Quantifying heterogeneity to drug response in cancer-stroma kinetics.

A crucial challenge in medicine is choosing which drug (or combination) will be the most advantageous for a particular patient. Usually, drug response rates differ substantially, and the reasons for this response unpredictability remain ambiguous. Consequently, it is central to classify features that contribute to the observed drug response variability. Pancreatic cancer is one of the deadliest cancers with limited therapeutic achievements due to the massive presence of stroma that generates an environment that enables tumor growth, metastasis, and drug resistance. To understand the cancer-stroma cross talk within the tumor microenvironment and to develop personalized adjuvant therapies, there is a necessity for effective approaches that offer measurable data to monitor the effect of drugs at the single-cell level. Here, we develop a computational approach, based on cell imaging, that quantifies the cellular cross talk between pancreatic tumor cells (L3.6pl or AsPC1) and pancreatic stellate cells (PSCs), coordinating their kinetics in presence of the chemotherapeutic agent gemcitabine. We report significant heterogeneity in the organization of cellular interactions in response to the drug. For L3.6pl cells, gemcitabine sensibly decreases stroma-stroma interactions but increases stroma-cancer interactions, overall enhancing motility and crowding. In the AsPC1 case, gemcitabine promotes the interactions among tumor cells, but it does not affect stroma-cancer interplay, possibly suggesting a milder effect of the drug on cell dynamics.

Deregulation of microtubule organization and RNA metabolism in Arx models for lissencephaly and developmental epileptic encephalopathy.

X-linked lissencephaly with abnormal genitalia (XLAG) and developmental epileptic encephalopathy-1 (DEE1) are caused by mutations in the Aristaless-related homeobox (ARX) gene, which encodes a transcription factor responsible for brain development. It has been unknown whether the phenotypically diverse XLAG and DEE1 phenotypes may converge on shared pathways. To address this question, a label-free quantitative proteomic approach was applied to the neonatal brain of Arx knockout (ArxKO/Y) and knock-in polyalanine (Arx(GCG)7/Y) mice that are respectively models for XLAG and DEE1. Gene ontology and protein-protein interaction analysis revealed that cytoskeleton, protein synthesis and splicing control are deregulated in an allelic-dependent manner. Decreased α-tubulin content was observed both in Arx mice and Arx/alr-1(KO) Caenorhabditis elegans ,and a disorganized neurite network in murine primary neurons was consistent with an allelic-dependent secondary tubulinopathy. As distinct features of Arx(GCG)7/Y mice, we detected eIF4A2 overexpression and translational suppression in cortex and primary neurons. Allelic-dependent differences were also established in alternative splicing (AS) regulated by PUF60 and SAM68. Abnormal AS repertoires in Neurexin-1, a gene encoding multiple pre-synaptic organizers implicated in synaptic remodelling, were detected in Arx/alr-1(KO) animals and in Arx(GCG)7/Y epileptogenic brain areas and depolarized cortical neurons. Consistent with a conserved role of ARX in modulating AS, we propose that the allelic-dependent secondary synaptopathy results from an aberrant Neurexin-1 repertoire. Overall, our data reveal alterations mirroring the overlapping and variant effects caused by null and polyalanine expanded mutations in ARX. The identification of these effects can aid in the design of pathway-guided therapy for ARX endophenotypes and NDDs with overlapping comorbidities.

From Pavlov Conditioning to Hebb Learning.

Hebb's learning traces its origin in Pavlov's classical conditioning; however, while the former has been extensively modeled in the past decades (e.g., by the Hopfield model and countless variations on theme), as for the latter, modeling has remained largely unaddressed so far. Furthermore, a mathematical bridge connecting these two pillars is totally lacking. The main difficulty toward this goal lies in the intrinsically different scales of the information involved: Pavlov's theory is about correlations between concepts that are (dynamically) stored in the synaptic matrix as exemplified by the celebrated experiment starring a dog and a ringing bell; conversely, Hebb's theory is about correlations between pairs of neurons as summarized by the famous statement that neurons that fire together wire together. In this letter, we rely on stochastic process theory to prove that as long as we keep neurons' and synapses' timescales largely split, Pavlov's mechanism spontaneously takes place and ultimately gives rise to synaptic weights that recover the Hebbian kernel.

