Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealisations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with MATLAB implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community

Bayesian score calibration for approximate models

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often intractable and model simulation may be computationally burdensome. Fortunately, in many of these situations, it is possible to adopt a surrogate model or approximate likelihood function. It may be convenient to conduct Bayesian inference directly with the surrogate, but this can result in bias and poor uncertainty quantification. In this paper we propose a new method for adjusting approximate posterior samples to reduce bias and produce more accurate uncertainty quantification. We do this by optimizing a transform of the approximate posterior that maximizes a scoring rule. Our approach requires only a (fixed) small number of complex model simulations and is numerically stable. We demonstrate good performance of the new method on several examples of increasing complexity.Comment: 27 pages, 8 figures, 5 table

Rapid Bayesian inference for expensive stochastic models

Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the simulation of models are growing even faster. This is largely due to the increase in model complexity, often including stochastic dynamics, that is necessary to describe and characterize phenomena observed using modern, high resolution, experimental techniques. Such models are rarely analytically tractable, meaning that extremely large numbers of stochastic simulations are required for parameter inference. In such cases, parameter inference can be practically impossible. In this work, we present new computational Bayesian techniques that accelerate inference for expensive stochastic models by using computationally inexpensive approximations to inform feasible regions in parameter space, and through learning transforms that adjust the biased approximate inferences to closer represent the correct inferences under the expensive stochastic model. Using topical examples from ecology and cell biology, we demonstrate a speed improvement of an order of magnitude without any loss in accuracy. This represents a substantial improvement over current state-of-the-art methods for Bayesian computations when appropriate model approximations are available

Generalised likelihood profiles for models with intractable likelihoods

Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models without a tractable likelihood function. Such models are typical in many fields of science, rendering these classical approaches impractical in these settings. To address this limitation, we develop a new approach to generalising the methods of likelihood profiling for situations when the likelihood cannot be evaluated but stochastic simulations of the assumed data generating process are possible. Our approach is based upon recasting developments from generalised Bayesian inference into a frequentist setting. We derive a method for constructing generalised likelihood profiles and calibrating these profiles to achieve desired frequentist coverage for a given coverage level. We demonstrate the performance of our method on realistic examples from the literature and highlight the capability of our approach for the purpose of practical identifability analysis for models with intractable likelihoods

Comorbidity of self-harm and disordered eating in young people:Evidence from a UK population-based cohort

BACKGROUND: Self-harm and eating disorders are often comorbid in clinical samples but their co-occurrence in the general population is unclear. Given that only a small proportion of individuals who self-harm or have disordered eating present to clinical services, and that both self-harm and eating disorders are associated with substantial morbidity and mortality, it is important to study these behaviours at a population level. METHODS: We assessed the co-occurrence of self-harm and disordered eating behaviours in 3384 females and 2326 males from a UK population-based cohort: the Avon Longitudinal Study of Parents and Children (ALSPAC). Participants reported on their self-harm and disordered eating behaviours (fasting, purging, binge-eating and excessive exercise) in the last year via questionnaire at 16 and 24 years. At each age we assessed how many individuals who self-harm also reported disordered eating, and how many individuals with disordered eating also reported self-harm. RESULTS: We found high comorbidity of self-harm and disordered eating. Almost two-thirds of 16-year-old females, and two-in-five 24-year old males who self-harmed also reported some form of disordered eating. Young people with disordered eating reported higher levels of self-harm at both ages compared to those without disordered eating. LIMITATIONS: We were not able to measure whether participants identified their disordered eating as a method of self-harm. CONCLUSIONS: Self-harm and disordered eating commonly co-occur in young people in the general population. It is important to screen for both sets of difficulties to provide appropriate treatment

Cell cycle-dependent activation of Ras

AbstractBackground Ras proteins play an essential role in the transduction of signals from a wide range of cell-surface receptors to the nucleus. These signals may promote cellular proliferation or differentiation, depending on the cell background. It is well established that Ras plays an important role in the transduction of mitogenic signals from activated growth-factor receptors, leading to cell-cycle entry. However, important questions remain as to whether Ras controls signalling events during cell-cycle progression and, if so, at which point in the cell-cycle it is activated.Results To address these questions we have developed a novel, functional assay for the detection of cellular activated Ras. Using this assay, we found that Ras was activated in HeLa cells, following release from mitosis, and in NIH 3T3 fibroblasts, following serum-stimulated cell-cycle entry. In each case, peak Ras activation occurred in mid-G1 phase. Ras activation in HeLa cells at mid-G1 phase was dependent on RNA and protein synthesis and was not associated with tyrosine phosphorylation of Shc proteins and their binding to Grb2. Significantly, activation of Ras and the extracellular-signal regulated (ERK) subgroup of mitogen-activated protein kinases were not temporally correlated during G1-phase progression.Conclusions Activation of Ras during mid-G1 phase appears to differ in many respects from its rapid activation by growth factors, suggesting a novel mechanism of regulation that may be intrinsic to cell-cycle progression. Furthermore, the temporal dissociation between Ras and ERK activation suggests that Ras targets alternate effector pathways during G1-phase progression

The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data

We present constraints on cosmological and astrophysical parameters from high-resolution microwave background maps at 148 GHz and 218 GHz made by the Atacama Cosmology Telescope (ACT) in three seasons of observations from 2008 to 2010. A model of primary cosmological and secondary foreground parameters is fit to the map power spectra and lensing deflection power spectrum, including contributions from both the thermal Sunyaev-Zeldovich (tSZ) effect and the kinematic Sunyaev-Zeldovich (kSZ) effect, Poisson and correlated anisotropy from unresolved infrared sources, radio sources, and the correlation between the tSZ effect and infrared sources. The power ell^2 C_ell/2pi of the thermal SZ power spectrum at 148 GHz is measured to be 3.4 +\- 1.4 muK^2 at ell=3000, while the corresponding amplitude of the kinematic SZ power spectrum has a 95% confidence level upper limit of 8.6 muK^2. Combining ACT power spectra with the WMAP 7-year temperature and polarization power spectra, we find excellent consistency with the LCDM model. We constrain the number of effective relativistic degrees of freedom in the early universe to be Neff=2.79 +\- 0.56, in agreement with the canonical value of Neff=3.046 for three massless neutrinos. We constrain the sum of the neutrino masses to be Sigma m_nu < 0.39 eV at 95% confidence when combining ACT and WMAP 7-year data with BAO and Hubble constant measurements. We constrain the amount of primordial helium to be Yp = 0.225 +\- 0.034, and measure no variation in the fine structure constant alpha since recombination, with alpha/alpha0 = 1.004 +/- 0.005. We also find no evidence for any running of the scalar spectral index, dns/dlnk = -0.004 +\- 0.012.Comment: 26 pages, 22 figures. This paper is a companion to Das et al. (2013) and Dunkley et al. (2013). Matches published JCAP versio