Prediction of Time Series Gene Expression and Structural Analysis of Gene Regulatory Networks Using Recurrent Neural Networks.

Methods for time series prediction and classification of gene regulatory networks (GRNs) from gene expression data have been treated separately so far. The recent emergence of attention-based recurrent neural network (RNN) models boosted the interpretability of RNN parameters, making them appealing for the understanding of gene interactions. In this work, we generated synthetic time series gene expression data from a range of archetypal GRNs and we relied on a dual attention RNN to predict the gene temporal dynamics. We show that the prediction is extremely accurate for GRNs with different architectures. Next, we focused on the attention mechanism of the RNN and, using tools from graph theory, we found that its graph properties allow one to hierarchically distinguish different architectures of the GRN. We show that the GRN responded differently to the addition of noise in the prediction by the RNN and we related the noise response to the analysis of the attention mechanism. In conclusion, this work provides a way to understand and exploit the attention mechanism of RNNs and it paves the way to RNN-based methods for time series prediction and inference of GRNs from gene expression data.

Beyond the Maximum Storage Capacity Limit in Hopfield Recurrent Neural Networks.

In a neural network, an autapse is a particular kind of synapse that links a neuron onto itself. Autapses are almost always not allowed neither in artificial nor in biological neural networks. Moreover, redundant or similar stored states tend to interact destructively. This paper shows how autapses together with stable state redundancy can improve the storage capacity of a recurrent neural network. Recent research shows how, in an N-node Hopfield neural network with autapses, the number of stored patterns (P) is not limited to the well known bound 0.14 N , as it is for networks without autapses. More precisely, it describes how, as the number of stored patterns increases well over the 0.14 N threshold, for P much greater than N, the retrieval error asymptotically approaches a value below the unit. Consequently, the reduction of retrieval errors allows a number of stored memories, which largely exceeds what was previously considered possible. Unfortunately, soon after, new results showed that, in the thermodynamic limit, given a network with autapses in this high-storage regime, the basin of attraction of the stored memories shrinks to a single state. This means that, for each stable state associated with a stored memory, even a single bit error in the initial pattern would lead the system to a stationary state associated with a different memory state. This thus limits the potential use of this kind of Hopfield network as an associative memory. This paper presents a strategy to overcome this limitation by improving the error correcting characteristics of the Hopfield neural network. The proposed strategy allows us to form what we call an absorbing-neighborhood of state surrounding each stored memory. An absorbing-neighborhood is a set defined by a Hamming distance surrounding a network state, which is an absorbing because, in the long-time limit, states inside it are absorbed by stable states in the set. We show that this strategy allows the network to store an exponential number of memory patterns, each surrounded with an absorbing-neighborhood with an exponentially growing size.

Photonic Stochastic Emergent Storage for deep classification by scattering-intrinsic patterns.

Disorder is a pervasive characteristic of natural systems, offering a wealth of non-repeating patterns. In this study, we present a novel storage method that harnesses naturally-occurring random structures to store an arbitrary pattern in a memory device. This method, the Stochastic Emergent Storage (SES), builds upon the concept of emergent archetypes, where a training set of imperfect examples (prototypes) is employed to instantiate an archetype in a Hopfield-like network through emergent processes. We demonstrate this non-Hebbian paradigm in the photonic domain by utilizing random transmission matrices, which govern light scattering in a white-paint turbid medium, as prototypes. Through the implementation of programmable hardware, we successfully realize and experimentally validate the capability to store an arbitrary archetype and perform classification at the speed of light. Leveraging the vast number of modes excited by mesoscopic diffusion, our approach enables the simultaneous storage of thousands of memories without requiring any additional fabrication efforts. Similar to a content addressable memory, all stored memories can be collectively assessed against a given pattern to identify the matching element. Furthermore, by organizing memories spatially into distinct classes, they become features within a higher-level categorical (deeper) optical classification layer.

A recurrent Hopfield network for estimating meso-scale effective connectivity in MEG.

