Approximate parameter inference in systems biology using gradient matching: a comparative evaluation

Background

A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes (GPs), combined with a parallel tempering scheme, and conducts a comparative evaluation with current state-of-the-art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method.

Methods

Methodology for the recently proposed adaptive gradient matching method using GPs, upon which we build our new method, is provided. Details of a competing method using RKHS are also described here.

Results

We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques.

Conclusions

Our study reveals that for known noise variance, our proposed method based on GPs and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust.

     

Individual variation in early‐life telomere length and survival in a wild mammal

Individual variation in survival probability due to differential responses to early‐life environmental conditions is important in the evolution of life histories and senescence. A biomarker allowing quantification of such individual variation, and which links early‐life environmental conditions with survival by providing a measure of conditions experienced, is telomere length. Here, we examined telomere dynamics among 24 cohorts of European badgers (Meles meles). We found a complex cross‐sectional relationship between telomere length and age, with no apparent loss over the first 29 months, but with both decreases and increases in telomere length at older ages. Overall, we found low within‐individual consistency in telomere length across individual lifetimes. Importantly, we also observed increases in telomere length within individuals, which could not be explained by measurement error alone. We found no significant sex differences in telomere length, and provide evidence that early‐life telomere length predicts lifespan. However, while early‐life telomere length predicted survival to adulthood (≥1 year old), early‐life telomere length did not predict adult survival probability. Furthermore, adult telomere length did not predict survival to the subsequent year. These results show that the relationship between early‐life telomere length and lifespan was driven by conditions in early‐life, where early‐life telomere length varied strongly among cohorts. Our data provide evidence for associations between early‐life telomere length and individual life history, and highlight the dynamics of telomere length across individual lifetimes due to individuals experiencing different early‐life environments.     

Cyclin ET, a new splice variant of human cyclin E with a unique expression pattern during cell cycle progression and differentiation.

Cyclin E is the regulatory subunit of the cdc2-related protein kinase cdk2 and is a rate limiting factor for the entry into S phase. To date, cyclin E is the only cyclin for which alternative splicing has been described. We report here the isolation of a new splice variant of cyclin E, termed cyclin ET, which has an internal deletion of 45 amino acids compared with the full-length cyclin E protein. Even though cyclin ETcontains an intact cyclin box, it is unable to complement a triple cln mutant strain of Saccharomyces cerevisiae or to interfere with rescue by cyclin E, indicating that an intact cyclin box is functionally insufficient. The expression pattern of cyclin ET during cell cycle entry, progression and differentiation differs from that of cyclin E. Thus, ET expression precedes that of the other isoforms during the G0-->S progression; it shows a sharp peak in early G1 in cells released from a mitotic block and is strongly down-regulated in terminally differentiated myeloid cells. These observations point to different functions for cyclin ET and E and show for the first time that the alternative splicing of cyclin E is a regulated mechanism governed by the cell cycle and differentiation.     

e-Cow: an animal model that predicts herbage intake, milk yield and live weight change in dairy cows grazing temperate pastures, with and without supplementary feeding

This animal simulation model, named e-Cow, represents a single dairy cow at grazing. The model integrates algorithms from three previously published models: a model that predicts herbage dry matter (DM) intake by grazing dairy cows, a mammary gland model that predicts potential milk yield and a body lipid model that predicts genetically driven live weight (LW) and body condition score (BCS). Both nutritional and genetic drives are accounted for in the prediction of energy intake and its partitioning. The main inputs are herbage allowance (HA; kg DM offered/cow per day), metabolisable energy and NDF concentrations in herbage and supplements, supplements offered (kg DM/cow per day), type of pasture (ryegrass or lucerne), days in milk, days pregnant, lactation number, BCS and LW at calving, breed or strain of cow and genetic merit, that is, potential yields of milk, fat and protein. Separate equations are used to predict herbage intake, depending on the cutting heights at which HA is expressed. The e-Cow model is written in Visual Basic programming language within Microsoft Excel^R. The model predicts whole-lactation performance of dairy cows on a daily basis, and the main outputs are the daily and annual DM intake, milk yield and changes in BCS and LW. In the e-Cow model, neither herbage DM intake nor milk yield or LW change are needed as inputs; instead, they are predicted by the e-Cow model. The e-Cow model was validated against experimental data for Holstein–Friesian cows with both North American (NA) and New Zealand (NZ) genetics grazing ryegrass-based pastures, with or without supplementary feeding and for three complete lactations, divided into weekly periods. The model was able to predict animal performance with satisfactory accuracy, with concordance correlation coefficients of 0.81, 0.76 and 0.62 for herbage DM intake, milk yield and LW change, respectively. Simulations performed with the model showed that it is sensitive to genotype by feeding environment interactions. The e-Cow model tended to overestimate the milk yield of NA genotype cows at low milk yields, while it underestimated the milk yield of NZ genotype cows at high milk yields. The approach used to define the potential milk yield of the cow and equations used to predict herbage DM intake make the model applicable for predictions in countries with temperate pastures.