High levels of somatic DNA diversity at the myotonic dystrophy type 1 locus are driven by ultra-frequent expansion and contraction mutations.

Several human genetic diseases are associated with inheriting an abnormally large unstable DNA simple sequence repeat. These sequences mutate, by changing the number of repeats, many times during the lifetime of those affected, with a bias towards expansion. These somatic changes lead not only to the presence of cells with different numbers of repeats in the same tissue, but also produce increasingly longer repeats, contributing towards the progressive nature of the symptoms. Modelling the progression of repeat length throughout the lifetime of individuals has potential for improving prognostic information as well as providing a deeper understanding of the underlying biological process. A large data set comprising blood DNA samples from individuals with one such disease, myotonic dystrophy type 1, provides an opportunity to parameterize a mathematical model for repeat length evolution that we can use to infer biological parameters of interest. We developed new mathematical models by modifying a proposed stochastic birth process to incorporate possible contraction. A hierarchical Bayesian approach was used as the basis for inference, and we estimated the distribution of mutation rates in the population. We used model comparison analysis to reveal, for the first time, that the expansion bias observed in the distributions of repeat lengths is likely to be the cumulative effect of many expansion and contraction events. We predict that mutation events can occur as frequently as every other day, which matches the timing of regular cell activities such as DNA repair and transcription but not DNA replication.

Somatic instability of the expanded CTG triplet repeat in myotonic dystrophy type 1 is a heritable quantitative trait and modifier of disease severity.

Deciphering the contribution of genetic instability in somatic cells is critical to our understanding of many human disorders. Myotonic dystrophy type 1 (DM1) is one such disorder that is caused by the expansion of a CTG repeat that shows extremely high levels of somatic instability. This somatic instability has compromised attempts to measure intergenerational repeat dynamics and infer genotype-phenotype relationships. Using single-molecule PCR, we have characterized more than 17 000 de novo somatic mutations from a large cohort of DM1 patients. These data reveal that the estimated progenitor allele length is the major modifier of age of onset. We find no evidence for a threshold above which repeat length does not contribute toward age at onset, suggesting pathogenesis is not constrained to a simple molecular switch such as nuclear retention of the DMPK transcript or haploinsufficiency for DMPK and/or SIX5. Importantly, we also show that age at onset is further modified by the level of somatic instability; patients in whom the repeat expands more rapidly, develop the symptoms earlier. These data establish a primary role for somatic instability in DM1 severity, further highlighting it as a therapeutic target. In addition, we show that the level of instability is highly heritable, implying a role for individual-specific trans-acting genetic modifiers. Identifying these trans-acting genetic modifiers will facilitate the formulation of novel therapies that curtail the accumulation of somatic expansions and may provide clues to the role these factors play in the development of cancer, aging and inherited disease in the general population.

A Bayesian approach for parameter estimation in the extended clock gene circuit of Arabidopsis thaliana.

The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.

Quantum deep learning by sampling neural nets with a quantum annealer.

We demonstrate the feasibility of framing a classically learned deep neural network as an energy based model that can be processed on a one-step quantum annealer in order to exploit fast sampling times. We propose approaches to overcome two hurdles for high resolution image classification on a quantum processing unit (QPU): the required number and the binary nature of the model states. With this novel method we successfully transfer a pretrained convolutional neural network to the QPU. By taking advantage of the strengths of quantum annealing, we show the potential for classification speedup of at least one order of magnitude.

Deep Learnability: Using Neural Networks to Quantify Language Similarity and Learnability.

Learning a second language (L2) usually progresses faster if a learner's L2 is similar to their first language (L1). Yet global similarity between languages is difficult to quantify, obscuring its precise effect on learnability. Further, the combinatorial explosion of possible L1 and L2 language pairs, combined with the difficulty of controlling for idiosyncratic differences across language pairs and language learners, limits the generalizability of the experimental approach. In this study, we present a different approach, employing artificial languages, and artificial learners. We built a set of five artificial languages whose underlying grammars and vocabulary were manipulated to ensure a known degree of similarity between each pair of languages. We next built a series of neural network models for each language, and sequentially trained them on pairs of languages. These models thus represented L1 speakers learning L2s. By observing the change in activity of the cells between the L1-speaker model and the L2-learner model, we estimated how much change was needed for the model to learn the new language. We then compared the change for each L1/L2 bilingual model to the underlying similarity across each language pair. The results showed that this approach can not only recover the facilitative effect of similarity on L2 acquisition, but can also offer new insights into the differential effects across different domains of similarity. These findings serve as a proof of concept for a generalizable approach that can be applied to natural languages.

Deep learning for real-time single-pixel video.

