Beyond Boolean networks, a multi-valued approach.

Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory networks involving genes, proteins, and metabolites. Since genes can have several modes of action, depending on their expression levels, binary variables are often not sufficiently rich, requiring the use of multi-valued networks instead. The steady state analysis of Boolean networks is computationally complex, and increasing the number of variable values beyond $2$ adds substantially to this complexity, and no general methods are available beyond simulation. The main contribution of this paper is to give an algorithm to compute the steady states of a multi-valued network that has a complexity that, in many cases, is essentially the same as that for the case of binary values. Our approach is based on a representation of multi-valued networks using multi-valued logic functions, providing a biologically intuitive representation of the network. Furthermore, it uses tools to compute lattice points in rational polytopes, tapping a rich area of algebraic combinatorics as a source for combinatorial algorithms for Boolean network analysis. An implementation of the algorithm is provided.

Digital twins in medicine.

Medical digital twins, which are potentially vital for personalized medicine, have become a recent focus in medical research. Here we present an overview of the state of the art in medical digital twin development, especially in oncology and cardiology, where it is most advanced. We discuss major challenges, such as data integration and privacy, and provide an outlook on future advancements. Emphasizing the importance of this technology in healthcare, we highlight the potential for substantial improvements in patient-specific treatments and diagnostics.

Building digital twins of the human immune system: toward a roadmap.

Digital twins, customized simulation models pioneered in industry, are beginning to be deployed in medicine and healthcare, with some major successes, for instance in cardiovascular diagnostics and in insulin pump control. Personalized computational models are also assisting in applications ranging from drug development to treatment optimization. More advanced medical digital twins will be essential to making precision medicine a reality. Because the immune system plays an important role in such a wide range of diseases and health conditions, from fighting pathogens to autoimmune disorders, digital twins of the immune system will have an especially high impact. However, their development presents major challenges, stemming from the inherent complexity of the immune system and the difficulty of measuring many aspects of a patient's immune state in vivo. This perspective outlines a roadmap for meeting these challenges and building a prototype of an immune digital twin. It is structured as a four-stage process that proceeds from a specification of a concrete use case to model constructions, personalization, and continued improvement.

A modular computational framework for medical digital twins.

This paper presents a modular software design for the construction of computational modeling technology that will help implement precision medicine. In analogy to a common industrial strategy used for preventive maintenance of engineered products, medical digital twins are computational models of disease processes calibrated to individual patients using multiple heterogeneous data streams. They have the potential to help improve diagnosis, prognosis, and personalized treatment for a wide range of medical conditions. Their large-scale development relies on both mechanistic and data-driven techniques and requires the integration and ongoing update of multiple component models developed across many different laboratories. Distributed model building and integration requires an open-source modular software platform for the integration and simulation of models that is scalable and supports a decentralized, community-based model building process. This paper presents such a platform, including a case study in an animal model of a respiratory fungal infection.

PlantSimLab - a modeling and simulation web tool for plant biologists.

BACKGROUND: At the molecular level, nonlinear networks of heterogeneous molecules control many biological processes, so that systems biology provides a valuable approach in this field, building on the integration of experimental biology with mathematical modeling. One of the biggest challenges to making this integration a reality is that many life scientists do not possess the mathematical expertise needed to build and manipulate mathematical models well enough to use them as tools for hypothesis generation. Available modeling software packages often assume some modeling expertise. There is a need for software tools that are easy to use and intuitive for experimentalists. RESULTS: This paper introduces PlantSimLab, a web-based application developed to allow plant biologists to construct dynamic mathematical models of molecular networks, interrogate them in a manner similar to what is done in the laboratory, and use them as a tool for biological hypothesis generation. It is designed to be used by experimentalists, without direct assistance from mathematical modelers. CONCLUSIONS: Mathematical modeling techniques are a useful tool for analyzing complex biological systems, and there is a need for accessible, efficient analysis tools within the biological community. PlantSimLab enables users to build, validate, and use intuitive qualitative dynamic computer models, with a graphical user interface that does not require mathematical modeling expertise. It makes analysis of complex models accessible to a larger community, as it is platform-independent and does not require extensive mathematical expertise.

Optimization and Control of Agent-Based Models in Biology: A Perspective.

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Stabilizing gene regulatory networks through feedforward loops.

The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this robustness has been identified as the action of so-called microRNAs that operate via feedforward loops. We present results of a computational study, using the modeling framework of stochastic Boolean networks, which explores the role that such network motifs play in stabilizing global dynamics. The paper introduces a new measure for the stability of stochastic networks. The results show that certain types of feedforward loops do indeed buffer the network against stochastic effects.

The core control system of intracellular iron homeostasis: a mathematical model.

Iron is a metal essential for cellular metabolism. However, excess iron available for reactions contributes to the formation of dangerous reactive oxygen species, such as the hydroxyl radical, via the Fenton reaction. Therefore, intracellular iron levels are tightly constrained by a control system of proteins. This paper contains a mathematical model, in the form of a system of five ordinary differential equations, of the core of this control system, including the labile iron pool as well as proteins that regulate uptake, storage, and export and are connected through negative feedback loops. The model is validated using data from an overexpression experiment with cultured human breast epithelial cells. The parameters in the mathematical model are not known for this particular cell culture system, so the analysis of the model was done for a generic choice of parameters. Through a mixture of analytical arguments and extensive simulations it is shown that for any choice of parameters the model reaches a unique stable steady state, thereby ruling out oscillatory behavior. It is shown furthermore that the model parameters are identifiable through suitable experiments.

A virtual look at Epstein-Barr virus infection: simulation mechanism.

Epstein-Barr virus (EBV) is an important human pathogen that establishes a life-long persistent infection and for which no precise animal model exists. In this paper, we describe in detail an agent-based model and computer simulation of EBV infection. Agents representing EBV and sets of B and T lymphocytes move and interact on a three-dimensional grid approximating Waldeyer's ring, together with abstract compartments for lymph and blood. The simulation allows us to explore the development and resolution of virtual infections in a manner not possible in actual human experiments. Specifically, we identify parameters capable of inducing clearance, persistent infection, or death.

Using formal concept analysis for microarray data comparison.

Microarray technologies, which can measure tens of thousands of gene expression values simultaneously in a single experiment, have become a common research method for biomedical researchers. Computational tools to analyze microarray data for biological discovery are needed. In this paper, we investigate the feasibility of using formal concept analysis (FCA) as a tool for microarray data analysis. The method of FCA builds a (concept) lattice from the experimental data together with additional biological information. For microarray data, each vertex of the lattice corresponds to a subset of genes that are grouped together according to their expression values and some biological information related to gene function. The lattice structure of these gene sets might reflect biological relationships in the dataset. Similarities and differences between experiments can then be investigated by comparing their corresponding lattices according to various graph measures. We apply our method to microarray data derived from influenza-infected mouse lung tissue and healthy controls. Our preliminary results show the promise of our method as a tool for microarray data analysis.

Reverse engineering of dynamic networks.

We consider the problem of reverse-engineering dynamic models of biochemical networks from experimental data using polynomial dynamic systems. In earlier work, we developed an algorithm to identify minimal wiring diagrams, that is, directed graphs that represent the causal relationships between network variables. Here we extend this algorithm to identify a most likely dynamic model from the set of all possible dynamic models that fit the data over a fixed wiring diagram. To illustrate its performance, the method is applied to simulated time-course data from a published gene regulatory network in the fruitfly Drosophila melanogaster.