Ensemble Behavior Research Articles

The cellular Ising model: a framework for phase transitions in multicellular environments.

Inspired by the Ising model, we introduce a gene regulatory network that induces a phase transition that coordinates robustly the behaviour of cell ensembles. The building blocks of the design are the so-called toggle switch interfaced with two quorum sensing modules, Las and Lux. We show that as a function of the transport rate of signalling molecules across the cell membrane the population undergoes a spontaneous symmetry breaking from cells individually switching their phenotypes to a global collective phenotypic organization. By characterizing the critical behaviour, we reveal some properties, such as phenotypic memory and hypersensitivity, with relevance in the field of synthetic biology. We argue that our results can be extrapolated to other multicellular systems and be a generic framework for collective decision-making processes.

Surface induced magnetization reversal of MnP nanoclusters embedded in GaP

We investigate the quasi-static magnetic behavior of ensembles of ferromagnetic nanoparticles consisting of MnP nanoclusters embedded in GaP(001) epilayers grown at 600, 650, and 700 °C. We use a phenomenological model, in which surface effects are included, to reproduce the experimental hysteresis curves measured as a function of temperature (120–260 K) and direction of the applied field. The slope of the hysteresis curve during magnetization reversal is determined by the MnP nanoclusters size distribution, which is a function of the growth temperature. Our results show that the coercive field is very sensitive to the strength of the surface anisotropy, which reduces the energy barrier between the two states of opposite magnetization. Notably, this reduction in the energy barrier increases by a factor of 3 as the sample temperature is lowered from 260 to 120 K.

Cooperative Transport by Populations of Fast and Slow Kinesins Uncovers Novel Family-Dependent Motor Characteristics Important for in Vivo Function

Intracellular cargo transport frequently involves multiple motor types, either having opposite directionality or having the same directionality but different speeds. Although significant progress has been made in characterizing kinesin motors at the single-molecule level, predicting their ensemble behavior is challenging and requires tight coupling between experiments and modeling to uncover the underlying motor behavior. To understand how diverse kinesins attached to the same cargo coordinate their movement, we carried out microtubule gliding assays using pairwise mixtures of motors from the kinesin-1, 2, 3, 5 and 7 families engineered to have identical run lengths and surface attachments. Uniform motor densities were used and microtubule gliding speeds were measured for varying proportions of fast and slow motors. A coarse-grained computational model of gliding assays was developed and found to recapitulate the experiments. The simulations show that the force-dependence of detachment is the key parameter that determines gliding speed in multi-motor assays and provide estimates for force-dependent dissociation rates suggesting that kinesin-1 and the mitotic motors kinesin-5 and −7 maintain microtubule association against loads, while kinesin-2 and −3 readily detach. Using these predictions, we are investigating how these motors carry scaffold proteins in teams to carry out distinct mechanical tasks in cells. Our work uncovers unexpected motor behavior in multi-motor ensembles and clarifies functional differences between kinesins.

NMR-Based Molecular view of the Biology and Biophysics of WIP, An Intrinsically Disordered Protein

Intrinsically disordered proteins (IDPs) are multi-conformational polypeptides that lack a stable three-dimensional structure, forcing structural biology to reconsider the structure-function paradigm. The versatile IDPs play key roles in a multitude of biological processes, and, given their inherently flexible nature, nuclear magnetic resonance (NMR) is a leading method for investigating IDP behavior on the molecular level. Our research has focused on the intrinsically disordered WASp Interacting Protein (WIP) from human T cells, whose C-terminal binds Wiskott-Aldrich syndrome protein (WASp), and N-terminal interacts with actin, both crucial factors in mediating the cytoskeletal changes accompanying cell activation.A range of NMR experiments tailored for IDP study was employed to discover transient structural motifs in the two terminal WIP domains. Chemical shifts, relaxation rates, residual dipolar couplings and solvent exposure all concurred in identifying WIP segments exhibiting a secondary structure bias in their conformational ensemble. Remarkably, these transient structural elements echo the conformation of WIP bound to actin or WASp. In addition, in each domain we identified a previously unrecognized binding epitope, and later confirmed these with binding-induced effects observed by NMR.IDPs are essentially an ensemble of multiple fast-interchanging conformations, and we have utilized WIP also as a model to monitor this ensemble behavior under various conditions. Temperature effects were consistent with thermal unfolding and exhibited a strong correlation with structural propensities. Similarly, the effects of denaturing or crowding conditions could be evaluated with this approach. Finally, we obtain insight into how proteins fold and interact with peptidic ligands by following the effects of sub-stochiometric actin concentrations on the WIP conformational ensemble. Our findings highlight the potential impact of high-resolution NMR upon the field of IDPs, which can be enhanced by complementary biophysical and computational approaches.

