Imperial College London

Dr Nick Jones

Faculty of Natural SciencesDepartment of Mathematics

Reader in Applied Mathematics and Mathematical Physics



+44 (0)20 7594 1146nick.jones




301aSir Ernst Chain BuildingSouth Kensington Campus





Publication Type

77 results found

Burgstaller J, Kolbe T, Havlicek V, Hembach S, Poulton J, Piálek J, Steinborn R, Rulicke T, Brem G, Jones NS, Johnston Iet al., 2019, Large-scale genetic analysis reveals mammalian mtDNA heteroplasmy dynamics and variance increase through lifetimes and generations, Nature Communications, Vol: 9, ISSN: 2041-1723

Vital mitochondrial DNA (mtDNA) populations exist in cells and may consist of heteroplasmic mixtures of mtDNA types. The evolution of these heteroplasmic populations through development, ageing, and generations is central to genetic diseases, but is poorly understood in mammals. Here we dissect these population dynamics using a dataset of unprecedented size and temporal span, comprising 1947 single-cell oocyte and 899 somatic measurements of heteroplasmy change throughout lifetimes and generations in two genetically distinct mouse models. We provide a novel and detailed quantitative characterisation of the linear increase in heteroplasmy variance throughout mammalian life courses in oocytes and pups. We find that differences in mean heteroplasmy are induced between generations, and the heteroplasmy of germline and somatic precursors diverge early in development, with a haplotype-specific direction of segregation. We develop stochastic theory predicting the implications of these dynamics for ageing and disease manifestation and discuss its application to human mtDNA dynamics.


Brittain R, Jones N, Ouldridge T, Biochemical Szilard engines for memory-limited inference, New Journal of Physics, ISSN: 1367-2630

By designing and leveraging an explicit molecular realisation of a measurement-and-feedback-powered Szilard engine, we investigate the extraction of work from complex environments by minimalmachines with finite capacity for memory and decision-making. Living systems perform inferenceto exploit complex structure, or correlations, in their environment, but the physical limits andunderlying cost/benefit trade-offs involved in doing so remain unclear. To probe these questions,we consider a minimal model for a structured environment—a correlated sequence of molecules—and explore mechanisms based on extended Szilard engines for extracting the work stored in thesenon-equilibrium correlations. We consider systems limited to a single bit of memory making binary‘choices’ at each step. We demonstrate that increasingly complex environments allow increasinglysophisticated inference strategies to extract more free energy than simpler alternatives, and arguethat optimal design of such machines should also consider the free energy reserves required to ensurerobustness against fluctuations due to mistakes.


Lubba CH, Le Guen Y, Jarvis S, Jones NS, Cork SC, Eftekhar A, Schultz SRet al., 2019, Correction to: PyPNS: Multiscale Simulation of a Peripheral Nerve in Python., Neuroinformatics

The original version of this article unfortunately contained a mistake. The following text: "This project has received funding from European Research Council (ERC) Synergy Grant no. 319818." is missing in the Acknowledgments.


Insalata F, Hoitzing H, Jones N, 2019, A mathematical model of expansion of disadvantaged but altruistic mitochondrial mutants in skeletal muscle fibres, Publisher: WILEY, Pages: 61-61, ISSN: 0014-2972


Aryaman J, Johnston I, Jones N, 2019, Mitochondrial heterogeneity, Frontiers in Genetics, Vol: 9, ISSN: 1664-8021

