arXiv subjects

Michele Castellana

Publications and source records attributed to Michele Castellana.

At least 19 recordsLinked to original sources

arXiv2026

Interaction between cell membranes and protein inclusions in the large-deformation regime

Biological membranes are dynamic surfaces whose shape and function are critically influenced by protein inclusions (PIs). While membrane deformations induced by PIs have been extensively studied in the small-deformation regime, a variety of processes involves strong membrane deformations. We investigate the interaction between lipid membranes and PIs in the large deformation (LD) regime, with the finite-element method. We develop an approximate analytical solution that captures key features of the LD regime. We show that the force exerted by the membrane on a PI displays a non-monotonic behavior with respect to the PI vertical displacement. The qualitative features of this force appear to be independent of the protein geometry. For two interacting PIs, the membrane-mediated potential exhibits sub-power-law decay with inter-protein distance, reflecting the complex nature of the elastic medium. The interaction potential shows that conical PIs with identical and opposite orientations repel and attract, respectively, confirming the analogy between PI orientation and electric charge, in the LD regime. In the presence of membrane flows, we identify a characteristic velocity that separates two regimes in which bending rigidity and viscous effects dominate, respectively, implying the onset of flow-induced deformations above such velocity threshold. Overall, our results provide quantitative predictions for membrane-protein systems in biologically relevant scenarios involving LDs, with implications for protein sorting, clustering, and membrane trafficking.

physics.bio-ph↗

arXiv2025

IRENE: a fluId layeR finitE-elemeNt softwarE

We present a finite-element software library, IRENE, which allows to solve numerically the dynamics of a viscous fluid layer embedded in three-dimensional space. Unlike finite-element libraries present in the literature, IRENE can handle two-dimensional open surfaces with a wide range of boundary conditions, and inter-surface obstacles with any shapes, and is built upon the user-friendly and versatile finite element computational software (FEniCS). Also, the library can describe a wide range of physical regimes--both low-Reynolds-number and inertia-dominated ones--capturing the complex coupling between in-plane flows, out-of-plane deformations, surface tension, and elastic response. We validate IRENE against known analytical and numerical results, and demonstrate its capabilities through physical examples. Overall, IRENE provides a versatile and efficient tool for understanding fluid-layer dynamics on multiple physical scales, from flows of lipidic membranes on a microscopic level, to fluid flows on a macroscopic scale, to atmospheric air flows on a planetary level.

physics.flu-dyn↗

arXiv2025

Order parameter for non-mean-field spin glasses

We propose a novel renormalization group (RG) method for non mean-field models of spin glasses, which leads to the emergence of a novel order parameter. Unlike previous approaches where the RG procedure is based on a priori notions on the system, our analysis follows a minimality principle, where no a priori assumption is made. We apply our approach to a spin-glass model built on a hierarchical lattice. In the RG decimation procedure, a novel order parameter spontaneously emerges from the system symmetries, and self-similarity features of the RG transformation only. This order parameter is the projection of the spin configurations on the ground state of the system. Kadanoff's majority rule for ferromagnetic systems is replaced by a more complex scheme, which involves such novel order parameter. The ground state thus acts as a pattern which translates spin configurations from one length scale to another. The rescaling RG procedure is based on a minimal, information-theory approach and, combined with the decimation, it yields a complete RG transformation. Below the upper critical dimension, the predictions for the critical exponent $ν$, which describes the critical divergence of the correlation length, are in excellent agreement with numerical simulations from both this and previous studies. Overall, this study opens new avenues in the understanding of the critical ordering of realistic spin glasses, and it can be applied to spin-glass models on a cubic lattice and nearest-neighbor couplings which directly model spin-glass materials, such as AuFe, CuMn and other magnetic alloys.

cond-mat.dis-nn↗

arXiv2024

Parallelization of Gillespie algorithm based on binary words

We present an improvement of the Gillespie Exact Stochastic Simulation Algorithm, which leverages a bitwise representation of variables to perform independent simulations in parallel. We show that the subsequent gain in computational yield is significant, and it may allow to perform simulations of non-well mixed chemical systems. We illustrate this idea with simulations of Frank model, originally introduced to explain the emergence of homochirality in prebiotic systems.

cond-mat.stat-mech↗

arXiv2024

Inverse modeling of time-delayed interactions via the dynamic-entropy formalism

Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically-measured equal-time correlation functions. Focusing on collective motion of active units, this constraint is reasonable when the interaction timescale is much faster than that of the interacting units, as in starling flocks, yet it fails in a number of counter examples, as in leukocyte coordination (where signalling proteins diffuse among two cells). Here, we relax this assumption and develop a path integral approach to maximum-entropy framework, which includes delay in signalling. Our method is able to infer the strength of couplings and fields, but also the time required by the couplings to completely transfer information among the units. We demonstrate the validity of our approach providing excellent results on synthetic datasets of non-Markovian trajectories generated by the Heisenberg-Kuramoto and Vicsek models equipped with delayed interactions. As a proof of concept, we also apply the method to experiments on dendritic migration, where matching equal-time correlations results in a significant information loss.