Reduced order models for assessing CO2 impacts in shallow unconfined aquifers

Risk assessment studies of potential CO2 sequestration projects consider many factors, including the possibility of brine and/or CO2 leakage from the storage reservoir. Detailed multiphase reactive transport simulations have been developed to predict the impact of such leaks on shallow groundwater quality; however, these simulations are computationally expensive and thus difficult to directly embed in a probabilistic risk assessment analysis. Here we present a process for developing computationally fast reduced-order models which emulate key features of the more detailed reactive transport simulations. A large ensemble of simulations that take into account uncertainty in aquifer characteristics and CO2/brine leakage scenarios were performed. Twelve simulation outputs of interest were used to develop response surfaces (RSs) using a MARS (multivariate adaptive regression splines) algorithm (Milborrow, 2015).A key part of this study is to compare different measures of ROM accuracy. We show that for some computed outputs, MARS performs very well in matching the simulation data. The capability of the RS to predict simulation outputs for parameter combinations not used in RS development was tested using cross-validation. Again, for some outputs, these results were quite good. For other outputs, however, the method performs relatively poorly. Performance was best for predicting the volume of depressed-pH-plumes, and was relatively poor for predicting organic and trace metal plume volumes. We believe several factors, including the non-linearity of the problem, complexity of the geochemistry, and granularity in the simulation results, contribute to this varied performance.The reduced order models were developed principally to be used in probabilistic performance analysis where a large range of scenarios are considered and ensemble performance is calculated. We demonstrate that they effectively predict the ensemble behavior. However, the performance of the RSs is much less accurate when used to predict time-varying outputs from a single simulation. If an analysis requires only a small number of scenarios to be investigated, computationally expensive physics-based simulations would likely provide more reliable results. If the aggregate behavior of a large number of realizations is the focus, as will be the case in probabilistic quantitative risk assessment, the methodology presented here is relatively robust.

Identification of DEM simulation parameters by Artificial Neural Networks and bulk experiments

In Discrete Element Method (DEM) simulations, particle–particle contact laws determine the macroscopic simulation results. Particle-based contact laws, in turn, commonly rely on semi-empirical parameters which are difficult to obtain by direct microscopic measurements. In this study, we present a method for the identification of DEM simulation parameters that uses artificial neural networks to link macroscopic experimental results to microscopic numerical parameters. In the first step, a series of DEM simulations with varying simulation parameters is used to train a feed-forward artificial neural network by backward-propagation reinforcement. In the second step, this artificial neural network is used to predict the macroscopic ensemble behaviour in relation to additional sets of particle-based simulation parameters. Thus, a comprehensive database is obtained which links particle-based simulation parameters to specific macroscopic bulk behaviours of the ensemble. The trained artificial neural network is able to predict the behaviours of additional sets of input parameters accurately and highly efficiently. Furthermore, this method can be used generically to identify DEM material parameters. For each set of calibration experiments, the neural network needs to be trained only once. After the training, the neural network provides a generic link between the macroscopic experimental results and the microscopic DEM simulation parameters. Based on these experiments, the DEM simulation parameters of any given non-cohesive granular material can be identified.

Numerical simulation of plastic strain localization and failure mode transition in metals under dynamic loading

The research is focused on simulation and experimental investigation of high-strain rate loading to study the mechanisms of plastic flow localization and failure mode transition in metals (AlMg6). The task of breaking down barriers by metal shell was examined. Model based on the statistical-thermodynamic description of deformation of solids with mesoscopic defects (microshears and micro-cracks) was used to simulate the behavior of metals under dynamic loading. Experimental studies were also carried out. The real-time lateral surface temperature was measured by high speed infrared camera CEDIP Silver 450M. The consistent result of “in-situ” experiment is the elevated temperature of strain localization area that doesn’t exceed 72°C. The results of numerical simulation are in a good agreement with the in-situ measured infrared experimental data. Experimental and theoretical (numerical) study of dynamic strain localization allowed us to establish the structure induced mechanism of plastic strain localization as possible mechanism of transition to the adiabatic shear failure. Evaluated temperature in the strain localization area (72°C) will not support conventionally used mechanisms of plastic strain localization as autocatalytic temperature control visco-plastic phenomena. Structural study of defect induced scaling properties revealed the correlated behavior of microshear ensemble that can be classified as structural transition providing the dynamic strain localization.

