Biology subjects

Parag, K. V.

Publications and source records attributed to Parag, K. V..

3 recordsLinked to original sources

bioRxiv2018

On the Biological Signalling, Information and Estimation Limits of Birth Processes

Understanding and uncovering the mechanisms or motifs that molecular networks employ to regulate noise is a key problem in cell biology. As it is often difficult to obtain direct and detailed insight into these mechanisms, many studies instead focus on assessing the best precision attainable on the signalling pathways that compose these networks. Molecules signal one another over such pathways to solve noise regulating estimation and control problems. Quantifying the maximum precision of these solutions delimits what is achievable and allows hypotheses about underlying motifs to be tested without requiring detailed biological knowledge. The pathway capacity, which defines the maximum rate of transmitting information along it, is a widely used proxy for precision. Here it is shown, for estimation problems involving elementary yet biologically relevant birth-process networks, that capacity can be surprisingly misleading. A time-optimal signalling motif, called birth-following, is derived and proven to better the precision expected from the capacity, provided the maximum signalling rate constraint is large and the mean one above a certain threshold. When the maximum constraint is relaxed, perfect estimation is predicted by the capacity. However, the true achievable precision is found highly variable and sensitive to the mean constraint. Since the same capacity can map to different combinations of rate constraints, it can only equivocally measure precision. Deciphering the rate constraints on a signalling pathway may therefore be more important than computing its capacity.

systems biology↗

bioRxiv2018

Robust Design for Coalescent Model Inference

--The coalescent process describes how changes in the size of a population influence the genealogical patterns of sequences sampled from that population. The estimation of population size changes from genealogies that are reconstructed from these sequence samples, is an important problem in many biological fields. Often, population size is characterised by a piecewise-constant function, with each piece serving as a population size parameter to be estimated. Estimation quality depends on both the statistical coalescent inference method employed, and on the experimental protocol, which controls variables such as the sampling of sequences through time and space, or the transformation of model parameters. While there is an extensive literature devoted to coalescent inference methodology, there is surprisingly little work on experimental design. The research that does exist is largely simulation based, precluding the development of provable or general design theorems. We examine three key design problems: temporal sampling of sequences under the skyline demographic coalescent model, spatio-temporal sampling for the structured coalescent model, and time discretisation for sequentially Markovian coalescent models. In all cases we prove that (i) working in the logarithm of the parameters to be inferred (e.g. population size), and (ii) distributing informative coalescent events uniformly among these log-parameters, is uniquely robust. Robust means that the total and maximum uncertainty of our estimates are minimised, and are also insensitive to their unknown (true) parameter values. Given its persistence among models, this formally derived two-point theorem may form the basis of an experimental design paradigm for coalescent inference.

bioinformatics↗

bioRxiv2017

Optimal Point Process Filtering for Birth-Death Model Estimation

The discrete space, continuous time birth-death model is a key process for describing phylogenies in the absence of coalescent approximations. Extensively used in macroevolution for analysing diversification, and in epidemiology for estimating viral dynamics, the birth-death process (BDP) is an important null model for inferring the parameters of reconstructed phylogenies. In this paper we show how optimal, point process (Snyder) filtering techniques can be used for parametric inference on BDPs. Specifically, we introduce the Bayesian Snyder filter (SF) to estimate birth and death rate parameters, given a reconstructed phylogeny. Our estimation procedure makes use of the equivalent Markov birth process description for a reconstructed birth-death phylogeny (Nee et al, 1994). We first analyse the popular constant rate BDP and show that our method gives results consistent with previous work. Among these results is an analytic solution to the special case of the Yule-Furry model. We also find an equivalence between the SF Poisson likelihood and two standard conditioned birth-death model likelihoods. We then generalise our estimation problem to BDPs with time varying rates and numerically solve the SF for two illustrative cases. Our results compare well with a recent Markov chain Monte Carlo method by Hohna et al (2016) and we numericaly show that both methods are solving the same likelihood functions. Lastly we apply the SF to a model selection problem on empirical data. We use the Australian Agamid dataset and predict the same relative model fit as that of the original maximum likelihood technique developed and used by Rabosky (2006) for this dataset. While several capable parametric and non-parametric birth-death estimators already exist, ours is the first to take the Nee et al approach, and directly computes the posterior distribution of the parameters. The SF makes no approximations, beyond those required for parameter space discretisation and numerical integration, and is mean square error optimal. It is deterministic, easily implementable and flexible. We think SFs present a promising alternative parametric BDP inference engine.

ecology↗