physics.bio-ph↗

arXiv2022

On non-ideal chemical-reaction networks and phase separation

Much of the theory on chemical-reaction networks (CRNs) has been developed in the ideal-solution limit, where interactions between the solutes are negligible. However, there is a large variety of phenomena in biological cells and soft-matter physics which appear to deviate from the ideal-solution behaviour. Particularly striking is the case of liquid-liquid phase separation, which is typically caused by inter-particle interactions. Here, we revisit a number of known results in the domain of ideal CRNs, and we generalise and adapt them to arbitrary interactions between the solutes which stem from a given free energy. Among these is the form of the steady-state probability distribution and Lyapunov functions for complex-balanced networks, where the creation and annihilation rates are equal for all chemical complexes which appear as reactants or products in the CRN. Finally, we draw a phase diagram for complex-balanced reaction-diffusion solutions based on the minimisation of such Lyapunov function with a rationale similar to that of equilibrium thermodynamics, but for systems that may sustain non-equilibrium chemical currents at steady state. Nevertheless, we find that complex-balanced networks are not sufficient to create diffusion currents at steady state.

physics.bio-ph↗

arXiv2021

Long-time diffusion and energy transfer in polydisperse mixtures of particles with different temperatures

Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different temperatures, we probe these effects in dilute solutions and derive long-time friction and self-diffusion coefficients as functions of volume fractions, sizes and temperatures of particles in $d=2$ and 3 dimensions. Thus, we model excluded-volume interactions for nonequilibrium systems but also extend the scope to short-range soft potentials and compare our results to Brownian-dynamics simulations. Remarkably, we show that both viscosity and energy flux display a nonlinear dependence on size. The simplicity of our formalism allows to discover various interesting scenarios that can be relevant for biological systems and active colloids.

cond-mat.soft↗

arXiv2021

Steric interactions and out-of-equilibrium processes control the internal organization of bacteria

Despite the absence of a membrane-enclosed nucleus, the bacterial DNA is typically condensed into a compact body - the nucleoid. This compaction influences the localization and dynamics of many cellular processes including transcription, translation, and cell division. Here, we develop a model that takes into account steric interactions among the components of the Escherichia coli transcriptional-translational machinery (TTM) and out-of-equilibrium effects of mRNA transcription, translation, and degradation, in order to explain many observed features of the nucleoid. We show that steric effects, due to the different molecular shapes of the TTM components, are sufficient to drive equilibrium phase separation of the DNA, explaining the formation and size of the nucleoid. In addition, we show that the observed positioning of the nucleoid at midcell is due to the out-of-equilibrium process of messenger RNA (mRNA) synthesis and degradation: mRNAs apply a pressure on both sides of the nucleoid, localizing it to midcell. We demonstrate that, as the cell grows, the production of these mRNAs is responsible for the nucleoid splitting into two lobes, and for their well-known positioning to 1/4 and 3/4 positions on the long cell axis. Finally, our model quantitatively accounts for the observed expansion of the nucleoid when the pool of cytoplasmic mRNAs is depleted. Overall, our study suggests that steric interactions and out-of-equilibrium effects of the TTM are key drivers of the internal spatial organization of bacterial cells.

q-bio.CB↗

arXiv2021

Two timescales control the creation of large protein aggregates in cells

Protein aggregation is of particular interest due to its connection with many diseases and disorders. Many factors can alter the dynamics and result of this process, one of them being the diffusivity of the monomers and aggregates in the system. Here, we study experimentally and theoretically an aggregation process in cells, and we identify two distinct physical timescales that set the number and size of aggregates. The first timescale involves fast aggregation of small clusters freely diffusing in the cytoplasm, while, in the second one, the aggregates are larger than the pore size of the cytoplasm and thus barely diffuse, and the aggregation process is slowed down. However, the process is not entirely halted, potentially reflecting a myriad of active but random forces forces that stir the aggregates. Such slow timescale is essential to account for the experimental results of the aggregation process. These results could also have implications in other processes of spatial organization in cell biology, such as phase-separated droplets.

physics.bio-ph↗

arXiv2021

Reply to comment on 'Real-space renormalization-group methods for hierarchical spin glasses'

