assumed responsibility for Biophysical Reviews as the second Chief Editor (2014-2019). Under his stewardship, Biophysical Reviews has become a six issue per year journal, publishing approximately 100 reviews per year. At the conclusion of his five-year tenure as Chief Editor (and at the age of 78), Cris is stepping down, leaving the journal well placed to apply for (and receive) an impact factor in 2020. On behalf of the journal, I would like to take the occasion of his retirement as Chief Editor to thank Cris for his dedicated service to Biophysical Reviews, and also welcome him to his new position as Emeritus Chief Editor.

Na+ microdomains and sparks: Role in cardiac excitation-contraction coupling and arrhythmias in ankyrin-B deficiency

Cardiac sodium (Na⁺) potassium ATPase (NaK) pumps, neuronal sodium channels (I_Na), and sodium calcium (Ca²⁺) exchangers (NCX1) may co-localize to form a Na⁺ microdomain. It remains controversial as to whether neuronal I_Na contributes to local Na⁺ accumulation, resulting in reversal of nearby NCX1 and influx of Ca²⁺ into the cell. Therefore, there has been great interest in the possible roles of a Na⁺ microdomain in cardiac Ca²⁺-induced Ca²⁺ release (CICR). In addition, the important role of co-localization of NaK and NCX1 in regulating localized Na⁺ and Ca²⁺ levels and CICR in ankyrin-B deficient (ankyrin-B^+/-) cardiomyocytes has been examined in many recent studies. Altered Na⁺ dynamics may contribute to the appearance of arrhythmias, but the mechanisms underlying this relationship remain unclear. In order to investigate this, we present a mechanistic canine cardiomyocyte model which reproduces independent local dyadic junctional SR (JSR) Ca²⁺ release events underlying cell-wide excitation-contraction coupling, as well as a three-dimensional super-resolution model of the Ca²⁺ spark that describes local Na⁺ dynamics as governed by NaK pumps, neuronal I_Na, and NCX1. The model predicts the existence of Na⁺ sparks, which are generated by NCX1 and exhibit significantly slower dynamics as compared to Ca²⁺ sparks. Moreover, whole-cell simulations indicate that neuronal I_Na in the cardiac dyad plays a key role during the systolic phase. Rapid inward neuronal I_Na can elevate dyadic [Na⁺] to 35-40 mM, which drives reverse-mode NCX1 transport, and therefore promotes Ca²⁺ entry into the dyad, enhancing the trigger for JSR Ca²⁺ release. The specific role of decreased co-localization of NaK and NCX1 in ankyrin-B^+/- cardiomyocytes was examined. Model results demonstrate that a reduction in the local NCX1- and NaK-mediated regulation of dyadic [Ca²⁺] and [Na⁺] results in an increase in Ca²⁺ spark activity during isoproterenol stimulation, which in turn stochastically activates NCX1 in the dyad. This alteration in NCX1/NaK co-localization interrupts the balance between NCX1 and NaK currents in a way that leads to enhanced depolarizing inward current during the action potential plateau, which ultimately leads to a higher probability of L-type Ca²⁺ channel reopening and arrhythmogenic early-afterdepolarizations.

Do Skeletal Dynamics Mediate Sugar Uptake and Transport in Human Erythrocytes?

We explore, herein, the hypothesis that transport of molecules or ions into erythrocytes may be affected and directly stimulated by the dynamics of the spectrin/actin skeleton. Skeleton/actin motions are driven by thermal fluctuations that may be influenced by ATP hydrolysis as well as by structural alterations of the junctional complexes that connect the skeleton to the cell's lipid membrane. Specifically, we focus on the uptake of glucose into erythrocytes via glucose transporter 1 and on the kinetics of glucose disassociation at the endofacial side of glucose transporter 1. We argue that glucose disassociation is affected by both hydrodynamic forces induced by the actin/spectrin skeleton and by probable contact of the swinging 37-nm-long F-actin protofilament with glucose, an effect we dub the "stickball effect." Our hypothesis and results are interpreted within the framework of the kinetic measurements and compartmental kinetic models of Carruthers and co-workers; these experimental results and models describe glucose disassociation as the "slow step" (i.e., rate-limiting step) in the uptake process. Our hypothesis is further supported by direct simulations of skeleton-enhanced transport using our molecular-based models for the actin/spectrin skeleton as well as by experimental measurements of glucose uptake into cells subject to shear deformations, which demonstrate the hydrodynamic effects of advection. Our simulations have, in fact, previously demonstrated enhanced skeletal dynamics in cells in shear deformations, as they occur naturally within the skeleton, which is an effect also supported by experimental observations.

Fractal analysis of lateral movement in biomembranes

Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.