Cell-to-cell heterogeneity drives a range of (patho)physiologically important phenomena, such as cell fate and chemotherapeutic resistance. The role of metabolism, and particularly of mitochondria, is increasingly being recognized as an important explanatory factor in cell-to-cell heterogeneity. Most eukaryotic cells possess a population of mitochondria, in the sense that mitochondrial DNA (mtDNA) is held in multiple copies per cell, where the sequence of each molecule can vary. Hence, intra-cellular mitochondrial heterogeneity is possible, which can induce inter-cellular mitochondrial heterogeneity, and may drive aspects of cellular noise. In this review, we discuss sources of mitochondrial heterogeneity (variations between mitochondria in the same cell, and mitochondrial variations between supposedly identical cells) from both genetic and non-genetic perspectives, and mitochondrial genotype-phenotype links. We discuss the apparent homeostasis of mtDNA copy number, the observation of pervasive intra-cellular mtDNA mutation (which is termed “microheteroplasmy”), and developments in the understanding of inter-cellular mtDNA mutation (“macroheteroplasmy”). We point to the relationship between mitochondrial supercomplexes, cristal structure, pH, and cardiolipin as a potential amplifier of the mitochondrial genotype-phenotype link. We also discuss mitochondrial membrane potential and networks as sources of mitochondrial heterogeneity, and their influence upon the mitochondrial genome. Finally, we revisit the idea of mitochondrial complementation as a means of dampening mitochondrial genotype-phenotype links in light of recent experimental developments. The diverse sources of mitochondrial heterogeneity, as well as their increasingly recognized role in contributing to cellular heterogeneity, highlights the need for future single-cell mitochondrial measurements in the context of cellular noise studies.


Brittain R, Jones N, Ouldridge T, 2018, Biochemical Szilard engine for memory limited inference

Code and data for figures in 'Biochemical Szilard engine for memory limited inference'


Sethi S, Ewers R, Jones N, Orme D, Picinali Let al., 2018, Robust, real-time and autonomous monitoring of ecosystems with an open, low-cost, networked device, Methods in Ecology and Evolution, Vol: 9, Pages: 2383-2387, ISSN: 2041-210X

1. Automated methods of monitoring ecosystems provide a cost-effective way to track changes in natural system's dynamics across temporal and spatial scales. However, methods of recording and storing data captured from the field still require significant manual effort. 2. Here we introduce an open source, inexpensive, fully autonomous ecosystem monitoring unit for capturing and remotely transmitting continuous data streams from field sites over long time-periods. We provide a modular software framework for deploying various sensors, together with implementations to demonstrate proof of concept for continuous audio monitoring and time-lapse photography. 3. We show how our system can outperform comparable technologies for fractions of the cost, provided a local mobile network link is available. The system is robust to unreliable network signals and has been shown to function in extreme environmental conditions, such as in the tropical rainforests of Sabah, Borneo. 4. We provide full details on how to assemble the hardware, and the open-source software. Paired with appropriate automated analysis techniques, this system could provide spatially dense, near real-time, continuous insights into ecosystem and biodiversity dynamics at a low cost.


Garrod M, Jones NS, 2018, Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information, Physical Review E, Vol: 98, ISSN: 1539-3755

A random geometric graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the distributional properties of the algebraic connectivity which is informative of diffusion and synchronization time scales in graphs. We use numerical simulations to provide a characterization of the algebraic connectivity distribution for RGG ensembles. We find that the algebraic connectivity can show fluctuations relative to its mean on the order of 30%, even for relatively large RGG ensembles (N=105). We explore the factors driving these fluctuations for RGG ensembles with different choices of dimensionality, boundary conditions, and node distributions. Within a given ensemble, the algebraic connectivity can covary with the minimum degree and can also be affected by the presence of density inhomogeneities in the nodal distribution. We also derive a closed-form expression for the expected algebraic connectivity for RGGs with periodic boundary conditions for general dimension.


Keogh M, Wei W, Aryaman J, Walker L, van den Ameele J, Coxhead J, Wilson I, Bashton M, Beck J, West J, Chen R, Haudenschild C, Bartha G, Luo S, Morris C, Jones N, Attems J, Chinnery Pet al., 2018, High prevalence of focal and multi-focal somatic genetic variants in the human brain, Nature Communications, Vol: 9, ISSN: 2041-1723

Somatic mutations during stem cell division are responsible for several cancers. In principle, a similar process could occur during the intense cell proliferation accompanying human brain development, leading to the accumulation of regionally distributed foci of mutations. Using dual platform >5000-fold depth sequencing of 102 genes in 173 adult human brain samples, we detect and validate somatic mutations in 27 of 54 brains. Using a mathematical model of neurodevelopment and approximate Bayesian inference, we predict that macroscopic islands of pathologically mutated neurons are likely to be common in the general population. The detected mutation spectrum also includes DNMT3A and TET2 which are likely to have originated from blood cell lineages. Together, these findings establish developmental mutagenesis as a potential mechanism for neurodegenerative disorders, and provide a novel mechanism for the regional onset and focal pathology in sporadic cases.


