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Collective behavior spans several orders of magnitudes of biological organization, ranging from cell colonies, to flocks of birds, to herds of wildebeests. In this work, we investigate collective motion of glioblastoma cells in an ex-vivo experimental model of malignant brain tumors. Using time-resolved tracking of individual glioma cells, we observed collective motion characterized by weak polarization in the (directional) velocities of single cells, with fluctuations correlated over many cell lengths. The correlation length of these fluctuations scales approximately linearly with the total population size, and these scale-free correlations suggest that the system is poised near a critical point. To further investigate the source of this scale-free behavior, we used a data-driven maximum entropy model to estimate the effective length scale (nc) and strength (J) of local interactions between tumor cells. The model captures statistical features of the experimental data, including the shape of the velocity distributions and the existence of long range correlations, and suggests that nc and J vary substantially across different populations. However, the scale and strength of the interactions do not vary randomly, but instead occur on the boundary separating ordered and disordered motion, where the model exhibits classical signs of criticality, including divergences in generalized susceptibility and heat capacity. Our results suggest that brain tumor assemblies are poised near a critical point characterized by scale-free correlations in the absence of strong polarization.

We prove the asymptotic flocking behavior of a general model of swarming dynamics. The model describing interacting particles encompasses three types of behavior: repulsion, alignment and attraction. We refer to this dynamics as the three-zone model. Our result expands the analysis of the so-called Cucker-Smale model where only alignment rule is taken into account. Whereas in the Cucker-Smale model, the alignment should be strong enough at long distance to ensure flocking behavior, here we only require that the attraction is described by a confinement potential. The key for the proof is to use that the dynamics is dissipative thanks to the alignment term which plays the role of a friction term. Several numerical examples illustrate the result and we also extend the proof for the kinetic equation associated with the three-zone dynamics.

We study two agent based models of opinion formation—one stochastic in nature and one deterministic. Both models are defined in terms of an underlying graph; we study how the structure of the graph affects the long time behavior of the models in all possible cases of graph topology. We are especially interested in the emergence of a consensus among the agents and provide a condition on the graph that is necessary and sufficient for convergence to a consensus in both models. This investigation reveals several contrasts between the models—notably the convergence rates—which are explored through analytical arguments and several numerical experiments.

Tumor mesenchymal transformation (MT) is a hallmark of high-grade gliomas. The mesenchymal state is associated with specific changes related to cell adhesion, migration, and the extracellular matrix. Collagen 1a1 (COL1A1) is a main component of the extracellular matrix in gliomas, and its expression correlates inversely with patient survival. However, the cellular and molecular mechanisms of the tumor-associated COL1A1 matrix in gliomas remains elusive. Our study integrates histopathological features, spatially resolved transcriptomics, cellular dynamics and microenvironment alterations associated with MT in high-grade gliomas. Using deep learning analysis of mouse and human glioma histological samples we identified that the density of areas of MT, named oncostreams, correlates with tumor aggressiveness. Spatial transcriptomics analysis, using laser capture microdissection, identified a signature enriched in extracellular matrix related proteins, in which COL1A1 appeared as a key determinant of mesenchymal organization. Correspondingly, human and mouse high-grade gliomas showed prominent alignment of collagen fibers along these mesenchymal fascicles and higher COL1A1 expression compared to low-grade gliomas. Moreover, RNA fluorescent multiplex assays identified at single cell level that different cells within glioma tumors contribute to COL1A1 expression, including neoplastic cells and perivascular non-neoplastic cells such as ACTA2+, CYR61+ and FAP+. Inhibition of COL1A1 using genetically engineered mouse models decreased areas of mesenchymal transformation and increased survival. COL1A1 downregulation impaired tumor cell proliferation and remodeled the tumor microenvironment by reducing CD68+ macrophages/microglia cells, CD31+ endothelial cells, ACTA2+, CYR61+ and FAP+ perivascular cells, and increased GFAP+ astrocytes infiltration withing the tumor mass. Further studies, using ex-vivo glioma explants demonstrated that CO1A1 downregulation decreased collective invasion of the normal brain, supporting its importance in tumor progression. We propose that COL1A1 expression is a valuable marker for diagnosis, and COL1A1 depletion within glioma tumors is a promising direct or complementary therapeutic approach to reprogram mesenchymal transformation, and halt tumor growth.

