Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Single Cell Proteomics in Biomedicine: High-dimensional Data Acquisition, Visualization and Analysis

New insights on cellular heterogeneity in the last decade provoke the development of a variety of single cell omics tools at a lightning pace. The resultant high-dimensional single cell data generated by these tools require new theoretical approaches and analytical algorithms for effective visualization and interpretation. In this review, we briefly survey the state-of-the-art single cell proteomic tools with a particular focus on data acquisition and quantification, followed by an elaboration of a number of statistical and computational approaches developed to date for dissecting the high-dimensional single cell data. The underlying assumptions, unique features, and limitations of the analytical methods with the designated biological questions they seek to answer will be discussed. Particular attention will be given to those information theoretical approaches that are anchored in a set of first principles of physics and can yield detailed (and often surprising) predictions

Mathematical Modelling and Machine Learning Methods for Bioinformatics and Data Science Applications

Mathematical modeling is routinely used in physical and engineering sciences to help understand complex systems and optimize industrial processes. Mathematical modeling differs from Artificial Intelligence because it does not exclusively use the collected data to describe an industrial phenomenon or process, but it is based on fundamental laws of physics or engineering that lead to systems of equations able to represent all the variables that characterize the process. Conversely, Machine Learning methods require a large amount of data to find solutions, remaining detached from the problem that generated them and trying to infer the behavior of the object, material or process to be examined from observed samples. Mathematics allows us to formulate complex models with effectiveness and creativity, describing nature and physics. Together with the potential of Artificial Intelligence and data collection techniques, a new way of dealing with practical problems is possible. The insertion of the equations deriving from the physical world in the data-driven models can in fact greatly enrich the information content of the sampled data, allowing to simulate very complex phenomena, with drastically reduced calculation times. Combined approaches will constitute a breakthrough in cutting-edge applications, providing precise and reliable tools for the prediction of phenomena in biological macro/microsystems, for biotechnological applications and for medical diagnostics, particularly in the field of precision medicine

Combinatorial perturbation analysis reveals divergent regulations of mesenchymal genes during epithelial-to-mesenchymal transition

Epithelial-to-mesenchymal transition (EMT), a fundamental transdifferentiation process in development, produces diverse phenotypes in different physiological or pathological conditions. Many genes involved in EMT have been identified to date, but mechanisms contributing to the phenotypic diversity and those governing the coupling between the dynamics of epithelial (E) genes and that of the mesenchymal (M) genes are unclear. In this study, we employed combinatorial perturbations to mammary epithelial cells to induce a series of EMT phenotypes by manipulating two essential EMT-inducing elements, namely TGF-β and ZEB1. By measuring transcriptional changes in more than 700 E-genes and M-genes, we discovered that the M-genes exhibit a significant diversity in their dependency to these regulatory elements and identified three groups of M-genes that are controlled by different regulatory circuits. Notably, functional differences were detected among the M-gene clusters in motility regulation and in survival of breast cancer patients. We computationally predicted and experimentally confirmed that the reciprocity and reversibility of EMT are jointly regulated by ZEB1. Our integrative analysis reveals the key roles of ZEB1 in coordinating the dynamics of a large number of genes during EMT, and it provides new insights into the mechanisms for the diversity of EMT phenotypes

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Neural Correlates of Experience-Induced Deficits in Learned Vocal Communication

Songbirds are one of the few vertebrate groups (including humans) that evolved the ability to learn vocalizations. During song learning, social interactions with adult models are crucial and young songbirds raised without direct contacts with adults typically produce abnormal songs showing phonological and syntactical deficits. This raises the question of what functional representation of their vocalizations such deprived animals develop. Here we show that young starlings that we raised without any direct contact with adults not only failed to differentiate starlings' typical song classes in their vocalizations but also failed to develop differential neural responses to these songs. These deficits appear to be linked to a failure to acquire songs' functions and may provide a model for abnormal development of communicative skills, including speech