What do aquaporin knockout studies tell us about fluid transport in epithelia?

The investigation of near-isosmotic water transport in epithelia goes back over 100 years; however, debates over mechanism and pathway remain. Aquaporin (AQP) knockouts have been used by various research groups to test the hypothesis of an osmotic mechanism as well as to explore the paracellular versus transcellular pathway debate. Nonproportional reductions in the water permeability of a water-transporting epithelial cell (e.g., a reduction of around 80–90 %) compared to the reduction in overall water transport rate in the knockout animal (e.g., a reduction of 50–60 %) are commonly found. This nonproportionality has led to controversy over whether AQP knockout studies support or contradict the osmotic mechanism. Arguments raised for and against an interpretation supporting the osmotic mechanism typically have partially specified, implicit, or incorrect assumptions. We present a simple mathematical model of the osmotic mechanism with clear assumptions and, for models based on this mechanism, establish a baseline prediction of AQP knockout studies. We allow for deviations from isotonic/isosmotic conditions and utilize dimensional analysis to reduce the number of parameters that must be considered independently. This enables a single prediction curve to be used for multiple epithelial systems. We find that a simple, transcellular-only osmotic mechanism sufficiently predicts the results of knockout studies and find criticisms of this mechanism to be overstated. We note, however, that AQP knockout studies do not give sufficient information to definitively rule out an additional paracellular pathway

A hierarchical Bayesian model for understanding the spatiotemporal dynamics of the intestinal epithelium

Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions-uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales

Dlgap1 knockout mice exhibit alterations of the postsynaptic density and selective reductions in sociability

Abstract The scaffold protein DLGAP1 is localized at the post-synaptic density (PSD) of glutamatergic neurons and is a component of supramolecular protein complexes organized by PSD95. Gain-of-function variants of DLGAP1 have been associated with obsessive-compulsive disorder (OCD), while haploinsufficient variants have been linked to autism spectrum disorder (ASD) and schizophrenia in human genetic studies. We tested male and female Dlgap1 wild type (WT), heterozygous (HT), and knockout (KO) mice in a battery of behavioral tests: open field, dig, splash, prepulse inhibition, forced swim, nest building, social approach, and sucrose preference. We also used biochemical approaches to examine the role of DLGAP1 in the organization of PSD protein complexes. Dlgap1 KO mice were most notable for disruption of protein interactions in the PSD, and deficits in sociability. Other behavioral measures were largely unaffected. Our data suggest that Dlgap1 knockout leads to PSD disruption and reduced sociability, consistent with reports of DLGAP1 haploinsufficient variants in schizophrenia and ASD

Elevated apoptosis impairs epithelial cell turnover and shortens villi in TNF-driven intestinal inflammation

The intestinal epithelial monolayer, at the boundary between microbes and the host immune system, plays an important role in the development of inflammatory bowel disease (IBD), particularly as a target and producer of pro-inflammatory TNF. Chronic overexpression of TNF leads to IBD-like pathology over time, but the mechanisms driving early pathogenesis events are not clear. We studied the epithelial response to inflammation by combining mathematical models with in vivo experimental models resembling acute and chronic TNF-mediated injury. We found significant villus atrophy with increased epithelial cell death along the crypt-villus axis, most dramatically at the villus tips, in both acute and chronic inflammation. In the acute model, we observed overexpression of TNF receptor I in the villus tip rapidly after TNF injection and concurrent with elevated levels of intracellular TNF and rapid shedding at the tip. In the chronic model, sustained villus atrophy was accompanied by a reduction in absolute epithelial cell turnover. Mathematical modelling demonstrated that increased cell apoptosis on the villus body explains the reduction in epithelial cell turnover along the crypt-villus axis observed in chronic inflammation. Cell destruction in the villus was not accompanied by changes in proliferative cell number or division rate within the crypt. Epithelial morphology and immunological changes in the chronic setting suggest a repair response to cell damage although the villus length is not recovered. A better understanding of how this state is further destabilised and results in clinical pathology resembling IBD will help identify suitable pathways for therapeutic intervention

Research Projects (2018) - Oliver Maclaren

Short presentation on my research interests, aimed at potential postgraduate (PhD or Masters) students

Practical parameter identifiability for spatio-temporal models of cell invasion

We examine the practical identifiability of parameters in a spatio-temporal reaction–diffusion model of a scratch assay. Experimental data involve fluorescent cell cycle labels, providing spatial information about cell position and temporal information about the cell cycle phase. Cell cycle labelling is incorporated into the reaction–diffusion model by treating the total population as two interacting subpopulations. Practical identifiability is examined using a Bayesian Markov chain Monte Carlo (MCMC) framework, confirming that the parameters are identifiable when we assume the diffusivities of the subpopulations are identical, but that the parameters are practically non-identifiable when we allow the diffusivities to be distinct. We also assess practical identifiability using a profile likelihood approach, providing similar results to MCMC with the advantage of being an order of magnitude faster to compute. Therefore, we suggest that the profile likelihood ought to be adopted as a screening tool to assess practical identifiability before MCMC computations are performed