Intra-tumoral heterogeneity and diffuse infiltration are hallmarks of glioblastoma that challenge treatment efficacy. However, the mechanisms that set up both tumor heterogeneity and invasion remain poorly understood. Herein, we present a comprehensive spatiotemporal study that aligns distinctive intra-tumoral histopathological structures, oncostreams, with dynamic properties and a unique, actionable, spatial transcriptomic signature. Oncostreams are dynamic multicellular fascicles of spindle-like and aligned cells with mesenchymal properties, detected using ex vivo explants and in vivo intravital imaging. Their density correlates with tumor aggressiveness in genetically engineered mouse glioma models, and high-grade human gliomas. Oncostreams facilitate the intra-tumoral distribution of tumoral and non-tumoral cells, and the invasion of the normal brain. These fascicles are defined by a specific molecular signature that regulates their organization and function. Oncostreams structure and function depend on overexpression of COL1A1. COL1A1 is a central gene in the dynamic organization of glioma mesenchymal transformation, and a powerful regulator of glioma malignant behavior. Inhibition of COL1A1 eliminated oncostreams, reprogramed the malignant histopathological phenotype, reduced expression of the mesenchymal associated genes, induced changes in the tumor microenvironment and prolonged animal survival. Oncostreams represent a novel pathological marker of potential value for diagnosis, prognosis, and treatment.

Glioblastomas multiforme (GBMs) are the most lethal tumors of the brain. Tumoral mesenchymal transformation is a hallmark of GBMs associated with alterations in cellular morphology and dynamic organization. However, little is known about the mechanisms that control this pathological process. Here, we report a comprehensive spatiotemporal study integrating novel intra-tumoral histopathological structures, ‘oncostreams’, with tumor dynamic properties, microenvironment assets and spatial molecular features. Cellular analyses of genetic engineered mouse models of glioma identified that oncostreams are heterogenous structures formed by elongated and aligned neoplastic cells enriched in non-neoplastic cells such as ACTA2+ mesenchymal like cells and CD68+ tumor associated microglia/macrophages (TAM). Deep learning analysis of H&E glioma histological samples from mouse and human gliomas identified that oncostream density correlates with tumor aggressiveness. To determine whether oncostreams fascicles are characterized by a specific gene expression profile, we performed transcriptomic analysis using laser capture microdissection coupled to RNA-sequencing. We found that oncostreams are defined by a transcriptomic signature enriched in mesenchymal genes. Network analyses identified that COL1A1 is a critical gene that regulates oncostream organization and function. Correspondingly, human and mouse high-grade gliomas with high oncostream densities showed prominent alignment of collagen fibers along these fascicles and higher COL1A1 expression compared to low-grade gliomas. To evaluate the functional role of COL1A1 in oncostream formation we generated a COL1A1-deficient GEMM of glioma. We observed that COL1A1 inhibition decreased oncostream formation, impaired tumor cell proliferation and remodeled the tumor microenvironment by diminishing CD68+ TAM cells, CD31+ endothelial vascular proliferation and ACTA2+ perivascular mesenchymal cells, thus increasing animal survival. Further studies, using time lapse confocal imaging in ex vivo glioma explants, and intravital imaging in vivo demonstrated that oncostreams are organized collective dynamic structures present at the tumor core and the invasive tumor border. Oncostreams dynamics increased the intra-tumoral spread of cells within the tumor and foster glioma aggressiveness through collective invasion of the normal brain parenchyma. The analysis of glioma invasion in COL1A1 knockdown tumors exhibited a reduction in collective migration patterns, strongly supporting its importance in tumor progression. We propose that oncostreams represent a novel pathological marker of potential value for diagnosis and COL1A1 depletion within oncostreams is a promising approach and reprogram mesenchymal transformation to reduce the tumor malignancy. Citation Format: Andrea Comba, Syed Faisal, Patrick J. Dunn, Anna E. Argento, Todd C. Hollon, Wajd N. Al-Holou, Maria L. Varela, Daniel B. Zamler, Gunnar L. Quass, Pierre F. Apostolides, Christine E. Brown, Phillip E. E. Kish, Alon Kahana, Celina G. Kleer, Sebastien Motsch, Maria G. Castro, Pedro R. Lowenstein. Spatiotemporal analyses of preclinical glioma models reveal ‘oncostreams’ as dynamic fascicles regulating tumor mesenchymal transformation, invasion, and malignancy [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2476.

The Vicsek model is a prototype for the emergence of collective motion. In free space, it is characterized by a swarm of particles all moving in the same direction. Since this dynamic does not include attraction among particles, the swarm, while aligning in velocity space, has no spatial coherence. Adding specular reflection at the boundaries generates global spatial coherence of the swarms while maintaining its velocity alignment. We investigate numerically how the geometry of the domain influences the Vicsek model using three type of geometry: a channel, a disk and a rectangle. Varying the parameters of the Vicsek model (e.g. noise levels and influence horizons), we discuss the mechanisms that generate spatial coherence and show how they create new dynamical solutions of the swarming motions in these geometries. Several observables are introduced to characterize the simulated patterns (e.g. mass profile, center of mass, connectivity of the swarm).