Regulating the Membrane Transport Activity and Death of Cells via Electroosmotic Manipulation

Although the volume of living cells has been known to heavily influence their behavior and fate, a method allowing us to control the cell size in a programmable manner is still lacking. Here, we develop a technique in which precise changes in the cellular volume can be conveniently introduced by varying the voltage applied across a Nafion membrane that separates the culture medium from a reservoir. It is found that, unlike sudden osmotic shocks, active ion transport across the membrane of leukemia K562 cells will not be triggered by a gradual change in the extracellular osmolarity. Furthermore, when subjected to the same applied voltage, different lung and nasopharyngeal epithelial cancer cells will undergo larger volumetric changes and have a 5-10% higher death rate compared to their normal counterparts. We show that such distinct response is largely caused by the overexpression of aquaporin-4 in tumor cells, with knockout of this water channel protein resulting in a markedly reduced change in the cellular volume. Finally, by taking into account the exchange of water/ion molecules across the Nafion film and the cell membrane, a theoretical model is also proposed to describe the voltage-induced size changes of cells, which explain our experimental observations very well.

Ecology of aspergillosis: insights into the pathogenic potency of Aspergillus fumigatus and some other Aspergillus species

Fungi of the genus Aspergillus are widespread in the environment. Some Aspergillus species, most commonly Aspergillus fumigatus, may lead to a variety of allergic reactions and life-threatening systemic infections in humans. Invasive aspergillosis occurs primarily in patients with severe immunodeficiency, and has dramatically increased in recent years. There are several factors at play that contribute to aspergillosis, including both fungus and host-related factors such as strain virulence and host pulmonary structure/immune status, respectively. The environmental tenacity of Aspergilllus, its dominance in diverse microbial communities/habitats, and its ability to navigate the ecophysiological and biophysical challenges of host infection are attributable, in large part, to a robust stress-tolerance biology and exceptional capacity to generate cell-available energy. Aspects of its stress metabolism, ecology, interactions with diverse animal hosts, clinical presentations and treatment regimens have been well-studied over the past years. Here, we synthesize these findings in relation to the way in which some Aspergillus species have become successful opportunistic pathogens of human- and other animal hosts. We focus on the biophysical capabilities of Aspergillus pathogens, key aspects of their ecophysiology and the flexibility to undergo a sexual cycle or form cryptic species. Additionally, recent advances in diagnosis of the disease are discussed as well as implications in relation to questions that have yet to be resolved.

Theory of Crowding Effects on Bimolecular Reaction Rates

An analytical expression for the rate constant of a diffusion-influenced bimolecular reaction in a crowded environment is derived in the framework of a microscopic model that accounts for: (1) the slowdown of diffusion due to crowding and the dependence of the diffusivity on the distance between the reactants, (2) a crowding-induced attractive short-range potential of mean force, and (3) nonspecific reversible binding to the crowders. This expression spans the range from reaction to diffusion control. Crowding can increase the reaction-controlled rate by inducing an effective attraction between reactants but decrease the diffusion-controlled rate by reducing their relative diffusivity.

Diffusion NMR studies of macromolecular complex formation, crowding and confinement in soft materials

Label-free methods to obtain hydrodynamic size from diffusion measurements are desirable in environments that contain multiple macromolecular species at a high total concentration: one example is the crowded cellular environment. In complex, multi-species macromolecular environments - in this article, we feature aqueous systems involving polymers, surfactants and proteins - the link between dynamics and size is harder to unpack due to macromolecular crowding and confinement. In this review, we demonstrate that the pulsed-field gradient NMR technique, with its spectral separation of different chemical components, is ideal for studying the dynamics of the entire system simultaneously and without labelling, in a wide range of systems. The simultaneous measurement of the dynamics of multiple components allows for internal consistency checks and enables quantitative statements about the link between macromolecular dynamics, size, complex formation and crowding in soft materials.

A pH-driven transition of the cytoplasm from a fluid- to a solid-like state promotes entry into dormancy

Cells can enter into a dormant state when faced with unfavorable conditions. However, how cells enter into and recover from this state is still poorly understood. Here, we study dormancy in different eukaryotic organisms and find it to be associated with a significant decrease in the mobility of organelles and foreign tracer particles. We show that this reduced mobility is caused by an influx of protons and a marked acidification of the cytoplasm, which leads to widespread macromolecular assembly of proteins and triggers a transition of the cytoplasm to a solid-like state with increased mechanical stability. We further demonstrate that this transition is required for cellular survival under conditions of starvation. Our findings have broad implications for understanding alternative physiological states, such as quiescence and dormancy, and create a new view of the cytoplasm as an adaptable fluid that can reversibly transition into a protective solid-like state.

