Cortical propagation tracks functional recovery after stroke.

Stroke is a debilitating condition affecting millions of people worldwide. The development of improved rehabilitation therapies rests on finding biomarkers suitable for tracking functional damage and recovery. To achieve this goal, we perform a spatiotemporal analysis of cortical activity obtained by wide-field calcium images in mice before and after stroke. We compare spontaneous recovery with three different post-stroke rehabilitation paradigms, motor training alone, pharmacological contralesional inactivation and both combined. We identify three novel indicators that are able to track how movement-evoked global activation patterns are impaired by stroke and evolve during rehabilitation: the duration, the smoothness, and the angle of individual propagation events. Results show that, compared to pre-stroke conditions, propagation of cortical activity in the subacute phase right after stroke is slowed down and more irregular. When comparing rehabilitation paradigms, we find that mice treated with both motor training and pharmacological intervention, the only group associated with generalized recovery, manifest new propagation patterns, that are even faster and smoother than before the stroke. In conclusion, our new spatiotemporal propagation indicators could represent promising biomarkers that are able to uncover neural correlates not only of motor deficits caused by stroke but also of functional recovery during rehabilitation. In turn, these insights could pave the way towards more targeted post-stroke therapies.

Reconstruction scheme for excitatory and inhibitory dynamics with quenched disorder: application to zebrafish imaging.

An inverse procedure is developed and tested to recover functional and structural information from global signals of brains activity. The method assumes a leaky-integrate and fire model with excitatory and inhibitory neurons, coupled via a directed network. Neurons are endowed with a heterogenous current value, which sets their associated dynamical regime. By making use of a heterogenous mean-field approximation, the method seeks to reconstructing from global activity patterns the distribution of in-coming degrees, for both excitatory and inhibitory neurons, as well as the distribution of the assigned currents. The proposed inverse scheme is first validated against synthetic data. Then, time-lapse acquisitions of a zebrafish larva recorded with a two-photon light sheet microscope are used as an input to the reconstruction algorithm. A power law distribution of the in-coming connectivity of the excitatory neurons is found. Local degree distributions are also computed by segmenting the whole brain in sub-regions traced from annotated atlas.

Condensation transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation.

The thermodynamics of the discrete nonlinear Schrödinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a thermalized phase and a condensed (localized) one occurs at the infinite-temperature line. Inequivalence between statistical ensembles characterizes the condensed phase, where the grand-canonical representation does not apply. The control over finite-size corrections of the microcanonical partition function allows to design an experimental test of delocalized negative-temperature states in lattices of cold atoms.

Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion.

Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path ℓ. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence.

We perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of the Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1 A.U., with a power-law index of around -4. Based on our measurements, we demonstrate that either a significant (>50%) fraction of the total turbulent energy flux is dissipated in this range of scales, or the characteristic nonlinear interaction time of the turbulence decreases dramatically from the expectation based solely on the dispersive nature of nonlinearly interacting kinetic Alfvén waves.

Resilience for stochastic systems interacting via a quasi-degenerate network.

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network, two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear lattice, noise gets amplified via a self-consistent process, which we trace back to the degenerate spectrum of the embedding support. The same phenomenon holds when the system is bound to explore a quasidegenerate network. In this case, the eigenvalues of the Laplacian operator, which governs species diffusion, accumulate over a limited portion of the complex plane. The larger the network, the more pronounced the amplification. Beyond a critical network size, a system deemed deterministically stable, hence resilient, can develop seemingly regular patterns in the concentration amount. Non-normality and quasidegenerate networks may, therefore, amplify the inherent stochasticity and so contribute to altering the perception of resilience, as quantified via conventional deterministic methods.

Boundary-induced instabilities in coupled oscillators.

A novel class of nonequilibrium phase transitions at zero temperature is found in chains of nonlinear oscillators. For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schrödinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a nontrivial interfacial region where the kinetic temperature is finite. Dynamics in such a supercritical state displays anomalous chaotic properties whereby some observables are nonextensive and transport is superdiffusive. At finite temperatures, the transition is smoothed, but the temperature profile is still nonmonotonic.

Variation and constraints in species-specific promoter sequences.