A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining feature of these dynamics, which we name the No one left behind dynamics, is the introduction of a local control on the agents which preserves the connectivity of the interaction network. We rigorously demonstrate that these dynamics result in unconditional convergence to a consensus. The qualitative nature of our argument prevents us quantifying how fast a consensus emerges, however we present numerical evidence that sharp convergence rates would be challenging to obtain for such dynamics. Finally, we propose a relaxed version of the control. The dynamics that result maintain many of the qualitative features of the bounded confidence dynamics yet ultimately still converge to a consensus as the control still maintains connectivity of the interaction network.

Efficient transportation is crucial for urban mobility, cell function and the survival of animal groups. From humans driving on the highway, to ants running on a trail, the main challenge faced by all collective systems is how to prevent traffic jams in crowded environments. Here, we show that ants, despite their behavioral simplicity, have managed the tour de force of avoiding the formation of traffic jams at high density. At the macroscopic level, we demonstrated that ant traffic is best described by a two-phase flow function. At low densities there is a clear linear relationship between ant density and the flow, while at large density, the flow remains constant and no congestion occurs. From a microscopic perspective, the individual tracking of ants under varying densities revealed that ants adjust their speed and avoid time consuming interactions at large densities. Our results point to strategies by which ant colonies solve the main challenge of transportation by self-regulating their behavior., eLife digest Humans and ants are among the few species that engage in two-way traffic. Maintaining a smooth and efficient traffic flow while avoiding collisions is challenging for humans. Yet ants seem to be masters of traffic management. They can efficiently move back and forth between their nests and food without overtaking or passing each other, forming a steady stream of traffic. Few studies have looked at how ants maintain such a smooth flow even as the number of ants on a path increases. Now, Poissonnier, Motsch et al. have designed an experiment to investigate whether ants can maintain their steady stream of traffic when their path to food gets more crowded. This involved manipulating the density of ants using a combination of different sized colonies (ranging from 400 to 25,600 Argentine ants) and changing the width of the bridge connecting the ants to their source of food. The experiment was repeated 170 times, and data was collected on traffic flow, speed of the ants, and number of collisions. For pedestrians and car traffic, the flow of movement will slow down if occupancy levels reach over 40%. Whereas in ants, the flow of traffic showed no signs of declining even when bridge occupancy reached 80%. The experiments revealed that ants do this by adjusting their behavior to their circumstances. They speed up at intermediate densities, avoid collisions at large densities, and avoid entering overcrowded trails. Studying ant traffic management has been a source of inspiration for scientists working with large groups of interacting particles in many fields. This includes molecular biology, statistical physics, and telecommunications. It may also have relevance for managing human traffic, particularly as scientists develop autonomous vehicles that might be programmed to work together cooperatively as ants do.

In this paper, we are interested in studying self-alignment mechanisms described as jump processes. In the dynamics proposed, active particles are moving at a constant speed and align with their neighbors at random times following a Poisson process. This dynamics can be viewed as an asynchronous version of the so-called Vicsek model. Starting from this particle dynamics, we introduce the related kinetic description and then derive a continuum hydrodynamic model. We then introduce different discretization strategies for the hierarchy of proposed models, we numerically study the convergence of the schemes and compare the behaviors of the different systems for several test cases.

Intratumoral heterogeneity is a hallmark of high grade gliomas. However, whether heterogeneity is static or dynamic remains unknown. Here we demonstrate that gliomas’ core and border regions display areas of self-organized collective motion, which we have termed oncostreams. Histologically oncostreams appear as multicellular fascicles of elongated and aligned glioma cells with mesenchymal-like morphology, and their density correlates positively with tumor malignant behavior. Using time lapse confocal imaging of organotypic brain slices of experimental glioma we discovered oncostream dynamics, namely, as two self-organizing patterns of collective motion: streams (bidirectional motion) and flocks (unidirectional motion). Oncostreams were also present in human glioblastoma multiforme, and could also be detected using objective artificial indigent approaches. They were present in 47% of TCGA-GBM grade IV tumor tissues, in 8.6 % of TCGA-LGG grade III, and were absent in TCGA-LGG grade II. Oncostreams are heterogeneous, contain GFAP+ cells, Iba1+ microglia/macrophages cells, and ACTA2+ mesenchymal cells aligned along Sox2+ tumor cells. We propose that oncostreams function as highways possibly stimulating the spread of slower-moving glioma cells and/or non-tumor cells throughout the tumor mass, reinforcing a potential role of oncostreams in determining spatial heterogeneity and remodeling of the tumor microenvironment. To analyze the molecular landscape of oncostreams we used laser capture microdissection coupled to RNA-Seq and bioinformatics analysis: we detected the existence of genetic networks specific to oncostreams. Oncostreams were aligned along highly expressed extracellular matrix proteins, among them Col1a1 was the most differentially expressed. Genetic inhibition of Col1a1 dissembled oncostreams, decreased glioma heterogeneity and improved animal survival. We propose that oncostreams dynamics will be a promising avenue to understand glioma behavior, and treat these malignant tumors. Citation Format: Andrea Comba, Sebastien Motsch, Patrick Dunn, Todd Hollon, Daniel Zamler, Anna Argento, Alon Kahana, Phillip Kish, Maria Castro, Pedro Lowenstein. The dynamic tumor microenvironment: Oncostreams are self-organizing structures that modulate glioma progression and treatment [abstract]. In: Proceedings of the AACR Virtual Special Conference on the Evolving Tumor Microenvironment in Cancer Progression: Mechanisms and Emerging Therapeutic Opportunities; in association with the Tumor Microenvironment (TME) Working Group; 2021 Jan 11-12. Philadelphia (PA): AACR; Cancer Res 2021;81(5 Suppl):Abstract nr PR005.

