Force and kinetics of fast and slow muscle myosin determined with a synthetic sarcomere-like nanomachine.

Myosin II is the muscle molecular motor that works in two bipolar arrays in each thick filament of the striated (skeletal and cardiac) muscle, converting the chemical energy into steady force and shortening by cyclic ATP-driven interactions with the nearby actin filaments. Different isoforms of the myosin motor in the skeletal muscles account for the different functional requirements of the slow muscles (primarily responsible for the posture) and fast muscles (responsible for voluntary movements). To clarify the molecular basis of the differences, here the isoform-dependent mechanokinetic parameters underpinning the force of slow and fast muscles are defined with a unidimensional synthetic nanomachine powered by pure myosin isoforms from either slow or fast rabbit skeletal muscle. Data fitting with a stochastic model provides a self-consistent estimate of all the mechanokinetic properties of the motor ensemble including the motor force, the fraction of actin-attached motors and the rate of transition through the attachment-detachment cycle. The achievements in this paper set the stage for any future study on the emergent mechanokinetic properties of an ensemble of myosin molecules either engineered or purified from mutant animal models or human biopsies.

Application limits of the scaling relations for Monte Carlo simulations in diffuse optics. Part 1: theory.

Monte Carlo (MC) is a powerful tool to study photon migration in scattering media, yet quite time-consuming to solve inverse problems. To speed up MC-simulations, scaling relations can be applied to an existing initial MC-simulation to generate a new data-set with different optical properties. We named this approach trajectory-based since it uses the knowledge of the detected photon trajectories of the initial MC-simulation, in opposition to the slower photon-based approach, where a novel MC-simulation is rerun with new optical properties. We investigated the convergence and applicability limits of the scaling relations, both related to the likelihood that the sample of trajectories considered is representative also for the new optical properties. For absorption, the scaling relation contains smoothly converging Lambert-Beer factors, whereas for scattering it is the product of two quickly diverging factors, whose ratio, for NIRS cases, can easily reach ten orders of magnitude. We investigated such instability by studying the probability-distribution for the number of scattering events in trajectories of given length. We propose a convergence test of the scattering scaling relation based on the minimum-maximum number of scattering events in recorded trajectories. We also studied the dependence of MC-simulations on optical properties, most critical in inverse problems, finding that scattering derivatives are ascribed to small deviations in the distribution of scattering events from a Poisson distribution. This paper, which can also serve as a tutorial, helps to understand the physics of the scaling relations with the causes of their limitations and devise new strategies to deal with them.

Integrins regulate hERG1 dynamics by girdin-dependent Gαi3: signaling and modeling in cancer cells.

The hERG1 potassium channel is aberrantly over expressed in tumors and regulates the cancer cell response to integrin-dependent adhesion. We unravel a novel signaling pathway by which integrin engagement by the ECM protein fibronectin promotes hERG1 translocation to the plasma membrane and its association with ß1 integrins, by activating girdin-dependent Gαi3 proteins and protein kinase B (Akt). By sequestering hERG1, ß1 integrins make it avoid Rab5-mediated endocytosis, where unbound channels are degraded. The cycle of hERG1 expression determines the resting potential (Vrest) oscillations and drives the cortical f-actin dynamics and thus cell motility. To interpret the slow biphasic kinetics of hERG1/ß1 integrin interplay, we developed a mathematical model based on a generic balanced inactivation-like module. Integrin-mediated cell adhesion triggers two contrary responses: a rapid stimulation of hERG1/ß1 complex formation, followed by a slow inhibition which restores the initial condition. The protracted hERG1/ß1 integrin cycle determines the slow time course and cyclic behavior of cell migration in cancer cells.

Stochastic Turing patterns of trichomes in Arabidopsis leaves.

Biological patterns that emerge during the morphogenesis of multicellular organisms can display high precision at large scales, while at cellular scales, cells exhibit large fluctuations stemming from cell-cell differences in molecular copy numbers also called demographic noise. We study the conflicting interplay between high precision and demographic noise in trichome patterns on the epidermis of wild-type Arabidopsis thaliana leaves, as a two-dimensional model system. We carry out a statistical characterization of these patterns and show that their power spectra display fat tails-a signature compatible with noise-driven stochastic Turing patterns-which are absent in power spectra of patterns driven by deterministic instabilities. We then present a theoretical model that includes demographic noise stemming from birth-death processes of genetic regulators which we study analytically and by stochastic simulations. The model captures the observed experimental features of trichome patterns.

Brain-wide neuron quantification toolkit reveals strong sexual dimorphism in the evolution of fear memory.