Magnetostatic nearest neighbor interactions in a Co48Fe52 nanowire array probed by in-field magnetic force microscopy

The magnetization behavior of nanowires embedded in an array is influenced by the sum of the dipolar fields produced by all surrounding nanowires. These magnetostatic interactions largely modify the array properties and thus complicate the reconstruction of the ensemble averaged behavior of the individual nanowires, such as the intrinsic switching field distribution. Simply correcting the shearing of the hysteresis in a mean-field approach does not account for the locally fluctuating demagnetizing field, which originates from the individual magnetization configuration in the close surrounding of each nanowire. We present an in-field Magnetic Force Microscopy study of electrochemically produced Co48Fe52 nanowires, in which the influence of the magnetic nearest neighbor configuration on the switching behavior of the individual embedded nanowires is clearly detected. Based on this finding, a statistical evaluation method of nearest neighbor histograms is proposed, which potentially allows to judge the strength of the local magnetostatic interactions against the magnitude of the intrinsic switching field distribution.

Critical behavior in topological ensembles

We consider the relation between three physical problems: 2D directed lattice random walks, ensembles of $T_{n,n+1}$ torus knots, and instanton ensembles in 5D SQED with one compact dimension in $\Omega$ background and with 5D Chern-Simons term at the level one. All these ensembles exhibit the critical behavior typical for the "area+length+corners" statistics of grand ensembles of 2D directed paths. Using the combinatorial description, we obtain an explicit expression of the generating function for $q$-Narayana numbers which amounts to the new critical behavior in the ensemble of $T_{n,n+1}$ torus knots and in the ensemble of instantons in 5D SQED. Depending on the number of the nontrivial fugacities, we get either the critical point, or cascade of critical lines and critical surfaces. In the 5D gauge theory the phase transition is of the 3rd order, while in the ensemble of paths and ensemble of knots it is typically of the 1st order. We also discuss the relation with the integrable models.

Some Dynamic Behaviour Aspects Related to a Vehicle Suspension

Some of the aspects of the vehicle suspension limiting performances from stress and vibrations point of view have been explored in this study. The vehicle is modeled as two DOF system and the suspension is considered a passive one. 3D CATIA model was built for both the spring and spring-damper ensemble, neglecting the tire influence. This can reasonably covers the studies of geometries and forces (bending or tensile stress), masses and stiffnesses (meaning vibration profiles). The theoretical analysis on the vibration behaviour of the spring-damper ensemble, regarded as the vehicle suspension, suggests a convenient operation regime at low frequencies below 15 Hz, if the damper piston displacement is limited.

Experimental evidence of statistical ensemble behavior in bed load sediment transport

AbstractA high‐resolution data set obtained from high‐speed imaging of coarse sand particles transported as bed load allows us to confidently describe the forms and qualities of the ensemble distributions of particle velocities, accelerations, hop distances, and traveltimes. Autocorrelation functions of frame‐averaged values (and the decay of these functions) support the idea that the forms of these distributions become time invariant within the 5 s imaging interval. Distributions of streamwise and cross‐stream particle velocities are exponential, consistent with previous experiments and theory. Importantly, streamwise particle velocities possess a “light” tail, where the largest velocities are limited by near‐bed fluid velocities. Distributions of streamwise and cross‐stream particle accelerations are Laplace in form and are centered on zero, consistent with equilibrium transport conditions. The majority of particle hops, measured start to stop, involve short displacements, and streamwise hop distances possess a Weibull distribution. In contrast to previous work, the distribution of traveltimes is exponential, consistent with a fixed temporal disentrainment rate. The Weibull distribution of hop distances is consistent with a decreasing spatial disentrainment rate and is related to the exponential distribution of traveltimes. By taking into account the effects of experimental censorship associated with a finite sampling window, the relationship between streamwise hop distances and traveltimes, , likely involves an exponent of α ∼ 2. These experimental results—an exponential distribution of traveltimes Tp and a Weibull distribution of hop distances Lx with shape parameter k < 1—are consistent with a nonlinear relationship between these quantities with α > 1.

