An important feature of Bayesian statistics is the opportunity to do sequential inference: The posterior distribution obtained after seeing a dataset can be used as prior for a second inference. However, when Monte Carlo sampling methods are used for inference, we only have a set of samples from the posterior distribution. To do sequential inference, we then either have to evaluate the second posterior at only these locations and reweight the samples accordingly, or we can estimate a functional description of the posterior probability distribution from the samples and use that as prior for the second inference. Here, we investigated to what extent we can obtain an accurate joint posterior from two datasets if the inference is done sequentially rather than jointly, under the condition that each inference step is done using Monte Carlo sampling. To test this, we evaluated the accuracy of kernel density estimates, Gaussian mixtures, mixtures of factor analyzers, vine copulas and Gaussian processes in approximating posterior distributions, and then tested whether these approximations can be used in sequential inference. In low dimensionality, Gaussian processes are more accurate, whereas in higher dimensionality Gaussian mixtures, mixtures of factor analyzers or vine copulas perform better. In our test cases of sequential inference, using posterior approximations gives more accurate results than direct sample reweighting, but joint inference is still preferable over sequential inference whenever possible. Since the performance is case-specific, we provide an R package mvdens with a unified interface for the density approximation methods. ... Read more

Cancer cell lines differ greatly in their sensitivity to anticancer drugs as a result of different oncogenic drivers and drug resistance mechanisms operating in each cell line. Althoughmany of these mechanisms have been discovered, it remains a challenge to understand how they interact to render an individual cell line sensitive or resistant to a particular drug. To better understand this variability, we profiled a panel of 30 breast cancer cell lines in the absence of drugs for their mutations, copy number aberrations, mRNA, protein expression and protein phosphorylation, and for response to seven different kinase inhibitors. We then constructed a knowledge-based, Bayesian computational model that integrates these data types and estimates the relative contribution of various drug sensitivity mechanisms. The resulting model of regulatory signaling explained the majority of the variability observed in drug response. The model also identified cell lines with an unexplained response, and for these we searched for novel explanatory factors. Among others, we found that 4E-BP1 protein expression, and not just the extent of phosphorylation, was a determinant of mTOR inhibitor sensitivity. We validated this finding experimentally and found that overexpression of 4E-BP1 in cell lines that normally possess low levels of this protein is sufficient to increase mTOR inhibitor sensitivity. Taken together, our work demonstrates that combining experimental characterization with integrative modeling can be used to systematically test and extend our understanding of the variability in anticancer drug response. Significance: By estimating how different oncogenic mutations and drug resistance mechanisms affect the response of cancer cells to kinase inhibitors, we can better understand and ultimately predict response to these anticancer drugs. ... Read more

Cancer patients often respond very differently to any given drug. Some patients respond very well, while others do not respond at all, leaving the cancer to grow unimpeded. If we have a good understanding of how this variability in response arises, we will be better able to choose the optimal treatment strategy for each patient. The variability in drug response observed in patients is also seen in cancer cell lines when they are cultured in vitro. Detailed cell-biological studies have revealed many different mechanisms which affect the response of cancer cells to anticancer drugs. Certain mutations can render cells sensitive to a certain drug, while other mutations, or changes in gene expression, can cause resistance. However, since any combination of these drug sensitivity mechanisms can be operating in a particular cell line, it is difficult to predict whether it will be sensitive or resistant to a particular drug. Computational modeling can be used to better understand this complexity. In this dissertation, we developed a novel method, which we call Inference of Signaling Activity, that can be used to infer the contributions of different drug sensitivity- and resistance mechanisms. We used the available knowledge of signal transduction in cells, and integrated multiple data types including mutations, gene amplifications and deletions, gene expression levels, protein phosphorylation, growth rates and drug response data to infer the signaling activities in each cell line. After an extensive characterization of thirty different breast cancer cell lines, we developed a model that can explain a large part of the variability in the response of these cell lines to seven different kinase inhibitors. At the same time, the response of some cell lines was not recapitulated exactly. Using further data-driven analysis, we found a novel determinant of mTOR inhibitor sensitivity. Overexpression of 4EBP1 in breast cancer cells renders them more sensitive to these inhibitors. This modeling approach can now be further developed to determine whether it can also be used to explain and predict the response of cancer patients. Initially this modeling framework did not permit the inclusion of feedback signaling mechanisms, even though we know feedback control to be an important feature of cellular signaling networks. We therefore subsequently extended our framework such that feedback could be included, and with this extension we were able to delineate signaling activities in regulatory networks with multiple, interrelated feedback loops, again taking into account different datasets. An important consideration in this dissertation was the quantification of uncertainty in model parameters, for which we used Bayesian statistics. If the uncertainty in parameter estimates is not taken into account, we can be lulled into a false sense of security and misinterpret which elements of the model are important. We developed a software package with efficient, multi-threaded implementations of various Monte Carlo sampling algorithms, which allowed the inference to be done in workable amounts of time. We further showed in a different biological system – cell cycle regulation in yeast – that the integration of different types of measurements can increase the identifiability of parameters. Finally, we investigated whether Bayesian inference with multiple datasets can be done sequentially using intermediate posterior approximations. Each of these contributions to Bayesian inference with multiple datasets may be used more broadly in modeling different biological systems. Although further development and validation of the drug response models is needed, the use of integrative computational modeling appears to be a promising approach for enabling precision medicine for cancer patients in the future. ... Read more

Motivation Computational models in biology are frequently underdetermined, due to limits in our capacity to measure biological systems. In particular, mechanistic models often contain parameters whose values are not constrained by a single type of measurement. It may be possible to achieve better model determination by combining the information contained in different types of measurements. Bayesian statistics provides a convenient framework for this, allowing a quantification of the reduction in uncertainty with each additional measurement type. We wished to explore whether such integration is feasible and whether it can allow computational models to be more accurately determined. Results We created an ordinary differential equation model of cell cycle regulation in budding yeast and integrated data from 13 different studies covering different experimental techniques. We found that for some parameters, a single type of measurement, relative time course mRNA expression, is sufficient to constrain them. Other parameters, however, were only constrained when two types of measurements were combined, namely relative time course and absolute transcript concentration. Comparing the estimates to measurements from three additional, independent studies, we found that the degradation and transcription rates indeed matched the model predictions in order of magnitude. The predicted translation rate was incorrect however, thus revealing a deficiency in the model. Since this parameter was not constrained by any of the measurement types separately, it was only possible to falsify the model when integrating multiple types of measurements. In conclusion, this study shows that integrating multiple measurement types can allow models to be more accurately determined. ... Read more

Background
Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model.
Results
We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers. It provides efficient, multithreaded implementations of eleven algorithms for sampling from posterior probability distributions and for calculating marginal likelihoods. BCM includes tools to simplify the process of model specification and scripts for visualizing the results. The flexible architecture allows it to be used on diverse types of biological computational models. In an example inference task using a model of the cell cycle based on ordinary differential equations, BCM is significantly more efficient than existing software packages, allowing more challenging inference problems to be solved.
Conclusions
BCM represents an efficient one-stop-shop for computational modelers wishing to use sampler-based Bayesian statistics. ... Read more