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Interplay between morphology and competition in two-dimensional colony expansion

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Physical Review E 2023年第3期108卷 L032301-L032301页

作者： Daniel W. Swartz Hyunseok Lee Mehran Kardar Kirill S. Korolev Department of Physics Graduate Program in Bioinformatics and Biological Design Center Boston University Boston Massachusetts 02215 USA

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (Kardar-Parisi-Zhang equation). We solve these equations and find three regimes, which are controlled solely by the expansion rates, solely by the competitive abilities, or by both. Collectively, our results provide a simple framework to study spatial competition.

关键词： Ecological population dynamics Front propagation Surface growth Coarse graining

Mechanically-driven growth and competition in a Voronoi model of tissues

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arXiv 2024年

作者： Brézin, Louis Korolev, Kirill S. Department of Physics Graduate Program in Bioinformatics Biological Design Center Boston University BostonMA02215 United States

The mechanisms leading cells to acquire a fitness advantage and establish themselves in a population are paramount to understanding the development and growth of cancer. Although there are many works that study separately either the evolutionary dynamics or the mechanics of cancer, little has been done to couple evolutionary dynamics to mechanics. To address this question, we study a confluent model of tissue using a Self-Propelled Voronoi (SPV) model with stochastic growth rates that depend on the mechanical variables of the system. The SPV model is an out-of-equilibrium model of tissue derived from an energy functional that has a jamming/unjamming transition between solid-like and liquid-like states. By considering several scenarios of mutants invading a resident population in both phases, we determine the range of parameters that confer a fitness advantage and show that the preferred area and perimeter are the most relevant ones. We find that the liquid-like state is more resistant to invasion and show that the outcome of the competition can be determined from the simulation of a non-growing mixture. Moreover, a mean-field approximation can accurately predict the fate of a mutation affecting mechanical properties of a cell. Our results can be used to infer evolutionary dynamics from tissue images, understand cancer-suppressing effects of tissue mechanics, and even search for mechanics-based therapies. © 2024, CC BY.

关键词： Tissue

New sector morphologies emerge from anisotropic colony growth

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arXiv 2024年

作者： Swartz, Daniel W. Lee, Hyunseok Kardar, Mehran Korolev, Kirill S. Department of Physics Massachusetts Institute of Technology CambridgeMA02139 United States Department of Physics Graduate Program in Bioinformatics and Biological Design Center Boston University BostonMA02215 United States

Competition during range expansions is of great interest from both practical and theoretical view points. Experimentally, range expansions are often studied in homogeneous Petri dishes, which lack spatial anisotropy that might be present in realistic populations. Here, we analyze a model of anisotropic growth, based on coupled Kardar-Parisi-Zhang and Fisher-Kolmogorov-Petrovsky-Piskunov equations that describe surface growth and lateral competition. Compared to a previous study of isotropic growth, anisotropy relaxes a constraint between parameters of the model. We completely characterize spatial patterns and invasion velocities in this generalized model. In particular, we find that strong anisotropy results in a distinct morphology of spatial invasion with a kink in the displaced strain ahead of the boundary between the strains. This morphology of the out-competed strain is similar to a shock wave and serves as a signature of anisotropic growth. Copyright © 2024, The Authors. All rights reserved.

关键词： Strain

Connecting polymer collapse and the onset of jamming

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Physical Review E 2024年第3期109卷 034406-034406页

作者： Alex T. Grigas Aliza Fisher Mark D. Shattuck Corey S. O'Hern Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA Integrated Graduate Program in Physical and Engineering Biology Yale University New Haven Connecticut 06520 USA Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA

Previous studies have shown that the interiors of proteins are densely packed, reaching packing fractions that are as large as those found for static packings of individual amino-acid-shaped particles. How can the interiors of proteins take on such high packing fractions given that amino acids are connected by peptide bonds and many amino acids are hydrophobic with attractive interactions? We investigate this question by comparing the structural and mechanical properties of collapsed attractive disk-shaped bead-spring polymers to those of three reference systems: static packings of repulsive disks, of attractive disks, and of repulsive disk-shaped bead-spring polymers. We show that the attractive systems quenched to temperatures below the glass transition T≪Tg and static packings of both repulsive disks and bead-spring polymers possess similar interior packing fractions. Previous studies have shown that static packings of repulsive disks are isostatic at jamming onset, i.e., the number of interparticle contacts Nc matches the number of degrees of freedom, which strongly influences their mechanical properties. We find that repulsive polymer packings are hypostatic at jamming onset (i.e., with fewer contacts than degrees of freedom) but are effectively isostatic when including stabilizing quartic modes, which give rise to quartic scaling of the potential energy with displacements along these modes. While attractive disk and polymer packings are often considered hyperstatic with excess contacts over the isostatic number, we identify a definition for interparticle contacts for which they can also be considered as effectively isostatic. As a result, we show that the mechanical properties (e.g., scaling of the potential energy with excess contact number and low-frequency contribution to the density of vibrational modes) of weakly attractive disk and polymer packings are similar to those of isostatic repulsive disk and polymer packings. Our results demonstrate that static

关键词： Jamming Polymer folding Protein folding Single polymer chains

Competition on the edge of an expanding population

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arXiv 2023年

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). We solved these equations and found three regimes, which are controlled solely by the expansion rates, solely by the competitive abilities, or by both. Collectively, our results provide a simple framework to study spatial competition. Copyright © 2023, The Authors. All rights reserved.

关键词：

Characterizing the mechanical response of metallic glasses to uniaxial tension using a spring network model

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Physical Review Materials 2023年第7期7卷 073605-073605页

作者： Aya Nawano Weiwei Jin Jan Schroers Mark D. Shattuck Corey S. O'Hern Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

A coarse-grained spring network model is proposed for the prediction of the mechanical response of metallic glasses as a function of the microstructure prior to loading. This model describes the mechanical response of metallic glasses using a network of parallel springs that can break and reform, mimicking atomic rearrangements during deformation. We compare predictions of the spring network model for stress versus strain to results from numerical simulations of athermal quasistatic, uniaxial tensile deformation of Cu50Zr50 metallic glasses using Lennard-Jones (LJ) and embedded atom method (EAM) atomic interactions. We show that both the LJ and EAM models possess qualitatively similar stress σ versus strain γ curves. By specifying five parameters [ultimate strength, strain at ultimate strength, slopes of σ(γ) at γ=0 and at large strain, and strain at fracture where σ=0], we demonstrate that the spring network model can accurately describe the form of the stress-strain curves during uniaxial tension for the computational studies of Cu50Zr50, as well as recent experimental studies of several Zr-based metallic glasses.

关键词： Alloys Amorphous materials Glasses Packing & jamming problems Molecular dynamics

Local and global measures of the shear moduli of jammed disk packings

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Physical Review E 2023年第5期107卷 054903-054903页

作者： Shiyun Zhang Weiwei Jin Dong Wang Ding Xu Jerry Zhang Mark D. Shattuck Corey S. O'Hern Department of Physics University of Science and Technology of China Hefei Anhui 230026 China Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1−F−)〈G+〉+F−〈G−〉, where F− is the fraction of jammed packings with negative shear moduli and 〈G+〉 and 〈G−〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G+〉 and 〈|G−|〉 obey different power-law scaling relations above and below pN2∼1. For pN2>1, both 〈G+〉N and 〈|G−|〉N∼(pN2)β, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN2)β′ with β′≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN2 and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN2≪1 limit. As pN2 increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN2≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r⃗) displays weak correlations for pnsub2<10−2, where nsub is the number of particles within each subsystem. However, C(r⃗) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pnsub2≳10−2.

关键词： Jamming Packing & jamming problems Granular materials

Identifying the minimal sets of distance restraints for FRET-assisted protein structural modeling

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arXiv 2024年

作者： Liu, Zhuoyi Grigas, Alex T. Sumner, Jacob Knab, Edward Davis, Caitlin M. O’Hern, Corey S. Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Integrated Graduate Program in Physical and Engineering Biology Yale University New HavenCT06520 United States Graduate Program in Computational Biology and Bioinformatics Yale University New HavenCT06520 United States Department of Chemistry Yale University New HavenCT06520 United States Department of Physics Yale University New HavenCT06520 United States Department of Applied Physics Yale University New HavenCT06520 United States

Proteins naturally occur in crowded cellular environments and interact with other proteins, nucleic acids, and organelles. Since most previous experimental protein structure determination techniques require that proteins occur in idealized, non-physiological environments, the effects of realistic cellular environments on protein structure are largely unexplored. Recently, Förster resonance energy transfer (FRET) has been shown to be an effective experimental method for investigating protein structure in vivo. Inter-residue distances measured in vivo can be incorporated as restraints in molecular dynamics (MD) simulations to model protein structural dynamics in vivo. Since most FRET studies only obtain inter-residue separations for a small number of amino acid pairs, it is important to determine the minimum number of restraints in the MD simulations that are required to achieve a given root-mean-square deviation (RMSD) from the experimental structural ensemble. Further, what is the optimal method for selecting these inter-residue restraints? Here, we implement several methods for selecting the most important FRET pairs and determine the number of pairs Nr that are needed to induce conformational changes in proteins between two experimentally determined structures. We find that enforcing only a small fraction of restraints, Nr/N 0.08, where N is the number of amino acids, can induce the conformational changes. These results establish the efficacy of FRET-assisted MD simulations for atomic scale structural modeling of proteins in vivo. © 2024, CC BY.

关键词： Conformations

Protein folding as a jamming transition

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arXiv 2024年

作者： Grigas, Alex T. Liu, Zhuoyi Logan, Jack A. Shattuck, Mark D. O’Hern, Corey S. Graduate Program in Computational Biology and Bioinformatics Yale University New HavenCT06520 United States Integrated Graduate Program in Physical and Engineering Biology Yale University New HavenCT06520 United States Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Benjamin Levich Institute and Physics Department The City College of New York New YorkNY10031 United States Department of Physics Yale University New HavenCT06520 United States Department of Applied Physics Yale University New HavenCT06520 United States

Proteins fold to a specific functional conformation with a densely packed hydrophobic core that controls their stability. We develop a geometric, yet all-atom model for proteins that explains the universal core packing fraction of φc = 0.55 found in experimental measurements. We show that as the hydrophobic interactions increase relative to the temperature, a novel jamming transition occurs when the core packing fraction exceeds φc. The model also recapitulates the global structure of proteins since it can accurately refold to native-like structures from partially unfolded states. © 2024, CC BY.

关键词： Proteins