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Nezhadhaghighi MG. Anomalous phase diagram of the elastic interface with nonlocal hydrodynamic interactions in the presence of quenched disorder. Phys Rev E 2024; 109:024115. [PMID: 38491668 DOI: 10.1103/physreve.109.024115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2023] [Accepted: 01/29/2024] [Indexed: 03/18/2024]
Abstract
We investigate the influence of quenched disorder on the steady states of driven systems of the elastic interface with nonlocal hydrodynamic interactions. The generalized elastic model (GEM), which has been used to characterize numerous physical systems such as polymers, membranes, single-file systems, rough interfaces, and fluctuating surfaces, is a standard approach to studying the dynamics of elastic interfaces with nonlocal hydrodynamic interactions. The criticality and phase transition of the quenched generalized elastic model are investigated numerically and the results are presented in a phase diagram spanned by two tuning parameters. We demonstrate that in the one-dimensional disordered driven GEM, three qualitatively different behavior regimes are possible with a proper specification of the order parameter (mean velocity) for this system. In the vanishing order parameter regime, the steady-state order parameter approaches zero in the thermodynamic limit. A system with a nonzero mean velocity can be in either the continuous regime, which is characterized by a second-order phase transition, or the discontinuous regime, which is characterized by a first-order phase transition. The focus of this research is to investigate the critical scaling features near the pinning-depinning threshold. The behavior of the quenched generalized elastic model at the critical depinning force is explored. Near the depinning threshold, the critical exponent is obtained numerically.
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2
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Valizadeh N, Hamzehpour H, Samadpour M, Najafi MN. Edwards-Wilkinson depinning transition in fractional Brownian motion background. Sci Rep 2023; 13:12300. [PMID: 37516759 PMCID: PMC10387108 DOI: 10.1038/s41598-023-39191-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 07/21/2023] [Indexed: 07/31/2023] Open
Abstract
There are various reports about the critical exponents associated with the depinning transition. In this study, we investigate how the disorder strength present in the support can account for this diversity. Specifically, we examine the depinning transition in the quenched Edwards-Wilkinson (QEW) model on a correlated square lattice, where the correlations are modeled using fractional Brownian motion (FBM) with a Hurst exponent of H.We identify a crossover time [Formula: see text] that separates the dynamics into two distinct regimes: for [Formula: see text], we observe the typical behavior of pinned surfaces, while for [Formula: see text], the behavior differs. We introduce a novel three-variable scaling function that governs the depinning transition for all considered H values. The associated critical exponents exhibit a continuous variation with H, displaying distinct behaviors for anti-correlated ([Formula: see text]) and correlated ([Formula: see text]) cases. The critical driving force decreases with increasing H, as the host medium becomes smoother for higher H values, facilitating fluid mobility. This fact causes the asymptotic velocity exponent [Formula: see text] to increase monotonically with H.
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Affiliation(s)
- N Valizadeh
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran
| | - H Hamzehpour
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran.
| | - M Samadpour
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran
| | - M N Najafi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
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Young E, Melaugh G, Allen RJ. Active layer dynamics drives a transition to biofilm fingering. NPJ Biofilms Microbiomes 2023; 9:17. [PMID: 37024470 PMCID: PMC10079924 DOI: 10.1038/s41522-023-00380-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 03/13/2023] [Indexed: 04/08/2023] Open
Abstract
The emergence of spatial organisation in biofilm growth is one of the most fundamental topics in biofilm biophysics and microbiology. It has long been known that growing biofilms can adopt smooth or rough interface morphologies, depending on the balance between nutrient supply and microbial growth; this 'fingering' transition has been linked with the average width of the 'active layer' of growing cells at the biofilm interface. Here we use long-time individual-based simulations of growing biofilms to investigate in detail the driving factors behind the biofilm-fingering transition. We show that the transition is associated with dynamical changes in the active layer. Fingering happens when gaps form in the active layer, which can cause local parts of the biofilm interface to pin, or become stationary relative to the moving front. Pinning can be transient or permanent, leading to different biofilm morphologies. By constructing a phase diagram for the transition, we show that the controlling factor is the magnitude of the relative fluctuations in the active layer thickness, rather than the active layer thickness per se. Taken together, our work suggests a central role for active layer dynamics in controlling the pinning of the biofilm interface and hence biofilm morphology.
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Affiliation(s)
- Ellen Young
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Gavin Melaugh
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Rosalind J Allen
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom.