Motion of nanoprobes in complex liquids within the framework of the length-scale dependent viscosity model

This paper deals with the recent phenomenological model of the motion of nanoscopic objects (colloidal particles, proteins, nanoparticles, molecules) in complex liquids. We analysed motion in polymer, micellar, colloidal and protein solutions and the cytoplasm of living cells using the length-scale dependent viscosity model. Viscosity monotonically approaches macroscopic viscosity as the size of the object increases and thus gives a single, coherent picture of motion at the nano and macro scale. The model includes interparticle interactions (solvent-solute), temperature and the internal structure of a complex liquid. The depletion layer ubiquitously occurring in complex liquids is also incorporated into the model. We also discuss the biological aspects of crowding in terms of the length-scale dependent viscosity model.

FOUNDATIONS FOR MODELING THE DYNAMICS OF GENE REGULATORY NETWORKS: A MULTILEVEL-PERSPECTIVE REVIEW

A promising alternative for unraveling the principles under which the dynamic interactions among genes lead to cellular phenotypes relies on mathematical and computational models at different levels of abstraction, from the molecular level of protein-DNA interactions to the system level of functional relationships among genes. This review article presents, under a bottom–up perspective, a hierarchy of approaches to modeling gene regulatory network dynamics, from microscopic descriptions at the single-molecule level in the spatial context of an individual cell to macroscopic models providing phenomenological descriptions at the population-average level. The reviewed modeling approaches include Molecular Dynamics, Particle-Based Brownian Dynamics, the Master Equation approach, Ordinary Differential Equations, and the Boolean logic abstraction. Each of these frameworks is motivated by a particular biological context and the nature of the insight being pursued. The setting of gene network dynamic models from such frameworks involves assumptions and mathematical artifacts often ignored by the non-specialist. This article aims at providing an entry point for biologists new to the field and computer scientists not acquainted with some recent biophysically-inspired models of gene regulation. The connections promoting intuition between different abstraction levels and the role that approximations play in the modeling process are highlighted throughout the paper.

Cardiac sodium transport and excitation-contraction coupling

The excitation-contraction coupling (EC-coupling) links membrane depolarization with contraction in cardiomyocytes. Ca(2+) induced opening of ryanodine receptors (RyRs) leads to Ca(2+) induced Ca(2+) release (CICR) from the sarcoplasmic reticulum (SR) into the dyadic cleft between the t-tubules and SR. Ca(2+) is removed from the cytosol by the SR Ca(2+) ATPase (SERCA2) and the Na,Ca-exchanger (NCX). The NCX connects cardiac Ca(2+) and Na(+)-transport, leading to Na(+)-dependent regulation of EC-coupling by several mechanisms of which some still lack firm experimental evidence. Firstly, NCX might contribute to CICR during an action potential (AP) as Na(+)-accumulation at the intracellular site together with depolarization will trigger reverse mode exchange bringing Ca(2+) into the dyadic cleft. The controversial issue is the nature of the compartment in which Na(+) accumulates. It seems not to be the bulk cytosol, but is it part of a widespread subsarcolemmal space, a localized microdomain ("fuzzy space"), or as we propose, a more localized "spot" to which only a few membrane proteins have shared access (nanodomains)? Also, there seems to be spots where the Na,K-pump (NKA) will cause local Na(+) depletion. Secondly, Na(+) determines the rate of cytosolic Ca(2+) removal and SR Ca(2+) load by regulating the SERCA2/NCX-balance during the decay of the Ca(2+) transient. The aim of this review is to describe available data and current concepts of Na(+)-mediated regulation of cardiac EC-coupling, with special focus on subcellular microdomains and the potential roles of Na(+) transport proteins in regulating CICR and Ca(2+) extrusion in cardiomyocytes. We propose that voltage gated Na(+) channels, NCX and the NKA α2-isoform all regulate cardiac EC-coupling through control of the "Na(+) concentration in specific subcellular nanodomains in cardiomyocytes. This article is part of a Special Issue entitled "Na(+) Regulation in Cardiac Myocytes."

A paradox of state-dependent diffusion and how to resolve it

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region, the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal proportions of time in the two regions in the long term? Statistical mechanics would suggest yes, since the number of accessible states in each region is presumably the same. However, another line of reasoning suggests that the particle should spend less time in the region with faster diffusion, since it will exit that region more quickly. We demonstrate with a simple microscopic model system that both predictions are consistent with the information given. Thus, specifying the diffusion rate as a function of position is not enough to characterize the behaviour of a system, even assuming the absence of external forces. We propose an alternative framework for modelling diffusive dynamics in which both the diffusion rate and equilibrium probability density for the position of the particle are specified by the modeller. We introduce a numerical method for simulating dynamics in our framework that samples from the equilibrium probability density exactly and is suitable for discontinuous diffusion coefficients.

