Spatial Interaction Range Research Articles

Both electrical and metabolic coupling shape the collective multimodal activity and functional connectivity patterns in beta cell collectives: A computational model perspective.

Pancreatic beta cells are coupled excitable oscillators that synchronize their activity via different communication pathways. Their oscillatory activity manifests itself on multiple timescales and consists of bursting electrical activity, subsequent oscillations in the intracellular Ca^{2+}, as well as oscillations in metabolism and exocytosis. The coordination of the intricate activity on the multicellular level plays a key role in the regulation of physiological pulsatile insulin secretion and is incompletely understood. In this paper, we investigate theoretically the principles that give rise to the synchronized activity of beta cell populations by building up a phenomenological multicellular model that incorporates the basic features of beta cell dynamics. Specifically, the model is composed of coupled slow and fast oscillatory units that reflect metabolic processes and electrical activity, respectively. Using a realistic description of the intercellular interactions, we study how the combination of electrical and metabolic coupling generates collective rhythmicity and shapes functional beta cell networks. It turns out that while electrical coupling solely can synchronize the responses, the addition of metabolic interactions further enhances coordination, the spatial range of interactions increases the number of connections in the functional beta cell networks, and ensures a better consistency with experimental findings. Moreover, our computational results provide additional insights into the relationship between beta cell heterogeneity, their activity profiles, and functional connectivity, supplementing thereby recent experimental results on endocrine networks.

Spatial Tumor Microenvironment Characterization and Outcome of Relapsed/Refractory Classic Hodgkin Lymphoma

INTRODUCTION: Despite recent treatment advances, about half of relapsed or refractory classic Hodgkin lymphoma (r/r CHL) patients succumb to their disease after high dose chemotherapy followed by autologous stem cell transplantation (HDT/ASCT). Our group has previously developed a gene expression based prognostic assay (RHL30) that identifies high-risk r/r CHL patients treated with HDT/ASCT (J Clin Oncol 2017). However, RHL30 does not incorporate important information about cellular interactions, specific expression features of Hodgkin and Reed-Sternberg (HRS) cells and the spatial architecture of the tumor-microenvironment (TME). Here, we aimed to determine spatially resolved TME ecosystems and establish novel biomarkers associated with treatment failure in r/r CHL. METHODS: Using a customized marker panel specific for CHL biology, we performed imaging mass cytometry (IMC) using a tissue microarray containing formalin-fixed paraffin-embedded tissues from 169 CHL tumors, including 73 patients with paired primary and relapse samples, as well as 23 pretreatment diagnostic samples from patients in long-term remission. Segmentation was performed by the Ilastik machine learning package following the Bodenmiller IMC segmentation pipeline to obtain single cell level data. We used the Phenograph clustering algorithm to identify major cell types and functional subsets. For each cell, we calculated a spatial cell enrichment score, called 'spatial score', of a given cell type as the distance to the five nearest neighbor cells, capped at the spatial interaction range (50um). Patients were classified as having early relapse disease if their CHL progressed within 12 months after initial diagnosis. For prognostic model development, we used an empirical Bayesian approach based on LPS (linear prediction score). RESULTS: We obtained highly multiplexed images for a total of 7,146,042 cells that could be broadly clustered into T cell, macrophage, B cell as well as HRS cells using the phenograph tool. We also identified subsets within the HRS cell cluster, such as GATA3-high HRS cells and CXCR5-high HRS cells. We, then, investigated the difference of TME characteristics according to the disease status. Overall, CHL biopsies from early relapse demonstrated shared TME patterns between diagnostic and relapse samples, and were characterized by a lesser extent of CD8+ cells (P < 0.01) as well as enrichment of a myeloid cell population (P < 0.05). In contrast, late relapse samples often demonstrated significant TME changes between diagnostic and relapse biopsies (P < 0.01). Considering the previous finding of the superiority of relapse biopsies for outcome prediction in comparison to pretreatment diagnostic samples in r/r CHL, we again focused our prognostic model development on relapse biopsies. Using LASSO based analyses, four variables, CXCR5+ HRS cells (Hazard Ratio [HR]: 2.86), PD1+ CD4+ T cells (HR: 2.80), macrophage (HR: 1.99), and CXCR5+ B cells (HR: 0.19) were identified as factors that were significantly associated with post-ASCT failure free survival (FFS). Using these 4 variables, we developed a spatial score-based prognostic model (RHL-4S) and compared performance with a classical protein%-based model. The RHL-4S produced a high-risk group of patients with significantly inferior post-ASCT FFS compared with the low-risk group (5-year post-ASCT FFS: high risk, 38% vs low risk, 96%; P < 0.0001, Figure A) as well as inferior post-ASCT overall survival (OS) (5-year post-ASCT OS: high risk, 45% vs low risk, 95%; P < 0.0025). IMC analyses furthermore identified unique spatial architecture defined by CXCR5+ HRS cells. In particular, CXCR5+ HRS cells were spatially arranged together with other HRS cells forming cell clusters as an architectural feature (P < 0.05, Figure B). CXCR5+ HRS cells in these clusters were also characterized by a lower abundance of neighboring non-malignant immune cells, including CD4+ T cells and CD20+ B cells when compared to CXCR5- HRS cells. CONCLUSION We developed a novel prognostic model, RHL-4S, applicable to relapse biopsies of r/r CHL patients who were treated with ASCT. In particular, we have shown the interaction between CXCR5 on HRS cells with ligand-expressing CXCL13+ follicular T helper cells (Aoki et al, PNAS 2021) and macrophages as a prominent crosstalk axis in relapsed disease. This insight opens new avenues to predictive biomarker development. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