- Theoretical Microbial Ecology, Institute of Microbiology, Faculty of Biological Sciences, Friedrich Schiller University Jena, Buchaer Strasse 6, 07745, Jena, Germany.
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4
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Azimzade Y. Invasion front dynamics of interactive populations in environments with barriers. Sci Rep 2022; 12:826. [PMID: 35039586 PMCID: PMC8764055 DOI: 10.1038/s41598-022-04806-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Accepted: 01/03/2022] [Indexed: 11/20/2022] Open
Abstract
Invading populations normally comprise different subpopulations that interact while trying to overcome existing barriers against their way to occupy new areas. However, the majority of studies so far only consider single or multiple population invasion into areas where there is no resistance against the invasion. Here, we developed a model to study how cooperative/competitive populations invade in the presence of a physical barrier that should be degraded during the invasion. For one dimensional (1D) environment, we found that a Langevin equation as [Formula: see text] describing invasion front position. We then obtained how [Formula: see text] and [Formula: see text] depend on population interactions and environmental barrier intensity. In two dimensional (2D) environment, for the average interface position movements we found a Langevin equation as [Formula: see text]. Similar to the 1D case, we calculate how [Formula: see text] and [Formula: see text] respond to population interaction and environmental barrier intensity. Finally, the study of invasion front morphology through dynamic scaling analysis showed that growth exponent, [Formula: see text], depends on both population interaction and environmental barrier intensity. Saturated interface width, [Formula: see text], versus width of the 2D environment (L) also exhibits scaling behavior. Our findings show revealed that competition among subpopulations leads to more rough invasion fronts. Considering the wide range of shreds of evidence for clonal diversity in cancer cell populations, our findings suggest that interactions between such diverse populations can potentially participate in the irregularities of tumor border.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran, 14395-547, Iran.
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5
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Valizadeh N, Samadpour M, Hamzehpour H, Najafi MN. Edwards-Wilkinson depinning transition in random Coulomb potential background. Phys Rev E 2021; 104:064140. [PMID: 35030907 DOI: 10.1103/physreve.104.064140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 12/01/2021] [Indexed: 06/14/2023]
Abstract
The quenched Edwards-Wilkinson growth of the 1+1 interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a critical driving force F[over ̃]_{c}≈0.037 (in terms of disorder strength unit) in the vicinity of which the final velocity of the interface varies linearly with time. Our data collapse analysis for the velocity shows a crossover time t^{*} at which the velocity is size independent. Based on a two-variable scaling analysis, we extract the exponents, which are different from all universality classes we are aware of. Especially noting that the dynamic and roughness exponents are z_{w}=1.55±0.05, and α_{w}=1.05±0.05 at the criticality, we conclude that the system is different from both Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) universality classes. Our analysis shows therefore that making the noise long-range correlated, drives the system out of the EW universality class. The simulations on the tilted lattice show that the nonlinearity term (λ term in the KPZ equations) goes to zero in the thermodynamic limit.
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Affiliation(s)
- N Valizadeh
- Department of Physics, K.N. Toosi University of Technology, Tehran 15875-4416, Iran
| | - M Samadpour
- Department of Physics, K.N. Toosi University of Technology, Tehran 15875-4416, Iran
| | - H Hamzehpour
- Department of Physics, K.N. Toosi University of Technology, Tehran 15875-4416, Iran
| | - M N Najafi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
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Möbius W, Tesser F, Alards KMJ, Benzi R, Nelson DR, Toschi F. The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions. J R Soc Interface 2021; 18:20210579. [PMID: 34665975 PMCID: PMC8526172 DOI: 10.1098/rsif.2021.0579] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here, we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speed-up, which we characterize as function of hotspot strength and density. Our findings emphasize the importance of taking the dimensionality of the environment into account.
