Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Basic Properties and Information Theory of Audic-Claverie Statistic for Analyzing cDNA Arrays

BACKGROUND: The Audic-Claverie method [1] has been and still continues to be a popular approach for detection of differentially expressed genes in the SAGE framework. The method is based on the assumption that under the null hypothesis tag counts of the same gene in two libraries come from the same but unknown Poisson distribution. The problem is that each SAGE library represents only a single measurement. We ask: Given that the tag count samples from SAGE libraries are extremely limited, how useful actually is the Audic-Claverie methodology? We rigorously analyze the A-C statistic that forms a backbone of the methodology and represents our knowledge of the underlying tag generating process based on one observation. RESULTS: We show that the A-C statistic and the underlying Poisson distribution of the tag counts share the same mode structure. Moreover, the K-L divergence from the true unknown Poisson distribution to the A-C statistic is minimized when the A-C statistic is conditioned on the mode of the Poisson distribution. Most importantly, the expectation of this K-L divergence never exceeds 1/2 bit. CONCLUSION: A rigorous underpinning of the Audic-Claverie methodology has been missing. Our results constitute a rigorous argument supporting the use of Audic-Claverie method even though the SAGE libraries represent very sparse samples

Temporal Networks

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

On Optical Detection of Densely Labeled Synapses in Neuropil and Mapping Connectivity with Combinatorially Multiplexed Fluorescent Synaptic Markers

We propose a new method for mapping neural connectivity optically, by utilizing Cre/Lox system Brainbow to tag synapses of different neurons with random mixtures of different fluorophores, such as GFP, YFP, etc., and then detecting patterns of fluorophores at different synapses using light microscopy (LM). Such patterns will immediately report the pre- and post-synaptic cells at each synaptic connection, without tracing neural projections from individual synapses to corresponding cell bodies. We simulate fluorescence from a population of densely labeled synapses in a block of hippocampal neuropil, completely reconstructed from electron microscopy data, and show that high-end LM is able to detect such patterns with over 95% accuracy. We conclude, therefore, that with the described approach neural connectivity in macroscopically large neural circuits can be mapped with great accuracy, in scalable manner, using fast optical tools, and straightforward image processing. Relying on an electron microscopy dataset, we also derive and explicitly enumerate the conditions that should be met to allow synaptic connectivity studies with high-resolution optical tools

Contributions of synaptic filters to models of synaptically stored memory

The question of how neural systems encode memories in one-shot without immediately disrupting previously stored information has puzzled theoretical neuroscientists for years and it is the central topic of this thesis. Previous attempts on this topic, have proposed that synapses probabilistically update in response to plasticity inducing stimuli to effectively delay the degradation of old memories in the face of ongoing memory storage. Indeed, experiments have shown that synapses do not immediately respond to plasticity inducing stimuli, since these must be presented many times before synaptic plasticity is expressed. Such a delay could be due to the stochastic nature of synaptic plasticity or perhaps because induction signals are integrated before overt strength changes occur.The later approach has been previously applied to control fluctuations in neural development by low-pass filtering induction signals before plasticity is expressed. In this thesis we consider memory dynamics in a mathematical model with synapses that integrate plasticity induction signals to a threshold before expressing plasticity. We report novel recall dynamics and considerable improvements in memory lifetimes against a prominent model of synaptically stored memory. With integrating synapses the memory trace initially rises before reaching a maximum and then falls. The memory signal dissociates into separate oblivescence and reminiscence components, with reminiscence initially dominating recall. Furthermore, we find that integrating synapses possess natural timescales that can be used to consider the transition to late-phase plasticity under spaced repetition patterns known to lead to optimal storage conditions. We find that threshold crossing statistics differentiate between massed and spaced memory repetition patterns. However, isolated integrative synapses obtain an insufficient statistical sample to detect the stimulation pattern within a few memory repetitions. We extend the modelto consider the cooperation of well-known intracellular signalling pathways in detecting storage conditions by utilizing the profile of postsynaptic depolarization. We find that neuron wide signalling and local synaptic signals can be combined to detect optimal storage conditions that lead to stable forms of plasticity in a synapse specific manner.These models can be further extended to consider heterosynaptic and neuromodulatory interactions for late-phase plasticity.<br/