A vast literature is nowadays devoted to the search of correlations between transcription related functions and the composition of sequences upstream the Transcription Start Site. Little is known about the possible functional effects of nucleotide distributions on the conformational landscape of DNA in such regions. We have used suitable statistical indicators for identifying sequences that may play an important role in regulating transcription processes. In particular, we have analyzed base composition, periodicity and information content in sets of aligned promoters clustered according to functional information in order to obtain an insight on the main structural differences between promoters regulating genes with different functions. Our results show that when we select promoters according to some biological information, in a single species, at least in vertebrates, we observe structurally different classes of sequences. The highly variable and differentiated gene expression patterns may explain the great extent of structural differentiation observed in complex organisms. In fact, despite our analysis is focused on Homo sapiens, we provide also a comparison with other species, selected at different positions in the phylogenetic tree.

Evolutionary trends of GC/AT distribution patterns in promoters.

Nucleotide distributions in genomes is known not to be random, showing the presence of specific motifs, long and short range correlations, periodicities, etc. Particularly, motifs are critical for the recognition by specific proteins affecting chromosome organization, transcription and DNA replication but little is known about the possible functional effects of nucleotide distributions on the conformational landscape of DNA, putatively leading to differential selective pressures throughout evolution. Promoter sequences have a fundamental role in the regulation of gene activity and a vast literature suggests that their conformational landscapes may be a critical factor in gene expression dynamics. On these grounds, with the aim of investigating the putative existence of phylogenetic patterns of promoter base distributions, we analyzed GC/AT ratios along the 1000 nucleotide sequences upstream of TSS in wide sets of promoters belonging to organisms ranging from bacteria to pluricellular eukaryotes. The data obtained showed very clear phylogenetic trends throughout evolution of promoter sequence base distributions. Particularly, in all cases either GC-rich or AT-rich monotone gradients were observed: the former being present in eukaryotes, the latter in bacteria along with strand biases. Moreover, within eukaryotes, GC-rich gradients increased in length from unicellular organisms to plants, to vertebrates and, within them, from ancestral to more recent species. Finally, results were thoroughly discussed with particular attention to the possible correlation between nucleotide distribution patterns, evolution, and the putative existence of differential selection pressures, deriving from structural and/or functional constraints, between and within prokaryotes and eukaryotes.

Fragment 101-108 of myelin oligodendrocyte glycoprotein: a possible lead compound for multiple sclerosis.

Multiple Sclerosis (MS) is a highly invalidating autoimmune disease of the central nervous system, leading to progressive paralysis and, sometimes, to premature death. One of the potential targets of the autoimmune reaction is the myelin protein MOG (Myelin Oligodendrocyte Glycoprotein). Since the 101-108 fragment of MOG plays a key role in the interaction with the MS-autoantibody 8-18C5, we performed an analysis of the equilibrium conformations of this peptide using the Replica Exchange Molecular Dynamics technique in conjunction with the Generalized Born continuum solvent model. Four variants of the peptide, stabilized by a disulfide bond, were also studied. We found that a significant fraction of the equilibrium population retains the original beta-hairpin conformation, and the amount of crystal-like conformations increases in the disulfide-closed analogues. When the equilibrium structures were used in docking simulations with the 8-18C5 autoantibody, we discovered the existence of a docking funnel whose bottom is populated by stable complexes where the peptide occupies the same region of space that was occupied in the crystal. It follows that the MOG 101-108 fragment represents a promising starting point for the design of a drug capable of blocking the 8-18C5 antibody. The molecule may also be used for the development of a diagnostic assay for multiple sclerosis.

Stochastic dynamics of model proteins on a directed graph.

A method for reconstructing the potential energy landscape of simple polypeptidic chains is described. We show how to obtain a faithful representation of the energy landscape in terms of a suitable directed graph. Topological and dynamical indicators of the graph are shown to yield an effective estimate of the time scales associated with both folding and equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined as a temperature-dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into "hubs" while redefining their connectivity. We show that the dynamical properties at large time scales are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to distinguish between "fast" and "slow" folders, one has to look at the kinetic properties of the corresponding directed graphs. In particular, we find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time while for the bad folder these time scales are comparable.

Desynchronization and pattern formation in a noisy feed-forward oscillator network.

We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is studied in a region of the parameters that would yield deterministic synchronization. Non-normal directed couplings seed a coherent amplification of the perturbation: this latter manifests as a modulation, transversal to the limit cycle, which gains in potency node after node. If the lattice extends long enough, the initial synchrony gets eventually lost, and the system moves toward a nontrivial attractor, which can be analytically characterized as an asymptotic splay state. The noise assisted instability, ultimately vehiculated and amplified by the non-normal nature of the imposed couplings, eventually destabilizes also this second attractor. This phenomenon yields spatiotemporal patterns, which cannot be anticipated by a conventional linear stability analysis.

