Minimum energy paths for conformational changes of viral capsids

In this work we study how a viral capsid can change conformation using techniques of Large Deviations Theory for stochastic differential equations. The viral capsid is a model of a complex system in which many units - the proteins forming the capsomers - interact by weak forces to form a structure with exceptional mechanical resistance. The destabilization of such a structure is interesting both per se, since it is related either to infection or maturation processes, and because it yields insights into the stability of complex structures in which the constitutive elements interact by weak attractive forces. We focus here on a simplified model of a dodecahederal viral capsid, and assume that the capsomers are rigid plaquettes with one degree of freedom each. We compute the most probable transition path from the closed capsid to the final configuration using minimum energy paths, and discuss the stability of intermediate states.Comment: 27 pages, 4 figures. New version, to appear in Physical Review

Γ\Gamma-limit of the cut functional on dense graph sequences

A sequence of graphs with diverging number of nodes is a dense graph sequence if the number of edges grows approximately as for complete graphs. To each such sequence a function, called graphon, can be associated, which contains information about the asymptotic behavior of the sequence. Here we show that the problem of subdividing a large graph in communities with a minimal amount of cuts can be approached in terms of graphons and the $\Gamma$-limit of the cut functional, and discuss the resulting variational principles on some examples. Since the limit cut functional is naturally defined on Young measures, in many instances the partition problem can be expressed in terms of the probability that a node belongs to one of the communities. Our approach can be used to obtain insights into the bisection problem for large graphs, which is known to be NP-complete.Comment: 25 pages, 5 figure

Preys’ exploitation of predators’ fear: when the caterpillar plays the Gruffalo

Alike the little mouse of the Gruffalo's tale, many harmless preys use intimidating deceptive signals as anti-predator strategies. For example, several caterpillars display eyespots and face-like colour patterns that are thought to mimic the face of snakes as deterrents to insectivorous birds. We develop a theoretical model to investigate the hypothesis that these defensive strategies exploit adaptive cognitive biases of birds, which make them much more likely to confound caterpillars with snakes than vice versa. By focusing on the information-processing mechanisms of decision-making, the model assumes that, during prey assessment, the bird accumulates noisy evidence supporting either the snake-escape or the caterpillar-attack motor responses, which compete against each other for execution. Competition terminates when the evidence for either one of the responses reaches a critical threshold. This model predicts a strong asymmetry and a strong negative correlation between the prey- and the predator-decision thresholds, which increase with the increasing risk of snake predation and assessment uncertainty. The threshold asymmetry causes an asymmetric distribution of false-negative and false-positive errors in the snake–caterpillar decision plane, which makes birds much more likely to be deceived by the intimidating signals of snake-mimicking caterpillars than by the alluring signals of caterpillar-mimicking snakes

A machine-learning procedure to detect network attacks

The goal of this note is to assess whether simple machine learning algorithms can be used to determine whether and how a given network has been attacked. The procedure is based on the $k$-Nearest Neighbor and the Random Forest classification schemes, using both intact and attacked Erd\H{o}s-R\'enyi, Barabasi-Albert and Watts-Strogatz networks to train the algorithm. The types of attacks we consider here are random failures and maximum-degree or maximum-betweenness node deletion. Each network is characterized by a list of 4 metrics, namely the normalized reciprocal maximum degree, the global clustering coefficient, the normalized average path length and the assortativity: a statistical analysis shows that this list of graph metrics is indeed significantly different in intact or damaged networks. We test the procedure by choosing both artificial and real networks, performing the attacks and applying the classification algorithms to the resulting graphs: the procedure discussed here turns out to be able to distinguish between intact networks and those attacked by the maximum-degree of maximum-betweenness deletions, but cannot detect random failures. Our results suggest that this approach may provide a basis for the analysis and detection of network attacks.Comment: 18 pages, 4 tables, 1 figur

Surface stresses in complex viral capsids and non-quasiequivalent viral architectures

Many larger and more complex viruses deviate from the capsid layouts predicted in the seminal Caspar-Klug theory of icosahedral viruses. Instead of being built from one type of capsid protein, they code for multiple distinct structural proteins that either break the local symmetry of the capsid protein building blocks (capsomers) in specific positions, or exhibit auxiliary proteins that stabilise the capsid shell. We investigate here the hypothesis that this occurs as a response to mechanical stress. For this, we construct a coarse-grained model of a viral capsid, derived from the experimentally determined atomistic positions of the capsid proteins, that represents the basic features of protein organisation in the viral capsid as described in Caspar-Klug theory. We focus here on viruses in the PRD1-adenovirus lineage. For T=28 viruses in this lineage, that have capsids formed from two distinct structural proteins, we show that the tangential shear stress in the viral capsid concentrates at the sites of local symmetry breaking. In the T=21,25 and 27 capsids, we show that stabilizing proteins decrease the tangential stress. These results suggest that mechanical properties can act as selective pressures on the evolution of capsid components, offsetting the coding cost imposed by the need for such additional protein components

Multi-Phase Equilibrium of Crystalline Solids

A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at interfaces, and the kinematics of such defects is discussed in some detail. A Gibbsian variational argument is used to derive the necessary bulk and interfacial conditions for multi-phase equilibrium (crystal-crystal and crystal-melt) where the allowed lattice variations involve the creation and transport of defects in the bulk and at the phase interface. An interfacial energy, assumed to depend on the interfacial dislocation density and the orientation of the interface with respect to the lattices of both phases, is also included in the analysis. Previous equilibrium results based on nonlinear elastic models for incoherent and coherent interfaces are recovered as special cases for when the lattice distortion is constrained to coincide with the macroscopic deformation gradient, thereby excluding bulk dislocations. The formulation is purely spatial and needs no recourse to a fixed reference configuration or an elastic-plastic decomposition of the strain. Such a decomposition can be introduced however through an incremental elastic deformation superposed onto an already dislocated state, but leads to additional equilibrium conditions. The presentation emphasizes the role of {configurational forces} as they provide a natural framework for the description and interpretation of singularities and phase transitions.Comment: 32 pages, to appear in Journal of the Mechanics and Physics of Solid