From microscopy data to in silico environments for in vivo-oriented simulations

ABSTRACT

: In our previous study, we introduced a combination methodology of Fluorescence Correlation Spectroscopy (FCS) and Transmission Electron Microscopy (TEM), which is powerful to investigate the effect of intracellular environment to biochemical reaction processes. Now, we developed a reconstruction method of realistic simulation spaces based on our TEM images. Interactive raytracing visualization of this space allows the perception of the overall 3D structure, which is not directly accessible from 2D TEM images. Simulation results show that the diffusion in such generated structures strongly depends on image post-processing. Frayed structures corresponding to noisy images hinder the diffusion much stronger than smooth surfaces from denoised images. This means that the correct identification of noise or structure is significant to reconstruct appropriate reaction environment in silico in order to estimate realistic behaviors of reactants in vivo. Static structures lead to anomalous diffusion due to the partial confinement. In contrast, mobile crowding agents do not lead to anomalous diffusion at moderate crowding levels. By varying the mobility of these non-reactive obstacles (NRO), we estimated the relationship between NRO diffusion coefficient (Dnro) and the anomaly in the tracer diffusion (α). For Dnro=21.96 to 44.49 μm2/s, the simulation results match the anomaly obtained from FCS measurements. This range of the diffusion coefficient from simulations is compatible with the range of the diffusion coefficient of structural proteins in the cytoplasm. In addition, we investigated the relationship between the radius of NRO and anomalous diffusion coefficient of tracers by the comparison between different simulations. The radius of NRO has to be 58 nm when the polymer moves with the same diffusion speed as a reactant, which is close to the radius of functional protein complexes in a cell.

Brownian dynamics simulations on CPU and GPU with BD_BOX

There has been growing interest in simulating biological processes under in vivo conditions due to recent advances in experimental techniques dedicated to study single particle behavior in crowded environments. We have developed a software package, BD_BOX, for multiscale Brownian dynamics simulations. BD_BOX can simulate either single molecules or multicomponent systems of diverse, interacting molecular species using flexible, coarse-grained bead models. BD_BOX is written in C and employs modern computer architectures and technologies; these include MPI for distributed-memory architectures, OpenMP for shared-memory platforms, NVIDIA CUDA framework for GPGPU, and SSE vectorization for CPU.

Agent-based simulation of reactions in the crowded and structured intracellular environment: Influence of mobility and location of the reactants

Background

In this paper we apply a novel agent-based simulation method in order to model intracellular reactions in detail. The simulations are performed within a virtual cytoskeleton enriched with further crowding elements, which allows the analysis of molecular crowding effects on intracellular diffusion and reaction rates. The cytoskeleton network leads to a reduction in the mobility of molecules. Molecules can also unspecifically bind to membranes or the cytoskeleton affecting (i) the fraction of unbound molecules in the cytosol and (ii) furthermore reducing the mobility. Binding of molecules to intracellular structures or scaffolds can in turn lead to a microcompartmentalization of the cell. Especially the formation of enzyme complexes promoting metabolic channeling, e.g. in glycolysis, depends on the co-localization of the proteins.

Results

While the co-localization of enzymes leads to faster reaction rates, the reduced mobility decreases the collision rate of reactants, hence reducing the reaction rate, as expected. This effect is most prominent in diffusion limited reactions. Furthermore, anomalous diffusion can occur due to molecular crowding in the cell. In the context of diffusion controlled reactions, anomalous diffusion leads to fractal reaction kinetics. The simulation framework is used to quantify and separate the effects originating from molecular crowding or the reduced mobility of the reactants. We were able to define three factors which describe the effective reaction rate, namely f ^diff for the diffusion effect, f ^volume for the crowding, and f ^access for the reduced accessibility of the molecules.

Conclusions

Molecule distributions, reaction rate constants and structural parameters can be adjusted separately in the simulation allowing a comprehensive study of individual effects in the context of a realistic cell environment. As such, the present simulation can help to bridge the gap between in vivo and in vitro kinetics.

Diffusion in crowded biological environments: applications of Brownian dynamics

Biochemical reactions in living systems occur in complex, heterogeneous media with total concentrations of macromolecules in the range of 50 - 400 mgml. Molecular species occupy a significant fraction of the immersing medium, up to 40% of volume. Such complex and volume-occupied environments are generally termed 'crowded' and/or 'confined'. In crowded conditions non-specific interactions between macromolecules may hinder diffusion - a major process determining metabolism, transport, and signaling. Also, the crowded media can alter, both qualitatively and quantitatively, the reactions in vivo in comparison with their in vitro counterparts. This review focuses on recent developments in particle-based Brownian dynamics algorithms, their applications to model diffusive transport in crowded systems, and their abilities to reproduce and predict the behavior of macromolecules under in vivo conditions.