An agent model of crowd behavior in emergencies

An agent model of crowd (ensemble) behavior in emergencies was presented. This model is distinguished for the allowance for dynamics of each agent from the ensemble under consideration. The crowd effect manifests itself mostly as attraction or repulsion of closely set agents with a probability depending on the agent's psychological type. Consideration was given to the effects associated with the crowd turbulence. Operation of the intelligent rescue agents was simulated. The impact of the configuration of spatial agent allocation on the dynamics of their evacuation in emergencies was analyzed. The influence of the intelligent rescue agents on the system was studied, and an adaptive procedure for training such agents was developed.

Synchronization versus neighborhood similarity in complex networks of nonidentical oscillators.

Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of nonidentical interacting oscillators. Three types of connection configurations are considered: Similar, Dissimilar, and Neutral patterns. These different groups correspond, respectively, to oscillators alike, distinct, and indifferent relative to their neighbors. To construct such scenarios we define a vertex-weighted graph measure, the total dissonance, which comprises the sum of the dissonances between all neighbor oscillators in the network. Our numerical simulations show that the more homogeneous a network, the higher tend to be both the coupling strength required for phase locking and the associated final phase configuration spread over the circle. On the other hand, the initial spread of partial synchronization occurs faster for Similar patterns in comparison to Dissimilar ones, while neutral patterns are an intermediate situation between both extremes.

Ensemble magnetic behavior of interacting CoFe nanoparticles

Ferromagnetic nanoparticles in the 10-14 nm size range are examined for their size and interaction dependent magnetic properties. From X-ray magnetic circular dichroism the orbital-to-spin magnetic moment ratio is determined and found to decrease significantly with particle size. This is in accordance with previous complementary studies on smaller particles and highlights the difficulty of fitting to a simple core-shell model. Vibrating sample magnetometry experiments on samples with more than 1000 particles per square micron show a wide distribution of blocking temperatures from 50 to greater than 650 K. This is attributed to the dipole-dipole magnetic coupling forces between particles. The blocking temperatures show an unexpected negative correlation with increasing particle density.

Intracellular dynamics and fate of polystyrene nanoparticles in A549 Lung epithelial cells monitored by image (cross-) correlation spectroscopy and single particle tracking

Novel insights in nanoparticle (NP) uptake routes of cells, their intracellular trafficking and subcellular targeting can be obtained through the investigation of their temporal and spatial behavior. In this work, we present the application of image (cross-) correlation spectroscopy (IC(C)S) and single particle tracking (SPT) to monitor the intracellular dynamics of polystyrene (PS) NPs in the human lung carcinoma A549 cell line. The ensemble kinetic behavior of NPs inside the cell was characterized by temporal and spatiotemporal image correlation spectroscopy (TICS and STICS). Moreover, a more direct interpretation of the diffusion and flow detected in the NP motion was obtained by SPT by monitoring individual NPs. Both techniques demonstrate that the PS NP transport in A549 cells is mainly dependent on microtubule-assisted transport. By applying spatiotemporal image cross-correlation spectroscopy (STICCS), the correlated motions of NPs with the early endosomes, late endosomes and lysosomes are identified. PS NPs were equally distributed among the endolysosomal compartment during the time interval of the experiments. The cotransport of the NPs with the lysosomes is significantly larger compared to the other cell organelles. In the present study we show that the complementarity of ICS-based techniques and SPT enables a consistent elaborate model of the complex behavior of NPs inside biological systems.

Fluorescence Recovery after Photobleaching and Single-Molecule Tracking Measurements of Anisotropic Diffusion within Identical Regions of a Cylinder-Forming Diblock Copolymer Film.