Understanding cellular differentiation by modelling of single-cell gene expression data

Over the course of the last decade single-cell RNA sequencing (scRNA-seq) has revolutionized the study of cellular heterogeneity, as one experiment routinely covers the expression of thousands of genes in tens or hundreds of thousands of cells. By quantifying differences between the single cell transcriptomes it is possible to reconstruct the process that gives rise to different cell fates from a progenitor population and gain access to trajectories of gene expression over developmental time. Tree reconstruction algorithms must deal with the high levels of noise, the high dimensionality of gene expression space, and strong non-linear dependencies between genes. In this thesis we address three aspects of working with scRNA-seq data: (1) lineage tree reconstruction, where we propose MERLoT, a novel trajectory inference method, (2) method comparison, where we propose PROSSTT, a novel algorithm that simulates scRNA-seq count data of complex differentiation trajectories, and (3) noise modelling, where we propose a novel probabilistic description of count data, a statistically motivated local averaging strategy, and an adaptation of the cross validation approach for the evaluation of gene expression imputation strategies. While statistical modelling of the data was our primary motivation, due to time constraints we did not manage to fully realize our plans for it. Increasingly complex processes like whole-organism development are being studied by single-cell transcriptomics, producing large amounts of data. Methods for trajectory inference must therefore efficiently reconstruct \textit{a priori} unknown lineage trees with many cell fates. We propose MERLoT, a method that can reconstruct trees in sub-quadratic time by utilizing a local averaging strategy, scaling very well on large datasets. MERLoT compares favorably to the state of the art, both on real data and a large synthetic benchmark. The absence of data with known complex underlying topologies makes it challenging to quantitatively compare tree reconstruction methods to each other. PROSSTT is a novel algorithm that simulates count data from complex differentiation processes, facilitating comparisons between algorithms. We created the largest synthetic dataset to-date, and the first to contain simulations with up to 12 cell fates. Additionally, PROSSTT can learn simulation parameters from reconstructed lineage trees and produce cells with expression profiles similar to the real data. Quantifying similarity between single-cell transcriptomes is crucial for clustering scRNA-seq profiles to cell types or inferring developmental trajectories, and appropriate statistical modelling of the data should improve such similarity calculations. We propose a Gaussian mixture of negative binomial distributions where gene expression variance depends on the square of the average expression. The model hyperparameters can be learned via the hybrid Monte Carlo algorithm, and a good initialization of average expression and variance parameters can be obtained by trajectory inference. A way to limit noise in the data is to apply local averaging, using the nearest neighbours of each cell to recover expression of non-captured mRNA. Our proposal, nearest neighbour smoothing with optimal bias-variance trade-off, optimizes the k-nearest neighbours approach by reducing the contribution of inappropriate neighbours. We also propose a way to assess the quality of gene expression imputation. After reconstructing a trajectory with imputed data, each cell can be projected to the trajectory using non-overlapping subsets of genes. The robustness of these assignments over multiple partitions of the genes is a novel estimator of imputation performance. Finally, I was involved in the planning and initial stages of a mouse ovary cell atlas as a collaboration

Exploring long-term determinants of chronological lifespan using system-wide approaches