Glioblastoma multiforme (GBM) is the most frequent and lethal tumor of the central nervous system. GBM are characterized by diffuse invasion and cellular heterogeneity which challenges treatment efficacy. Tumors with mesenchymal properties display the most aggressive phenotype. However, the biological function and molecular mechanisms underlying GBM mesenchymal transformation remain unknown. Analysis of mouse and human malignant gliomas revealed the presence of organized multicellular structures formed by elongated and aligned cells. These structures resemble areas of GBM mesenchymal transformation that we named Oncostreams. We determined the molecular signature underlying oncostreams function by performing laser capture microdissection followed by transcriptomic analysis. We found that oncostreams overexpressed Col1a1, ACTA2, MMP9, MMP10 and ADAMTS2 genes, all of them associated with regulation of extracellular matrix organization, collagen catabolic process and cellular migration pathways. Functional network analysis indicated that Col1a1 was a primary regulator gene. To analyze whether these structures display migratory properties we used time lapse imagining in a 3D organotypic glioma model. Morphological and statistical analysis revealed that oncostreams displayed a collective motion pattern, organized as streams or flocks. This dynamic patterns participate in local invasion and function as tumoral highways to facilitate the spread of several cells as intra-. Further analysis showed that oncostreams presence correlates with increased collagen expression and decreased animal survival. Patient's glioma biopsies also evidenced that these areas of Col1a1 overexpression were present in high grade but no in low-grade gliomas. We corroborated by immune-hystochemistry that Col1a1 were overexpressed and co-localized within GFP positive tumoral cells. Further, to analyze the origin and role of Col1a1 in glioma malignancy we generated genetically engineered mouse glioma models (GEMM) with Col1a1 downregulation. Interestingly, Col1a1 was retained only surrounding the blood vessel but was completed absent within the tumor parenchyma. We demonstrated that Col1a1 downregulation ablates oncostreams structures, reversed the malignant phenotype resembling low grade glioma histopathology and prolonged animal survival. This study reveals that oncostreams are organized dynamic structures that regulate glioma growth and invasion. They are areas of mesenchymal transformation defined by a molecular signature associated to extracellular matrix proteins expressed as Col1a1. Oncostreams with high expression of Col1a1 within glioma cells represent a novel potential targets for future translational development. Disruption of oncostreams will provide a new avenue to treat GBM. Citation Format: Andrea Comba, Patrick Dunn, Anna E. Argento, Padma Kadiyala, Sebastien Motsch, Daniel Zamler, Alon Kahana, Phillips E. Kish, Maria G. Castro, Pedro R. Lowenstein. Spatiotemporal analysis of gliomas: Dynamics of mesenchymal multicellular structures as novel target for tumor treatment [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 3950.

Self-organization is a ubiquitous phenomenon in nature which can be observed in a variety of different contexts and scales, with examples ranging from schools of fish, swarms of birds or locusts to flocks of bacteria. The observation of such global patterns can often be reproduced in models based on simple interactions between neighboring particles. In this paper we focus on two particular interaction dynamics closely related to the one described in the seminal paper of Vicsek and collaborators. After reviewing the current state of the art in the subject, we study a numerical scheme for the kinetic equation associated with the Vicsek models which has the specificity of reproducing many physical properties of the continuous models, like the preservation of energy and positivity and the diminution of an entropy functional. We describe a stable pattern of bands emerging in the dynamics proposed by Degond–Frouvelle–Liu dynamics and give some insights about their formation.

In this paper we present the first numerical method for a kinetic description of the Vicsek swarming model. The kinetic model poses a unique challenge, as there is a distribution dependent collision invariant to satisfy when computing the interaction term. We use a spectral representation linked with a discrete constrained optimization to compute these interactions. To test the numerical scheme we investigate the kinetic model at different scales and compare the solution with the microscopic and macroscopic descriptions of the Vicsek model. We observe that the kinetic model captures key features such as vortex formation and traveling waves.

International audience; Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying real-time crowd optimization strategies.