Histone demethylase KDM5C is a SAHA-sensitive central hub at the crossroads of transcriptional axes involved in multiple neurodevelopmental disorders.

A disproportional large number of neurodevelopmental disorders (NDDs) is caused by variants in genes encoding transcription factors and chromatin modifiers. However, the functional interactions between the corresponding proteins are only partly known. Here, we show that KDM5C, encoding a H3K4 demethylase, is at the intersection of transcriptional axes under the control of three regulatory proteins ARX, ZNF711 and PHF8. Interestingly, mutations in all four genes (KDM5C, ARX, ZNF711 and PHF8) are associated with X-linked NDDs comprising intellectual disability as a core feature. in vitro analysis of the KDM5C promoter revealed that ARX and ZNF711 function as antagonist transcription factors that activate KDM5C expression and compete for the recruitment of PHF8. Functional analysis of mutations in these genes showed a correlation between phenotype severity and the reduction in KDM5C transcriptional activity. The KDM5C decrease was associated with a lack of repression of downstream target genes Scn2a, Syn1 and Bdnf in the embryonic brain of Arx-null mice. Aiming to correct the faulty expression of KDM5C, we studied the effect of the FDA-approved histone deacetylase inhibitor suberanilohydroxamic acid (SAHA). In Arx-KO murine ES-derived neurons, SAHA was able to rescue KDM5C depletion, recover H3K4me3 signalling and improve neuronal differentiation. Indeed, in ARX/alr-1-deficient Caenorhabditis elegans animals, SAHA was shown to counteract the defective KDM5C/rbr-2-H3K4me3 signalling, recover abnormal behavioural phenotype and ameliorate neuronal maturation. Overall, our studies indicate that KDM5C is a conserved and druggable effector molecule across a number of NDDs for whom the use of SAHA may be considered a potential therapeutic strategy.

Neural Networks with a Redundant Representation: Detecting the Undetectable.

We consider a three-layer Sejnowski machine and show that features learnt via contrastive divergence have a dual representation as patterns in a dense associative memory of order P=4. The latter is known to be able to Hebbian store an amount of patterns scaling as N^{P-1}, where N denotes the number of constituting binary neurons interacting P wisely. We also prove that, by keeping the dense associative network far from the saturation regime (namely, allowing for a number of patterns scaling only linearly with N, while P>2) such a system is able to perform pattern recognition far below the standard signal-to-noise threshold. In particular, a network with P=4 is able to retrieve information whose intensity is O(1) even in the presence of a noise O(sqrt[N]) in the large N limit. This striking skill stems from a redundancy representation of patterns-which is afforded given the (relatively) low-load information storage-and it contributes to explain the impressive abilities in pattern recognition exhibited by new-generation neural networks. The whole theory is developed rigorously, at the replica symmetric level of approximation, and corroborated by signal-to-noise analysis and Monte Carlo simulations.

Identification of the first dominant mutation of LAMA5 gene causing a complex multisystem syndrome due to dysfunction of the extracellular matrix.

BACKGROUND: The laminin alpha 5 gene (LAMA5) plays a master role in the maintenance and function of the extracellular matrix (ECM) in mammalian tissues, which is critical in developmental patterning, stem cell niches, cancer and genetic diseases. Its mutations have never been reported in human disease so far. The aim of this study was to associate the first mutation in LAMA5 gene to a novel multisystem syndrome. METHODS: A detailed characterisation of a three-generation family, including clinical, biochemical, instrumental and morphological analysis, together with genetics and expression (WES and RNAseq) studies, was performed. RESULTS: The heterozygous LAMA5 mutation c.9418G>A (p.V3140M) was associated with skin anomalies, impaired scarring, night blindness, muscle weakness, osteoarthritis, joint and internal organs ligaments laxity, malabsorption syndrome and hypothyroidism. We demonstrated that the mutation alters the amount of LAMA5 peptides likely derived from protein cleavage and perturbs the activation of the epithelial-mesenchymal signalling, producing an unbalanced expression of Sonic hedgehog and GLI1, which are upregulated in cells from affected individuals, and of ECM proteins (COL1A1, MMP1 and MMP3), which are strongly inhibited. Studies carried out using human skin biopsies showed alteration of dermal papilla with a reduction of the germinative layer and an early arrest of hair follicle downgrowth. The knock-in mouse model, generated in our laboratory, shows similar changes in the tissues studied so far. CONCLUSIONS: This is the first report of a disease phenotype associated with LAMA5 mutation in humans.