Ageing is a great research challenge. Age is the primary risk factor for many complex diseases, including cardiovascular disease, neurodegeneration and cancer. Anti-ageing interventions aim to delay the onset of these diseases and extend health span. Ageing remains enigmatic, however, and its proximal cause and mechanisms are not understood. This partly reflects the laborious nature of ageing experiments, typically requiring large timeframes and numerous individuals, which creates a bottleneck for systematic ageing studies. Yeast can be grown under highly parallelised experimental platforms and are well suited to systematic studies. However, ageing research is a notable exception, with the traditional colony-forming unit (CFU) assay for chronological lifespan being notoriously time- and resource-consuming. I present two alternative assays which circumnavigate this bottleneck. One is a high throughput CFU assay that is automated by robotics and supported by an R package to estimate culture viability by constructing a statistical model based on colony patterns. The second assay employs barcode sequencing to monitor strain viability in competitively ageing pools of deletion libraries, providing genome-scale functional insights into the genetics of lifespan. I employ this assay to dissect the genetic basis of rapamycin-mediated longevity, providing insights into the condition-specific nature of lifespan-extending mutations and the anti-ageing action of rapamycin. Experimental reproducibility is essential for research. Ageing studies, including those in yeast, are notably sensitive to batch effects: genetically identical cells grown under identical conditions can exhibit substantial phenotypic differences. I systematically test typically neglected factors, and demonstrate that chronological lifespan is strongly affected by pre-culture protocol such as the amount of colony picked for the pre-culture – suggesting a ‘memory’ which is passed across cell divisions from pre-culture to non-dividing, ageing cells. Hence, this work addresses key issues in yeast ageing research, both technological and biological, establishing a platform to robustly perform future studies at large scales

True single-cell proteomics using advanced ion mobility mass spectrometry

In this thesis, I present the development of a novel mass spectrometry (MS) platform and scan modes in conjunction with a versatile and robust liquid chromatography (LC) platform, which addresses current sensitivity and robustness limitations in MS-based proteomics. I demonstrate how this technology benefits the high-speed and ultra-high sensitivity proteomics studies on a large scale. This culminated in the first of its kind label-free MS-based single-cell proteomics platform and its application to spatial tissue proteomics. I also investigate the vastly underexplored ‘dark matter’ of the proteome, validating novel microproteins that contribute to human cellular function. First, we developed a novel trapped ion mobility spectrometry (TIMS) platform for proteomics applications, which multiplies sequencing speed and sensitivity by ‘parallel accumulation – serial fragmentation’ (PASEF) and applied it to first high-sensitivity and large-scale projects in the biomedical arena. Next, to explore the collisional cross section (CCS) dimension in TIMS, we measured over 1 million peptide CCS values, which enabled us to train a deep learning model for CCS prediction solely based on the linear amino acid sequence. We also translated the principles of TIMS and PASEF to the field of lipidomics, highlighting parallel benefits in terms of throughput and sensitivity. The core of my PhD is the development of a robust ultra-high sensitivity LC-MS platform for the high-throughput analysis of single-cell proteomes. Improvements in ion transfer efficiency, robust, very low flow LC and a PASEF data independent acquisition scan mode together increased measurement sensitivity by up to 100-fold. We quantified single-cell proteomes to a depth of up to 1,400 proteins per cell. A fundamental result from the comparisons to single-cell RNA sequencing data revealed that single cells have a stable core proteome, whereas the transcriptome is dominated by Poisson noise, emphasizing the need for both complementary technologies. Building on our achievements with the single-cell proteomics technology, we elucidated the image-guided spatial and cell-type resolved proteome in whole organs and tissues from minute sample amounts. We combined clearing of rodent and human organs, unbiased 3D-imaging, target tissue identification, isolation and MS-based unbiased proteomics to describe early-stage β-amyloid plaque proteome profiles in a disease model of familial Alzheimer’s. Automated artificial intelligence driven isolation and pooling of single cells of the same phenotype allowed us to analyze the cell-type resolved proteome of cancer tissues, revealing a remarkable spatial difference in the proteome. Last, we systematically elucidated pervasive translation of noncanonical human open reading frames combining state-of-the art ribosome profiling, CRISPR screens, imaging and MS-based proteomics. We performed unbiased analysis of small novel proteins and prove their physical existence by LC-MS as HLA peptides, essential interaction partners of protein complexes and cellular function

Proceedings of the 35th International Workshop on Statistical Modelling : July 20- 24, 2020 Bilbao, Basque Country, Spain

466 p.The InternationalWorkshop on Statistical Modelling (IWSM) is a reference workshop in promoting statistical modelling, applications of Statistics for researchers, academics and industrialist in a broad sense. Unfortunately, the global COVID-19 pandemic has not allowed holding the 35th edition of the IWSM in Bilbao in July 2020. Despite the situation and following the spirit of the Workshop and the Statistical Modelling Society, we are delighted to bring you the proceedings book of extended abstracts