J. M. Schwarz

VU University Amsterdam, Amsterdam, North Holland, Netherlands

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Publications (38)58.8 Total impact

  • J. H. Lopez, Moumita Das, J. M. Schwarz
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    ABSTRACT: Experiments suggest that the migration of some cells in the three-dimensional extra cellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell made of two beads and an active spring moving along a rigid track. The active spring models the stress fibers with their myosin-driven contractility and alpha-actinin-driven extendability, while the friction coefficients of the two beads describe the catch/slip bond behavior of the integrins in focal adhesions. In the absence of active noise, net motion arises from an interplay between active contractility (and passive extendability) of the stress fibers and an asymmetry between the front and back of the cell due to catch bond behavior of integrins at the front of the cell and slip bond behavior of integrins at the back. We obtain reasonable cell speeds with independently estimated parameters. We also study the effects of hysteresis in the active spring, due to catch bond behavior and the dynamics of cross-linking, and the addition of active noise on the motion of the cell. Our model highlights the role of alpha-actinin in three-dimensional cell motility and does not require Arp2/3 actin filament nucleation for net motion.
    06/2014;
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    ABSTRACT: Recent observations demonstrate that confluent tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. Here we develop numerical and theoretical models to calculate energy barriers to cell rearrangements, which help govern cell migration in cell monolayers. In contrast to work on sheared foams, we find that energy barrier heights are exponentially distributed and depend systematically on the cell's number of neighbors. Based on these results, we predict glassy two-time correlation functions for cell motion, with a timescale that increases rapidly as cell activity decreases. These correlation functions are used to construct simple random walks that reproduce the caging behavior observed for cell trajectories in experiments. This work provides a theoretical framework for predicting collective motion of cells in wound-healing, embryogenesis and cancer tumorogenesis.
    Soft Matter 02/2014; 10(12):1885-90. · 3.91 Impact Factor
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    Jorge H Lopez, L Cao, J M Schwarz
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    ABSTRACT: We revisit the concept of minimal rigidity as applied to frictionless, repulsive soft sphere packings in two dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's theorem in two dimensions. It constrains the global, average coordination number of the graph, for example. However, minimal rigidity does not address the geometry of local mechanical stability. The jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability. We demonstrate how jamming graphs can be constructed using local moves via the Henneberg construction such that these graphs fall under the jurisdiction of correlated percolation. We then probe how jamming graphs destabilize, or become unjammed, by deleting a bond and computing the resulting rigid cluster distribution. We also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra (redundant) contacts destabilizes. The latter endeavor allows us to probe a disk packing in the rigid phase and uncover a potentially new diverging length scale associated with the random deletion of contacts as compared to the study of cut-out (or frozen-in) subsystems.
    Physical Review E 12/2013; 88(6-1):062130. · 2.31 Impact Factor
  • Moumita Das, J. M. Schwarz
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    ABSTRACT: Cell migration is integral to several physiological processes such as immune response, wound healing, tissue formation, fertilization etc. Previous studies, both theoretical and experimental, have attempted to model different aspects of cell migration, including adhesion, protrusion and retraction at the level of single cells, and collective motion at the multicellular level. The entire motility process of a single cell and its ability to navigate a landscape containing obstacles is, however, not well understood. We attempt to address this issue by modeling a single moving cell as a Brownian inchworm composed of two beads attached by a spring that can sense and respond to the mechanical properties and architecture of its environment. The elastic interaction between inchworm and the substrate is modeled by molecular clutches. We study the dynamics of this inchworm in a corrugated potential. In particular we focus on the interplay between confinement and adhesion in the motility of this inchworm. This model may provide important insights on cell movement through a biological maze of other cellular and extracellular structures.
    03/2013;
  • J. M. Schwarz, Tao Zhang, Moumita Das
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    ABSTRACT: At the leading edge of a crawling cell, the actin cytoskeleton extends itself in a particular direction via a branched crosslinked network of actin filaments with some overall alignment. This network is known as the lamellipodium. Branching via the complex Arp2/3 occurs at a reasonably well-defined angle of 70 degrees from the plus end of the mother filament such that Arp2/3 can be modeled as an angle-constraining crosslinker. Freely-rotating crosslinkers, such as alpha-actinin, are also present in lamellipodia. Therefore, we study the interplay between these two types of crosslinkers, angle-constraining and free-rotating, both analytically and numerically, to begin to quantify the mechanics of lamellipodia. We also investigate how the orientational ordering of the filaments affects this interplay. Finally, while role of Arp2/3 as a nucleator for filaments along the leading edge of a crawling cell has been studied intensely, much less is known about its mechanical contribution. Our work seeks to fill in this important gap in modeling the mechanics of lamellipodia.
    03/2013;
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    ABSTRACT: The behavior of cellular aggregates strongly influences morphogenesis, cancer growth and wound healing. While single cell mechanics has been extensively studied, the collective dynamics of cells inside a tissue is not well understood. Recent experiments have shown cells in tissues behave like fluids on long timescales and solids on shorter timescales, and exhibit caging behavior at intermediate timescales as they are more tightly packed. These observations are reminiscent of dynamic slowing down and dynamical heterogeneities due to mutual confinement and crowding of particles glassy systems. A common and crucial feature of glassy systems is the existence of a Potential Energy Landscape (PEL) for local rearrangements. For thermal glassy materials, when these barriers are large compared to thermal fluctuations, its rheology is dependent on the PEL and external mechanical driving. In contrast, cells in a tissue are non-thermal and overcome energy barriers in the PEL mainly through local active processes, i.e. making new adhesions and cell shape changes. We numerically map the PEL of a confluent tissue as functions of different transition pathways and single cell properties. Analytical calculations are also performed to find the minimal energy shapes for 2-D confluent cell packings.
    03/2013;
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    L Cao, J M Schwarz
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    ABSTRACT: The recent proliferation of correlated percolation models-models where the addition of edges and/or vertices is no longer independent of other edges and/or vertices-has been motivated by the quest to find discontinuous percolation transitions. The leader in this proliferation is what is known as explosive percolation. A recent proof demonstrates that a large class of explosive percolation-type models does not, in fact, exhibit a discontinuous transition [Riordan and Warnke, Science, 333, 322 (2011)]. Here, we discuss two lesser known correlated percolation models-the k≥3-core model on random graphs and the counter-balance model in two-dimensions-both exhibiting discontinuous transitions. To search for tricriticality, we construct mixtures of these models with other percolation models exhibiting the more typical continuous transition. Using a powerful rate equation approach, we demonstrate that a mixture of k=2-core and k=3-core vertices on the random graph exhibits a tricritical point. However, for a mixture of k-core and counter-balance vertices in two dimensions, as the fraction of counter-balance vertices is increased, numerics and heuristic arguments suggest that there is a line of continuous transitions with the line ending at a discontinuous transition, i.e., when all vertices are counter-balanced. Interestingly, these heuristic arguments may help identify the ingredients needed for a discontinuous transition in low dimensions. In addition, our results may have potential implications for glassy and jamming systems.
    Physical Review E 12/2012; 86(6-1):061131. · 2.31 Impact Factor
  • Tao Zhang, Moumita Das, D. A. Quint, J. M. Schwarz
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    ABSTRACT: At the leading edge of a crawling cell, the actin cytoskeleton extends itself via a branched, crosslinked network of filaments, otherwise known as the lamellipodium. The filaments in this network have an average preferred orientation of around ± 30 degrees with respect to the normal of the leading edge. This preferred orientation of filaments leads to a material that is structurally anisotropic. To better understand the forces generated by the lamellipodium, we analytically and numerically study the mechanical properties of a model branched and crosslinked filamentous network where the filaments are preferentially oriented along one direction. We investigate the interplay between geometry, elasticity and anisotropy in the network. In particular, we show how anisotropy modulates the onset of rigidity and non-linear mechanical response of the network.
