Easy parameter identifiability analysis with COPASI

Physics-informed machine learning for automatic model reduction in chemical reaction networks

Physics-informed machine learning bridges the gap between the high fidelity of mechanistic models and the adaptive insights of artificial intelligence. In chemical reaction network modeling, this synergy proves valuable, addressing the high computational costs of detailed mechanistic models while leveraging the predictive power of machine learning. This study applies this fusion to the biomedical challenge of Aβ fibril aggregation, a key factor in Alzheimer's disease. Central to the research is the introduction of an automatic reaction order model reduction framework, designed to optimize reduced-order kinetic models. This framework represents a shift in model construction, automatically determining the appropriate level of detail for reaction network modeling. The proposed approach significantly improves simulation efficiency and accuracy, particularly in systems like Aβ aggregation, where precise modeling of nucleation and growth kinetics can reveal potential therapeutic targets. Additionally, the automatic model reduction technique has the potential to generalize to other network models. The methodology offers a scalable and adaptable tool for applications beyond biomedical research. Its ability to dynamically adjust model complexity based on system-specific needs ensures that models remain both computationally feasible and scientifically relevant, accommodating new data and evolving understandings of complex phenomena.

Ganglioside-Enriched Phospholipid Vesicles Induce Cooperative Aβ Oligomerization and Membrane Disruption

A major hallmark of Alzheimer's disease (AD) is the accumulation of extracellular aggregates of amyloid-β (Aβ). Structural polymorphism observed among Aβ fibrils in AD brains seem to correlate with the clinical subtypes suggesting a link between fibril polymorphism and pathology. Since fibrils emerge from a templated growth of low-molecular-weight oligomers, understanding the factors affecting oligomer generation is important. Membrane lipids are key factors to influence early stages of Aβ aggregation and oligomer generation, which cause membrane disruption. We have previously demonstrated that conformationally discrete Aβ oligomers can be generated by modulating the charge, composition, and chain length of lipids and surfactants. Here, we extend our studies into liposomal models by investigating Aβ oligomerization on large unilamellar vesicles (LUVs) of total brain extracts (TBE), reconstituted lipid rafts (LRs), or 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). Varying the vesicle composition by specifically increasing the amount of GM1 gangliosides as a constituent, we found that only GM1-enriched liposomes induce the formation of toxic, low-molecular-weight oligomers. Furthermore, we found that the aggregation on liposome surface and membrane disruption are highly cooperative and sensitive to membrane surface characteristics. Numerical simulations confirm such a cooperativity and reveal that GM1-enriched liposomes form twice as many pores as those formed in the absence GM1. Overall, this study uncovers mechanisms of cooperativity between oligomerization and membrane disruption under controlled lipid compositional bias, and refocuses the significance of the early stages of Aβ aggregation in polymorphism, propagation, and toxicity in AD.

Mechanism of actin filament nucleation

We used computational methods to analyze the mechanism of actin filament nucleation. We assumed a pathway where monomers form dimers, trimers, and tetramers that then elongate to form filaments but also considered other pathways. We aimed to identify the rate constants for these reactions that best fit experimental measurements of polymerization time courses. The analysis showed that the formation of dimers and trimers is unfavorable because the association reactions are orders of magnitude slower than estimated in previous work rather than because of rapid dissociation of dimers and trimers. The 95% confidence intervals calculated for the four rate constants spanned no more than one order of magnitude. Slow nucleation reactions are consistent with published high-resolution structures of actin filaments and molecular dynamics simulations of filament ends. One explanation for slow dimer formation, which we support with computational analysis, is that actin monomers are in a conformational equilibrium with a dominant conformation that cannot participate in the nucleation steps.