The architecture of communication within the brain, represented by the human connectome, has gained a paramount role in the neuroscience community. Several features of this communication, e.g., the frequency content, spatial topology, and temporal dynamics are currently well established. However, identifying generative models providing the underlying patterns of inhibition/excitation is very challenging. To address this issue, we present a novel generative model to estimate large-scale effective connectivity from MEG. The dynamic evolution of this model is determined by a recurrent Hopfield neural network with asymmetric connections, and thus denoted Recurrent Hopfield Mass Model (RHoMM). Since RHoMM must be applied to binary neurons, it is suitable for analyzing Band Limited Power (BLP) dynamics following a binarization process. We trained RHoMM to predict the MEG dynamics through a gradient descent minimization and we validated it in two steps. First, we showed a significant agreement between the similarity of the effective connectivity patterns and that of the interregional BLP correlation, demonstrating RHoMM's ability to capture individual variability of BLP dynamics. Second, we showed that the simulated BLP correlation connectomes, obtained from RHoMM evolutions of BLP, preserved some important topological features, e.g, the centrality of the real data, assuring the reliability of RHoMM. Compared to other biophysical models, RHoMM is based on recurrent Hopfield neural networks, thus, it has the advantage of being data-driven, less demanding in terms of hyperparameters and scalable to encompass large-scale system interactions. These features are promising for investigating the dynamics of inhibition/excitation at different spatial scales.

Two Receptor Binding Strategy of SARS-CoV-2 Is Mediated by Both the N-Terminal and Receptor-Binding Spike Domain.

It is not well understood why severe acute respiratory syndrome (SARS)-CoV-2 spreads much faster than other ß-coronaviruses such as SARS-CoV and Middle East respiratory syndrome (MERS)-CoV. In a previous publication, we predicted the binding of the N-terminal domain (NTD) of SARS-CoV-2 spike to sialic acids (SAs). Here, we experimentally validate this interaction and present simulations that reveal a second possible interaction between SAs and the spike protein via a binding site located in the receptor-binding domain (RBD). The predictions from molecular-dynamics simulations and the previously-published 2D-Zernike binding-site recognition approach were validated through flow-induced dispersion analysis (FIDA)─which reveals the capability of the SARS-CoV-2 spike to bind to SA-containing (glyco)lipid vesicles, and flow-cytometry measurements─which show that spike binding is strongly decreased upon inhibition of SA expression on the membranes of angiotensin converting enzyme-2 (ACE2)-expressing HEK cells. Our analyses reveal that the SA binding of the NTD and RBD strongly enhances the infection-inducing ACE2 binding. Altogether, our work provides in silico, in vitro, and cellular evidence that the SARS-CoV-2 virus utilizes a two-receptor (SA and ACE2) strategy. This allows the SARS-CoV-2 spike to use SA moieties on the cell membrane as a binding anchor, which increases the residence time of the virus on the cell surface and aids in the binding of the main receptor, ACE2, via 2D diffusion.

Electrostatic complementarity at the interface drives transient protein-protein interactions.

Understanding the mechanisms driving bio-molecules binding and determining the resulting complexes' stability is fundamental for the prediction of binding regions, which is the starting point for drug-ability and design. Characteristics like the preferentially hydrophobic composition of the binding interfaces, the role of van der Waals interactions, and the consequent shape complementarity between the interacting molecular surfaces are well established. However, no consensus has yet been reached on the role of electrostatic. Here, we perform extensive analyses on a large dataset of protein complexes for which both experimental binding affinity and pH data were available. Probing the amino acid composition, the disposition of the charges, and the electrostatic potential they generated on the protein molecular surfaces, we found that (i) although different classes of dimers do not present marked differences in the amino acid composition and charges disposition in the binding region, (ii) homodimers with identical binding region show higher electrostatic compatibility with respect to both homodimers with non-identical binding region and heterodimers. Interestingly, (iii) shape and electrostatic complementarity, for patches defined on short-range interactions, behave oppositely when one stratifies the complexes by their binding affinity: complexes with higher binding affinity present high values of shape complementarity (the role of the Lennard-Jones potential predominates) while electrostatic tends to be randomly distributed. Conversely, complexes with low values of binding affinity exploit Coulombic complementarity to acquire specificity, suggesting that electrostatic complementarity may play a greater role in transient (or less stable) complexes. In light of these results, (iv) we provide a novel, fast, and efficient method, based on the 2D Zernike polynomial formalism, to measure electrostatic complementarity without the need of knowing the complex structure. Expanding the electrostatic potential on a basis of 2D orthogonal polynomials, we can discriminate between transient and permanent protein complexes with an AUC of the ROC of [Formula: see text] 0.8. Ultimately, our work helps shedding light on the non-trivial relationship between the hydrophobic and electrostatic contributions in the binding interfaces, thus favoring the development of new predictive methods for binding affinity characterization.

Collective behavior and self-organization in neural rosette morphogenesis.

