Dynamic modelling of signalling pathways when ordinary differential equations are not feasible

MOTIVATION

Mathematical modelling plays a crucial role in understanding inter- and intracellular signalling processes. Currently, ordinary differential equations (ODEs) are the predominant approach in systems biology for modelling such pathways. While ODE models offer mechanistic interpretability, they also suffer from limitations, including the need to consider all relevant compounds, resulting in large models difficult to handle numerically and requiring extensive data.

RESULTS

In previous work, we introduced the retarded transient function (RTF) as an alternative method for modelling temporal responses of signalling pathways. Here, we extend the RTF approach to integrate concentration or dose-dependencies into the modelling of dynamics. With this advancement, RTF modelling now fully encompasses the application range of ODE models, which comprises predictions in both time and concentration domains. Moreover, characterizing dose-dependencies provides an intuitive way to investigate and characterize signalling differences between biological conditions or cell types based on their response to stimulating inputs. To demonstrate the applicability of our extended approach, we employ data from time- and dose-dependent inflammasome activation in bone marrow-derived macrophages treated with nigericin sodium salt. Our results show the effectiveness of the extended RTF approach as a generic framework for modelling dose-dependent kinetics in cellular signalling. The approach results in intuitively interpretable parameters that describe signal dynamics and enables predictive modelling of time- and dose-dependencies even if only individual cellular components are quantified.

AVAILABILITY AND IMPLEMENTATION

The presented approach is available within the MATLAB-based Data2Dynamics modelling toolbox at https://github.com/Data2Dynamics and https://zenodo.org/records/14008247 and as R code at https://github.com/kreutz-lab/RTF.

High-speed parameter search of dynamic biological pathways from time-course transcriptomic profiles using high-level Petri net

Dynamic simulation promises a deeper understanding of complex molecular mechanisms of biological pathways. How to determine the reaction kinetic parameters which govern the simulation results is still an open question in the field of systems biology. (1) Background: To execute simulation experiments, it is an essential first step to search effective values of model parameters. The complexity of biological systems and the experimental measurement technology severely limit the acquirement of accurate kinetic parameters. Previously proposed genomic data assimilation (GDA) approach enables users to handle parameter estimation using time-course information. However, it highly depends on successive time points and costs massive computational resource; (2) Methods: To address this problem, we present a new high-speed parameter search method for estimating the kinetic parameters of quantitative biological pathways using time-course transcriptomic profiles. The key idea of our method is to interactively prune the search space by introducing Probabilistic Linear-time Temporal Logic (PLTL) based model checking into GDA. (3) Results and conclusion: We demonstrated the effectiveness of our method by comparing with GDA on Mus musculus transcription circuits modelled by hybrid functional Petri net with extension. As a result, our method works faster and more accurate than GDA for both time-course datasets with dense and sparse observed values.

Discovering epistasis in large scale genetic association studies by exploiting graphics cards

Despite the enormous investments made in collecting DNA samples and generating germline variation data across thousands of individuals in modern genome-wide association studies (GWAS), progress has been frustratingly slow in explaining much of the heritability in common disease. Today's paradigm of testing independent hypotheses on each single nucleotide polymorphism (SNP) marker is unlikely to adequately reflect the complex biological processes in disease risk. Alternatively, modeling risk as an ensemble of SNPs that act in concert in a pathway, and/or interact non-additively on log risk for example, may be a more sensible way to approach gene mapping in modern studies. Implementing such analyzes genome-wide can quickly become intractable due to the fact that even modest size SNP panels on modern genotype arrays (500k markers) pose a combinatorial nightmare, require tens of billions of models to be tested for evidence of interaction. In this article, we provide an in-depth analysis of programs that have been developed to explicitly overcome these enormous computational barriers through the use of processors on graphics cards known as Graphics Processing Units (GPU). We include tutorials on GPU technology, which will convey why they are growing in appeal with today's numerical scientists. One obvious advantage is the impressive density of microprocessor cores that are available on only a single GPU. Whereas high end servers feature up to 24 Intel or AMD CPU cores, the latest GPU offerings from nVidia feature over 2600 cores. Each compute node may be outfitted with up to 4 GPU devices. Success on GPUs varies across problems. However, epistasis screens fare well due to the high degree of parallelism exposed in these problems. Papers that we review routinely report GPU speedups of over two orders of magnitude (>100x) over standard CPU implementations.

Model selection in systems and synthetic biology

Developing mechanistic models has become an integral aspect of systems biology, as has the need to differentiate between alternative models. Parameterizing mathematical models has been widely perceived as a formidable challenge, which has spurred the development of statistical and optimisation routines for parameter inference. But now focus is increasingly shifting to problems that require us to choose from among a set of different models to determine which one offers the best description of a given biological system. We will here provide an overview of recent developments in the area of model selection. We will focus on approaches that are both practical as well as build on solid statistical principles and outline the conceptual foundations and the scope for application of such methods in systems biology.

Improved statistical model checking methods for pathway analysis

Statistical model checking techniques have been shown to be effective for approximate model checking on large stochastic systems, where explicit representation of the state space is impractical. Importantly, these techniques ensure the validity of results with statistical guarantees on errors. There is an increasing interest in these classes of algorithms in computational systems biology since analysis using traditional model checking techniques does not scale well. In this context, we present two improvements to existing statistical model checking algorithms. Firstly, we construct an algorithm which removes the need of the user to define the indifference region, a critical parameter in previous sequential hypothesis testing algorithms. Secondly, we extend the algorithm to account for the case when there may be a limit on the computational resources that can be spent on verifying a property; i.e, if the original algorithm is not able to make a decision even after consuming the available amount of resources, we resort to a p-value based approach to make a decision. We demonstrate the improvements achieved by our algorithms in comparison to current algorithms first with a straightforward yet representative example, followed by a real biological model on cell fate of gustatory neurons with microRNAs.