Parameter identifiability and model selection for sigmoid population growth models

Sigmoid growth models, such as the logistic, Gompertz and Richards’ models, are widely used to study population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and parameter estimation are critical if these models are to be used to make practical inferences. However, the question of parameter identifiability – whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates – is often overlooked. We use a profile-likelihood approach to explore practical parameter identifiability using data describing the re-growth of hard coral. With this approach, we explore the relationship between parameter identifiability and model misspecification, finding that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards’ models encounter practical non-identifiability issues. This analysis of parameter identifiability and model selection is important because different growth models are in biological modelling without necessarily considering whether parameters are identifiable. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and potentially misleading mechanistic interpretations. For example, using the Gompertz model, the estimate of the time scale of coral re-growth is 625 days when we estimate the initial density from the data, whereas it is 1429 days using a more standard approach where variability in the initial density is ignored. While tools developed here focus on three standard sigmoid growth models only, our theoretical developments are applicable to any sigmoid growth model and any appropriate data set. MATLAB implementations of all software are available on GitHub

Where next for the reproducibility agenda in computational biology?

Background: The concept of reproducibility is a foundation of the scientific method. With the arrival of fast and powerful computers over the last few decades, there has been an explosion of results based on complex computational analyses and simulations. The reproducibility of these results has been addressed mainly in terms of exact replicability or numerical equivalence, ignoring the wider issue of the reproducibility of conclusions through equivalent, extended or alternative methods. Results: We use case studies from our own research experience to illustrate how concepts of reproducibility might be applied in computational biology. Several fields have developed ‘minimum information’ checklists to support the full reporting of computational simulations, analyses and results, and standardised data formats and model description languages can facilitate the use of multiple systems to address the same research question. We note the importance of defining the key features of a result to be reproduced, and the expected agreement between original and subsequent results. Dynamic, updatable tools for publishing methods and results are becoming increasingly common, but sometimes come at the cost of clear communication. In general, the reproducibility of computational research is improving but would benefit from additional resources and incentives. Conclusions: We conclude with a series of linked recommendations for improving reproducibility in computational biology through communication, policy, education and research practice. More reproducible research will lead to higher quality conclusions, deeper understanding and more valuable knowledge

Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models

Stochastic individual-based mathematical models are attractive for modelling biological phenomena because they naturally capture the stochasticity and variability that is often evident in biological data. Such models also allow us to track the motion of individuals within the population of interest. Unfortunately, capturing this microscopic detail means that simulation and parameter inference can become computationally expensive. One approach for overcoming this computational limitation is to coarse-grain the stochastic model to provide an approximate continuum model that can be solved using far less computational effort. However, coarse-grained continuum models can be biased or inaccurate, particularly for certain parameter regimes. In this work, we combine stochastic and continuum mathematical models in the context of lattice-based models of two-dimensional cell biology experiments by demonstrating how to simulate two commonly used experiments: cell proliferation assays and barrier assays. Our approach involves building a simple statistical model of the discrepancy between the expensive stochastic model and the associated computationally inexpensive coarse-grained continuum model. We form this statistical model based on a limited number of expensive stochastic model evaluations at design points sampled from a user-chosen distribution, corresponding to a computer experiment design problem. With straightforward design point selection schemes, we show that using the statistical model of the discrepancy in tandem with the computationally inexpensive continuum model allows us to carry out prediction and inference while correcting for biases and inaccuracies due to the continuum approximation. We demonstrate this approach by simulating a proliferation assay, where the continuum limit model is the well-known logistic ordinary differential equation, as well as a barrier assay where the continuum limit model is closely related to the well-known Fisher-KPP partial differential equation. We construct an approximate likelihood function for parameter inference, both with and without discrepancy correction terms. Using maximum likelihood estimation, we provide point estimates of the unknown parameters, and use the profile likelihood to characterise the uncertainty in these estimates and form approximate confidence intervals. For the range of inference problems considered, working with the continuum limit model alone leads to biased parameter estimation and confidence intervals with poor coverage. In contrast, incorporating correction terms arising from the statistical model of the model discrepancy allows us to recover the parameters accurately with minimal computational overhead. The main tradeoff is that the associated confidence intervals are typically broader, reflecting the additional uncertainty introduced by the approximation process. All algorithms required to replicate the results in this work are written in the open source Julia language and are available at GitHub

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether this data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the expected moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers