Searcharxiv⌕ Search

arXiv subjects

Robijn Bruinsma

Publications and source records attributed to Robijn Bruinsma.

At least 19 recordsLinked to original sources
arXiv2024

Active Liquid-Liquid Phase-Separation in a Confining Environment

Active liquid-liquid phase separation (LLPS) in a confining environment is believed to play an important role in cell biology. Recently, it was shown that when active noise at the microscopic level is included in the classical theory of nucleation and growth then this does not cause the breakdown of detailed balance at the \textit{macroscopic} level provided that the droplet radius is the only collective coordinate. Here, we present a simple model for active LLPS in a confining environment, with the droplet location in a confining potential as a second collective coordinate, and find that detailed balance \textit{is} broken at the macroscopic level in an unusual fashion, using the Fluctuation-Dissipation Theorem as a diagnostic.

cond-mat.soft↗
arXiv2022

The Spanning Tree Model and the Assembly Kinetics of RNA Viruses

Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules and it is not known whether this also can be understood by free energy minimization. We address this question using a simple mathematical model recently proposed for the assembly of small ssRNA viruses (submitted to PLOS Biocomputation). We present a statistical physics analysis of the properties of the model finding an effect kinetic RNA selection mechanism with selection taking place during the formation of the nucleation complex. Surprisingly, kinetic selectivity is greatly enhanced by a modest level of supersaturation and by reduced protein to RNA concentration ratios. The mechanism is related to the Hopfield kinetic proofreading scenario.

physics.bio-ph↗
arXiv2021

Quantum Gates Robust to Secular Amplitude Drifts

Quantum gates are typically vulnerable to imperfections in the classical control fields applied to physical qubits to drive the gates. One approach to reduce this source of error is to break the gate into parts, known as composite pulses (CPs), that typically leverage the constancy of the error over time to mitigate its impact on gate fidelity. Here we extend this technique to suppress secular drifts in Rabi frequency by regarding them as sums of power-law drifts whose first-order effects on over- or under-rotation of the state vector add linearly. Power-law drifts have the form $t^p$ where $t$ is time and the constant $p$ is its power. We show that composite pulses that suppress all power-law drifts with $p \leq n$ are also high-pass filters of filter order $n+1$ arXiv:1410.1624. We present sequences that satisfy our proposed power-law amplitude criteria, $\text{PLA}(n)$, obtained with this technique, and compare their simulated performance under time-dependent amplitude errors to some traditional composite pulse sequences. We find that there is a range of noise frequencies for which the $\text{PLA}(n)$ sequences provide more error suppression than the traditional sequences, but in the low frequency limit, non-linear effects become more important for gate fidelity than frequency roll-off. As a result, the previously known $F_1$ sequence, which is one of the two solutions to the $\text{PLA}(1)$ criteria and furnishes suppression of both linear secular drift and the first order nonlinear effects, is a sharper noise filter than any of the other $\text{PLA}(n)$ sequences in the low frequency limit.

quant-ph↗
arXiv2021

The Spanning Tree Model and the Assembly Kinetics of RNA Viruses

Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and the viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization of rather simple models. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules. It is known that the assembly process takes the form of preferential heterogeneous nucleation of capsid proteins on viral RNA molecules ("selective nucleation"). Recently, a simple mathematical model was proposed for the selective nucleation of small ssRNA viruses. In this paper we present a statistical physics analysis of the thermal equilibrium and kinetic properties of that model and show that it can account, at least qualitatively, for numerous observations of the self-assembly of small ssRNA viruses.

physics.bio-ph↗
arXiv2021

The Spanning Tree Model for the Assembly Kinetics of RNA Viruses

We present a simple kinetic model for the assembly of small single-stranded RNA viruses that can be used to carry out analytical packaging contests between different types of RNA molecules. The RNA selection mechanism is purely kinetic and based on small differences between the assembly energy profiles. RNA molecules that win these packaging contests are characterized by having a minimum "Maximum Ladder Distance" and a maximum "Wrapping Number".The former is a topological invariant that measures the "branchiness" of the genome molecule while the latter measures the ability of the genome molecule to maximally associate with the capsid proteins. The model can also be used study the applicability of the theory of nucleation and growth to viral assembly, which breaks down with increasing strength of the RNA-protein interaction.

