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• Journal article
  Fricker M, Heaton L, Jones N, Obara B, Müller SJ, Meyer AJet al., 2018,

  Quantitation of ER Structure and Function.

  , Methods Mol Biol, Vol: 1691, Pages: 43-66

  The plant endoplasmic reticulum forms a network of tubules connected by three-way junctions or sheet-like cisternae. Although the network is three-dimensional, in many plant cells, it is constrained to a thin volume sandwiched between the vacuole and plasma membrane, effectively restricting it to a 2-D planar network. The structure of the network, and the morphology of the tubules and cisternae can be automatically extracted following intensity-independent edge-enhancement and various segmentation techniques to give an initial pixel-based skeleton, which is then converted to a graph representation. Collectively, this approach yields a wealth of quantitative metrics for ER structure and can be used to describe the effects of pharmacological treatments or genetic manipulation. The software is publicly available.

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• Journal article
  Salnikov V, Cassese D, Lambiotte R, Jones NSet al., 2018,

  Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge.

  , Appl Netw Sci, Vol: 3

  In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose for the first time a simplicial complex approach to word co-occurrences, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the conceptual landscape of mathematical research, focusing on homological holes, regions with low connectivity in the simplicial structure. We find that homological holes are ubiquitous, which suggests that they capture some essential feature of research practice in mathematics. k-dimensional holes die when every concept in the hole appears in an article together with other k+1 concepts in the hole, hence their death may be a sign of the creation of new knowledge, as we show with some examples. We find a positive relation between the size of a hole and the time it takes to be closed: larger holes may represent potential for important advances in the field because they separate conceptually distant areas. We provide further description of the conceptual space by looking for the simplicial analogs of stars and explore the likelihood of edges in a star to be also part of a homological cycle. We also show that authors' conceptual entropy is positively related with their contribution to homological holes, suggesting that polymaths tend to be on the frontier of research.

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• Journal article
  Thomas P, 2017,

  Making sense of snapshot data: ergodic principle for clonal cell populations

  , Journal of the Royal Society Interface, Vol: 14, ISSN: 1742-5662

  Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations.

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• Journal article
  Aryaman J, Johnston IG, Jones NS, 2017,

  Mitochondrial DNA Density Homeostasis Accounts for a Threshold Effect in a Cybrid Model of a Human Mitochondrial Disease

  , Biochemical Journal, Vol: 474, Pages: 4019-4034, ISSN: 1470-8728

  Mitochondrial dysfunction is involved in a wide array of devastating diseases, but the heterogeneity and complexity of the symptoms of these diseases challenges theoretical understanding of their causation. With the explosion of omics data, we have the unprecedented opportunity to gain deep understanding of the biochemical mechanisms of mitochondrial dysfunction. This goal raises the outstanding need to make these complex datasets interpretable. Quantitative modelling allows us to translate such datasets into intuition and suggest rational biomedical treatments. Taking an interdisciplinary approach, we use a recently published large-scale dataset and develop a descriptive and predictive mathematical model of progressive increase in mutant load of the MELAS 3243A>G mtDNA mutation. The experimentally observed behaviour is surprisingly rich, but we find that our simple, biophysically motivated model intuitively accounts for this heterogeneity and yields a wealth of biological predictions. Our findings suggest that cells attempt to maintain wild-type mtDNA density through cell volume reduction, and thus power demand reduction, until a minimum cell volume is reached. Thereafter, cells toggle from demand reduction to supply increase, up-regulating energy production pathways. Our analysis provides further evidence for the physiological significance of mtDNA density and emphasizes the need for performing single-cell volume measurements jointly with mtDNA quantification. We propose novel experiments to verify the hypotheses made here to further develop our understanding of the threshold effect and connect with rational choices for mtDNA disease therapies.

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• Journal article
  Fulcher B, Jones NS, 2017,

  hctsa: A computational framework for automated timeseriesphenotyping using massive feature extraction

  , Cell Systems, Vol: 5, Pages: 527-531.e3, ISSN: 2405-4712

  Phenotype measurements frequently take the form of time series, but we currently lack a systematic method for relating these complex data streams to scientifically meaningful outcomes, such as relating the movement dynamics of organisms to their genotype or measurements of brain dynamics of a patient to their disease diagnosis. Previous work addressed this problem by comparing implementations of thousands of diverse scientific time-series analysis methods in an approach termed highly comparative time-series analysis. Here, we introduce hctsa, a software tool for applying this methodological approach to data. hctsa includes an architecture for computing over 7,700 time-series features and a suite of analysis and visualization algorithms to automatically select useful and interpretable time-series features for a given application. Using exemplar applications to high-throughput phenotyping experiments, we show how hctsa allows researchers to leverage decades of time-series research to quantify and understand informative structure in time-series data.

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• Journal article
  Liu Z, Barahona M, 2017,

  Geometric multiscale community detection: Markov stability and vector partitioning

  , Journal of Complex Networks, Vol: 6, Pages: 157-172, ISSN: 2051-1329

  Multiscale community detection can be viewed from a dynamical perspective within the Markov stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we reformulate multiscale community detection as a max-sum length vector partitioning problem with respect to the set of time-dependent node vectors expressed in terms of eigenvectors of the transition matrix. This formulation provides a geometric interpretation of Markov stability in terms of a time-dependent spectral embedding, where the Markov time acts as an inhomogeneous geometric resolution factor that zooms the components of the node vectors at different rates. Our geometric formulation encompasses both modularity and the multi-resolution Potts model, which are shown to correspond to vector partitioning in a pseudo-Euclidean space, and is also linked to spectral partitioning methods, where the number of eigenvectors used corresponds to the dimensionality of the underlying embedding vector space. Inspired by the Louvain optimization for community detection, we then propose an algorithm based on a graph-theoretical heuristic for the vector partitioning problem. We apply the algorithm to the spectral optimization of modularity and Markov stability community detection. The spectral embedding based on the transition matrix eigenvectors leads to improved partitions with higher information content and higher modularity than the eigen-decomposition of the modularity matrix. We illustrate the results with random network benchmarks.