Neural rosettes develop from the self-organization of differentiating human pluripotent stem cells. This process mimics the emergence of the embryonic central nervous system primordium, i.e., the neural tube, whose formation is under close investigation as errors during such process result in severe diseases like spina bifida and anencephaly. While neural tube formation is recognized as an example of self-organization, we still do not understand the fundamental mechanisms guiding the process. Here, we discuss the different theoretical frameworks that have been proposed to explain self-organization in morphogenesis. We show that an explanation based exclusively on stem cell differentiation cannot describe the emergence of spatial organization, and an explanation based on patterning models cannot explain how different groups of cells can collectively migrate and produce the mechanical transformations required to generate the neural tube. We conclude that neural rosette development is a relevant experimental 2D in-vitro model of morphogenesis because it is a multi-scale self-organization process that involves both cell differentiation and tissue development. Ultimately, to understand rosette formation, we first need to fully understand the complex interplay between growth, migration, cytoarchitecture organization, and cell type evolution.

Differences in the organization of interface residues tunes the stability of the SARS-CoV-2 spike-ACE2 complex.

The continuous emergence of novel variants represents one of the major problems in dealing with the SARS-CoV-2 virus. Indeed, also due to its prolonged circulation, more than ten variants of concern emerged, each time rapidly overgrowing the current viral version due to improved spreading features. As, up to now, all variants carry at least one mutation on the spike Receptor Binding Domain, the stability of the binding between the SARS-CoV-2 spike protein and the human ACE2 receptor seems one of the molecular determinants behind the viral spreading potential. In this framework, a better understanding of the interplay between spike mutations and complex stability can help to assess the impact of novel variants. Here, we characterize the peculiarities of the most representative variants of concern in terms of the molecular interactions taking place between the residues of the spike RBD and those of the ACE2 receptor. To do so, we performed molecular dynamics simulations of the RBD-ACE2 complexes of the seven variants of concern in comparison with a large set of complexes with different single mutations taking place on the RBD solvent-exposed residues and for which the experimental binding affinity was available. Analyzing the strength and spatial organization of the intermolecular interactions of the binding region residues, we found that (i) mutations producing an increase of the complex stability mainly rely on instaurating more favorable van der Waals optimization at the cost of Coulombic ones. In particular, (ii) an anti-correlation is observed between the shape and electrostatic complementarities of the binding regions. Finally, (iii) we showed that combining a set of dynamical descriptors is possible to estimate the outcome of point mutations on the complex binding region with a performance of 0.7. Overall, our results introduce a set of dynamical observables that can be rapidly evaluated to probe the effects of novel isolated variants or different molecular systems.

Microglia reactivity entails microtubule remodeling from acentrosomal to centrosomal arrays.

Microglia reactivity entails a large-scale remodeling of cellular geometry, but the behavior of the microtubule cytoskeleton during these changes remains unexplored. Here we show that activated microglia provide an example of microtubule reorganization from a non-centrosomal array of parallel and stable microtubules to a radial array of more dynamic microtubules. While in the homeostatic state, microglia nucleate microtubules at Golgi outposts, and activating signaling induces recruitment of nucleating material nearby the centrosome, a process inhibited by microtubule stabilization. Our results demonstrate that a hallmark of microglia reactivity is a striking remodeling of the microtubule cytoskeleton and suggest that while pericentrosomal microtubule nucleation may serve as a distinct marker of microglia activation, inhibition of microtubule dynamics may provide a different strategy to reduce microglia reactivity in inflammatory disease.

Hedgehog-GLI and Notch Pathways Sustain Chemoresistance and Invasiveness in Colorectal Cancer and Their Inhibition Restores Chemotherapy Efficacy.

Colorectal cancer (CRC) is a leading cause of cancer-related mortality and chemoresistance is a major medical issue. The epithelial-to-mesenchymal transition (EMT) is the primary step in the emergence of the invasive phenotype and the Hedgehog-GLI (HH-GLI) and NOTCH signaling pathways are associated with poor prognosis and EMT in CRC. CRC cell lines harboring KRAS or BRAF mutations, grown as monolayers and organoids, were treated with the chemotherapeutic agent 5-Fluorouracil (5-FU) alone or combined with HH-GLI and NOTCH pathway inhibitors GANT61 and DAPT, or arsenic trioxide (ATO) to inhibit both pathways. Treatment with 5-FU led to the activation of HH-GLI and NOTCH pathways in both models. In KRAS mutant CRC, HH-GLI and NOTCH signaling activation co-operate to enhance chemoresistance and cell motility, while in BRAF mutant CRC, the HH-GLI pathway drives the chemoresistant and motile phenotype. We then showed that 5-FU promotes the mesenchymal and thus invasive phenotype in KRAS and BRAF mutant organoids and that chemosensitivity could be restored by targeting the HH-GLI pathway in BRAF mutant CRC or both HH-GLI and NOTCH pathways in KRAS mutant CRC. We suggest that in KRAS-driven CRC, the FDA-approved ATO acts as a chemotherapeutic sensitizer, whereas GANT61 is a promising chemotherapeutic sensitizer in BRAF-driven CRC.