Whether tumors in general and gliomas in particular are self-organized has not been determined. Brain tumor self-organization would be revealed through individual recognizable structures. Here we demonstrate that brain tumors are indeed self-organized. Brain tumor self-organization is evidenced by the existence of oncostreams, multicellular structures composed of elongated glioma cells. Oncostream structure, function and molecular makeup was studied in several glioma models. In experimental mouse models, and in human GBM tumors, oncostreams were demarcated anatomically as multicellular arrangements of fusiform cells, 10–20 cells wide, of various lengths and distributed throughout the tumors. Using genetically engineered glioma models we found a negative correlation between oncostream density and survival, suggesting that oncostreams contribute to tumor aggressiveness. As oncostreams also reached tumor borders, it is likely that they participate in glioma invasion. Further, by placing slow moving glioma stem cells into oncostreams we detected that these function as streams that distribute glioma cells throughout the tumors. Importantly, we performed the molecular analysis of oncostreams using a Laser Microdissection Microscope to dissect oncostreams from surrounding tumor. The transcriptome landscape was analyzed by next generation sequencing using RNA-Seq and advanced bioinformatics algorithms. The molecular analysis showed that oncostreams are defined by a distinctive transcriptome landscape. We hereby show that oncostreams: (i) are anatomically discrete structures that reveal the existence of glioma self-organization, (ii) are functionally unique as they regulate glioma growth, invasion and spread, and (iii) molecularly distinct, their genetic landscape and associated gene networks differentiate oncostreams from surrounding glioma. Understanding glioma self-organization and its molecular basis will contribute to uncover novel targets for future translational development.

Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of a & “crowd forecasting system„whereby real-time observations of crowds are coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying real-time crowd optimization strategies.

International audience; In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view of its possible extensions to other kinds of collective motion.

In this review, we present an example of a system of collectively moving agents which exhibit spontaneous self-organization: this example consist of a model of ant-trail formation. We use this example to illustrate what are the challenges in the mathematical modeling of these systems and to outline some possible methodological tracks.

Mesenchymal gliomas are the most aggressive tumors that carry the worst prognosis. The origins of mesenchymal cells within brain tumors, remains poorly understood. They could originate either from invading mesenchymal cells, from perivascular smooth muscle actin+ cells, or from a mesenchymal transformation of tumor cells. Identifying the origin and function of mesenchymal cells within gliomas is essential as these cells contribute to increased glioma aggressiveness and tumor progression. In this study we used human biopsies and implantable and genetically engineered mouse models (GEMM) of GBM to study tumor mesenchymal transformation. GBM implantable models were used to analyze the molecular landscape by laser microdissection followed by RNA-Seq and bioinformatics analysis. Time lapse confocal imagining was implemented to analyze GBM cells dynamics. Our results indicate the existence of a complex intratumoral and peritumoral dynamic organization of glioma cells (i.e., Oncostreams). Multicellular structures of elongated cells compatible with mesenchymal differentiation. These structures play important roles in intratumoral movements, peritumoral invasion of normal brain, and overall glioma progression. We also show that oncostreams are molecularly distinct and display increased expression of mesenchymal genes such as Col1a1. Knocking down of Col1a1 in a GEMM of aggressive gliomas reduced tumor progression and significantly increased animal survival. Histological examination confirmed absence of Col1a1, and absence of morphologically identifiable oncostreams. Our results show that tumor cells, especially within oncostreams, display a fibroblastic-like morphology and express proteins typical of mesenchymal cells. The knockout of Col1a1 from tumoral cells eliminated oncostreams from tumors and delayed tumor progression. These data suggest that tumor cells expressing mesenchymal genes regulate the organization of mesenchymal multicellular structures, and determine glioma progression. We propose that inhibiting mesenchymal transformation of glioma cells will assist in the treatment of glioblastoma.

We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or “agents,” with the tendency to adjust to their “environmental averages.” This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, rendezvous in mobile networks, etc. A natural question which arises in this context is to ask when and how clusters emerge through the self-alignment of agents, and what types of “rules of engagement” influence the formation of such clusters. Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking of birds, fish, or cells, rendezvous of mobile agents, and, in general, concentration of other traits intrinsic to the dynamics. Many standard models for self-organized dynamics in social, biological, and physical sciences assume that the intensity of alignment in...

