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Journal of the Royal Society, Interface Mar 2021Swarming has been observed in various biological systems from collective animal movements to immune cells. In the cellular context, swarming is driven by the secretion...
Swarming has been observed in various biological systems from collective animal movements to immune cells. In the cellular context, swarming is driven by the secretion of chemotactic factors. Despite the critical role of chemotactic swarming, few methods to robustly identify and quantify this phenomenon exist. Here, we present a novel method for the analysis of time series of positional data generated from realizations of agent-based processes. We convert the positional data for each individual time point to a function measuring agent aggregation around a given area of interest, hence generating a functional time series. The functional time series, and a more easily visualized of agent aggregation derived from these functions, provide useful information regarding the evolution of the underlying process over time. We extend our method to build upon the modelling of collective motility using drift-diffusion partial differential equations (PDEs). Using a functional linear model, we are able to use the functional time series to estimate the drift and diffusivity terms associated with the underlying PDE. By producing an accurate estimate for the drift coefficient, we can infer the strength and range of attraction or repulsion exerted on agents, as in chemotaxis. Our approach relies solely on using agent positional data. The spatial distribution of diffusing chemokines is not required, nor do individual agents need to be tracked over time. We demonstrate our approach using random walk simulations of chemotaxis and experiments investigating cytotoxic T cells interacting with tumouroids.
Topics: Animals; Cell Tracking; Chemotactic Factors; Chemotaxis; Diffusion; Models, Biological; Movement
PubMed: 33715400
DOI: 10.1098/rsif.2020.0879 -
Biophysical Journal Apr 2020In cell membranes, the functional constituents such as peptides, proteins, and polysaccharides diffuse in a sea of lipids as single molecules and molecular aggregates....
In cell membranes, the functional constituents such as peptides, proteins, and polysaccharides diffuse in a sea of lipids as single molecules and molecular aggregates. Thus, the fluidity of the heterogeneous multicomponent membrane is important for understanding the roles of the membrane in cell functionality. Recently, Henle and Levine described the hydrodynamics of molecular diffusion in a spherical membrane. A tangential point force at the north pole induces a pair of vortices whose centers lie on a line perpendicular to the point force and are symmetrical with respect to the point force. The position of the vortex center depends on η/Rη, where R is the radius of the spherical membrane, and η and η are the viscosities of the membrane and the surrounding medium, respectively. Based on this theoretical prediction, we applied a point force to a phase-separated spherical vesicle composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine/1,2-dioleoyl-sn-glycero-3-phosphocholine/cholesterol by means of a microinjection technique. The pathlines were visualized by trajectories of microdomains. We determined the position of the vortex center and estimated the membrane viscosity using the dependence of the position of the vortex center on η/Rη. The obtained apparent membrane viscosities for various compositions are mapped on the phase diagram. The membrane viscosity is almost constant in the range of 0 <ϕ ≤ 0.5 (ϕ: area fraction of the liquid ordered phase), whereas that in the range of 0.5 ≤ ϕ < 1.0 exponentially increases with increase of ϕ. The obtained viscosity landscape provides a basic understanding of the fluidity of heterogeneous multicomponent membranes.
Topics: Cell Membrane; Cholesterol; Diffusion; Lipid Bilayers; Lipids; Phosphatidylcholines; Viscosity
PubMed: 32053773
DOI: 10.1016/j.bpj.2020.01.009 -
Journal of Colloid and Interface Science Jan 2022The use of isotropic potential models of simple colloids for describing complex protein-protein interactions is a topic of ongoing debate in the biophysical community....
The use of isotropic potential models of simple colloids for describing complex protein-protein interactions is a topic of ongoing debate in the biophysical community. This contention stems from the unavailability of synthetic protein-like model particles that are amenable to systematic experimental characterization. In this article, we test the utility of colloidal theory to capture the solution structure, interactions and dynamics of novel globular protein-mimicking, computationally designed peptide assemblies called bundlemers that are programmable model systems at the intersection of colloids and proteins. Small-angle neutron scattering (SANS) measurements of semi-dilute bundlemer solutions in low and high ionic strength solution indicate that bundlemers interact locally via repulsive interactions that can be described by a screened repulsive potential. We also present neutron spin echo (NSE) spectroscopy results that show high-Q freely-diffusive dynamics of bundlemers. Importantly, formation of clusters due to short-range attractive, inter-bundlemer interactions is observed in SANS even at dilute bundlemer concentrations, which is indicative of the complexity of the bundlemer charged surface. The similarities and differences between bundlemers and simple colloidal as well as complex protein-protein interactions is discussed in detail.