A multi-inverse approach for a holistic understanding of applied animal science systems

Technological and mathematical advances have provided opportunities to investigate new approaches for the holistic quantification of complex biological systems. One objective of these approaches, including the multi-inverse deterministic approach proposed in this paper, is to deepen the understanding of biological systems through the structural development of a useful, best-fitted inverse mechanistic model. The objective of the present work was to evaluate the capacity of a deterministic approach, that is, the multi-inverse approach (MIA), to yield meaningful quantitative nutritional information. To this end, a case study addressing the effect of diet composition on sheep weight was performed using data from a previous experiment on saccharina (a sugarcane byproduct), and an inverse deterministic model (named Paracoa) was developed. The MIA successfully revealed an increase in the final weight of sheep with an increase in the percentage of corn in the diet. Although the soluble fraction also increased with increasing corn percentage, the effective nonsoluble degradation increased fourfold, indicating that the increased weight gain resulted from the nonsoluble substrate. A profile likelihood analysis showed that the potential best-fitted model had identifiable parameters, and that the parameter relationships were affected by the type of data, number of parameters and model structure. It is necessary to apply the MIA to larger and/or more complex datasets to obtain a clearer understanding of its potential.

PyCoTools: a Python toolbox for COPASI

Motivation

COPASI is an open source software package for constructing, simulating and analyzing dynamic models of biochemical networks. COPASI is primarily intended to be used with a graphical user interface but often it is desirable to be able to access COPASI features programmatically, with a high level interface.

Results

PyCoTools is a Python package aimed at providing a high level interface to COPASI tasks with an emphasis on model calibration. PyCoTools enables the construction of COPASI models and the execution of a subset of COPASI tasks including time courses, parameter scans and parameter estimations. Additional ‘composite’ tasks which use COPASI tasks as building blocks are available for increasing parameter estimation throughput, performing identifiability analysis and performing model selection. PyCoTools supports exploratory data analysis on parameter estimation data to assist with troubleshooting model calibrations. We demonstrate PyCoTools by posing a model selection problem designed to show case PyCoTools within a realistic scenario. The aim of the model selection problem is to test the feasibility of three alternative hypotheses in explaining experimental data derived from neonatal dermal fibroblasts in response to TGF-β over time. PyCoTools is used to critically analyze the parameter estimations and propose strategies for model improvement.

Availability and implementation

PyCoTools can be downloaded from the Python Package Index (PyPI) using the command ’pip install pycotools’ or directly from GitHub (https://github.com/CiaranWelsh/pycotools). Documentation at http://pycotools.readthedocs.io.

Supplementary information

Supplementary data are available at Bioinformatics online.

An important role for periplasmic storage in Pseudomonas aeruginosa copper homeostasis revealed by a combined experimental and computational modeling study

Biological systems require precise copper homeostasis enabling metallation of cuproproteins while preventing metal toxicity. In bacteria, sensing, transport, and storage molecules act in coordination to fulfill these roles. However, there is not yet a kinetic schema explaining the system integration. Here, we report a model emerging from experimental and computational approaches that describes the dynamics of copper distribution in Pseudomonas aeruginosa. Based on copper uptake experiments, a minimal kinetic model describes well the copper distribution in the wild-type bacteria but is unable to explain the behavior of the mutant strain lacking CopA1, a key Cu+ efflux ATPase. The model was expanded through an iterative hypothesis-driven approach, arriving to a mechanism that considers the induction of compartmental pools and the parallel function of CopA and Cus efflux systems. Model simulations support the presence of a periplasmic copper storage with a crucial role under dyshomeostasis conditions in P. aeruginosa. Importantly, the model predicts not only the interplay of periplasmic and cytoplasmic pools but also the existence of a threshold in the concentration of external copper beyond which cells lose their ability to control copper levels.

Transmembrane NADH Oxidation with Tetracyanoquinodimethane

The design of efficient schemes for nicotinamide adenine dinucleotide (NAD) regeneration is essential for the development of enzymatic biotechnological processes in order to sustain continuous production. In line with our motivation for the encapsulation of redox cascades in liposomes to serve as microbioreactors, we developed a straightforward strategy for the interfacial oxidation of entrapped NADH by ferricyanide as an external electron acceptor. Instead of the commonly applied enzymatic regeneration methods, we employed a hydrophobic redox shuttle embedded in the liposome bilayer. Tetracyanoquinodimethane (TCNQ) mediated electron transfer across the membrane and thus allowed us to shortcut and emulate part of the electron transfer chain functionality without the involvement of membrane proteins. To describe the experimental system, we developed a mathematical model which allowed for the determination of rate constants and exhibited handy predictive utility.