Fear responses are functionally adaptive behaviors that are strengthened as memories. Indeed, detailed knowledge of the neural circuitry modulating fear memory could be the turning point for the comprehension of this emotion and its pathological states. A comprehensive understanding of the circuits mediating memory encoding, consolidation, and retrieval presents the fundamental technological challenge of analyzing activity in the entire brain with single-neuron resolution. In this context, we develop the brain-wide neuron quantification toolkit (BRANT) for mapping whole-brain neuronal activation at micron-scale resolution, combining tissue clearing, high-resolution light-sheet microscopy, and automated image analysis. The robustness and scalability of this method allow us to quantify the evolution of activity patterns across multiple phases of memory in mice. This approach highlights a strong sexual dimorphism in recruited circuits, which has no counterpart in the behavior. The methodology presented here paves the way for a comprehensive characterization of the evolution of fear memory.

Prestrain-induced contraction in one-dimensional random elastic chains.

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. Motivated by this observation, we here consider a minimal model in one dimension to set the stage for understanding the response of such networks as a function of the prestrain. To this end we consider a chain [one-dimensional (1D) network] of elastic springs upon which a random, zero mean, finite variance prestrain is imposed. Numerical simulations and analytical predictions quantify the magnitude of the contraction as a function of the variance of the prestrain, and show that the chain always shrinks. To test these predictions, we vary the topology of the chain, consider more complex connectivity and show that our results are relatively robust to these changes.

Spectral pruning of fully connected layers.

Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the eigenvalues can be used to rank the nodes' importance within the ensemble. Indeed, we will prove that sorting the nodes based on their associated eigenvalues, enables effective pre- and post-processing pruning strategies to yield massively compacted networks (in terms of the number of composing neurons) with virtually unchanged performance. The proposed methods are tested for different architectures, with just a single or multiple hidden layers, and against distinct classification tasks of general interest.

Fast whole-brain imaging of seizures in zebrafish larvae by two-photon light-sheet microscopy.

Light-sheet fluorescence microscopy (LSFM) enables real-time whole-brain functional imaging in zebrafish larvae. Conventional one-photon LSFM can however induce undesirable visual stimulation due to the use of visible excitation light. The use of two-photon (2P) excitation, employing near-infrared invisible light, provides unbiased investigation of neuronal circuit dynamics. However, due to the low efficiency of the 2P absorption process, the imaging speed of this technique is typically limited by the signal-to-noise-ratio. Here, we describe a 2P LSFM setup designed for non-invasive imaging that enables quintuplicating state-of-the-art volumetric acquisition rate of the larval zebrafish brain (5 Hz) while keeping low the laser intensity on the specimen. We applied our system to the study of pharmacologically-induced acute seizures, characterizing the spatial-temporal dynamics of pathological activity and describing for the first time the appearance of caudo-rostral ictal waves (CRIWs).

Training of sparse and dense deep neural networks: Fewer parameters, same performance.

Deep neural networks can be trained in reciprocal space by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues while freezing the eigenvectors yields a substantial compression of the parameter space. This latter scales by definition with the number of computing neurons. The classification scores as measured by the displayed accuracy are, however, inferior to those attained when the learning is carried in direct space for an identical architecture and by employing the full set of trainable parameters (with a quadratic dependence on the size of neighbor layers). In this paper, we propose a variant of the spectral learning method as in Giambagli et al. [Nat. Commun. 12, 1330 (2021)2041-172310.1038/s41467-021-21481-0], which leverages on two sets of eigenvalues for each mapping between adjacent layers. The eigenvalues act as veritable knobs which can be freely tuned so as to (1) enhance, or alternatively silence, the contribution of the input nodes and (2) modulate the excitability of the receiving nodes with a mechanism which we interpret as the artificial analog of the homeostatic plasticity. The number of trainable parameters is still a linear function of the network size, but the performance of the trained device gets much closer to those obtained via conventional algorithms, these latter requiring, however, a considerably heavier computational cost. The residual gap between conventional and spectral trainings can be eventually filled by employing a suitable decomposition for the nontrivial block of the eigenvectors matrix. Each spectral parameter reflects back on the whole set of internode weights, an attribute which we effectively exploit to yield sparse networks with stunning classification abilities as compared to their homologs trained with conventional means.

Deep learning and alignment of spatially resolved single-cell transcriptomes with Tangram.

Charting an organs' biological atlas requires us to spatially resolve the entire single-cell transcriptome, and to relate such cellular features to the anatomical scale. Single-cell and single-nucleus RNA-seq (sc/snRNA-seq) can profile cells comprehensively, but lose spatial information. Spatial transcriptomics allows for spatial measurements, but at lower resolution and with limited sensitivity. Targeted in situ technologies solve both issues, but are limited in gene throughput. To overcome these limitations we present Tangram, a method that aligns sc/snRNA-seq data to various forms of spatial data collected from the same region, including MERFISH, STARmap, smFISH, Spatial Transcriptomics (Visium) and histological images. Tangram can map any type of sc/snRNA-seq data, including multimodal data such as those from SHARE-seq, which we used to reveal spatial patterns of chromatin accessibility. We demonstrate Tangram on healthy mouse brain tissue, by reconstructing a genome-wide anatomically integrated spatial map at single-cell resolution of the visual and somatomotor areas.