Processes affecting size of fish schools in agent‐based model

AbstractFish school size varies with several factors, such as environmental conditions, individual size, time of day, and variations between individuals. In this study, we investigate the mean size of fish schools formed in a simple agent‐based model, wherein each individual swims at a fixed speed with the direction modified by interactions with the neighbors. If alignment (tendency to swim in their neighbors' direction) is stronger than cohesion (tendency to swim toward the neighbors), then “marches” are formed, in which individuals swim in the same direction. If alignment is weaker than cohesion, then “circles” are formed, in which individuals chase one another and the entire group moves minimally. We analyzed various processes that control the shape and mean size of the schools. The school's shape is primarily affected by the magnitude of alignment, cohesion, and individual noises. In contrast, the mean size of the group is affected by several factors, including the spatial interaction range, initial configuration, individual differences in swimming speed, and sudden encounters with predators.

Discovering significant situational profiles of crime occurrence by modeling complex spatial interactions

The joint influence of different facilities plays an important role in understanding situational profiles of crime incidents. While spatial conjunctive analysis of case configurations (CACC) is widely used to explore situational profiles of crime, complex spatial interactions (e.g., spatial autocorrelation of crime incidents, spatial interactions among multiple facilities) have not been fully considered. Drawing on previous environmental criminology research, this study extends the CACC by modeling complex spatial interactions between crime and facilities. First, the spatial interaction range between single facility and crime incidents is quantitatively measured by the cross-type pair-correlation function. Then, the relationship between different situational profiles is modeled, and a “bottom-up” strategy is applied to generate potential situational profiles. Finally, significant situational profiles are selected via Monte Carlo testing by modeling the complex structure of crime incidents. The effectiveness of the proposed approach is evaluated by both a synthetic and real dataset. The experimental result manifests that the proposed approach can effectively eliminate the influence of independent facilities and more accurately identify those significant situation profiles. The discovered significant situational profiles have a positive guiding effect in understanding the spatial context for crime occurrence, thereby facilitating crime prevention.