Wei W, Keogh MJ, Aryaman J, Golder Z, Kullar PJ, Wilson I, Talbot K, Turner MR, McKenzie C-A, Troakes C, Attems J, Smith C, Sarraj SA, Morris CM, Ansorge O, Jones NS, Ironside JW, Chinnery PFet al., 2018, Frequency and signature of somatic variants in 1461 human brain exomes, Genetics in Medicine, ISSN: 1098-3600

PURPOSE: To systematically study somatic variants arising during development in the human brain across a spectrum of neurodegenerative disorders. METHODS: In this study we developed a pipeline to identify somatic variants from exome sequencing data in 1461 diseased and control human brains. Eighty-eight percent of the DNA samples were extracted from the cerebellum. Identified somatic variants were validated by targeted amplicon sequencing and/or PyroMark® Q24. RESULTS: We observed somatic coding variants present in >10% of sampled cells in at least 1% of brains. The mutational signature of the detected variants showed a predominance of C>T variants most consistent with arising from DNA mismatch repair, occurred frequently in genes that are highly expressed within the central nervous system, and with a minimum somatic mutation rate of 4.25 × 10-10 per base pair per individual. CONCLUSION: These findings provide proof-of-principle that deleterious somatic variants can affect sizeable brain regions in at least 1% of the population, and thus have the potential to contribute to the pathogenesis of common neurodegenerative diseases.


Keogh MJ, Wei W, Aryaman J, Wilson I, Talbot K, Turner MR, McKenzie C-A, Troakes C, Attems J, Smith C, Al Sarraj S, Morris CM, Ansorge O, Pickering-Brown S, Jones N, Ironside JW, Chinnery PFet al., 2018, Oligogenic genetic variation of neurodegenerative disease genes in 980 postmortem human brains, JOURNAL OF NEUROLOGY NEUROSURGERY AND PSYCHIATRY, Vol: 89, Pages: 813-816, ISSN: 0022-3050


Lubba CT, Le Guen Y, Jarvis S, Jones N, Cork S, Eftekhar A, Schultz Set al., 2018, PyPNS: multiscale simulation of a peripheral nerve in Python, Neuroinformatics, ISSN: 1539-2791

Bioelectronic Medicines that modulate the activity patterns on peripheral nerves have promise as a new way of treating diverse medical conditions from epilepsy to rheumatism. Progress in the field builds upon time consuming and expensive experiments in living organisms. To reduce experimentation load and allow for a faster, more detailed analysis of peripheral nerve stimulation and recording, computational models incorporating experimental insights will be of great help.We present a peripheral nerve simulator that combines biophysical axon models and numerically solved and idealised extracellular space models in one environment. We modeled the extracellular space as a three-dimensional resistive continuum governed by the electro-quasistatic approximation of the Maxwell equations. Potential distributions were precomputed in finite element models for different media (homogeneous, nerve in saline, nerve in cuff) and imported into our simulator. Axons, on the other hand, were modeled more abstractly as one-dimensional chains of compartments. Unmyelinated fibres were based on the Hodgkin- Huxley model; for myelinated fibres, we adapted the model proposed by McIntyre et al. in 2002 to smaller diameters. To obtain realistic axon shapes, an iterative algorithm positioned fibres along the nerve with a variable tortuosity fit to imaged trajectories. We validated our model with data from the stimulated rat vagus nerve. Simulation results predicted that tortuosity alters recorded signal shapes and increases stimulation thresholds. The model we developed can easily be adapted to different nerves, and may be of use for Bioelectronic Medicine research in the future.


Pezet M, Gomez-Duran A, Aryaman J, Jones NS, Chinnery PFet al., 2018, Understanding the mechanism underpinning the transmission of mtDNA mutations, 11th UK Neuromuscular Translational Research Conference, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: S35-S35, ISSN: 0960-8966


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.