An improved hybrid of particle swarm optimization and the gravitational search algorithm to produce a kinetic parameter estimation of aspartate biochemical pathways

Mathematical modelling is fundamental to understand the dynamic behavior and regulation of the biochemical metabolisms and pathways that are found in biological systems. Pathways are used to describe complex processes that involve many parameters. It is important to have an accurate and complete set of parameters that describe the characteristics of a given model. However, measuring these parameters is typically difficult and even impossible in some cases. Furthermore, the experimental data are often incomplete and also suffer from experimental noise. These shortcomings make it challenging to identify the best-fit parameters that can represent the actual biological processes involved in biological systems. Computational approaches are required to estimate these parameters. The estimation is converted into multimodal optimization problems that require a global optimization algorithm that can avoid local solutions. These local solutions can lead to a bad fit when calibrating with a model. Although the model itself can potentially match a set of experimental data, a high-performance estimation algorithm is required to improve the quality of the solutions. This paper describes an improved hybrid of particle swarm optimization and the gravitational search algorithm (IPSOGSA) to improve the efficiency of a global optimum (the best set of kinetic parameter values) search. The findings suggest that the proposed algorithm is capable of narrowing down the search space by exploiting the feasible solution areas. Hence, the proposed algorithm is able to achieve a near-optimal set of parameters at a fast convergence speed. The proposed algorithm was tested and evaluated based on two aspartate pathways that were obtained from the BioModels Database. The results show that the proposed algorithm outperformed other standard optimization algorithms in terms of accuracy and near-optimal kinetic parameter estimation. Nevertheless, the proposed algorithm is only expected to work well in small scale systems. In addition, the results of this study can be used to estimate kinetic parameter values in the stage of model selection for different experimental conditions.

Quantitative interactome of a membrane Bcl-2 network identifies a hierarchy of complexes for apoptosis regulation

The Bcl-2 proteins form a complex interaction network that controls mitochondrial permeabilization and apoptosis. The relative importance of different Bcl-2 complexes and their spatio-temporal regulation is debated. Using fluorescence cross-correlation spectroscopy to quantify the interactions within a minimal Bcl-2 network, comprised by cBid, Bax, and Bcl-xL, we show that membrane insertion drastically alters the pattern of Bcl-2 complexes, and that the C-terminal helix of Bcl-xL determines its binding preferences. At physiological temperature, Bax can spontaneously activate in a self-amplifying process. Strikingly, Bax also recruits Bcl-xL to membranes, which is sufficient to retrotranslocate Bax back into solution to secure membrane integrity. Our study disentangles the hierarchy of Bcl-2 complex formation in relation to their environment: Bcl-xL association with cBid occurs in solution and in membranes, where the complex is stabilized, whereas Bcl-xL binding to Bax occurs only in membranes and with lower affinity than to cBid, leading instead to Bax retrotranslocation.

The permeabilization of the mitochondrial outer membrane to induce apoptosis is regulated by complex interactions between Bcl-2 family members. Here the authors develop a quantitative interactome of a membrane Bcl-2 network and identify a hierarchy of protein complexes in apoptosis induction.

COPASI and its applications in biotechnology

COPASI is software used for the creation, modification, simulation and computational analysis of kinetic models in various fields. It is open-source, available for all major platforms and provides a user-friendly graphical user interface, but is also controllable via the command line and scripting languages. These are likely reasons for its wide acceptance. We begin this review with a short introduction describing the general approaches and techniques used in computational modeling in the biosciences. Next we introduce the COPASI package, and its capabilities, before looking at typical applications of COPASI in biotechnology.