    02/2012;
  • D. A. Quint, S. Henkes, J. M. Schwarz
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    ABSTRACT: While the frictionless jamming transition has been intensely studied in recent years, more realistic frictional packings are less well understood. In frictionless sphere packings, the transition is predicted by a simple mean-field constraint counting argument, the isostaticity argument. For frictional packings, a modified constraint counting argument, which includes slipping contacts at the Coulomb threshold, has had limited success in accounting for the transition. We propose that the frictional jamming transition is not mean field and is triggered by the nucleation of unstable regions, which are themselves dynamical objects due to the Coulomb criterion. We create frictional packings using MD simulations and test for the presence and shape of rigid clusters with the pebble game to identify the partition of the packing into stable and unstable regions. To understand the dynamics of these unstable regions we follow perturbations at contacts crucial to the stability of the ``frictional house of cards.''
    02/2012;
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    Moumita Das, D A Quint, J M Schwarz
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    ABSTRACT: The cytoskeleton of living cells contains many types of crosslinkers. Some crosslinkers allow energy-free rotations between filaments and others do not. The mechanical interplay between these different crosslinkers is an open issue in cytoskeletal mechanics. Therefore, we develop a theoretical framework based on rigidity percolation to study a generic filamentous system containing both stretching and bond-bending forces to address this issue. The framework involves both analytical calculations via effective medium theory and numerical simulations on a percolating triangular lattice with very good agreement between both. We find that the introduction of angle-constraining crosslinkers to a semiflexible filamentous network with freely rotating crosslinks can cooperatively lower the onset of rigidity to the connectivity percolation threshold-a result argued for years but never before obtained via effective medium theory. This allows the system to ultimately attain rigidity at the lowest concentration of material possible. We further demonstrate that introducing angle-constraining crosslinks results in mechanical behaviour similar to just freely rotating crosslinked semflexible filaments, indicating redundancy and universality. Our results also impact upon collagen and fibrin networks in biological and bio-engineered tissues.
    PLoS ONE 01/2012; 7(5):e35939. · 3.73 Impact Factor
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    S. -L. -Y. Xu, J. M. Schwarz
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    ABSTRACT: A vicious walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to the position. We numerically compute the survival probability exponent, {\alpha}, for this system, which characterizes the probability for any two walkers not to meet. For example, for N = 3, {\alpha} = 0.71 \pm 0.01. Based on our numerical data, we conjecture that 1/8N(N - 1) is an upper bound on {\alpha}. We also numerically study N vicious Levy flights and find, for instance, for N = 3 and a Levy index {\mu} = 1 that {\alpha} = 1.31 \pm 0.03. Vicious accelerating walkers relate to no-crossing configurations of semiflexible polymer brushes and may prove relevant for a non-Markovian extension of Dyson's Brownian motion model.
    EPL (Europhysics Letters) 08/2011; 96(5). · 2.26 Impact Factor
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    ABSTRACT: Understanding the effect of motor proteins, such as myosins, on the elasticity of crosslinked actin networks is essential to our understanding of cell mechanics. Both in vivo and in vitro, these active networks have radically different mechanical properties from their equilibrium counterparts, including contractile behavior and higher elastic moduli. Existing theoretical models do not address the relative role of passive and active crosslinkers in controlling the network contractility and stiffening. We construct a one dimensional lattice model with minimal ingredients, that is, rigid polar filaments, spring-like passive crosslinks and active crosslinks with on/ off dynamics implemented through non-equilibrium Monte Carlo solution of the corresponding master equations. We find, consistent with experiments, that the network needs to be percolated through the passive crosslinks to be mechanically stable. Contractile behavior is observed for all concentrations of active crosslinks. We study the mechanical properties of the gel in the phase space of motor processivity, crosslink stiffness, and concentration of active crosslinks.
