Understanding cellular functions, particularly in their intricate complexity, can greatly benefit from the spatial mapping of diverse molecules through multitarget single-molecule localization microscopy (SMLM). Exist...
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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 fitn...
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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.
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 separa...
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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 t...
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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 int...
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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
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 fitn...
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...
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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.
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 contrib...
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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.
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 prote...
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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 packin...
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