Extensive nature of long range interactions: role of disorder

The omnipresent disorder in physical systems makes it imperative to investigate its effect on the spatial range of interactions for which system remains thermodynamically extensive. Previously known bounds on the statistical free energy for clean systems [] indicate it to be extensive only for the spatially short range interactions (decaying faster than r−d at large distance r with d as system dimension). We analyze the bounds for quantum systems with different types of disordered many body potentials e.g. annealed, quenched, Gaussian or power law distributed. Our results indicate the dependence of the bounds on the multiple distribution parameters representing the potential which in turn permits, in contrast to clean potentials, more freedom to achieve the extensive limits even for arbitrary spatial ranges of the interactions.

Creeplike behavior in athermal threshold dynamics: Effects of disorder and stress.

We study the dynamical aspects of a statistical-mechanical model for fracture of heterogeneous media: the fiber bundle model with various interaction ranges. Although the model does not include any nontrivial elementary processes such as nonlinear rheology or stochasticity, the system exhibits creeplike behaviors under a constant load being slightly above the critical value. These creeplike behaviors comprise three stages: primary, secondary, and tertiary. In the primary and tertiary stages, the strain rate exhibits power-law behaviors with time, which are well described by the Omori-Utsu and the inverse Omori laws, respectively, although the exponents are larger than those typically observed in experiments. A characteristic time that defines the onset of power-law behavior in the Omori-Utsu law is found to decrease with the strength of disorder in the system. The analytical solution, which agrees with the above numerical results, is obtained for the mean-field limit. Beyond the mean-field limit, the exponent for the Omori-Utsu law tends to be even larger but decreases with the disorder in the system. Increasing the spatial range of interactions, this exponent is found to be independent of disorder and to converge to the mean-field value. In contrast, the inverse Omori law remains independent of the spatial range of interaction and the disorder strength.

Diffusion maps for edge-aware image editing

Edge-aware operations, such as edge-preserving smoothing and edge-aware interpolation, require assessing the degree of similarity between pairs of pixels, typically defined as a simple monotonic function of the Euclidean distance between pixel values in some feature space. In this work we introduce the idea of replacing these Euclidean distances with diffusion distances , which better account for the global distribution of pixels in their feature space. These distances are approximated using diffusion maps : a set of the dominant eigenvectors of a large affinity matrix, which may be computed efficiently by sampling a small number of matrix columns (the Nyström method). We demonstrate the benefits of using diffusion distances in a variety of image editing contexts, and explore the use of diffusion maps as a tool for facilitating the creation of complex selection masks. Finally, we present a new analysis that establishes a connection between the spatial interaction range between two pixels, and the number of samples necessary for accurate Nyström approximations.

Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via power-law coupling is considered. Furthermore, each unit in the one-dimensional chain is linked to the corresponding one in the replica via a local coupling. The synchronization transition is studied as a nonequilibrium phase transition, and its critical properties are analyzed at varying the spatial interaction range as well as the nonlinearity of the dynamical units composing each system. In particular, continuous and discontinuous local maps are considered. In both cases the transitions are of the second order with critical indices varying with the exponent characterizing the interaction range. For discontinuous maps it is numerically shown that the transition belongs to the anomalous directed percolation (ADP) family of universality classes, previously identified for Lévy-flight spreading of epidemic processes. For continuous maps, the critical exponents are different from those characterizing ADP, but apart from the nearest-neighbor case, the identification of the corresponding universality classes remains an open problem. Finally, to test the influence of deterministic correlations for the studied synchronization transitions, the chaotic dynamical evolutions are substituted by suitable stochastic models. In this framework and for the discontinuous case, it is possible to derive an effective Langevin description that corresponds to that proposed for ADP.

Invasion and adaptive evolution for individual-based spatially structured populations

The interplay between space and evolution is an important issue in population dynamics, that is particularly crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution are closely related. Here, we model the interplay between space and evolution starting with an individual-based approach and show the important role of parameter scalings on clustering and invasion. We consider a stochastic discrete model with birth, death, competition, mutation and spatial diffusion, where all the parameters may depend both on the position and on the phenotypic trait of individuals. The spatial motion is driven by a reflected diffusion in a bounded domain. The interaction is modelled as a trait competition between individuals within a given spatial interaction range. First, we give an algorithmic construction of the process. Next, we obtain large population approximations, as weak solutions of nonlinear reaction-diffusion equations. As the spatial interaction range is fixed, the nonlinearity is nonlocal. Then, we make the interaction range decrease to zero and prove the convergence to spatially localized nonlinear reaction-diffusion equations. Finally, a discussion of three concrete examples is proposed, based on simulations of the microscopic individual-based model. These examples illustrate the strong effects of the spatial interaction range on the emergence of spatial and phenotypic diversity (clustering and polymorphism) and on the interplay between invasion and evolution. The simulations focus on the qualitative differences between local and nonlocal interactions.