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Affiliation(s)
- Wolfram Möbius
- Living Systems Institute, University of Exeter, Exeter, UK.,Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK.,Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.,Department of Physics, Harvard University, Cambridge, MA, USA
| | - Francesca Tesser
- Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.,PMMH, ESPCI Paris-PSL, Paris, France
| | - Kim M J Alards
- Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands
| | - Roberto Benzi
- Universitá di Roma 'Tor Vergata' and INFN, Rome, Italy
| | - David R Nelson
- Department of Physics, Harvard University, Cambridge, MA, USA.,Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, USA
| | - Federico Toschi
- Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.,Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Rome, Italy
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Azimzade Y, Sasar M, Maleki I. Invasion front dynamics in disordered environments. Sci Rep 2020; 10:18231. [PMID: 33106618 PMCID: PMC7588433 DOI: 10.1038/s41598-020-75366-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 10/15/2020] [Indexed: 12/25/2022] Open
Abstract
Invasion occurs in environments that are normally spatially disordered, however, the effect of such a randomness on the dynamics of the invasion front has remained less understood. Here, we study Fisher's equation in disordered environments both analytically and numerically. Using the Effective Medium Approximation, we show that disorder slows down invasion velocity and for ensemble average of invasion velocity in disordered environment we have [Formula: see text] where [Formula: see text] is the amplitude of disorder and [Formula: see text] is the invasion velocity in the corresponding homogeneous environment given by [Formula: see text]. Additionally, disorder imposes fluctuations on the invasion front. Using a perturbative approach, we show that these fluctuations are Brownian with a diffusion constant of: [Formula: see text]. These findings were approved by numerical analysis. Alongside this continuum model, we use the Stepping Stone Model to check how our findings change when we move from the continuum approach to a discrete approach. Our analysis suggests that individual-based models exhibit inherent fluctuations and the effect of environmental disorder becomes apparent for large disorder intensity and/or high carrying capacities.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, 14395-547, Tehran, Iran.
| | - Mahdi Sasar
- Department of Physics, University of Tehran, 14395-547, Tehran, Iran
| | - Iraj Maleki
- Department of Physics, University of Tehran, 14395-547, Tehran, Iran
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Azimzade Y, Saberi AA, Sahimi M. Effect of heterogeneity and spatial correlations on the structure of a tumor invasion front in cellular environments. Phys Rev E 2019; 100:062409. [PMID: 31962455 DOI: 10.1103/physreve.100.062409] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2019] [Indexed: 06/10/2023]
Abstract
Analysis of invasion front has been widely used to decipher biological properties, as well as the growth dynamics of the corresponding populations. Likewise, the invasion front of tumors has been investigated, from which insights into the biological mechanisms of tumor growth have been gained. We develop a model to study how tumors' invasion front depends on the relevant properties of a cellular environment. To do so, we develop a model based on a nonlinear reaction-diffusion equation, the Fisher-Kolmogorov-Petrovsky-Piskunov equation, to model tumor growth. Our study aims to understand how heterogeneity in the cellular environment's stiffness, as well as spatial correlations in its morphology, the existence of both of which has been demonstrated by experiments, affects the properties of tumor invasion front. It is demonstrated that three important factors affect the properties of the front, namely the spatial distribution of the local diffusion coefficients, the spatial correlations between them, and the ratio of the cells' duplication rate and their average diffusion coefficient. Analyzing the scaling properties of tumor invasion front computed by solving the governing equation, we show that, contrary to several previous claims, the invasion front of tumors and cancerous cell colonies cannot be described by the well-known models of kinetic growth, such as the Kardar-Parisi-Zhang equation.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
| | - Abbas Ali Saberi
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
- Institut für Theoretische Physik, Universitat zu Köln, 50937 Köln, Germany
| | - Muhammad Sahimi
- Mork Family Department of Chemical Engineering Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
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9
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Gralka M, Hallatschek O. Environmental heterogeneity can tip the population genetics of range expansions. eLife 2019; 8:e44359. [PMID: 30977724 PMCID: PMC6513619 DOI: 10.7554/elife.44359] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Accepted: 04/11/2019] [Indexed: 12/12/2022] Open
Abstract
The population genetics of most range expansions is thought to be shaped by the competition between Darwinian selection and random genetic drift at the range margins. Here, we show that the evolutionary dynamics during range expansions is highly sensitive to additional fluctuations induced by environmental heterogeneities. Tracking mutant clones with a tunable fitness effect in bacterial colonies grown on randomly patterned surfaces we found that environmental heterogeneity can dramatically reduce the efficacy of selection. Time-lapse microscopy and computer simulations suggest that this effect arises generically from a local 'pinning' of the expansion front, whereby stretches of the front are slowed down on a length scale that depends on the structure of the environmental heterogeneity. This pinning focuses the range expansion into a small number of 'lucky' individuals with access to expansion paths, altering the neutral evolutionary dynamics and increasing the importance of chance relative to selection.
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Affiliation(s)
- Matti Gralka
- Department of PhysicsUniversity of California, BerkeleyBerkeleyUnited States
| | - Oskar Hallatschek
- Department of PhysicsUniversity of California, BerkeleyBerkeleyUnited States
- Department of Integrative BiologyUniversity of California, BerkeleyBerkeleyUnited States
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