Retrieval capabilities of hierarchical networks: from Dyson to Hopfield.

We consider statistical-mechanics models for spin systems built on hierarchical structures, which provide a simple example of non-mean-field framework. We show that the coupling decay with spin distance can give rise to peculiar features and phase diagrams much richer than their mean-field counterpart. In particular, we consider the Dyson model, mimicking ferromagnetism in lattices, and we prove the existence of a number of metastabilities, beyond the ordered state, which become stable in the thermodynamic limit. Such a feature is retained when the hierarchical structure is coupled with the Hebb rule for learning, hence mimicking the modular architecture of neurons, and gives rise to an associative network able to perform single pattern retrieval as well as multiple-pattern retrieval, depending crucially on the external stimuli and on the rate of interaction decay with distance; however, those emergent multitasking features reduce the network capacity with respect to the mean-field counterpart. The analysis is accomplished through statistical mechanics, Markov chain theory, signal-to-noise ratio technique, and numerical simulations in full consistency. Our results shed light on the biological complexity shown by real networks, and suggest future directions for understanding more realistic models.

Anergy in self-directed B lymphocytes: A statistical mechanics perspective.

Self-directed lymphocytes may evade clonal deletion at ontogenesis but still remain harmless due to a mechanism called clonal anergy. For B-lymphocytes, two major explanations for anergy developed over the last decades: according to Varela theory, anergy stems from a proper orchestration of the whole B-repertoire, such that self-reactive clones, due to intensive feed-back from other clones, display strong inertia when mounting a response. Conversely, according to the model of cognate response, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy. Through statistical mechanics we show that helpers do not prompt activation of a sub-group of B-cells: remarkably, the latter are just those broadly interacting in the idiotypic network. Hence Varela theory can finally be reabsorbed into the prevailing framework of the cognate response model. Further, we show how the B-repertoire architecture may emerge, where highly connected clones are self-directed as a natural consequence of ontogenetic learning.

Oral-facial-digital type I protein is required for primary cilia formation and left-right axis specification.

The oral-facial-digital type I (OFD1) syndrome (OMIM 311200) is a human developmental disorder; affected individuals have craniofacial and digital abnormalities and, in 15% of cases, polycystic kidney. The disease is inherited as an X-linked dominant male-lethal trait. Using a Cre-loxP system, we generated knockout animals lacking Ofd1 and reproduced the main features of the disease, albeit with increased severity, possibly owing to differences of X inactivation patterns between human and mouse. We found failure of left-right axis specification in mutant male embryos, and ultrastructural analysis showed a lack of cilia in the embryonic node. Formation of cilia was defective in cystic kidneys from heterozygous females, implicating ciliogenesis as a mechanism underlying cyst development. In addition, we found impaired patterning of the neural tube and altered expression of the 5' Hoxa and Hoxd genes in the limb buds of mice lacking Ofd1, suggesting that Ofd1 could have a role beyond primary cilium organization and assembly.

Extensive parallel processing on scale-free networks.