Single-pixel cameras capture images without the requirement for a multi-pixel sensor, enabling the use of state-of-the-art detector technologies and providing a potentially low-cost solution for sensing beyond the visible spectrum. One limitation of single-pixel cameras is the inherent trade-off between image resolution and frame rate, with current compressive (compressed) sensing techniques being unable to support real-time video. In this work we demonstrate the application of deep learning with convolutional auto-encoder networks to recover real-time 128 × 128 pixel video at 30 frames-per-second from a single-pixel camera sampling at a compression ratio of 2%. In addition, by training the network on a large database of images we are able to optimise the first layer of the convolutional network, equivalent to optimising the basis used for scanning the image intensities. This work develops and implements a novel approach to solving the inverse problem for single-pixel cameras efficiently and represents a significant step towards real-time operation of computational imagers. By learning from examples in a particular context, our approach opens up the possibility of high resolution for task-specific adaptation, with importance for applications in gas sensing, 3D imaging and metrology.

Neural network identification of people hidden from view with a single-pixel, single-photon detector.

Light scattered from multiple surfaces can be used to retrieve information of hidden environments. However, full three-dimensional retrieval of an object hidden from view by a wall has only been achieved with scanning systems and requires intensive computational processing of the retrieved data. Here we use a non-scanning, single-photon single-pixel detector in combination with a deep convolutional artificial neural network: this allows us to locate the position and to also simultaneously provide the actual identity of a hidden person, chosen from a database of people (N = 3). Artificial neural networks applied to specific computational imaging problems can therefore enable novel imaging capabilities with hugely simplified hardware and processing times.

Modelling and inference reveal nonlinear length-dependent suppression of somatic instability for small disease associated alleles in myotonic dystrophy type 1 and Huntington disease.

More than 20 human genetic diseases are associated with inheriting an unstable expanded DNA simple sequence tandem repeat, for example, CTG (cytosine-thymine-guanine) repeats in myotonic dystrophy type 1 (DM1) and CAG (cytosine-adenine-guanine) repeats in Huntington disease (HD). These sequences mutate by changing the number of repeats not just between generations, but also during the lifetime of affected individuals. Levels of somatic instability contribute to disease onset and progression but as changes are tissue-specific, age- and repeat length-dependent, interpretation of the level of somatic instability in an individual is confounded by these considerations. Mathematical models, fitted to CTG repeat length distributions derived from blood DNA, from a large cohort of DM1-affected or at risk individuals, have recently been used to quantify inherited repeat lengths and mutation rates. Taking into account age, the estimated mutation rates are lower than predicted among individuals with small alleles (inherited repeat lengths less than 100 CTGs), suggesting that these rates may be suppressed at the lower end of the disease-causing range. In this study, we propose that a length-specific effect operates within this range and tested this hypothesis using a model comparison approach. To calibrate the extended model, we used data derived from blood DNA from DM1 individuals and, for the first time, buccal DNA from HD individuals. In a novel application of this extended model, we identified individuals whose effective repeat length, with regards to somatic instability, is less than their actual repeat length. A plausible explanation for this distinction is that the expanded repeat tract is compromised by interruptions or other unusual features. We quantified effective length for a large cohort of DM1 individuals and showed that effective length better predicts age of onset than inherited repeat length, thus improving the genotype-phenotype correlation. Under the extended model, we removed some of the bias in mutation rates making them less length-dependent. Consequently, rates adjusted in this way will be better suited as quantitative traits to investigate cis- or trans-acting modifiers of somatic mosaicism, disease onset and progression.

Bifurcation analysis informs Bayesian inference in the Hes1 feedback loop.

BACKGROUND: Ordinary differential equations (ODEs) are an important tool for describing the dynamics of biological systems. However, for ODE models to be useful, their parameters must first be calibrated. Parameter estimation, that is, finding parameter values given experimental data, is an inference problem that can be treated systematically through a Bayesian framework.A Markov chain Monte Carlo approach can then be used to sample from the appropriate posterior probability distributions, provided that suitable prior distributions can be found for the unknown parameter values. Choosing these priors is therefore a vital first step in the inference process. We study here a negative feedback loop in gene regulation where an ODE incorporating a time delay has been proposed as a realistic model and where experimental data is available. Our aim is to show that a priori mathematical analysis can be exploited in the choice of priors. RESULTS: By focussing on the onset of oscillatory behaviour through a Hopf Bifurcation, we derive a range of analytical expressions and constraints that link the model parameters to the observed dynamics of the system. Computational tests on both simulated and experimental data emphasise the usefulness of this analysis. CONCLUSION: Mathematical analysis not only gives insights into the possible dynamical behaviour of gene expression models, but can also be used to inform the choice of priors when parameters are inferred from experimental data in a Bayesian setting.