In their comment, Angelini et al. object to the conclusion of [J. Phys. A: Math. Theor., 52:445002, 2019] (1), where we show that in [Phys. Rev. B, 87:134201, 2013] the exponent $ν$ has been obtained by applying a mathematical relation in a regime where this relation is not valid. We observe that the criticism above on the mathematical validity of such relation has not been addressed in the comment. Our criticism thus remains valid, and disproves the conclusions of the comment. This constitutes the main point of this reply. We also provide a point-by-point response and discussion of Angelini et al.'s claims. First, Angelini et al. claim that the prediction $2^{1/ν}=1$ of [1] is incorrect, because it results from the relation $λ_{\rm max}=2^{1/ν}$ between the largest eigenvalue of the linearized renormalization-group (RG) transformation and $ν$, which cannot be applied to the ensemble renormalization group (ERG) method, because for the ERG $λ_{\rm max} =1 $. However, the feature $λ_{\rm max}=1$ is specific to the ERG transformation and it does not give any grounds for questioning the validity of the general relation $λ_{\rm max}=2^{1/ν}$ specifically for the ERG transformation. Second, Angelini et al. claim that $ν$ should be extracted from an early RG regime (A), as opposed to the asymptotic regime (B) used to estimate $ν$ in [1] and that (B) is dominated by finite-size effects. Still, (A) is a small-wavelength, non-critical regime, which cannot characterize the critical exponent $ν$ related to the divergence of the correlation length. Also, the fact that (B) involves finite-size effects is a feature specific to the ERG, and gives no rationale for extracting $ν$ from (A). Finally, we refute the remaining claims made by Angelini et al., and thus stand by our assertion that the ERG method yields a prediction given by $2^{1/ν}=1$.

cond-mat.dis-nn↗

arXiv2019

A statistical-inference approach to reconstruct inter-cellular interactions in cell-migration experiments

Migration of cells can be characterized by two, prototypical types of motion: individual and collective migration. We propose a statistical-inference approach designed to detect the presence of cell-cell interactions that give rise to collective behaviors in cell-motility experiments. Such inference method has been first successfully tested on synthetic motional data, and then applied to two experiments. In the first experiment, cell migrate in a wound-healing model: when applied to this experiment, the inference method predicts the existence of cell-cell interactions, correctly mirroring the strong intercellular contacts which are present in the experiment. In the second experiment, dendritic cells migrate in a chemokine gradient. Our inference analysis does not provide evidence for interactions, indicating that cells migrate by sensing independently the chemokine source. According to this prediction, we speculate that mature dendritic cells disregard inter-cellular signals that could otherwise delay their arrival to lymph vessels.

q-bio.CB↗

arXiv2019

Real-space renormalization-group methods for hierarchical spin glasses

We focus on two real-space renormalization-group (RG) methods recently proposed for a hierarchical model of a spin glass: A sample-by-sample method, in which the RG transformation is performed separately on each disorder sample, and an ensemble RG (ERG) method [M. C. Angelini, G. Parisi, and F. Ricci-Tersenghi. Ensemble renormalization group for disordered systems. $\textit{Phys. Rev. B}$, 87(13):134201, 2013] in which the transformation is based on an average over samples. Above the upper critical dimension, the sample-by-sample method yields the correct mean-field value for the critical exponent $ν$ related to the divergence of the correlation length, while it does not predict the correct qualitative behavior of $ν$ below the upper critical dimension. On the other hand, the ERG procedure has been claimed to predict the correct behavior of $ν$ both above and below the upper critical dimension. Here, we straighten out the reasons for the discrepancy between the two methods above, by demonstrating that the ERG method predicts a marginally stable critical fixed point, thus implying a prediction for the critical exponent $ν$ given by $2^{1/ν} = 1$. This prediction disagrees, on a qualitative and quantitative level, both with the mean-field value of $ν$ above the critical dimension, and with numerical estimates of $ν$ below the upper critical dimension. Therefore, our results show that finding a real-space RG method for spin glasses which yields the correct prediction for universal quantities below the upper critical dimension is still an open problem, for which our analysis may provide some general guidance for future studies.

cond-mat.dis-nn↗

arXiv2019

Symmetry reduction of the three-body problem based on Euler angles

We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and orientation, respectively, of a triangle with the three bodies located at the vertices. The radial variables are given by the distances between a reference body and the other two, and by the angle at the reference body between the other two. Such radial variables set the potential energy of the system, and they are reminiscent of the inter-body distance in the two-body problem. On the other hand, the angular variables are the Euler angles relative to a rigid rotation of the triangle, and they are analogous to the polar and azimuthal angle of the vector between the two bodies in the two-body problem. We show that the rotational symmetry allows us to obtain a closed set of eight Hamilton equations of motion, whose generalized coordinates are the thee radial variables and one additional angle, for which we provide the following geometrical interpretation. Given a reference body, we consider the plane through it which is orthogonal to the line between the reference and a second body. We show that the angular variable above is the angle between the plane projection of the angular-momentum vector, and the projection of the radius between the reference and the third body.