SBpipe: a collection of pipelines for automating repetitive simulation and analysis tasks

BACKGROUND

The rapid growth of the number of mathematical models in Systems Biology fostered the development of many tools to simulate and analyse them. The reliability and precision of these tasks often depend on multiple repetitions and they can be optimised if executed as pipelines. In addition, new formal analyses can be performed on these repeat sequences, revealing important insights about the accuracy of model predictions.

RESULTS

Here we introduce SBpipe, an open source software tool for automating repetitive tasks in model building and simulation. Using basic YAML configuration files, SBpipe builds a sequence of repeated model simulations or parameter estimations, performs analyses from this generated sequence, and finally generates a LaTeX/PDF report. The parameter estimation pipeline offers analyses of parameter profile likelihood and parameter correlation using samples from the computed estimates. Specific pipelines for scanning of one or two model parameters at the same time are also provided. Pipelines can run on multicore computers, Sun Grid Engine (SGE), or Load Sharing Facility (LSF) clusters, speeding up the processes of model building and simulation. SBpipe can execute models implemented in COPASI, Python or coded in any other programming language using Python as a wrapper module. Future support for other software simulators can be dynamically added without affecting the current implementation.

CONCLUSIONS

SBpipe allows users to automatically repeat the tasks of model simulation and parameter estimation, and extract robustness information from these repeat sequences in a solid and consistent manner, facilitating model development and analysis. The source code and documentation of this project are freely available at the web site: https://pdp10.github.io/sbpipe/ .

Increasing extracellular H2O2 produces a bi-phasic response in intracellular H2O2, with peroxiredoxin hyperoxidation only triggered once the cellular H2O2-buffering capacity is overwhelmed

Reactive oxygen species, such as H2O2, can damage cells but also promote fundamental processes, including growth, differentiation and migration. The mechanisms allowing cells to differentially respond to toxic or signaling H2O2 levels are poorly defined. Here we reveal that increasing external H2O2 produces a bi-phasic response in intracellular H2O2. Peroxiredoxins (Prx) are abundant peroxidases which protect against genome instability, ageing and cancer. We have developed a dynamic model simulating in vivo changes in Prx oxidation. Remarkably, we show that the thioredoxin peroxidase activity of Prx does not provide any significant protection against external rises in H2O2. Instead, our model and experimental data are consistent with low levels of extracellular H2O2 being efficiently buffered by other thioredoxin-dependent activities, including H2O2-reactive cysteines in the thiol-proteome. We show that when extracellular H2O2 levels overwhelm this buffering capacity, the consequent rise in intracellular H2O2 triggers hyperoxidation of Prx to thioredoxin-resistant, peroxidase-inactive form/s. Accordingly, Prx hyperoxidation signals that H2O2 defenses are breached, diverting thioredoxin to repair damage.

Development of a robust DNA damage model including persistent telomere-associated damage with application to secondary cancer risk assessment

Mathematical modelling has been instrumental to understand kinetics of radiation-induced DNA damage repair and associated secondary cancer risk. The widely accepted two-lesion kinetic (TLK) model assumes two kinds of double strand breaks, simple and complex ones, with different repair rates. Recently, persistent DNA damage associated with telomeres was reported as a new kind of DNA damage. We therefore extended existing versions of the TLK model by new categories of DNA damage and re-evaluated those models using extensive data. We subjected different versions of the TLK model to a rigorous model discrimination approach. This enabled us to robustly select a best approximating parsimonious model that can both recapitulate and predict transient and persistent DNA damage after ionizing radiation. Models and data argue for i) nonlinear dose-damage relationships, and ii) negligible saturation of repair kinetics even for high doses. Additionally, we show that simulated radiation-induced persistent telomere-associated DNA damage foci (TAF) can be used to predict excess relative risk (ERR) of developing secondary leukemia after fractionated radiotherapy. We suggest that TAF may serve as an additional measure to predict cancer risk after radiotherapy using high dose rates. This may improve predicting risk-dose dependency of ionizing radiation especially for long-term therapies.