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.


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.


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.


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.


Poole W, Ortiz-Muñoz A, Behera A, Jones NS, Ouldridge TE, Winfree E, Gopalkrishnan Met al., 2017, Chemical Boltzmann Machines, Lecture Notes in Computer Science, Vol: 10467, Pages: 210-231, ISSN: 0302-9743

How smart can a micron-sized bag of chemicals be? How can an artificial orreal cell make inferences about its environment? From which kinds ofprobability distributions can chemical reaction networks sample? We begintackling these questions by showing four ways in which a stochastic chemicalreaction network can implement a Boltzmann machine, a stochastic neural networkmodel that can generate a wide range of probability distributions and computeconditional probabilities. The resulting models, and the associated theorems,provide a road map for constructing chemical reaction networks that exploittheir native stochasticity as a computational resource. Finally, to show thepotential of our models, we simulate a chemical Boltzmann machine to classifyand generate MNIST digits in-silico.


Deshpande A, Gopalkrishnan M, Ouldridge TE, Jones Net al., 2017, Designing the Optimal Bit: Balancing Energetic Cost, Speed and Reliability, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 473, ISSN: 1364-5021

We consider the technologically relevant costs of operating a reliable bitthat can be erased rapidly. We find that both erasing and reliability times arenon-monotonic in the underlying friction, leading to a trade-off betweenerasing speed and bit reliability. Fast erasure is possible at the expense oflow reliability at moderate friction, and high reliability comes at the expenseof slow erasure in the underdamped and overdamped limits. Within a given classof bit parameters and control strategies, we define "optimal" designs of bitsthat meet the desired reliability and erasing time requirements with the lowestoperational work cost. We find that optimal designs always saturate the boundon the erasing time requirement, but can exceed the required reliability timeif critically damped. The non-trivial geometry of the reliability and erasingtime-scales allows us to exclude large regions of parameter space assub-optimal. We find that optimal designs are either critically damped or closeto critical damping under the erasing procedure.


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.


Fricker MD, Akita D, Heaton LLM, Jones N, Obara B, Nakagaki Tet al., 2017, Automated analysis of Physarum network structure and dynamics, JOURNAL OF PHYSICS D-APPLIED PHYSICS, Vol: 50, ISSN: 0022-3727


Brittain RA, Jones NS, Ouldridge TE, 2017, What we learn from the learning rate, Journal of Statistical Mechanics-Theory and Experiment, Vol: 2017, ISSN: 1742-5468

The learning rate is an information-theoretical quantity for bipartite Markovchains describing two coupled subsystems. It is defined as the rate at whichtransitions in the downstream subsystem tend to increase the mutual informationbetween the two subsystems, and is bounded by the dissipation arising fromthese transitions. Its physical interpretation, however, is unclear, althoughit has been used as a metric for the sensing performance of the downstreamsubsystem. In this paper we explore the behaviour of the learning rate for anumber of simple model systems, establishing when and how its behaviour isdistinct from the instantaneous mutual information between subsystems. In thesimplest case, the two are almost equivalent. In more complex steady-statesystems, the mutual information and the learning rate behave qualitativelydistinctly, with the learning rate clearly now reflecting the rate at which thedownstream system must update its information in response to changes in theupstream system. It is not clear whether this quantity is the most naturalmeasure for sensor performance, and, indeed, we provide an example in whichoptimising the learning rate over a region of parameter space of the downstreamsystem yields an apparently sub-optimal sensor.


Colijn C, Jones N, Johnston I, Yaliraki SN, Barahona Met al., 2017, Towards precision healthcare: context and mathematical challenges, Frontiers in Physiology, Vol: 8, ISSN: 1664-042X

Precision medicine refers to the idea of delivering the right treatment to the right patient at the right time, usually with a focus on a data-centred approach to this task. In this perspective piece, we use the term "precision healthcare" to describe the development of precision approaches that bridge from the individual to the population, taking advantage of individual-level data, but also taking the social context into account. These problems give rise to a broad spectrum of technical, scientific, policy, ethical and social challenges, and new mathematical techniques will be required to meet them. To ensure that the science underpin-ning "precision" is robust, interpretable and well-suited to meet the policy, ethical and social questions that such approaches raise, the mathematical methods for data analysis should be transparent, robust and able to adapt to errors and uncertainties. In particular, precision methodologies should capture the complexity of data, yet produce tractable descriptions at the relevant resolution while preserving intelligibility and traceability, so that they can be used by practitioners to aid decision-making. Through several case studies in this domain of precision healthcare, we argue that this vision requires the development of new mathematical frameworks, both in modelling and in data analysis and interpretation.


