BioBayes: a software package for Bayesian inference in systems biology

MOTIVATION: There are several levels of uncertainty involved in the mathematical modelling of biochemical systems. There often may be a degree of uncertainty about the values of kinetic parameters, about the general structure of the model and about the behaviour of biochemical species which cannot be observed directly. The methods of Bayesian inference provide a consistent framework for modelling and predicting in these uncertain conditions. We present a software package for applying the Bayesian inferential methodology to problems in systems biology. RESULTS: Described herein is a software package, BioBayes, which provides a framework for Bayesian parameter estimation and evidential model ranking over models of biochemical systems defined using ordinary differential equations. The package is extensible allowing additional modules to be included by developers. There are no other such packages available which provide this functionality.     

Universally sloppy parameter sensitivities in systems biology models

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a “sloppy” spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.     

DNA-repair studies with sodium fluoride: comparative evaluation using density gradient ultracentrifugation and autoradiography

Sodium fluoride (NaF) was assayed for the induction of DNA-repair synthesis in WI-38 human diploid fibroblasts and in primary cultures of rat hepatocytes. DNA-repair synthesis in non-replicating DNA was measured by ultracentrifugation of density-labeled DNA in CsCl gradients. When this method was used, NaF did not induce DNA-repair synthesis in either of these cell types. However, when NaF was assayed for induction of unscheduled DNA synthesis (UDS) in rat hepatocytes by autoradiography, an increased net nuclear grain count was observed. Because the autoradiographic results were not confirmed by density-gradient ultracentrifugation of hepatocyte DNA, which is a more definitive technique, it is doubtful whether the autoradiographic results actually represent DNA-repair synthesis. Modifications of the UDS/autoradiography protocol to include more extensive washing resulted in no UDS response. Published reports (Hellung-Larsen and Klenow, 1969; Srivastava et al., 1981) describe the formation of precipitable complexes of Mg2+, F-, and [3H]thymidine triphosphate which suggests that autoradiographic measurement of UDS may lead to artifacts when testing NaF unless extensive washing of the cultures is employed.     

MTML-msBayes: Approximate Bayesian comparative phylogeographic inference from multiple taxa and multiple loci with rate heterogeneity

Background  

MTML-msBayes uses hierarchical approximate Bayesian computation (HABC) under a coalescent model to infer temporal patterns of divergence and gene flow across codistributed taxon-pairs. Under a model of multiple codistributed taxa that diverge into taxon-pairs with subsequent gene flow or isolation, one can estimate hyper-parameters that quantify the mean and variability in divergence times or test models of migration and isolation. The software uses multi-locus DNA sequence data collected from multiple taxon-pairs and allows variation across taxa in demographic parameters as well as heterogeneity in DNA mutation rates across loci. The method also allows a flexible sampling scheme: different numbers of loci of varying length can be sampled from different taxon-pairs.     

Practical limits for reverse engineering of dynamical systems: a statistical analysis of sensitivity and parameter inferability in systems biology models

The size and complexity of cellular systems make building predictive models an extremely difficult task. In principle dynamical time-course data can be used to elucidate the structure of the underlying molecular mechanisms, but a central and recurring problem is that many and very different models can be fitted to experimental data, especially when the latter are limited and subject to noise. Even given a model, estimating its parameters remains challenging in real-world systems. Here we present a comprehensive analysis of 180 systems biology models, which allows us to classify the parameters with respect to their contribution to the overall dynamical behaviour of the different systems. Our results reveal candidate elements of control in biochemical pathways that differentially contribute to dynamics. We introduce sensitivity profiles that concisely characterize parameter sensitivity and demonstrate how this can be connected to variability in data. Systematically linking data and model sloppiness allows us to extract features of dynamical systems that determine how well parameters can be estimated from time-course measurements, and associates the extent of data required for parameter inference with the model structure, and also with the global dynamical state of the system. The comprehensive analysis of so many systems biology models reaffirms the inability to estimate precisely most model or kinetic parameters as a generic feature of dynamical systems, and provides safe guidelines for performing better inferences and model predictions in the context of reverse engineering of mathematical models for biological systems.     

Dupuytren's: a systems biology disease

Dupuytren's disease (DD) is an ill-defined fibroproliferative disorder of the palm of the hands leading to digital contracture. DD commonly occurs in individuals of northern European extraction. Cellular components and processes associated with DD pathogenesis include altered gene and protein expression of cytokines, growth factors, adhesion molecules, and extracellular matrix components. Histology has shown increased but varying levels of particular types of collagen, myofibroblasts and myoglobin proteins in DD tissue. Free radicals and localised ischaemia have been suggested to trigger the proliferation of DD tissue. Although the existing available biological information on DD may contain potentially valuable (though largely uninterpreted) information, the precise aetiology of DD remains unknown. Systems biology combines mechanistic modelling with quantitative experimentation in studies of networks and better understanding of the interaction of multiple components in disease processes. Adopting systems biology may be the ideal approach for future research in order to improve understanding of complex diseases of multifactorial origin. In this review, we propose that DD is a disease of several networks rather than of a single gene, and show that this accounts for the experimental observations obtained to date from a variety of sources. We outline how DD may be investigated more effectively by employing a systems biology approach that considers the disease network as a whole rather than focusing on any specific single molecule.     