We investigate the large time behavior of an agent based model describing tumor growth. The microscopic model combines short-range repulsion and cell division. As the number of cells increases exponentially in time, the microscopic model is challenging in terms of computational time. To overcome this problem, we aim at deriving the associated macroscopic dynamics leading here to a porous media type equation. As we are interested in the long time behavior of the dynamics, the macroscopic equation obtained through usual derivation method fails at providing the correct qualitative behavior (e.g. stationary states differ from the microscopic dynamics). We propose a modified version of the macroscopic equation introducing a density threshold for the repulsion. We numerically validate the new formulation by comparing the solutions of the micro- and macro- dynamics. Moreover, we study the asymptotic behavior of the dynamics as the repulsion between cells becomes singular (leading to non-overlapping constraints in the microscopic model). We manage to show formally that such asymptotic limit leads to a Hele-Shaw type problem for the macroscopic dynamics. We compare the micro- and macro- dynamics in this asymptotic limit using explicit solutions of the Hele-Shaw problem (e.g. radially symmetric configuration). The numerical simulations reveal an excellent agreement between the two descriptions, validating the formal derivation of the macroscopic model. The macroscopic model derived in this paper therefore enables to overcome the problem of large computational time raised by the microscopic model, but stays closely linked to the microscopic dynamics.

The Vicsek model is a very popular individual based model which describes collective behavior among animal societies. A large-scale limit of the Vicsek model has been derived in [Math. Models Methods Appl. Sci., 18 (2008), pp. 1193–1215], leading to a macroscopic version of the model. In this work, we want to numerically validate this macroscopic Vicsek (MV) model. However, there is no standard theory to study analytically or numerically the MV model since it is a nonconservative hyperbolic system with a geometric constraint. Different formulations of the MV model are presented and lead to several nonequivalent numerical schemes. In particular, we derive a numerical scheme, denoted by the splitting method, based on a relaxation of the geometric constraint. To test the veracity of these schemes, we compare the simulations of the macroscopic and microscopic models with each other. The numerical simulations reveal that the microscopic and macroscopic models are in good agreement, provided that we use the spl...

OBJECTIVES/SPECIFIC AIMS: Oncostreams represent a novel growth pattern of GBM. In this study we uncovered the cellular and molecular mechanism that regulates the oncostreams function in GBM growth and invasion. METHODS/STUDY POPULATION: We studied oncostreams organization and function using genetically engineered mouse gliomas models (GEMM), mouse primary patient derived GBM model and human glioma biopsies. We evaluated the molecular landscape of oncostreams by laser capture microdissection (LCM) followed by RNA-Sequencing and bioinformatics analysis. RESULTS/ANTICIPATED RESULTS: Oncostreams are multicellular structures of 10-20 cells wide and 2-400 μm long. They are distributed throughout the tumors in mouse and human GBM. Oncostreams are heterogeneous structures positive for GFAP, Nestin, Olig2 and Iba1 cells and negative for Neurofilament. Using GEMM we found a negative correlation between oncostream density and animal survival. Moreover, examination of patient’s glioma biopsies evidenced that oncostreams are present in high grade but no in low grade gliomas. This suggests that oncostreams may play a role in tumor malignancy. Our data also indicated that oncostreams aid local invasion of normal brain. Transcriptome analysis of oncostreams revealed 43 differentially expressed (DE) genes. Functional enrichment analysis of DE genes showed that “collagen catabolic processes”, “positive regulation of cell migration”, and “extracellular matrix organization” were the most over-represented GO biological process. Network analysis indicated that Col1a1, ACTA2, MMP9 and MMP10 are primary target genes. These genes were also overexpressed in more malignant tumors (WT-IDH) compared to the less malignant (IDH1- R132H) tumors. Confocal time lapse imagining of 3D tumor slices demonstrated that oncostreams display a collective motion pattern within gliomas that has not been seen before. DISCUSSION/SIGNIFICANCE OF IMPACT: In summary, oncostreams are anatomically and molecularly distinctive, regulate glioma growth and invasion, display collective motion and are regulated by the extracellular matrix. We propose oncostreams as novel pathological markers valuable for diagnosis, prognosis and designing therapeutics for GBM patients.

GBM remains the deadliest primary malignant brain tumor. Given the importance of invading cells, less attention has been paid to the tumor mass, even if such a mass eventually kills the patient. We previously demonstrated that human and mouse transplantable or GEMM gliomas display regular anatomical multicellular structures containing elongated cells which we named ‘oncostreams’. Oncostreams are 10–20 cells wide, 2–400 um long, and are distributed throughout the tumors. Furthermore, we uncovered a negative correlation between oncostream density and animal survival suggesting that oncostreams play a role in tumor malignancy. Further data indicate that oncostreams aid local invasion of normal brain. Co-implantation experiments demonstrated that oncostreams facilitate the intratumoral spread of slow migrating cells. To determine a possible molecular distinctiveness of oncostreams we used laser capture microdissection followed by RNA-Seq, bioinformatics and network analysis. Evaluation of the transcriptome demonstrated differential expression (DE) of genes between oncostreams and adjacent tumor. Functional enrichment of DE genes showed that “collagen catabolic processes”, “positive regulation of cell migration”, and “extracellular matrix organization” were the most over-represented gene ontologies. Network analysis indicated that Col1a1, ACTA2, MMP9, MMP10 and ADAMTS2, genes important for cell migration and ECM interactions, are part of these networks. IHC and PCR were used to validate RNA-Seq expression changes. To understand the cellular dynamics in our system we used time lapse imagining and evaluated the results using high level statistical analyses. The following tests, i.e., velocity distribution, pair-wise correlation of local position, velocity correlation, etc. were used to characterize the dynamics of cellular intratumoral motility. These data demonstrate the existence of collective motion within glioma tumors. Taken together, our results show that oncostreams, move by collective motion, are anatomically and molecularly distinct, reveal the existence of glioma self-organization, and regulate glioma growth and invasion. Targeting oncostreams is a candidate therapeutic strategy.