This work demonstrates ensemble and single-molecule diffusion measurements within identical regions of a cylinder-forming polystyrene-poly(ethylene oxide) diblock copolymer (PS-b-PEO) film using fluorescence recovery after photobleaching (FRAP) and single-molecule tracking (SMT). A PS-b-PEO film (∼4 μm thick) with aligned cylindrical PEO microdomains containing 10 μM sulforhodamine B (SRB) was prepared by directional solvent-vapor penetration (SVP) of 1,4-dioxane. The ensemble diffusion behavior of SRB in the microdomains was assessed in FRAP studies of circular photobleached regions (∼7 μm in diameter). The SRB concentration was subsequently reduced by additional photobleaching, and the diffusion of individual SRB molecules was explored using SMT in the identical area (∼16 × 16 μm(2)). The FRAP data showed anisotropic fluorescence recovery, yielding the average microdomain orientation. The extent of fluorescence recovery observed (∼90%) demonstrated long-range microdomain connectivity, while the recovery time dependence provided an ensemble measurement of the SRB diffusion coefficient within the cylindrical microdomains. The SMT data exhibited one-dimensional diffusion of individual SRB molecules along the SVP direction across the entire film thickness, as consistent with the FRAP results. Importantly, the average of the single-molecule diffusion coefficients was close to the value obtained from FRAP in the identical area. In some cases, SMT offered smaller diffusion coefficients than FRAP, possibly due to contributions from SRB molecules confined within short PEO microdomains. The implementation of FRAP and SMT measurements in identical areas provides complementary information on molecular diffusion with minimal influence of sample heterogeneity, permitting direct comparison of ensemble and single-molecule diffusion behavior.

On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve.

Recent long-term studies showed an unsatisfactory recurrence rate of severe mitral regurgitation 3-5years after surgical repair, suggesting that excessive tissue stresses and the resulting strain-induced tissue failure are potential etiological factors controlling the success of surgical repair for treating mitral valve (MV) diseases. We hypothesized that restoring normal MV tissue stresses in MV repair techniques would ultimately lead to improved repair durability through the restoration of MV normal homeostatic state. Therefore, we developed a micro- and macro- anatomically accurate MV finite element model by incorporating actual fiber microstructural architecture and a realistic structure-based constitutive model. We investigated MV closing behaviors, with extensive in vitro data used for validating the proposed model. Comparative and parametric studies were conducted to identify essential model fidelity and information for achieving desirable accuracy. More importantly, for the first time, the interrelationship between the local fiber ensemble behavior and the organ-level MV closing behavior was investigated using a computational simulation. These novel results indicated not only the appropriate parameter ranges, but also the importance of the microstructural tuning (i.e., straightening and re-orientation) of the collagen/elastin fiber networks at the macroscopic tissue level for facilitating the proper coaptation and natural functioning of the MV apparatus under physiological loading at the organ level. The proposed computational model would serve as a logical first step toward our long-term modeling goal-facilitating simulation-guided design of optimal surgical repair strategies for treating diseased MVs with significantly enhanced durability.

Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties.

The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system's constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.

Synchronization of intermittent behavior in ensembles of multistable dynamical systems.

We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the basins of attraction of coexisting synchronous states. Then, we propose the use of the master stability function (MSF) for multistable systems to describe synchronizability, even during intermittent behavior, of a network of multistable oscillators, regardless of both the number of coupled oscillators and the interaction structure. In particular, we show that a network of multistable elements is synchronizable for a given range of topology spectra and coupling strengths, irrespective of specific attractor dynamics to which different oscillators are locked, and even in the presence of intermittency. Finally, we experimentally demonstrate the feasibility and robustness of the MSF approach with a network of multistable electronic circuits.

Динамика ансамбля активных броуновских частиц, управляемых шумом

Dynamics of an ensemble of small number of active Brownian particles is studied by means of numerical simulations. The particles are influenced by independent sources of noise, passive and active, and interact with each other through a global velocity field. We suppose that active noise affects to direction of the particle velocity only. Behaviour of the large ensemble and behaviour of the small one are compared. Mean velocity of particles of the large ensemble was analytically estimated earler. We show that a noise-induced "order- disorder" transition accompaniated by a bistability phenomena is observed in a small ensemble. A borderline of a coupling coefficient moves up while reducing the number of particles. Influence of passive noise leads to conversion of bistability to bimodality. There are two most probable values of a particle velocity in the last case. Borders of regions of bistability and bimodality are defined by the stochastic bifurcations of different kinds.