Approximate Monte Carlo conditional inference in exponential families

This article presents an algorithm for approximate frequentist conditional inference on two or more parameters for any regression model in the Generalized Linear Model (GLIM) family. We thereby extend highly accurate inference beyond the cases of logistic regression and contingency tables implimented in commercially available software. The method makes use of the double saddlepoint approximations of Skovgaard (1987, Journal of Applied Probability 24, 875-887) and Jensen (1992, Biometrika 79, 693-703) to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics. This approximation is then used in conjunction with noniterative Monte Carlo methods to generate a sample from a distribution that approximates the joint distribution of the sufficient statistics associated with the parameters of interest conditional on the observed values of the sufficient statistics associated with the nuisance parameters. This algorithm is an alternate approach to that presented by Kolassa and Tanner (1994, Journal of the American Statistical Association 89, 697-702), in which a Markov chain is generated whose equilibrium distribution under certain regularity conditions approximates the joint distribution of interest. In Kolassa and Tanner (1994), the Gibbs sampler was used in conjunction with these univariate conditional distribution function approximations. The method of this paper does not require the construction and simulation of a Markov chain, thus avoiding the need to develop regularity conditions under which the algorithm converges and the need for the data analyst to check convergence of the particular chain. Examples involving logistic and truncated Poisson regression are presented.     

Artificial cells: building bioinspired systems using small-scale biology

Artificial cells have generated much interest since the concept was introduced by Aleksandr Oparin in the 1920s, and they have had an impact on the pharmaceutical and biotechnology industry in various areas, including potential therapeutic applications. Here, we discuss the development of small-scale, bio-inspired artificial cell components that recreate the function of key cellular and physiological systems. We describe artificial cells, selected current applications and how small-scale biology could be used to provide what might be a next-generation approach in this area. We believe that this type of work is in its infancy and that exploiting small-scale biological inspiration in the field of artificial cells has great potential for successes in the future.     

PEtab—Interoperable specification of parameter estimation problems in systems biology

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been—so far—no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies.     

The Gegenbaur Transformation: a paradigm change in comparative biology

The leading experts in the development of phylogenetic systematics, Walter Zimmermann and Willi Hennig, formulated their research program in opposition to (neo-) idealistic morphology as expounded by authors such as Wilhelm Troll and Adolf Naef. Idealistic morphology was synonymous with systematic morphology for Naef, who wanted it to be strictly kept separate and independent of phylogenetics. Naef conceded, however, that the natural system researched by systematic morphology is to be causally explained by the theory of descent with modification. Naef went on to compile a dictionary that would regulate the translation of the language of systematic morphology into the language of phylogenetics. The switch from idealistic morphology to phylogenetic morphology is paradigmatically exemplified in the two editions (1859, 1870) of Carl Gegenbaur's Grundzüge der vergleichenden Anatomie. This paper traces the development of phylogenetic systematics from Gegenbaur through the work of Adolf Naef to Walter Zimmermann and Willi Hennig. Hennig added to Naef's systematic morphology the dimension of time, which required an ontological replacement: Naef's natural system, a nested hierarchy of intensionally defined sets subject to the membership relation, was replaced by Hennig's phylogenetic system, an enkaptic hierarchy subject to the part-to-whole relation.     

Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent

Background  

Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.     

Quantitative measures of gastrovascular flow in octocorals and hydroids: toward a comparative biology of transport systems in cnidarians

Using microscopy, the gastrovascular systems of four hydroids (Eirene viridula, Cordylophora lacustris, Hydractinia symbiolongicarpus, and Podocoryna carnea) and two distantly related alcyonacean octocorals (Acrossota amboinensis and Sarcothelia sp.) were examined and compared within a phylogenetic framework. Despite a range of stolon widths (means 53–160 μm), the hydroid species exhibited similar patterns of gastrovascular flow: sequentially bidirectional flow in the stolons, driven by myoepithelial contractions emanating from the center of the colony. Unlike the hydroids, the gastrovascular system of A. amboinensis (mean stolon widths for 5 colonies, 0.57–1.21 mm) exhibited simultaneously bidirectional flow with incomplete, medial baffles (width 4–20 μm) separating the flow. Baffles visualized with transmission electron microscopy consisted of endoderm, mesoglea, and occasionally another layer of tissue. Mean flow rates of the gastrovascular fluid for seven stolons ranged from 125 to 275 μm s^?1, with maximum rates of 225–700 μm s^?1. In Sarcothelia sp., stolons were of comparable width (means for 13 colonies 0.55–1.4 mm) to those of A. amboinensis. These stolons, however, were divided by several partitions (width 8–25 μm), both complete and incomplete, which were spaced every 100.5±5.1 μm (mean±SE; range 27.1–283.7 μm) and appeared structurally similar to baffles. In lanes defined by these partitions, ciliary motion was visible in image sequences, and flow was unidirectional. Within a single stolon, flow moved in different directions in different lanes and changed direction by moving from lane to lane via occasional spaces between the partitions. Mean flow rates for 30 stolons ranged from 75 to 475 μm s^?1, with maximum rates of 85–775 μm s^?1. For both octocorals, flow rates of the gastrovascular fluid were not correlated with the width of the stolon lumen. While octocoral gastrovascular systems probably exhibit differences based on phylogenetic affinities, in all species studied thus far, gastrovascular flow is entirely driven by cilia, in contrast to the hydroid taxa.     

Automatic control of biomass gasifiers using fuzzy inference systems

A fuzzy controller for biomass gasifiers is proposed. Although fuzzy inference systems do not need models to be tuned, a plant model is proposed which has turned out very useful to prove different combinations of membership functions and rules in the proposed fuzzy control. The global control scheme is shown, including the elements to generate the set points for the process variables automatically. There, the type of biomass and its moisture content are the only data which need to be introduced to the controller by a human operator at the beginning of operation to make it work autonomously. The advantages and good performance of the fuzzy controller with the automatic generation of set points, compared to controllers utilising fixed parameters, are demonstrated.