Growing networks under geographical constraints

Inspired by the structure of technological weblike systems, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, we suggest that the peculiar structure of transport and distribution networks is fundamentally determined by two factors. These are the dependence of the spatial interaction range of vertices on the vertex attractiveness (or importance within the network) and on the inhomogeneous distribution of vertices in space. We propose and analyze numerically a simple model based on these generating mechanisms which seems, for instance, to be able to reproduce known structural features of the Internet.

Cooperation among Microorganisms

Cooperation among Microorganisms

Space-time contraction and the dynamics of urban systems

An attempt is made to identify the dynamics of urban systems during the historical process of their evolution. An illustration is made with the case of European cities between 1200 and 1990, using harmonised historical data bases. First off, simple maps show a general expansion in cities number and size of cities over time, reflecting the ability of the system to continuously adapt its structure over time. A second trend is an increased hierarchisation in city size, which may be related to the continuous improvement in the speed and capacity of transportation means. Because of this space-time contraction, large cities short-circuit small towns, and inequalities in city size are widening. A third trend leading to a spatial reorganisation, emerges from maps of the urban population potentials. Among all possible mathematical equations and parameters values which could describe the intensity and the spatial range of interactions between cities, we choose those which give rather stable results and which are compatible with the analysis of urban historians, such as De Vries, Braudel, Bairoch, Hohenberg and Lees, for the centuries preceding the industrial revolution, by using evaluations of distances in terms of time and cost. Urban systems dynamics is better approached with reference to this relative space than on usual topographic maps.

The effects of surround contrast on contrast thresholds, perceived contrast and contrast discrimination.

Perceived contrast, contrast detection thresholds and contrast discrimination thresholds were measured in the presence and absence of surrounding patterns of a similar spatio-temporal makeup. In the foveal retina we found that the perceived contrast of the central pattern was reduced by the presence of the contrast surrounds with the effect being greatest at low test contrast. Detection thresholds were not affected and contrast discrimination thresholds were only affected over a small range of low test contrasts. However if the test pattern was made smaller, or if its central part was occluded detection thresholds were raised. In the peripheral retina detection thresholds were raised and discrimination thresholds were affected over most of the range of contrasts. We argue that the pattern of results resembles those produced in masking paradigms where the test and mask are coextensive if the spatial range of interactions is taken into account and hence the effects of the contrast surround may be merely a manifestation of normal masking processes.

Integral equation theory of block copolymer liquids. I. General formalism and analytic predictions for symmetric copolymers

The equilibrium properties of block copolymer liquids are studied using liquid state theory. We first present the formal extension of the polymer reference interaction site model theory to treat block copolymers of general architectures, and then apply this to the symmetric block copolymer using the Gaussian thread model. Contact with Leibler mean field theory is made by employing the ‘‘reference molecular mean spherical approximation’’ closure within the thread idealization. A host of density and concentration fluctuation effects are studied using the ‘‘reference molecular Percus–Yevick’’ closure. In particular, the dependence of the effective chi-parameter and peak scattering intensity on density, chain length, temperature, composition, and spatial range of interactions is examined. Within the thread-polymer/effective incompressibility assumption the chain length dependence of the fluctuation stabilization in the vicinity of the mean field spinodal is found to be the same as in the Brazovskii–Fredrickson–Helfand theory. However, a rich dependence on the nonuniversal prefactors, and the enthalpic origin of the feedback mechanism, distinguishes these results from previous field theoretic work.