We adapt belief-propagation techniques to study the equilibrium behavior of a bipartite spin glass, with interactions between two sets of N and P=αN spins each having an arbitrary degree, i.e., number of interaction partners in the opposite set. An equivalent view is then of a system of N neurons storing P diluted patterns via Hebbian learning, in the high storage regime. Our method allows analysis of parallel pattern processing on a broad class of graphs, including those with pattern asymmetry and heterogeneous dilution; previous replica approaches assumed homogeneity. We show that in a large part of the parameter space of noise, dilution, and storage load, delimited by a critical surface, the network behaves as an extensive parallel processor, retrieving all P patterns in parallel without falling into spurious states due to pattern cross talk, as would be typical of the structural glassiness built into the network. Parallel extensive retrieval is more robust for homogeneous degree distributions, and is not disrupted by asymmetric pattern distributions. For scale-free pattern degree distributions, Hebbian learning induces modularity in the neural network; thus, our Letter gives the first theoretical description for extensive information processing on modular and scale-free networks.

Hebbian dreaming for small datasets.

The dreaming Hopfield model constitutes a generalization of the Hebbian paradigm for neural networks, that is able to perform on-line learning when "awake" and also to account for off-line "sleeping" mechanisms. The latter have been shown to enhance storing in such a way that, in the long sleep-time limit, this model can reach the maximal storage capacity achievable by networks equipped with symmetric pairwise interactions. In this paper, we inspect the minimal amount of information that must be supplied to such a network to guarantee a successful generalization, and we test it both on random synthetic and on standard structured datasets (i.e., MNIST, Fashion-MNIST and Olivetti). By comparing these minimal thresholds of information with those required by the standard (i.e., always "awake") Hopfield model, we prove that the present network can save up to ∼90% of the dataset size, yet preserving the same performance of the standard counterpart. This suggests that sleep may play a pivotal role in explaining the gap between the large volumes of data required to train artificial neural networks and the relatively small volumes needed by their biological counterparts. Further, we prove that the model Cost function (typically used in statistical mechanics) admits a representation in terms of a standard Loss function (typically used in machine learning) and this allows us to analyze its emergent computational skills both theoretically and computationally: a quantitative picture of its capabilities as a function of its control parameters is achieved and consistency between the two approaches is highlighted. The resulting network is an associative memory for pattern recognition tasks that learns from examples on-line, generalizes correctly (in suitable regions of its control parameters) and optimizes its storage capacity by off-line sleeping: such a reduction of the training cost can be inspiring toward sustainable AI and in situations where data are relatively sparse.

Probing Single-Cell Fermentation Fluxes and Exchange Networks via pH-Sensing Hybrid Nanofibers.

The homeostatic control of their environment is an essential task of living cells. It has been hypothesized that, when microenvironmental pH inhomogeneities are induced by high cellular metabolic activity, diffusing protons act as signaling molecules, driving the establishment of exchange networks sustained by the cell-to-cell shuttling of overflow products such as lactate. Despite their fundamental role, the extent and dynamics of such networks is largely unknown due to the lack of methods in single-cell flux analysis. In this study, we provide direct experimental characterization of such exchange networks. We devise a method to quantify single-cell fermentation fluxes over time by integrating high-resolution pH microenvironment sensing via ratiometric nanofibers with constraint-based inverse modeling. We apply our method to cell cultures with mixed populations of cancer cells and fibroblasts. We find that the proton trafficking underlying bulk acidification is strongly heterogeneous, with maximal single-cell fluxes exceeding typical values by up to 3 orders of magnitude. In addition, a crossover in time from a networked phase sustained by densely connected "hubs" (corresponding to cells with high activity) to a sparse phase dominated by isolated dipolar motifs (i.e., by pairwise cell-to-cell exchanges) is uncovered, which parallels the time course of bulk acidification. Our method addresses issues ranging from the homeostatic function of proton exchange to the metabolic coupling of cells with different energetic demands, allowing for real-time noninvasive single-cell metabolic flux analysis.

Kidney-specific inactivation of Ofd1 leads to renal cystic disease associated with upregulation of the mTOR pathway.