Mathematical modelling of arsenic transport, distribution and detoxification processes in yeast

Arsenic has a dual role as causative and curative agent of human disease. Therefore, there is considerable interest in elucidating arsenic toxicity and detoxification mechanisms. By an ensemble modelling approach, we identified a best parsimonious mathematical model which recapitulates and predicts intracellular arsenic dynamics for different conditions and mutants, thereby providing novel insights into arsenic toxicity and detoxification mechanisms in yeast, which could partly be confirmed experimentally by dedicated experiments. Specifically, our analyses suggest that: (i) arsenic is mainly protein-bound during short-term (acute) exposure, whereas glutathione-conjugated arsenic dominates during long-term (chronic) exposure, (ii) arsenic is not stably retained, but can leave the vacuole via an export mechanism, and (iii) Fps1 is controlled by Hog1-dependent and Hog1-independent mechanisms during arsenite stress. Our results challenge glutathione depletion as a key mechanism for arsenic toxicity and instead suggest that (iv) increased glutathione biosynthesis protects the proteome against the damaging effects of arsenic and that (v) widespread protein inactivation contributes to the toxicity of this metalloid. Our work in yeast may prove useful to elucidate similar mechanisms in higher eukaryotes and have implications for the use of arsenic in medical therapy.

Profile likelihood in systems biology

Inferring knowledge about biological processes by a mathematical description is a major characteristic of Systems Biology. To understand and predict system's behavior the available experimental information is translated into a mathematical model. Since the availability of experimental data is often limited and measurements contain noise, it is essential to appropriately translate experimental uncertainty to model parameters as well as to model predictions. This is especially important in Systems Biology because typically large and complex models are applied and therefore the limited experimental knowledge might yield weakly specified model components. Likelihood profiles have been recently suggested and applied in the Systems Biology for assessing parameter and prediction uncertainty. In this article, the profile likelihood concept is reviewed and the potential of the approach is demonstrated for a model of the erythropoietin (EPO) receptor.

Modelling reveals novel roles of two parallel signalling pathways and homeostatic feedbacks in yeast

Ensemble modelling is used to study the yeast high osmolarity glycerol (HOG) pathway, a prototype for eukaryotic mitogen-activated kinase signalling systems. The best fit model provides new insights into the function of this system, some of which are then experimentally validated.

The main mechanism for osmo-adaptation is a fast and transient non-transcriptional Hog1-mediated activation of glycerol production.

The transcriptional response rather serves to maintain an increased steady-state glycerol production with low steady-state Hog1 activity after adaptation.

A fast negative feedback of activated Hog1 on the upstream signalling branches serves to stabilise the adaptation response by preventing oscillatory behaviour.

Two parallel redundant signalling branches elicit a more robust and swifter adaptation than a single branch alone, at least for low osmotic shock. This notion could be corroborated by dedicated measurements of single-cell volume recovery for the wild-type and single-branch mutants.

The high osmolarity glycerol (HOG) pathway in yeast serves as a prototype signalling system for eukaryotes. We used an unprecedented amount of data to parameterise 192 models capturing different hypotheses about molecular mechanisms underlying osmo-adaptation and selected a best approximating model. This model implied novel mechanisms regulating osmo-adaptation in yeast. The model suggested that (i) the main mechanism for osmo-adaptation is a fast and transient non-transcriptional Hog1-mediated activation of glycerol production, (ii) the transcriptional response serves to maintain an increased steady-state glycerol production with low steady-state Hog1 activity, and (iii) fast negative feedbacks of activated Hog1 on upstream signalling branches serves to stabilise adaptation response. The best approximating model also indicated that homoeostatic adaptive systems with two parallel redundant signalling branches show a more robust and faster response than single-branch systems. We corroborated this notion to a large extent by dedicated measurements of volume recovery in single cells. Our study also demonstrates that systematically testing a model ensemble against data has the potential to achieve a better and unbiased understanding of molecular mechanisms.