physics.bio-ph↗
arXiv2019

Invariant Theory and Orientational Phase Transitions

The Landau theory of phase transitions has been productively applied to phase transitions that involve rotational symmetry breaking, such as the transition from an isotropic fluid to a nematic liquid crystal. It even can be applied to the orientational symmetry breaking of simple atomic or molecular clusters that are not true phase transitions. In this paper we address fundamental problems that arise with the Landau theory when it is applied to rotational symmetry breaking transitions of more complex particle clusters that involve order parameters characterized by larger values of the $l$ index of the dominant spherical harmonic that describes the broken symmetry state. The problems are twofold. First, one may encounter a thermodynamic instability of the expected ground state with respect to states with lower symmetry. A second problem concerns the proliferation of quartic invariants that may or may not be physical. We show that the combination of a geometrical method based on the analysis of the space of invariants, developed by Kim to study symmetry breaking of the Higgs potential, with modern visualization tools provides a resolution to these problems. The approach is applied to the outcome of numerical simulations of particle ordering on a spherical surface and to the ordering of protein shells.

cond-mat.soft↗
arXiv2018

Generalized Flory Theory for Rotational Symmetry Breaking of Complex Macromolecules

We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. We analyze this transition using a variational mean-field theory that combines the Gibbs-Bogolyubov-Feynman inequality with the concept of the Laplacian matrix. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of this Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension Eventually, the variational free energy landscape develops a complex structure with multiple competing minima.

cond-mat.soft↗
arXiv2017

Orientational Phase Transitions and the Assembly of Viral Capsids

We present a generalized Landau-Brazovskii free energy for the solidification of chiral molecules on a spherical surface in the context of the assembly of viral shells. We encounter two types of icosahedral solidification transitions. The first type is a conventional first-order phase transition from the uniform to the icosahedral state. It can be described by a single icosahedral spherical harmonic of even $l$. The chiral pseudo-scalar term in the free energy creates secondary terms with chiral character but it does not affect the thermodynamics of the transition. The second type, associated with icosahedral spherical harmonics with odd $l$, is anomalous. Pure odd $l$ icosahedral states are unstable but stability is recovered if admixture with the neighboring $l+1$ icosahedral spherical harmonic is included, generated by the non-linear terms. This is in conflict with the principle of Landau theory that symmetry-breaking transitions are characterized by only a \textit{single} irreducible representation of the symmetry group of the uniform phase and we argue that this principle should be removed from Landau theory. The chiral term now directly affects the transition because it lifts the degeneracy between two isomeric mixed-$l$ icosahedral states. A direct transition is possible only over a limited range of parameters. Outside this range, non-icosahedral states intervene. For the important case of capsid assembly dominated by $l=15$, the intervening states are found to be based on octahedral symmetry.

physics.bio-ph↗
arXiv2016

Landau Theory and the Emergence of Chirality in Viral Capsids

We present a generalized Landau-Brazovskii theory for the solidification of chiral molecules on a spherical surface. With increasing sphere radius one encounters first intervals where robust achiral density modulations appear with icosahedral symmetry via first-order transitions. Next, one en- counters intervals where fragile but stable icosahedral structures still can be constructed but only by superposition of multiple irreducible representations. Chiral icoshedral structures appear via continuous or very weakly first-order transitions. Outside these parameter intervals, icosahedral symmetry is broken along a three-fold axis or a five-fold axis. The predictions of the theory are compared with recent numerical simulations.

physics.bio-ph↗
arXiv2014

Bose-Einstein Condensates: a model system for particle solvation?

We propose that impurities in Bose-Einstein condensates can serve as a minimal laboratory system to explore the effects of quantum and thermal fluctuations on solvation. Specifically, we show that the role of quantum fluctuations in the formation of solvation shells and the breakdown of linear response theory can be explored in detail.

cond-mat.quant-gas↗
arXiv2009

Statistical Mechanics of Integral Membrane Protein Assembly

During the synthesis of integral membrane proteins (IMPs), the hydrophobic amino acids of the polypeptide sequence are partitioned mostly into the membrane interior and hydrophilic amino acids mostly into the aqueous exterior. We analyze the minimum free energy state of polypeptide sequences partitioned into alpha-helical transmembrane (TM) segments and the role of thermal fluctuations using a many-body statistical mechanics model. Results suggest that IMP TM segment partitioning shares important features with general theories of protein folding. For random polypeptide sequences, the minimum free energy state at room temperature is characterized by fluctuations in the number of TM segments with very long relaxation times. Simple assembly scenarios do not produce a unique number of TM segments and jamming phenomena interfere with segment placement. For sequences corresponding to IMPs, the minimum free energy structure with the wildtype number of segments is free of number fluctuations due to an anomalous gap in the energy spectrum, and simple assembly scenarios produce this structure. There is a threshold number of random point mutations beyond which the size of this gap is reduced so that the wildtype groundstate is destabilized and number fluctuations reappear.