Deep learning for blind structured illumination microscopy.

Blind-structured illumination microscopy (blind-SIM) enhances the optical resolution without the requirement of nonlinear effects or pre-defined illumination patterns. It is thus advantageous in experimental conditions where toxicity or biological fluctuations are an issue. In this work, we introduce a custom convolutional neural network architecture for blind-SIM: BS-CNN. We show that BS-CNN outperforms other blind-SIM deconvolution algorithms providing a resolution improvement of 2.17 together with a very high Fidelity (artifacts reduction). Furthermore, BS-CNN proves to be robust in cross-database variability: it is trained on synthetically augmented open-source data and evaluated on experiments. This approach paves the way to the employment of CNN-based deconvolution in all scenarios in which a statistical model for the illumination is available while the specific realizations are unknown or noisy.

A novel computational strategy for defining the minimal protein molecular surface representation.

Most proteins perform their biological function by interacting with one or more molecular partners. In this respect, characterizing local features of the molecular surface, that can potentially be involved in the interaction with other molecules, represents a step forward in the investigation of the mechanisms of recognition and binding between molecules. Predictive methods often rely on extensive samplings of molecular patches with the aim to identify hot spots on the surface. In this framework, analysis of large proteins and/or many molecular dynamics frames is often unfeasible due to the high computational cost. Thus, finding optimal ways to reduce the number of points to be sampled maintaining the biological information (including the surface shape) carried by the molecular surface is pivotal. In this perspective, we here present a new theoretical and computational algorithm with the aim of defining a set of molecular surfaces composed of points not uniformly distributed in space, in such a way as to maximize the information of the overall shape of the molecule by minimizing the number of total points. We test our procedure's ability in recognizing hot-spots by describing the local shape properties of portions of molecular surfaces through a recently developed method based on the formalism of 2D Zernike polynomials. The results of this work show the ability of the proposed algorithm to preserve the key information of the molecular surface using a reduced number of points compared to the complete surface, where all points of the surface are used for the description. In fact, the methodology shows a significant gain of the information stored in the sampling procedure compared to uniform random sampling.

Inferring the stabilization effects of SARS-CoV-2 variants on the binding with ACE2 receptor.

As the SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) pandemic continues to spread, several variants of the virus, with mutations distributed all over the viral genome, are emerging. While most of the variants present mutations having little to no effects at the phenotypic level, some of these variants are spreading at a rate that suggests they may present a selective advantage. In particular, these rapidly spreading variants present specific mutations on the spike protein. These observations call for an urgent need to characterize the effects of these variants' mutations on phenotype features like contagiousness and antigenicity. With this aim, we performed molecular dynamics simulations on a selected set of possible spike variants in order to assess the stabilizing effect of particular amino acid substitutions on the molecular complex. We specifically focused on the mutations that are both characteristic of the top three most worrying variants at the moment, i.e the English, South African, and Amazonian ones, and that occur at the molecular interface between SARS-CoV-2 spike protein and its human ACE2 receptor. We characterize these variants' effect in terms of (i) residue mobility, (ii) compactness, studying the network of interactions at the interface, and (iii) variation of shape complementarity via expanding the molecular surfaces in the Zernike basis. Overall, our analyses highlighted greater stability of the three variant complexes with respect to both the wild type and two negative control systems, especially for the English and Amazonian variants. In addition, in the three variants, we investigate the effects a not-yet observed mutation in position 501 could provoke on complex stability. We found that a phenylalanine mutation behaves similarly to the English variant and may cooperate in further increasing the stability of the South African one, hinting at the need for careful surveillance for the emergence of these mutations in the population. Ultimately, we show that the proposed observables describe key features for the stability of the ACE2-spike complex and can help to monitor further possible spike variants.

Does blood type affect the COVID-19 infection pattern?