The oral-facial-digital type I syndrome (OFDI; MIM 311200) is a rare syndromic form of inherited renal cystic disease. It is transmitted as an X-linked dominant, male lethal disorder and is caused by mutations in the OFD1 gene. Previous studies demonstrated that OFDI belongs to the growing number of disorders ascribed to dysfunction of primary cilia. We generated a conditional inactivation of the mouse Ofd1 gene using the Ksp-Cre transgenic line, which resulted in a viable model characterized by renal cystic disease and progressive impairment of renal function. The study of this model allowed us to demonstrate that primary cilia initially form and then disappear after the development of cysts, suggesting that the absence of primary cilia is a consequence rather than the primary cause of renal cystic disease. Immunofluorescence and western blotting analysis revealed upregulation of the mTOR pathway in both dilated and non-dilated renal structures. Treatment with rapamycin, a specific inhibitor of the mTOR pathway, resulted in a significant reduction in the number and size of renal cysts and a decrease in the cystic index compared with untreated mutant animals, suggesting that dysregulation of this pathway in our model is mTOR-dependent. The animal model we have generated could thus represent a valuable tool to understand the molecular link between mTOR and cyst development, and eventually to the identification of novel drug targets for renal cystic disease.

Multitasking associative networks.

We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzmann machine and we show its thermodynamical equivalence to an associative working memory able to retrieve several patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky theory. Results obtained through statistical mechanics, the signal-to-noise technique, and Monte Carlo simulations are overall in perfect agreement and carry interesting biological insights. Indeed, these associative networks pave new perspectives in the understanding of multitasking features expressed by complex systems, e.g., neural and immune networks.

Outperforming RBM Feature-Extraction Capabilities by "Dreaming" Mechanism.

Inspired by a formal equivalence between the Hopfield model and restricted Boltzmann machines (RBMs), we design a Boltzmann machine, referred to as the dreaming Boltzmann machine (DBM), which achieves better performances than the standard one. The novelty in our model lies in a precise prescription for intralayer connections among hidden neurons whose strengths depend on features correlations. We analyze learning and retrieving capabilities in DBMs, both theoretically and numerically, and compare them to the RBM reference. We find that, in a supervised scenario, the former significantly outperforms the latter. Furthermore, in the unsupervised case, the DBM achieves better performances both in features extraction and representation learning, especially when the network is properly pretrained. Finally, we compare both models in simple classification tasks and find that the DBM again outperforms the RBM reference.

The emergence of a concept in shallow neural networks.

We consider restricted Boltzmann machine (RBMs) trained over an unstructured dataset made of blurred copies of definite but unavailable "archetypes" and we show that there exists a critical sample size beyond which the RBM can learn archetypes, namely the machine can successfully play as a generative model or as a classifier, according to the operational routine. In general, assessing a critical sample size (possibly in relation to the quality of the dataset) is still an open problem in machine learning. Here, restricting to the random theory, where shallow networks suffice and the "grandmother-cell" scenario is correct, we leverage the formal equivalence between RBMs and Hopfield networks, to obtain a phase diagram for both the neural architectures which highlights regions, in the space of the control parameters (i.e., number of archetypes, number of neurons, size and quality of the training set), where learning can be accomplished. Our investigations are led by analytical methods based on the statistical-mechanics of disordered systems and results are further corroborated by extensive Monte Carlo simulations.

Fully Automated Computational Approach for Precisely Measuring Organelle Acidification with Optical pH Sensors.

pH balance and regulation within organelles are fundamental to cell homeostasis and proliferation. The ability to track pH in cells becomes significantly important to understand these processes in detail. Fluorescent sensors based on micro- and nanoparticles have been applied to measure intracellular pH; however, an accurate methodology to precisely monitor acidification kinetics of organelles in living cells has not been established, limiting the scope of this class of sensors. Here, silica-based fluorescent microparticles were utilized to probe the pH of intracellular organelles in MDA-MB-231 and MCF-7 breast cancer cells. In addition to the robust, ratiometric, trackable, and bioinert pH sensors, we developed a novel dimensionality reduction algorithm to automatically track and screen massive internalization events of pH sensors. We found that the mean acidification time is comparable among the two cell lines (ΔTMCF-7 = 16.3 min; ΔTMDA-MB-231 = 19.5 min); however, MCF-7 cells showed a much broader heterogeneity in comparison to MDA-MB-231 cells. The use of pH sensors and ratiometric imaging of living cells in combination with a novel computational approach allow analysis of thousands of events in a computationally inexpensive and faster way than the standard routes. The reported methodology can potentially be used to monitor pH as well as several other parameters associated with endocytosis.