physics.class-ph↗

arXiv2019

Optimal localization patterns in bacterial protein synthesis

In $\textit{Escherichia coli}$ bacterium, the molecular compounds involved in protein synthesis, messenger RNAs (mRNAs) and ribosomes, show marked intracellular localization patterns. Yet a quantitative understanding of the physical principles which would allow one to control protein synthesis by designing, bioengineering, and optimizing these localization patterns is still lacking. In this study, we consider a scenario where a synthetic modification of mRNA reaction-diffusion properties allows for controlling the localization and stoichiometry of mRNAs and polysomes$\mathrm{-}$complexes of multiple ribosomes bound to mRNAs. Our analysis demonstrates that protein synthesis can be controlled, e.g., optimally enhanced or inhibited, by leveraging mRNA spatial localization and stoichiometry only, without resorting to alterations of mRNA expression levels. We identify the physical mechanisms that control the protein-synthesis rate, highlighting the importance of colocalization between mRNAs and freely diffusing ribosomes, and the interplay between polysome stoichiometry and excluded-volume effects due to the DNA nucleoid. The genome-wide, quantitative predictions of our work may allow for a direct verification and implementation in cell-biology experiments, where localization patterns and protein-synthesis rates may be monitored by fluorescence microscopy in single cells and populations.

physics.bio-ph↗

arXiv2016

Spatial organization of bacterial transcription and translation

In bacteria such as $\textit{Escherichia coli}$, DNA is compacted into a nucleoid near the cell center, while ribosomes$-$molecular complexes that translate messenger RNAs (mRNAs) into proteins$-$are mainly localized at the poles. We study the impact of this spatial organization using a minimal reaction-diffusion model for the cellular transcriptional-translational machinery. Our model predicts that $\sim 90\%$ of mRNAs are segregated to the poles and reveals a "circulation" of ribosomes driven by the flux of mRNAs, from synthesis in the nucleoid to degradation at the poles. To address the existence of non-specific, transient interactions between ribosomes and mRNAs, we developed a novel method to efficiently incorporate such transient interactions into reaction-diffusion equations, which allowed us to quantify the biological implications of such non-specific interactions, e.g. for ribosome efficiency.

q-bio.SC↗

arXiv2015

Non-perturbative effects in spin glasses

We present a numerical study of an Ising spin glass with hierarchical interactions - the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to $d\geq4$ and $d<4$ for the $d$-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the $ε$-expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent $ν$ in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only $\sim 2\%$ from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.

cond-mat.dis-nn↗

arXiv2015

Hierarchical spin glasses in a magnetic field: A renormalization-group study

By using renormalization-group (RG) methods, we study a non-mean-field model of a spin glass built on a hierarchical lattice, the hierarchical Edwards-Anderson model in a magnetic field. We investigate the spin-glass transition in a field by studying the existence of a stable critical RG fixed point (FP) with perturbation theory. In the parameter region where the model has a mean-field behavior - corresponding to $d \geq 4$ for a $d$-dimensional Ising model - we find a stable FP that corresponds to a spin-glass transition in a field. In the non-mean-field parameter region the FP above is unstable, and we determined exactly all other FPs: to our knowledge, this is the first time that all perturbative FPs for the full set of RG equations of a spin glass in a field have been characterized in the non-mean-field region. We find that all potentially stable FPs in the non-mean-field region have a nonzero imaginary part: this constitutes, to the best of our knowledge, the first demonstration for a spin glass in a field that there is no perturbative FP corresponding to a spin-glass transition in the non-mean-field region. Finally, we discuss the possible interpretations of this result, such as the absence of a phase transition in a field, or the existence of a transition associated with a non-perturbative FP.

cond-mat.dis-nn↗

arXiv2014

Entropic forces in a non-equilibrium system: Flocks of birds

When birds come together to form a flock, the distribution of their individual velocities narrows around the mean velocity of the flock. We argue that, in a broad class of models for the joint distribution of positions and velocities, this narrowing generates an entropic force that opposes the cohesion of the flock. The strength of this force depends strongly on the nature of the interactions among birds: if birds are coupled to a fixed number of neighbors, the entropic forces are weak, while if they couple to all other birds within a fixed distance, the entropic forces are sufficient to tear a flock apart. Similar entropic forces should occur in other non-equilibrium systems. For the joint distribution of protein structures and amino-acid sequences, these forces favor the occurrence of "highly designable" structures.

cond-mat.stat-mech↗