cond-mat.soft↗
arXiv2008

Conformation of single-stranded RNA in a virus capsid: implications of dimensional reduction

The statistical mechanics of a treelike polymer in a confining volume is relevant to the packaging of the genome in RNA viruses. Making use of the mapping of the grand partition function of this system onto the statistical mechanics of a hard-core gas in two fewer spatial dimensions and of techniques developed for the evaluation of the equilibrium properties of a one-dimensional hard rod gas, we show how it is possible to determine the density and other key properties of a collection of rooted excluded-volume tress confined between two walls, both in the absence and in the presence of a one-dimensional external potential. We find, somewhat surprisingly, that in the case of key quantities, the statistical mechanics of the excluded volume, randomly branched polymer map exactly into corresponding problems for an unrestricted linear polymer.

cond-mat.stat-mech↗
arXiv2008

The confinement free energies of non-ideal branched polymers and ideal unbranched polymers are the same

We use the method of dimensional reduction to show that a branching polymer with excluded volume interaction confined between two flat plates has, in the thermodynamic limit, a confinement free energy and density profile that is the same as that of an ideal linear polymer with the same number of monomers and the same monomer-plate interaction potential. Condensation due to branching is exactly compensated by swelling due to excluded volume interaction.

cond-mat.stat-mech↗
arXiv2007

Thermodynamic restrictions on evolutionary optimization of transcription factor proteins

Conformational fluctuations are believed to play an important role in the process by which transcription factor proteins locate and bind their target site on the genome of a bacterium. Using a simple model, we show that the binding time can be minimized, under selective pressure, by adjusting the spectrum of conformational states so that the fraction of time spent in more mobile conformations is matched with the target recognition rate. The associated optimal binding time is then within an order of magnitude of the limiting binding time imposed by thermodynamics, corresponding to an idealized protein with instant target recognition. Numerical estimates suggest that typical bacteria operate in this regime of optimized conformational fluctuations.

cond-mat.soft↗
arXiv2007

Melting of Branched RNA Molecules

Stability of the branching structure of an RNA molecule is an important condition for its function. In this letter we show that the melting thermodynamics of RNA molecules is very sensitive to their branching geometry for the case of a molecule whose groundstate has the branching geometry of a Cayley Tree and whose pairing interactions are described by the Go model. Whereas RNA molecules with a linear geometry melt via a conventional continuous phase transition with classical exponents, molecules with a Cayley Tree geometry are found to have a free energy that seems smooth, at least within our precision. Yet, we show analytically that this free energy in fact has a mathematical singularity at the stability limit of the ordered structure. The correlation length appears to diverge on the high-temperature side of this singularity.

q-bio.BM↗
arXiv2005

Soft elasticity of RNA gels and negative Poisson ratio

We propose a model for the elastic properties of RNA gels. The model predicts anomalous elastic properties in the form of a negative Poisson ratio and shape instabilities. The anomalous elasticity is generated by the non-Gaussian force-deformation relation of single-stranded RNA. The effect is greatly magnified by broken rotational symmetry produced by double-stranded sequences and the concomitant soft modes of uniaxial elastomers.

cond-mat.soft↗
arXiv2004

Physics of RecA-mediated homologous recognition

Most proteins involved in processing DNA accomplish their activities as a monomer or as a component of a multimer containing a relatively small number of other elements. They generally act locally, binding to one or a few small regions of the DNA substrate. Striking exceptions are the \textit{E. coli} protein RecA and its homologues in other species, whose activities are associated with homologous DNA recombination. The active form of RecA in DNA recombination is a stiff nucleoprotein filament formed by RecA and DNA, within which the DNA is extended by 50%. Invoking physical and geometrical ideas, we show that the filamentary organization greatly enhances the rate of homologous recognition while preventing the formation of topological traps originating from multi-site recognition.

q-bio.BM↗