A thermodynamic perspective of immune capabilities.

We consider the mutual interactions, via cytokine exchanges, among helper lymphocytes, B lymphocytes and killer lymphocytes, and we model them as a unique system by means of a tripartite network. Each part includes all the different clones of the same lymphatic subpopulation, whose couplings to the others are either excitatory or inhibitory (mirroring elicitation and suppression by cytokine). First of all, we show that this system can be mapped into an associative neural network, where helper cells directly interact with each other and are able to secrete cytokines according to "strategies" learn by the system and profitable to cope with possible antigenic stimulation; the ability of such a retrieval corresponds to a healthy reaction of the immune system. We then investigate the possible conditions for the failure of a correct retrieval and distinguish between the following outcomes: massive lymphocyte expansion/suppression (e.g. lymphoproliferative syndromes), subpopulation unbalance (e.g. HIV, EBV infections) and ageing (thought of as noise growth); the correlation of such states to autoimmune diseases is also highlighted. Lastly, we discuss how self-regulatory effects within each effector branch (i.e. B and killer lymphocytes) can be modeled in terms of a stochastic process, ultimately providing a consistent bridge between the tripartite-network approach introduced here and the immune networks developed in the last decades.

On the effective initialisation for restricted Boltzmann machines via duality with Hopfield model.

Restricted Boltzmann machines (RBMs) with a binary visible layer of size N and a Gaussian hidden layer of size P have been proved to be equivalent to a Hopfield neural network (HNN) made of N binary neurons and storing P patterns ξ, as long as the weights w in the former are identified with the patterns. Here we aim to leverage this equivalence to find effective initialisations for weights in the RBM when what is available is a set of noisy examples of each pattern, aiming to translate statistical mechanics background available for HNN to the study of RBM's learning and retrieval abilities. In particular, given a set of definite, structureless patterns we build a sample of blurred examples and prove that the initialisation where w corresponds to the empirical average ξ¯ over the sample is a fixed point under stochastic gradient descent. Further, as a toy application of the duality between HNN and RBM, we consider the simplest random auto-encoder (a three layer network made of two RBMs coupled by their hidden layer) and evidence that, as long as the parameter setting corresponds to the retrieval region of the dual HNN, reconstruction and denoising can be accomplished trivially, while when the system is in the spin-glass phase inference algorithms are necessary. This questions the need for larger retrieval regions which we obtain by applying a Gram-Schmidt orthogonalisation to the patterns: in fact, this procedure yields to a set of patterns devoid of correlations and for which the largest retrieval region can be accomplished. Finally we consider an application of duality also in a structured case: we test this approach on the MNIST dataset, and obtain that the network performs already ∼67% of successful classifications, suggesting it can be exploited as a computationally-cheap pre-training.

Generalized Guerra's interpolation schemes for dense associative neural networks.

In this work we develop analytical techniques to investigate a broad class of associative neural networks set in the high-storage regime. These techniques translate the original statistical-mechanical problem into an analytical-mechanical one which implies solving a set of partial differential equations, rather than tackling the canonical probabilistic route. We test the method on the classical Hopfield model - where the cost function includes only two-body interactions (i.e., quadratic terms) - and on the "relativistic" Hopfield model - where the (expansion of the) cost function includes p-body (i.e., of degree p) contributions. Under the replica symmetric assumption, we paint the phase diagrams of these models by obtaining the explicit expression of their free energy as a function of the model parameters (i.e., noise level and memory storage). Further, since for non-pairwise models ergodicity breaking is non necessarily a critical phenomenon, we develop a fluctuation analysis and find that criticality is preserved in the relativistic model.