McGrath T, Jones NS, ten Wolde PR, Ouldridge TEet al., 2017, Biochemical Machines for the Interconversion of Mutual Information and Work (vol 118, 028101, 2017), PHYSICAL REVIEW LETTERS, Vol: 118, ISSN: 0031-9007


McGrath T, Jones NS, Wolde PRT, Ouldridge TEet al., 2017, A biochemical machine for the interconversion of mutual information and work, Physical Review Letters, Vol: 118, ISSN: 1079-7114

We propose a physically-realisable biochemical device that is coupled to abiochemical reservoir of mutual information, fuel molecules and a chemicalbath. Mutual information allows work to be done on the bath even when the fuelmolecules appear to be in equilibrium; alternatively, mutual information can becreated by driving from the fuel or the bath. The system exhibits diversebehaviour, including a regime in which the information, despite increasingduring the reaction, enhances the extracted work. We further demonstrate that amodified device can function without the need for external manipulation,eliminating the need for a complex and potentially costly control.


Hoitzing H, Johnston IG, Jones NS, 2017, Stochastic models for evolving cellular populations of mitochondria: Disease, development, and ageing, Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, Pages: 287-314, ISBN: 9783319626260

© Springer International Publishing AG 2017. Mitochondria are essential cellular organelles whose dysfunction is associated with ageing, cancer, mitochondrial diseases, and many other disorders. They contain their own genomes (mtDNA), of which thousands can be present in a single cell. These genomes are repeatedly replicated and degraded over time, and are prone to mutations. If the fraction of mutated genomes (heteroplasmy) exceeds a certain threshold, cellular defects can arise. The dynamics of mtDNAs over time and the accumulation of mutant genomes form a rich and vital stochastic process, the understanding of which provides important insights into disease progression. Numerous mathematical models have been constructed to provide a better understanding of how mitochondrial dysfunctions arise and, importantly, how clinical interventions can alleviate disease symptoms. For a given mean heteroplasmy, an increased variance-and thus a wider cell-to-cell heteroplasmy distribution-implies a higher probability of exceeding a given threshold value, meaning that stochastic models are essential to describe mtDNA disease. Mitochondria can undergo fusion and fission events with each other making the mitochondrial population a dynamic network that continuously changes its morphology, and allowing for the possibility of exchange of mtDNA molecules: coupled stochastic physical and genetic dynamics thus govern cellular mtDNA populations. Here, an overview is given of the kinds of stochastic mathematical models constructed describing mitochondria, their implications, and currently existing open problems.


Johnston IG, Jones NS, 2016, Evolution of cell-to-cell variability in stochastic, controlled, heteroplasmic mtDNA populations, American Journal of Human Genetics, Vol: 99, Pages: 1150-1162, ISSN: 1537-6605

Populations of physiologically vital mitochondrial DNA (mtDNA) molecules evolve in cells under control from the nucleus. The evolution of populations of mixed mtDNA types is complicated and poorly understood, and variability of these controlled admixtures plays a central role in the inheritance and onset of genetic disease. Here, we develop a mathematical theory describing the evolution of, and variability in, these stochastic populations for any type of cellular control, showing that cell-to-cell variability in mtDNA and mutant load inevitably increases with time, according to rates that we derive and which are notably independent of the mechanistic details of feedback signaling. We show with a set of experimental case studies that this theory explains disparate quantitative results from classical and modern experimental and computational research on heteroplasmy variance in different species. We demonstrate that our general model provides a host of specific insights, including a modification of the often-used but hard-to-interpret Wright formula to correspond directly to biological observables, the ability to quantify selective and mutational pressure in mtDNA populations, and characterization of the pronounced variability inevitably arising from the action of possible mtDNA quality-control mechanisms. Our general theoretical framework, supported by existing experimental results, thus helps us to understand and predict the evolution of stochastic mtDNA populations in cell biology.


