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

Reconciling transport models across scales: the role of volume exclusion

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far

Multiscale control of flooding and riparian‐forest composition in Lower Michigan, USA

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/117201/1/ecy2009901145.pd

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

Bayesian uncertainty quantification for data-driven equation learning

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with relatively small amounts of noise, the relationship between observation noise and uncertainty in the learned differential equation models remains unexplored. We demonstrate that for noisy data sets there exists great variation in both the structure of the learned differential equation models as well as the parameter values. We explore how to combine data sets to quantify uncertainty in the learned models, and at the same time draw mechanistic conclusions about the target differential equations. We generate noisy data using a stochastic agent-based model and combine equation learning methods with approximate Bayesian computation (ABC) to show that the correct differential equation model can be successfully learned from data, while a quantification of uncertainty is given by a posterior distribution in parameter space

Twittering about research : a case study of the world's first Twitter poster competition

The Royal Society of Chemistry held, to our knowledge, the world’s first Twitter conference at 9am on February 5th, 2015. This paper reports the details of the event and discusses the outcomes, such as the potential for the use of social media to enhance scientific communication at conferences. In particular, the present work argues that social media outlets such as Twitter broaden audiences, speed up communication, and force clearer and more concise descriptions of a researcher’s work. The benefits of poster presentations are also discussed in terms of potential knowledge exchange and networking. This paper serves as a proof-of-concept approach for improving both the public opinion of the poster, and the enhancement of the poster through an innovative online format that some may feel more comfortable with, compared to face-to-face communication

Learning to predict: exposure to temporal sequences facilitates prediction of future events.

Previous experience is thought to facilitate our ability to extract spatial and temporal regularities from cluttered scenes. However, little is known about how we may use this knowledge to predict future events. Here we test whether exposure to temporal sequences facilitates the visual recognition of upcoming stimuli. We presented observers with a sequence of leftwards and rightwards oriented gratings that was interrupted by a test stimulus. Observers were asked to indicate whether the orientation of the test stimulus matched their expectation based on the preceding sequence. Our results demonstrate that exposure to temporal sequences without feedback facilitates our ability to predict an upcoming stimulus. In particular, observers' performance improved following exposure to structured but not random sequences. Improved performance lasted for a prolonged period and generalized to untrained stimulus orientations rather than sequences of different global structure, suggesting that observers acquire knowledge of the sequence structure rather than its items. Further, this learning was compromised when observers performed a dual task resulting in increased attentional load. These findings suggest that exposure to temporal regularities in a scene allows us to accumulate knowledge about its global structure and predict future events

Learning differential equation models from stochastic agent-based model simulations

Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology, and epidemiology. Analysis of the model dynamics can be challenging due to their inherent stochasticity and heavy computational requirements. Common approaches to the analysis of agent-based models include extensive Monte Carlo simulation of the model or the derivation of coarse-grained differential equation models to predict the expected or averaged output from the agent-based model. Both of these approaches have limitations, however, as extensive computation of complex agent-based models may be infeasible, and coarse-grained differential equation models can fail to accurately describe model dynamics in certain parameter regimes. We propose that methods from the equation learning field provide a promising, novel, and unifying approach for agent-based model analysis. Equation learning is a recent field of research from data science that aims to infer differential equation models directly from data. We use this tutorial to review how methods from equation learning can be used to learn differential equation models from agent-based model simulations. We demonstrate that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so. We highlight these advantages through several case studies involving two agent-based models that are broadly applicable to biological phenomena: a birth-death-migration model commonly used to explore cell biology experiments and a susceptible-infected-recovered model of infectious disease spread

De novo design of a homo-trimeric amantadine-binding protein.

The computational design of a symmetric protein homo-oligomer that binds a symmetry-matched small molecule larger than a metal ion has not yet been achieved. We used de novo protein design to create a homo-trimeric protein that binds the C3 symmetric small molecule drug amantadine with each protein monomer making identical interactions with each face of the small molecule. Solution NMR data show that the protein has regular three-fold symmetry and undergoes localized structural changes upon ligand binding. A high-resolution X-ray structure reveals a close overall match to the design model with the exception of water molecules in the amantadine binding site not included in the Rosetta design calculations, and a neutron structure provides experimental validation of the computationally designed hydrogen-bond networks. Exploration of approaches to generate a small molecule inducible homo-trimerization system based on the design highlight challenges that must be overcome to computationally design such systems