Topics: Colloids; Diffusion; Peptides; Proteins; Scattering, Small Angle
PubMed: 34749446
DOI: 10.1016/j.jcis.2021.09.184 -
Biophysical Journal Oct 2021Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration...
Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration of osteoblast tissue in zebrafish scales. These waves originate from a central source region, propagate as expanding rings, and impart cell growth, thus controlling tissue morphogenesis. Here, we present a minimal reaction-diffusion model for Erk activity waves. The model considers three components: Erk, a diffusible Erk activator, and an Erk inhibitor. Erk stimulates both its activator and inhibitor, forming a positive and negative feedback loop, respectively. Our model shows that this system can be excitable and propagate Erk activity waves. Waves originate from a pulsatile source that is modeled by adding a localized basal production of the activator, which turns the source region from an excitable to an oscillatory state. As Erk activity periodically rises in the source, it can trigger an excitable wave that travels across the entire tissue. Analysis of the model finds that positive feedback controls the properties of the traveling wavefront and that negative feedback controls the duration of Erk activity peak and the period of Erk activity waves. The geometrical properties of the waves facilitate constraints on the effective diffusivity of the activator, indicating that waves are an efficient mechanism to transfer growth factor signaling rapidly across a large tissue.
Topics: Animals; Diffusion; Models, Theoretical; Osteoblasts; Signal Transduction; Zebrafish
PubMed: 34022234
DOI: 10.1016/j.bpj.2021.05.004 -
Proceedings of the National Academy of... Aug 2022Some dividing cells sense their shape by becoming polarized along their long axis. Cell polarity is controlled in part by polarity proteins, like Rho GTPases, cycling...
Some dividing cells sense their shape by becoming polarized along their long axis. Cell polarity is controlled in part by polarity proteins, like Rho GTPases, cycling between active membrane-bound forms and inactive cytosolic forms, modeled as a "wave-pinning" reaction-diffusion process. Does shape sensing emerge from wave pinning? We show that wave pinning senses the cell's long axis. Simulating wave pinning on a curved surface, we find that high-activity domains migrate to peaks and troughs of the surface. For smooth surfaces, a simple rule of minimizing the domain perimeter while keeping its area fixed predicts the final position of the domain and its shape. However, when we introduce roughness to our surfaces, shape sensing can be disrupted, and high-activity domains can become localized to locations other than the global peaks and valleys of the surface. On rough surfaces, the domains of the wave-pinning model are more robust in finding the peaks and troughs than the minimization rule, although both can become trapped in steady states away from the peaks and valleys. We can control the robustness of shape sensing by altering the Rho GTPase diffusivity and the domain size. We also find that the shape-sensing properties of cell polarity models can explain how domains localize to curved regions of deformed cells. Our results help to understand the factors that allow cells to sense their shape-and the limits that membrane roughness can place on this process.
Topics: Cell Polarity; Cell Shape; Diffusion; Models, Biological; rho GTP-Binding Proteins
PubMed: 35905323
DOI: 10.1073/pnas.2121302119 -
Biophysical Journal Jun 2020Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell...
Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.
Topics: Cell Movement; Computer Simulation; Diffusion; Models, Biological; Motion
PubMed: 32407685
DOI: 10.1016/j.bpj.2020.04.024 -
Proceedings of the National Academy of... Nov 2018Using a microscopic theory to analyze experiments, we demonstrate that enzymes are active matter. Superresolution fluorescence measurements-performed across four orders...
Using a microscopic theory to analyze experiments, we demonstrate that enzymes are active matter. Superresolution fluorescence measurements-performed across four orders of magnitude of substrate concentration, with emphasis on the biologically relevant regime around or below the Michaelis-Menten constant-show that catalysis boosts the motion of enzymes to be superdiffusive for a few microseconds, enhancing their effective diffusivity over longer timescales. Occurring at the catalytic turnover rate, these fast ballistic leaps maintain direction over a duration limited by rotational diffusion, driving enzymes to execute wormlike trajectories by piconewton forces performing work of a few against viscosity. The boosts are more frequent at high substrate concentrations, biasing the trajectories toward substrate-poor regions, thus exhibiting antichemotaxis, demonstrated here experimentally over a wide range of aqueous concentrations. Alternative noncatalytic, passive mechanisms that predict chemotaxis, cross-diffusion, and phoresis, are critically analyzed. We examine the physical interpretation of our findings, speculate on the underlying mechanism, and discuss the avenues they open with biological and technological implications. These findings violate the classical paradigm that chemical reaction and motility are distinct processes, and suggest reaction-motion coupling as a general principle of catalysis.