GBM (WHO IV) histological structures used in glioma diagnosis are pseudopalisades, microvascular proliferation, and necrosis. To these we can add Scherer's structures: the perivascular, perineuronal, white matter, and subpial growth of glioma cells. Though CXCL12 is important in the organization of Scherer's structures, the molecular and cellular basis of the other histopathological structures is not fully understood. To determine the large scale organization of gliomas we studied various models, including transplantable gliomas (mouse, human glioma stem cells), and genetically induced gliomas using the Sleeping Beauty Transposase system (NRas, LgT, sh-p53, PDGF, sh-ATRX, IDH1mut). Examination of all glioma models indicates the existence of streams, a hallmark of self-organization. Streams are 10-20 cells across, of various lengths, and distributed throughout the tumors. Within streams cells are fusiform and at the tumor border participate in glioma invasion. Streams can be understood mathematically using models from statistical mechanics. Experimentally, streams facilitated the migration of slower migrating glioma stem cells. We propose that streams accelerate glioma growth; inhibiting stream formation may be beneficial therapeutically. We also detected the presence of vortices in which cells appear as if rotating around a central axis. Vortices were found in murine transplantable models and in genetically induced gliomas -independently of individual genetic mutations-. Vortices can be studied mathematically using the theories of fluid dynamics. We propose that vortices are cores of glioma stem cells that nucleate brain tumor growth around them. Disrupting vortex formation could also lead to novel therapies. Our work demonstrates that gliomas display large scale, non-random, self-organization. We show the existence of novel histopathological structures in glioblastoma, and their potential role in glioma growth and invasion. We are currently working to understand their cellular, molecular, and mathematical basis as this will make them into novel so far unknown therapeutic targets.

International audience; We present a macroscopic model for pedestrian dynamics in a corridor (or in any quasi one-dimensional system). The model is inspired from the Aw-Rascle model of car traffic but here, a two-directional flow is considered: in each point, two densities are defined, for left and right going pedestrians. The challenge is to bound the density even under congestion. This is enforced by a pressure term, modeling the interactions between pedestrians, that diverges when the density approaches the maximal density. The intensity of the divergence is controlled by a small parameter epsilon. In the limit where epsilon tends to zero, the system exhibits coexisting congested and uncongested phases separated by sharp interfaces.The lateral extension of the corridor can be taken into account through a multi-lane model, with appropriate lane changes. A characteristic of two-way models is that they can loose their hyperbolicity in some cases. Actually, this could be the counterpart of phenomena observed in real crowds, namely the instability of homogeneous flows towards lane-formation, or even crowd turbulence as observed at very high crowd densities.

International audience; This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. The starting point is the kinetic model considered in earlier work of Degond & Motsch with the addition of an attraction-repulsion interaction potential. Introducing different scalings than in Degond & Motsch, the non-local effects of the alignment and attraction-repulsion interactions can be kept in the hydrodynamic limit and result in extra pressure, viscosity terms and capillary force. The systems are shown to be symmetrizable hyperbolic systems with viscosity terms. A local-in-time existence result is proved in the 2D case for the viscous model and in the 3D case for the inviscid model. The proof relies on the energy method.

We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the influence between agents is scaled in term of their relative distance. Consequently, our model does not involve any explicit dependence on the number of agents; only their geometry in phase space is taken into account. The use of relative distances destroys the symmetry property of the original C-S model, which was the key for the various recent studies of C-S flocking behavior. To this end, we introduce here a new framework to analyze the phenomenon of flocking for a rather general class of dynamical systems, which covers systems with non-symmetric influence matrices. In particular, we analyze the flocking behavior of the proposed model as well as other strongly asymmetric models with "leaders". The methodology presented in this paper, based on the notion of active sets, carries over from the particle to kinetic and hydrodynamic descriptions. In particular, we discuss the hydrodynamic formulation of our proposed model, and prove its unconditional flocking for slowly decaying influence functions.