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• Journal article
  Shahrezaei V, Robertson B, Thomas P, Priestman Met al., 2017,

  Mycobacteria modify their cell size control under sub-optimal carbon sources

  , Frontiers in Cell and Developmental Biology, Vol: 5, ISSN: 2296-634X

  The decision to divide is the most important one that any cell must make. Recent single cell studies suggest that most bacteria follow an “adder” model of cell size control, incorporating a fixed amount of cell wall material before dividing. Mycobacteria, including the causative agent of tuberculosis Mycobacterium tuberculosis, are known to divide asymmetrically resulting in heterogeneity in growth rate, doubling time, and other growth characteristics in daughter cells. The interplay between asymmetric cell division and adder size control has not been extensively investigated. Moreover, the impact of changes in the environment on growth rate and cell size control have not been addressed for mycobacteria. Here, we utilize time-lapse microscopy coupled with microfluidics to track live Mycobacterium smegmatis cells as they grow and divide over multiple generations, under a variety of growth conditions. We demonstrate that, under optimal conditions, M. smegmatis cells robustly follow the adder principle, with constant added length per generation independent of birth size, growth rate, and inherited pole age. However, the nature of the carbon source induces deviations from the adder model in a manner that is dependent on pole age. Understanding how mycobacteria maintain cell size homoeostasis may provide crucial targets for the development of drugs for the treatment of tuberculosis, which remains a leading cause of global mortality.

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• Journal article
  Branch T, Barahona M, Dodson C, Ying Let al., 2017,

  Kinetic analysis reveals the identity of Aβ-metal complex responsible for the initial aggregation of Aβ in the synapse

  , ACS Chemical Neuroscience, Vol: 8, Pages: 1970-1979, ISSN: 1948-7193

  The mechanism of Aβ aggregation in the absence of metal ions is well established, yet the role that Zn2+ and Cu2+, the two most studied metal ions, released during neurotransmission, paly in promoting Aβ aggregation in the vicinity of neuronal synapses remains elusive. Here we report the kinetics of Zn2+ binding to Aβ and Zn2+/Cu2+ binding to Aβ-Cu to form ternary complexes under near physiological conditions (nM Aβ, μM metal ions). We find that these reactions are several orders of magnitude slower than Cu2+ binding to Aβ. Coupled reaction-diffusion simulations of the interactions of synaptically released metal ions with Aβ show that up to a third of Aβ is Cu2+-bound under repetitive metal ion release, while any other Aβ-metal complexes (including Aβ-Zn) are insignificant. We therefore conclude that Zn2+ is unlikely to play an important role in the very early stages (i.e., dimer formation) of Aβ aggregation, contrary to a widely held view in the subject. We propose that targeting the specific interactions between Cu2+ and Aβ may be a viable option in drug development efforts for early stages of AD.

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• Journal article
  Aryaman J, hoitzing H, burgstaller J, johnston I, Jones NSet al., 2017,

  Mitochondrial heterogeneity, metabolic scaling and cell death

  , Bioessays, Vol: 39, ISSN: 1521-1878

  Heterogeneity in mitochondrial content has been previously suggested as a major contributor to cellular noise, with multiple studies indicating its direct involvement in biomedically important cellular phenomena. A recently published dataset explored the connection between mitochondrial functionality and cell physiology, where a non-linearity between mitochondrial functionality and cell size was found. Using mathematical models, we suggest that a combination of metabolic scaling and a simple model of cell death may account for these observations. However, our findings also suggest the existence of alternative competing hypotheses, such as a non-linearity between cell death and cell size. While we find that the proposed non-linear coupling between mitochondrial functionality and cell size provides a compelling alternative to previous attempts to link mitochondrial heterogeneity and cell physiology, we emphasise the need to account for alternative causal variables, including cell cycle, size, mitochondrial density and death, in future studies of mitochondrial physiology.

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• Journal article
  Johnson S, Jones NS, 2017,

  Looplessness in networks is linked to trophic coherence

  , Proceedings of the National Academy of Sciences of USA, Vol: 114, Pages: 5618-5623, ISSN: 0027-8424

  Many natural, complex systems are remarkably stable thanks to anabsence of feedback acting on their elements. When described as net-works, these exhibit few or no cycles, and associated matrices have smallleading eigenvalues. It has been suggested that this architecture can con-fer advantages to the system as a whole, such as ‘qualitative stability’,but this observation does not in itself explain how a loopless structuremight arise. We show here that the number of feedback loops in a net-work, as well as the eigenvalues of associated matrices, are determined bya structural property called trophic coherence, a measure of how neatlynodes fall into distinct levels. Our theory correctly classifies a variety ofnetworks – including those derived from genes, metabolites, species, neu-rons, words, computers and trading nations – into two distinct regimesof high and low feedback, and provides a null model to gauge the signifi-cance of related magnitudes. Since trophic coherence suppresses feedback,whereas an absence of feedback alone does not lead to coherence, our worksuggests that the reasons for ‘looplessness’ in nature should be sought incoherence-inducing mechanisms.

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