Topics: Biocatalysis; Catalysis; Chemotaxis; Diffusion; Enzymes; Hydrodynamics; Kinetics
PubMed: 30385635
DOI: 10.1073/pnas.1814180115 -
Journal of Biomechanics Sep 2016The cartilage endplate (CEP) is implicated as the main pathway of nutrient supply to the healthy human intervertebral disc (IVD). In this study, the diffusivities of...
The cartilage endplate (CEP) is implicated as the main pathway of nutrient supply to the healthy human intervertebral disc (IVD). In this study, the diffusivities of nutrient/metabolite solutes in healthy CEP were assessed, and further correlated with tissue biochemical composition and structure. The CEPs from non-degenerated human IVD were divided into four regions: central, lateral, anterior, and posterior. The diffusivities of glucose and lactate were measured with a custom diffusion cell apparatus under 0%, 10%, and 20% compressive strains. Biochemical assays were conducted to quantify the water and glycosaminoglycan (GAG) contents. The Safranin-O and Ehrlich׳s hematoxylin and eosin staining and scanning electron microscopy (SEM) were performed to reveal the tissue structure of the CEP. Average diffusivities of glucose and lactate in healthy CEP were 2.68±0.93×10cm/s and 4.52±1.47×10cm/s, respectively. Solute diffusivities were region-dependent (p<0.0001) with the highest values in the central region, and mechanical strains impeded solute diffusion in the CEP (p<0.0001). The solute diffusivities were significantly correlated with the tissue porosities (glucose: p<0.0001, r=0.581; lactate: p<0.0001, r=0.534). Histological and SEM studies further revealed that the collagen fibers in healthy CEP are more compacted than those in the nucleus pulposus (NP) and annulus fibrosus (AF) and show no clear orientation. Compared to human AF and NP, much smaller solute diffusivities in human CEP suggested that it acts as a gateway for solute diffusion through the disc, maintaining the balance of nutritional environment in healthy human disc under mechanical loading and preventing the progression of disc degeneration.
Topics: Cartilage; Diffusion; Female; Glucose; Glycosaminoglycans; Humans; Intervertebral Disc; Intervertebral Disc Degeneration; Lactic Acid; Male; Middle Aged; Stress, Mechanical; Water
PubMed: 27338525
DOI: 10.1016/j.jbiomech.2016.06.008 -
Proceedings of the National Academy of... Dec 2022A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns...
A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which interconnect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex-like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks.
Topics: Diffusion; Motion; Neural Networks, Computer
PubMed: 36459639
DOI: 10.1073/pnas.2211359119 -
The Journal of Physical Chemistry. B Dec 2018A formalism is developed to describe how diffusion alters the kinetics of coupled reversible association-dissociation reactions in the presence of conformational changes...
A formalism is developed to describe how diffusion alters the kinetics of coupled reversible association-dissociation reactions in the presence of conformational changes that can modify the reactivity. The major difficulty in constructing a general theory is that, even to the lowest order, diffusion can change the structure of the rate equations of chemical kinetics by introducing new reaction channels (i.e., modifies the kinetic scheme). Therefore, the right formalism must be found that allows the influence of diffusion to be described in a concise and elegant way for networks of arbitrary complexity. Our key result is a set of non-Markovian rate equations involving stoichiometric matrices and net reaction rates (fluxes), in which these rates are coupled by a time-dependent pair association flux matrix, whose elements have a simple physical interpretation. Specifically, each element is the probability density that an isolated pair of reactants irreversibly associates at time t via one reaction channel on the condition that it started out with the dissociation products of another (or the same) channel. In the Markovian limit, the coupling of the chemical rates is described by committors (or splitting/capture probabilities). The committor is the probability that an isolated pair of reactants formed by dissociation at one site will irreversibly associate at another site rather than diffuse apart. We illustrate the use of our formalism by considering three reversible reaction schemes: (1) binding to a single site, (2) binding to two inequivalent sites, and (3) binding to a site whose reactivity fluctuates. In the first example, we recover the results published earlier, while in the second one we show that a new reaction channel appears, which directly connects the two bound states. The third example is particularly interesting because all species become coupled and an exchange-type bimolecular reaction appears. In the Markovian limit, some of the diffusion-modified rate constants that describe new transitions become negative, indicating that memory effects cannot be ignored.
Topics: Chemistry, Physical; Diffusion; Kinetics; Models, Chemical; Probability
PubMed: 30215520
DOI: 10.1021/acs.jpcb.8b07250