    03/2011;
  • D. A. Quint, J. M. Schwarz
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    ABSTRACT: In vitro experiments of growing dendritic actin networks demonstrate reversible stress-softening at high loads, above some critical load. The transition to the stress-softening regime has been attributed to the elastic buckling of individual actin filaments. To estimate the critical load above which softening should occur, we extend the elastic theory of buckling of individual filaments embedded in a network to include the buckling of branched filaments, a signature trait of growing dendritic actin networks. Under certain assumptions, there will be approximately a seven-fold increase in the classical critical bucking load, when compared to the unbranched filament, which is entirely due to the presence of a branch. Moreover, we go beyond the classical buckling regime to investigate the effect of entropic fluctuations. The result of compressing the filament in this case leads to an increase in these fluctuations and eventually the harmonic approximation breaks down signifying the onset of the buckling transition. We compute corrections to the classical critical buckling load near this breakdown.
    03/2011;
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    D A Quint, J M Schwarz
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    ABSTRACT: Actin cytoskeletal protrusions in crawling cells, or lamellipodia, exhibit various morphological properties such as two characteristic peaks in the distribution of filament orientation with respect to the leading edge. To understand these properties, using the dendritic nucleation model as a basis for cytoskeletal restructuring, a kinetic-population model with orientational-dependent branching (birth) and capping (death) is constructed and analyzed. Optimizing for growth yields a relation between the branch angle and filament orientation that explains the two characteristic peaks. The model also exhibits a subdominant population that allows for more accurate modeling of recent measurements of filamentous actin density along the leading edge of lamellipodia in keratocytes. Finally, we explore the relationship between orientational and spatial organization of filamentous actin in lamellipodia and address recent observations of a prevalence of overlapping filaments to branched filaments-a finding that is claimed to be in contradiction with the dendritic nucleation model.
    Journal of Mathematical Biology 12/2010; 63(4):735-55. · 2.37 Impact Factor
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    K-C Lee, A Gopinathan, J M Schwarz
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    ABSTRACT: Filopodia are bundles of actin filaments that extend out ahead of the leading edge of a crawling cell to probe its upcoming environment. In vitro experiments (Vignjevic et al. in J Cell Biol 160:951-962, 2003) have determined the minimal ingredients required for the formation of filopodia from the dendritic-like morphology of the leading edge. We model these experiments using kinetic aggregation equations for the density of growing bundle tips. In mean field, we determine the bundle size distribution to be broad for bundle sizes smaller than a characteristic bundle size above which the distribution decays exponentially. Two-dimensional simulations incorporating both bundling and cross-linking measure a bundle size distribution that agrees qualitatively with mean field. The simulations also demonstrate a nonmonotonicity in the radial extent of the dendritic region as a function of capping protein concentration, as was observed in experiments, due to the interplay between percolation and the ratcheting of growing filaments off a spherical obstacle.
    Journal of Mathematical Biology 10/2010; 63(2):229-61. · 2.37 Impact Factor
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    S. -L. -Y. Xu, X. Illa, J. M. Schwarz
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    ABSTRACT: Using a system of repulsive, soft particles as a model for a jammed solid, we analyze its force network as characterized by the magnitude of the contact force between two particles, the local contact angle subtended between three particles, and the local coordination number. In particular, we measure the local contact angle distribution as a function of the magnitude of the local contact force. We find the suppression of small contact angles for locally larger contact forces, suggesting the existence of chain-like correlations in the locally larger contact forces. We couple this information with a coordination number-spin state mapping to arrive at a Potts spin model with frustration and correlated disorder to draw a potential connection between jammed solids (no quenched disorder) and spin glasses (quenched disorder). We use this connection to measure chaos due to marginality in the jammed system. In addition, we present the replica solution of the one-dimensional, long-range Potts glass as a potential toy building block for a jammed solid, where a sea of weakly interacting spins provide for long-range interactions along a chain-like backbone of more strongly interacting spins. Comment: 15 pages, 9 figures
    08/2010;
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    M. Jeng, S.-L.-Y. Xu, E. Hawkins, J. M. Schwarz
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    ABSTRACT: A number of papers over the past eight years have claimed to solve the fractional Schrödinger equation for systems ranging from the one-dimensional infinite square well to the Coulomb potential to one-dimensional scattering with a rectangular barrier. However, some of the claimed solutions ignore the fact that the fractional diffusion operator is inherently nonlocal, preventing the fractional Schrödinger equation from being solved in the usual piecewise fashion. We focus on the one-dimensional infinite square well and show that the purported ground state, which is based on a piecewise approach, is definitely not a solution of the fractional Schrödinger equation for the general fractional parameter α. On a more positive note, we present a solution to the fractional Schrödinger equation for the one-dimensional harmonic oscillator with α = 1.