Among the many aspects that characterize the COVID-19 pandemic, two seem particularly challenging to understand: i) the great geographical differences in the degree of virus contagiousness and lethality that were found in the different phases of the epidemic progression, and, ii) the potential role of the infected people's blood type in both the virus infectivity and the progression of the disease. A recent hypothesis could shed some light on both aspects. Specifically, it has been proposed that, in the subject-to-subject transfer, SARS-CoV-2 conserves on its capsid the erythrocytes' antigens of the source subject. Thus these conserved antigens can potentially cause an immune reaction in a receiving subject that has previously acquired specific antibodies for the source subject antigens. This hypothesis implies a blood type-dependent infection rate. The strong geographical dependence of the blood type distribution could be, therefore, one of the factors at the origin of the observed heterogeneity in the epidemics spread. Here, we present an epidemiological deterministic model where the infection rules based on blood types are taken into account, and we compare our model outcomes with the exiting worldwide infection progression data. We found an overall good agreement, which strengthens the hypothesis that blood types do play a role in the COVID-19 infection.

2D Zernike polynomial expansion: Finding the protein-protein binding regions.

We present a method for efficiently and effectively assessing whether and where two proteins can interact with each other to form a complex. This is still largely an open problem, even for those relatively few cases where the 3D structure of both proteins is known. In fact, even if much of the information about the interaction is encoded in the chemical and geometric features of the structures, the set of possible contact patches and of their relative orientations are too large to be computationally affordable in a reasonable time, thus preventing the compilation of reliable interactome. Our method is able to rapidly and quantitatively measure the geometrical shape complementarity between interacting proteins, comparing their molecular iso-electron density surfaces expanding the surface patches in term of 2D Zernike polynomials. We first test the method against the real binding region of a large dataset of known protein complexes, reaching a success rate of 0.72. We then apply the method for the blind recognition of binding sites, identifying the real region of interaction in about 60 % of the analyzed cases. Finally, we investigate how the efficiency in finding the right binding region depends on the surface roughness as a function of the expansion order.

Alignment interactions drive structural transitions in biological tissues.

Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a nonequilibrium phase transition into a quasihexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of the alignment coupling. In this regime, the dynamics of cell centers and shape fluctuation show features typical of glassy systems.

In-Silico Evidence for a Two Receptor Based Strategy of SARS-CoV-2.

We propose a computational investigation on the interaction mechanisms between SARS-CoV-2 spike protein and possible human cell receptors. In particular, we make use of our newly developed numerical method able to determine efficiently and effectively the relationship of complementarity between portions of protein surfaces. This innovative and general procedure, based on the representation of the molecular isoelectronic density surface in terms of 2D Zernike polynomials, allows the rapid and quantitative assessment of the geometrical shape complementarity between interacting proteins, which was unfeasible with previous methods. Our results indicate that SARS-CoV-2 uses a dual strategy: in addition to the known interaction with angiotensin-converting enzyme 2, the viral spike protein can also interact with sialic-acid receptors of the cells in the upper airways.

Investigation of the binding between olfactory receptors and odorant molecules in C. elegans organism.

The molecular mechanisms regulating the complex sensory system that underlies olfaction are still not completely understood. The compounds formed from the interaction of Olfactory Receptors (ORs) with volatile molecules play a crucial role in producing the sense of olfaction. Therefore, it is necessary to investigate the binding mechanisms between these receptors and small ligands. In this work, we focus our attention on C.elegans, this is a particularly suitable model organism because it is characterized by a nervous system composed of only 302 neurons. To study olfaction in C.elegans, we select 21 ORs from its olfactory neurons, and present a pipeline, consisting of several computational methods, with the aim of proposing a set of possible candidates for binding the selected C.elegans ORs. This pipeline introduces an approach based on the selection of templates, and threading, that takes advantage of the structural redundancy among membrane receptors. This procedure is widely replicable because it is based on algorithms that are publicly available and are freely hosted on institutional servers.

Effect of dilution in asymmetric recurrent neural networks.

We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network dilution measures the fraction of neuron couples that are connected, and the network asymmetry measures to what extent the underlying connectivity matrix is asymmetric. For each given neural network, we study the dynamical evolution of all the different initial conditions, thus characterizing the full dynamical landscape without imposing any learning rule. Because of the deterministic dynamics, each trajectory converges to an attractor, that can be either a fixed point or a limit cycle. These attractors form the set of all the possible limit behaviors of the neural network. For each network we then determine the convergence times, the limit cycles' length, the number of attractors, and the sizes of the attractors' basin. We show that there are two network structures that maximize the number of possible limit behaviors. The first optimal network structure is fully-connected and symmetric. On the contrary, the second optimal network structure is highly sparse and asymmetric. The latter optimal is similar to what observed in different biological neuronal circuits. These observations lead us to hypothesize that independently from any given learning model, an efficient and effective biologic network that stores a number of limit behaviors close to its maximum capacity tends to develop a connectivity structure similar to one of the optimal networks we found.