Publications

Journal article

Thomas P, 2018,

Analysis of cell size homeostasis at the single-cell and population level

, Frontiers in Physics, Vol: 6, ISSN: 2296-424X

Growth pervades all areas of life from single cells to cell populations to tissues. Cell size often fluctuates significantly from cell to cell and from generation to generation. Here we present a unified framework to predict the statistics of cell size variations within a lineage tree of a proliferating population. We analytically characterize (i) the distributions of cell size snapshots, (ii) the distribution within a population tree, and (iii) the distribution of lineages across the tree. Surprisingly, these size distributions differ significantly from observing single cells in isolation. In populations, cells seemingly grow to different sizes, typically exhibit less cell-to-cell variability and often display qualitatively different sensitivities to cell cycle noise and division errors. We demonstrate the key findings using recent single-cell data and elaborate on the implications for the ability of cells to maintain a narrow size distribution and the emergence of different power laws in these distributions.

Journal article

Arnaudon A, 2018,

Structure preserving noise and dissipation in the Toda lattice

, Journal of Physics A: Mathematical and Theoretical, Vol: 51, ISSN: 1751-8113

In this paper, we use Flaschka's change of variables of the open Toda latticeand its interpretation in term of the group structure of the LU factorisationas a coadjoint motion on a certain dual of Lie algebra to implement a structurepreserving noise and dissipation. Both preserve the structure of coadjointorbit, that is the space of symmetric tri-diagonal matrices and arise as a newtype of multiplicative noise and nonlinear dissipation of the Toda lattice. Weinvestigate some of the properties of these deformations and in particular thecontinuum limit as a stochastic Burger equation with a nonlinear viscosity.This work is meant to be exploratory, and open more questions that we cananswer with simple mathematical tools and without numerical simulations.

Journal article

Tomazou M, Barahona M, Polizzi K, Stan Get al., 2018,

Computational re-design of synthetic genetic oscillators for independent amplitude and frequency modulation

, Cell Systems, Vol: 6, Pages: 508-520.e5, ISSN: 2405-4712

To perform well in biotechnology applications, synthetic genetic oscillators must be engineered to allow independent modulation of amplitude and period. This need is currently unmet. Here, we demonstrate computationally how two classic genetic oscillators, the dual-feedback oscillator and the repressilator, can be re-designed to provide independent control of amplitude and period and improve tunability—that is, a broad dynamic range of periods and amplitudes accessible through the input “dials.” Our approach decouples frequency and amplitude modulation by incorporating an orthogonal “sink module” where the key molecular species are channeled for enzymatic degradation. This sink module maintains fast oscillation cycles while alleviating the translational coupling between the oscillator's transcription factors and output. We characterize the behavior of our re-designed oscillators over a broad range of physiologically reasonable parameters, explain why this facilitates broader function and control, and provide general design principles for building synthetic genetic oscillators that are more precisely controllable.

Journal article

Kendall ML, Ayabina P, Xu Y, Stimson J, Colijn Cet al., 2018,

Estimating Transmission from Genetic and Epidemiological Data: A Metric to Compare Transmission Trees

, Statistical Science, Vol: 33, Pages: 70-85, ISSN: 0883-4237

Reconstructing who infected whom is a central challenge in analysing epidemiological data. Recently, advances in sequencing technology have led to increasing interest in Bayesian approaches to inferring who infected whom using genetic data from pathogens. The logic behind such approaches is that isolates that are nearly genetically identical are more likely to have been recently transmitted than those that are very different. A number of methods have been developed to perform this inference. However, testing their convergence, examining posterior sets of transmission trees and comparing methods’ performance are challenged by the fact that the object of inference—the transmission tree—is a complicated discrete structure. We introduce a metric on transmission trees to quantify distances between them. The metric can accommodate trees with unsampled individuals, and highlights differences in the source case and in the number of infections per infector. We illustrate its performance on simple simulated scenarios and on posterior transmission trees from a TB outbreak. We find that the metric reveals where the posterior is sensitive to the priors, and where collections of trees are composed of distinct clusters. We use the metric to define median trees summarising these clusters. Quantitative tools to compare transmission trees to each other will be required for assessing MCMC convergence, exploring posterior trees and benchmarking diverse methods as this field continues to mature.

Journal article

Arnaudon A, Ganaba N, Holm DD, 2017,

The stochastic energy-Casimir method

, Comptes Rendus. Mécanique, Vol: 346, Pages: 279-290

Journal article

McGrath TM, Murphy KG, Jones NS, 2018,

Quantitative approaches to energy and glucose homeostasis: machine learning and modelling for precision understanding and prediction

, Journal of the Royal Society Interface, Vol: 15, ISSN: 1742-5662

Obesity is a major global public health problem. Understanding how energy homeostasis is regulated, and can become dysregulated, is crucial for developing new treatments for obesity. Detailed recording of individual behaviour and new imaging modalities offer the prospect of medically relevant models of energy homeostasis that are both understandable and individually predictive. The profusion of data from these sources has led to an interest in applying machine learning techniques to gain insight from these large, relatively unstructured datasets. We review both physiological models and machine learning results across a diverse range of applications in energy homeostasis, and highlight how modelling and machine learning can work together to improve predictive ability. We collect quantitative details in a comprehensive mathematical supplement. We also discuss the prospects of forecasting homeostatic behaviour and stress the importance of characterizing stochasticity within and between individuals in order to provide practical, tailored forecasts and guidance to combat the spread of obesity.

Journal article

Grandjean L, Gilman RH, Iwamoto T, Köser CU, Coronel J, Zimic M, Török ME, Ayabina D, Kendall M, Fraser C, Harris S, Parkhill J, Peacock SJ, Moore DAJ, Colijn Cet al., 2017,

Convergent evolution and topologically disruptive polymorphisms among multidrug-resistant tuberculosis in Peru.

, PLoS ONE, Vol: 12, Pages: e0189838-e0189838, ISSN: 1932-6203

BACKGROUND: Multidrug-resistant tuberculosis poses a major threat to the success of tuberculosis control programs worldwide. Understanding how drug-resistant tuberculosis evolves can inform the development of new therapeutic and preventive strategies. METHODS: Here, we use novel genome-wide analysis techniques to identify polymorphisms that are associated with drug resistance, adaptive evolution and the structure of the phylogenetic tree. A total of 471 samples from different patients collected between 2009 and 2013 in the Lima suburbs of Callao and Lima South were sequenced on the Illumina MiSeq platform with 150bp paired-end reads. After alignment to the reference H37Rv genome, variants were called using standardized methodology. Genome-wide analysis was undertaken using custom written scripts implemented in R software. RESULTS: High quality homoplastic single nucleotide polymorphisms were observed in genes known to confer drug resistance as well as genes in the Mycobacterium tuberculosis ESX secreted protein pathway, pks12, and close to toxin/anti-toxin pairs. Correlation of homoplastic variant sites identified that many were significantly correlated, suggestive of epistasis. Variation in genes coding for ESX secreted proteins also significantly disrupted phylogenetic structure. Mutations in ESX genes in key antigenic epitope positions were also found to disrupt tree topology. CONCLUSION: Variation in these genes have a biologically plausible effect on immunogenicity and virulence. This makes functional characterization warranted to determine the effects of these polymorphisms on bacterial fitness and transmission.

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.

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.

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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