    Journal of Mathematical Physics 06/2010; 51(6):062102-062102-6. · 1.30 Impact Factor
  • D. A. Quint, J. M. Schwarz
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    ABSTRACT: Experiments measuring the orientation of extracted, in vivo-grown branched actin filaments with respect to the leading edge show a distribution prominently peaked at ±35^o, which is half of the measured branching angle. To understand this result, we model the successive generations of polymerizing, branched actin filaments as a set of coupled kinetic equations with a branching (birth) rate that depends on the orientation of the filament with respect to the leading edge of the cell and a constant capping (death) rate. We find in steady state that the orientation angle of the filament with respect to the leading edge optimizing for survival is in agreement with the observed values of ±35^o. A previous rate equation based model, introduced by Maly and Borisy, yields the same result but with an orientation dependent capping (death) rate. Given these similar outcomes, we investigate whether this result is generic for models where the birth and death rates are dependent on more general functions of the filament orientation. We also study the effects of fluctuations in the branching angle on the optimal orientation angle.
    03/2010;
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    M Jeng, J M Schwarz
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    ABSTRACT: We study models of correlated percolation where there are constraints on the occupation of sites that mimic force balance, i.e., for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We prove rigorously that p(c) < 1 for the two-dimensional models studied. Numerical data indicate that the force-balance percolation transition is discontinuous with a growing crossover length, with perhaps the same form as the jamming percolation models, suggesting that all models belong to the same universality class with the same underlying mechanism driving the transition in both cases. We find a lower bound for the correlation length in the connected phase and that the correlation function does not appear to be a power law at the transition. Finally, we study the dynamics of the culling procedure invoked to obtain the force-balance configurations and find a dynamical exponent similar to that found in sandpile models.
    Physical Review E 01/2010; 81(1 Pt 1):011134. · 2.31 Impact Factor
  • Liang Cao, M. Jeng, J. M. Schwarz
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    ABSTRACT: : Quantum percolation is the study of hopping transport of a quantum particle on randomly diluted percolation clusters. Inspired by correlated percolation models of geometrical jamming, we extend quantum percolation to investigate hopping transport on percolation clusters with geometric constraints on the occupation of bonds/sites. An example of a geometric constraint is each occupied site must have at least k occupied neighboring sites to remain occupied (k-core percolation). Another example is particular sets of neighboring sites containing at least one occupied site for an occupied site to remain occupied (spiral model). Both models exhibit long-range geometrical correlations differing from ordinary percolation and give rise to a discontinuous phase transition (in high dimensions for k-core percolation). To investigate how these atypical long-range geometrical correlations affect the hopping transport of a quantum particle, we numerically study the level statistics of quantum k-core percolation on the Bethe lattice and the two-dimensional quantum spiral model. While the quantum k-core model exhibits an insulator-to-metal transition as the occupation probability is increased, preliminary results indicate that there is no insulator-to-metal transition in the two-dimensional quantum spiral model. Studies of a three- dimensional quantum spiral model will also be addressed as will possible physical applications of quantum jamming.
    03/2009;

Publication Stats

105 Citations
58.80 Total Impact Points

Institutions

  • 2012
    • VU University Amsterdam
      • Department of Physics and Astronomy
      Amsterdam, North Holland, Netherlands
  • 2003–2012
    • Syracuse University
      • Department of Physics
      Syracuse, NY, United States
  • 2010
    • University of California, Davis
      • Department of Mathematics
      Davis, CA, United States
  • 2007
    • University of California, Merced
      • School of Natural Sciences
      Merced, CA, United States