Larson HJ, de Figueiredo A, Xiahong Z, Schulz WS, Verger P, Johnston IG, Cook AR, Jones NSet al., 2016, The state of vaccine confidence 2016: global insights through a 67-country survey, EBioMedicine, Vol: 12, Pages: 295-301, ISSN: 2352-3964

BackgroundPublic trust in immunization is an increasingly important global health issue. Losses in confidence in vaccines and immunization programmes can lead to vaccine reluctance and refusal, risking disease outbreaks and challenging immunization goals in high- and low-income settings. National and international immunization stakeholders have called for better monitoring of vaccine confidence to identify emerging concerns before they evolve into vaccine confidence crises.MethodsWe perform a large-scale, data-driven study on worldwide attitudes to immunizations. This survey – which we believe represents the largest survey on confidence in immunization to date – examines perceptions of vaccine importance, safety, effectiveness, and religious compatibility among 65,819 individuals across 67 countries. Hierarchical models are employed to probe relationships between individual- and country-level socio-economic factors and vaccine attitudes obtained through the four-question, Likert-scale survey.FindingsOverall sentiment towards vaccinations is positive across all 67 countries, however there is wide variability between countries and across world regions. Vaccine-safety related sentiment is particularly negative in the European region, which has seven of the ten least confident countries, with 41% of respondents in France and 36% of respondents in Bosnia & Herzegovina reporting that they disagree that vaccines are safe (compared to a global average of 13%). The oldest age group (65 +) and Roman Catholics (amongst all faiths surveyed) are associated with positive views on vaccine sentiment, while the Western Pacific region reported the highest level of religious incompatibility with vaccines. Countries with high levels of schooling and good access to health services are associated with lower rates of positive sentiment, pointing to an emerging inverse relationship between vaccine sentiments and socio-economic status.ConclusionsRegular monitoring of vaccine


de Figueiredo A, Johnston IG, Smith DM, Agarwal S, Larson HJ, Jones NSet al., 2016, Forecasted trends in vaccination coverage and correlations with socioeconomic factors: a global time-series analysis over 30 years., Lancet Global Health, Vol: 4, Pages: e726-e735, ISSN: 2214-109X

BACKGROUND: Incomplete immunisation coverage causes preventable illness and death in both developing and developed countries. Identification of factors that might modulate coverage could inform effective immunisation programmes and policies. We constructed a performance indicator that could quantitatively approximate measures of the susceptibility of immunisation programmes to coverage losses, with an aim to identify correlations between trends in vaccine coverage and socioeconomic factors. METHODS: We undertook a data-driven time-series analysis to examine trends in coverage of diphtheria, tetanus, and pertussis (DTP) vaccination across 190 countries over the past 30 years. We grouped countries into six world regions according to WHO classifications. We used Gaussian process regression to forecast future coverage rates and provide a vaccine performance index: a summary measure of the strength of immunisation coverage in a country. FINDINGS: Overall vaccine coverage increased in all six world regions between 1980 and 2010, with variation in volatility and trends. Our vaccine performance index identified that 53 countries had more than a 50% chance of missing the Global Vaccine Action Plan (GVAP) target of 90% worldwide coverage with three doses of DTP (DTP3) by 2015. These countries were mostly in sub-Saharan Africa and south Asia, but Austria and Ukraine also featured. Factors associated with DTP3 immunisation coverage varied by world region: personal income (Spearman's ρ=0·66, p=0·0011) and government health spending (0·66, p<0·0001) were informative of immunisation coverage in the Eastern Mediterranean between 1980 and 2010, whereas primary school completion was informative of coverage in Africa (0·56, p<0·0001) over the same period. The proportion of births attended by skilled health staff correlated significantly with immunisation coverage across many world regions. INTERPRETATION: Our vaccine performance inde


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