International audience; We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromones and interact with them through alignment interaction. The directed pheromones intend to model pieces of trails, while the alignment interaction translates the tendency for an ant to follow a trail when it meets it. Thanks to adequate quantitative descriptors of the trail patterns, the existence of a phase transition as the ant-pheromone interaction frequency is increased can be evidenced. Finally, we propose both kinetic and fluid descriptions of this model and analyze the capabilities of the fluid model to develop trail patterns. We observe that the development of patterns by fluid models require extra trail amplification mechanisms that are not needed at the Individual-Based Model level.

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian density cannot exceed a maximal density corresponding to contact between pedestrians. In a first step, we propose a singularly perturbed pressure relation which models the fact that the pedestrian velocity is considerably reduced, if not blocked, at congestion. In a second step, we carry over the singular limit into the model and show that abrupt transitions between compressible flow (in the uncongested regions) to incompressible flow (in congested regions) occur. We also investigate the hyperbolicity of the two-way models and show that they can lose their hyperbolicity in some cases. We study a diffusive correction of these models and discuss the characteristic time and length scales of the instability.

International audience; In this paper, we study the macroscopic limit of a new model of collective displacement. The model, called PTWA, is a combination of the Vicsek alignment model and the Persistent Turning Walker (PTW) model of motion by curvature control. The PTW model was designed to fit measured trajectories of individual fish. The PTWA model (Persistent Turning Walker with Alignment) describes the displacements of agents which modify their curvature in order to align with their neighbors. The derivation of its macroscopic limit uses the non-classical notion of generalized collisional invariant. The macroscopic limit of the PTWA model involves two physical quantities, the density and the mean velocity of individuals. It is a system of hyperbolic type but is non-conservative due to a geometric constraint on the velocity. This system has the same form as the macroscopic limit of the Vicsek model (the 'Vicsek hydrodynamics') but for the expression of the model coefficients. The numerical computations show that the numerical values of the coefficients are very close. The 'Vicsek Hydrodynamic model' appears in this way as a more generic macroscopic model of swarming behavior as originally anticipated.

International audience; The trajectories of Kuhlia mugil fish swimming freely in a tank are analyzed in order to develop a model of spontaneous fish movement. The data show that K. mugil displacement is best described by turning speed and its auto-correlation. The continuous-time process governing this new kind of displacement is modelled by a stochastic differential equation of Ornstein-Uhlenbeck family: the persistent turning walker. The associated diffusive dynamics are compared to the standard persistent random walker model and we show that the resulting diffusion coefficient scales non-linearly with linear swimming speed. In order to illustrate how interactions with other fish or the environment can be added to this spontaneous movement model we quantify the effect of tank walls on the turning speed and adequately reproduce the characteristics of the observed fish trajectories.

International audience; This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of diffusive type, and to provide an analytic expression of the diffusion coefficient. Two methods are investigated. In the first one, we compute the large time asymptotics of the variance of the individual stochastic trajectories. The second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories. The kinetic model is a Fokker-Planck type equation posed in an extended phase-space involving the curvature among the kinetic variables. We show that both methods lead to the same value of the diffusion constant. We present some numerical simulations to illustrate the theoretical results.

International audience; This paper concerns the homogenization of a one-dimensional elliptic equation with oscillatory random coefficients. It is well-known that the random solution to the elliptic equation converges to the solution of an effective medium elliptic equation in the limit of a vanishing correlation length in the random medium. It is also well-known that the corrector to homogenization, i.e., the difference between the random solution and the homogenized solution, converges in distribution to a Gaussian process when the correlations in the random medium are sufficiently short-range. Moreover, the limiting process may be written as a stochastic integral with respect to standard Brownian motion. We generalize the result to a large class of processes with long-range correlations. In this setting, the corrector also converges to a Gaussian random process, which has an interpretation as a stochastic integral with respect to fractional Brownian motion. Moreover, we show that the longer the range of the correlations, the larger is the amplitude of the corrector. Derivations are based on a careful analysis of random oscillatory integrals of processes with long-range correlations. We also make use of the explicit expressions for the solutions to the one-dimensional elliptic equation.

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic hypo-elliptic diffusion. This diffusion solves a kinetic Fokker-Planck equation based on an Ornstein-Uhlenbeck Gaussian process. The long time "diffusive" behavior of this model was recently studied by Degond & Motsch using partial differential equations techniques. This model is however intrinsically probabilistic. In the present paper, we show how the long time diffusive behavior of this model can be essentially recovered and extended by using appropriate tools from stochastic analysis. The approach can be adapted to many other kinetic "probabilistic" models., Accepted for publication in Asymptotic Analysis

International audience; We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator.

The discrete Couzin–Vicsek algorithm (CVA) has been proposed to model the interactions of individuals among animal societies such as schools of fish. In this Note, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity. The result is based on the introduction of a non-conventional concept of a collisional invariant of the collision operator. To cite this article: P. Degond, S. Motsch, C. R. Acad. Sci. Paris, Ser. I 345 (2007).