A Method for the Structure-Based, Genome-Wide Analysis of Bacterial Intergenic Sequences Identifies Shared Compositional and Functional Features.

In this paper, we propose a computational strategy for performing genome-wide analyses of intergenic sequences in bacterial genomes. Following similar directions of a previous paper, where a method for genome-wide analysis of eucaryotic Intergenic sequences was proposed, here we developed a tool for implementing similar concepts in bacteria genomes. This allows us to (i) classify intergenic sequences into clusters, characterized by specific global structural features and (ii) draw possible relations with their functional features.

Stability and kinetic properties of C5-domain from myosin binding protein C and its mutants.

The impact of three mutations of domain C5 from myosin binding protein C, correlated to Familial Hypertrophic Cardiomyopathy, has been assessed through molecular dynamics simulations based on a native centric protein modeling. The severity of the phenotype correlates with the shift in unfolding temperature determined by the mutations. A contact probability analysis reveals a folding process of the C5 domain originating in the region of DE and FG loops and propagating toward the area proximal to CD and EF loops. This suggests that mutation effects gain relevance in the proximity to the area where folding originates. The scenario is also confirmed by the analysis of the kinetics of 27 test mutations evenly distributed throughout the entire C5 domain.

Computational analysis of folding and mutation properties of C5 domain of myosin binding protein C.

Thermal folding molecular dynamics simulations of the domain C5 of Myosin binding protein C were performed using a native-centric model to study the role of three mutations related to Familial Hypertrophic Cardiomyopathy. Mutation of Asn755 causes the largest shift of the folding temperature, and the residue is located in the CFGA' beta-sheet featuring the highest phi-values. The mutation thus appears to reduce the thermodynamic stability in agreement with experimental data. The mutations on Arg654 and Arg668, conversely, cause little change in the folding temperature and they reside in the low phi-value BDE beta-sheet, so that their pathological role cannot be related to impairment of the folding process but possibly to the binding with target molecules. As the typical signature of Domain C5 is the presence of a longer and destibilizing CD-loop with respect to the other Ig-like domains, we completed the work with a bioinformatic analysis of this loop showing a high density of negative charge and low hydrophobicity. This indicates the CD-loop as a natively unfolded sequence with a likely coupling between folding and ligand binding.

Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs.

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power α of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards or from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For 0≤α<1, the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which such size is proportional to the system size N, the stationary current is independent on N. For α>1, heat transport mostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an α-dependent characteristic exponent.

Stability of the splay state in pulse-coupled networks.

The stability of the dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse width and the interspike interval. More precisely, the spectrum of Floquet exponents turns out to consist of three components: (i) one that coincides with the predictions of the mean-field analysis [Abbott and van Vreesvijk, Phys. Rev. E 48, 1483 (1993)], (ii) a component measuring the instability of "finite-frequency" modes, (iii) a number of "isolated" eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities (the Floquet exponent being proportional to the network size). Finally, as a side result, we find that the splay state can be stable even for inhibitory coupling.

Intertangled stochastic motifs in networks of excitatory-inhibitory units.

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust internode correlations that persist at large distances. Antiphase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns that invade the network as a whole. These patterns are lacking under the idealized deterministic scenario, and could provide hints on how living systems implement and handle a large gallery of delicate computational tasks.

Multiparticle collision simulations of two-dimensional one-component plasmas: Anomalous transport and dimensional crossovers.

By means of hybrid multiparticle collsion-particle-in-cell (MPC-PIC) simulations we study the dynamical scaling of energy and density correlations at equilibrium in moderately coupled two-dimensional (2D) and quasi-one-dimensional (1D) plasmas. We find that the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations in 1D systems with three global conservation laws hold true also for 2D systems that are more extended along one of the two spatial dimensions. Moreover, from the analysis of the equilibrium energy correlators and density structure factors of both 1D and 2D neutral plasmas, we find that neglecting the contribution of the fluctuations of the vanishing self-consistent electrostatic fields overestimates the interval of frequencies over which the anomalous transport is observed. Such violations of the expected scaling in the currents correlation are found in different regimes, hindering the observation of the asymptotic scaling predicted by the theory.

Noise-driven neuromorphic tuned amplifier.

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.