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.

Robust, coherent, and synchronized circadian clock-controlled oscillations along Anabaena filaments.

Circadian clocks display remarkable reliability despite significant stochasticity in biomolecular reactions. We study the dynamics of a circadian clock-controlled gene at the individual cell level in Anabaena sp. PCC 7120, a multicellular filamentous cyanobacterium. We found significant synchronization and spatial coherence along filaments, clock coupling due to cell-cell communication, and gating of the cell cycle. Furthermore, we observed low-amplitude circadian oscillatory transcription of kai genes encoding the post-transcriptional core oscillatory circuit and high-amplitude oscillations of rpaA coding for the master regulator transducing the core clock output. Transcriptional oscillations of rpaA suggest an additional level of regulation. A stochastic one-dimensional toy model of coupled clock cores and their phosphorylation states shows that demographic noise can seed stochastic oscillations outside the region where deterministic limit cycles with circadian periods occur. The model reproduces the observed spatio-temporal coherence along filaments and provides a robust description of coupled circadian clocks in a multicellular organism.

Machine learning in spectral domain.

Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvalues and eigenvectors of transfer operators in direct space. The proposed method is ductile and can be tailored to return either linear or non-linear classifiers. Adjusting the eigenvalues, when freezing the eigenvectors entries, yields performances that are superior to those attained with standard methods restricted to operate with an identical number of free parameters. To recover a feed-forward architecture in direct space, we have postulated a nested indentation of the eigenvectors. Different non-orthogonal basis could be employed to export the spectral learning to other frameworks, as e.g. reservoir computing.

Analysis and forecast of COVID-19 spreading in China, Italy and France.

In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window 22 / 01 - 15 / 03 / 2020 . A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-infected-recovered-deaths model indicates that the kinetic parameter that describes the rate of recovery seems to be the same, irrespective of the country, while the infection and death rates appear to be more variable. The model places the peak in Italy around March 21st 2020, with a peak number of infected individuals of about 26000 (not including recovered and dead) and a number of deaths at the end of the epidemics of about 18,000. Since the confirmed cases are believed to be between 10 and 20% of the real number of individuals who eventually get infected, the apparent mortality rate of COVID-19 falls between 4% and 8% in Italy, while it appears substantially lower, between 1% and 3% in China. Based on our calculations, we estimate that 2500 ventilation units should represent a fair figure for the peak requirement to be considered by health authorities in Italy for their strategic planning. Finally, a simulation of the effects of drastic containment measures on the outbreak in Italy indicates that a reduction of the infection rate indeed causes a quench of the epidemic peak. However, it is also seen that the infection rate needs to be cut down drastically and quickly to observe an appreciable decrease of the epidemic peak and mortality rate. This appears only possible through a concerted and disciplined, albeit painful, effort of the population as a whole.

Random walks on hypergraphs.

In the past 20 years network science has proven its strength in modeling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Nevertheless, in many relevant cases, interactions are not pairwise but involve larger sets of nodes at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multibody interactions. Here we propose and study a class of random walks defined on such higher-order structures and grounded on a microscopic physical model where multibody proximity is associated with highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterization of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalized random-walk Laplace operator that reduces to the standard random-walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have full control of the high-order structures and on real-world networks where higher-order interactions are at play. As the first application of the method, we compare the behavior of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As the second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unraveling the effect of higher-order interactions on diffusive processes in higher-order networks, shedding light on mechanisms at the heart of biased information spreading in complex networked systems.

Author Correction: Pattern invariance for reaction-diffusion systems on complex networks.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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.

Patterns of non-normality in networked systems.

Several mechanisms have been proposed to explain the spontaneous generation of self-organised patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the system under scrutiny displays a homogeneous equilibrium, which is destabilised via a symmetry breaking instability which reflects the specificity of the problem being inspected. The Turing instability is among the most celebrated paradigms for pattern formation. In its original form, the diffusion constants of the two mobile species need to be quite different from each other for the instability to develop. Unfortunately, this condition limits the applicability of the theory. To overcome this impediment, and with the ambitious long term goal to eventually reconcile theory and experiments, we here propose an alternative mechanism for promoting the onset of pattern. To this end a multi-species reactive model is studied, assuming a generalized transport on a discrete and directed network-like support: the instability is triggered by the non-normality of the embedding network. The non-normal character of the dynamics instigates a short time amplification of the imposed perturbation, thus making the system unstable for a choice of parameters that would yield stability under the conventional scenario. In other words, non-normality promotes the emergence of patterns in cases where a classical linear analysis would not predict them. The importance of our result relies also on the fact that non-normal networks are pervasively found, motivating the general interest of the mechanism discussed here.

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.