A model integration approach linking signalling and gene-regulatory logic with kinetic metabolic models

Physiological Indirect Response Model to Omics-Powered Quantitative Systems Pharmacology Model

Over the past several decades, mathematical modeling has been applied to increasingly wider scopes of questions in drug development. Accordingly, the range of modeling tools has also been evolving, as showcased by contributions of Jusko and colleagues: from basic pharmacokinetics/pharmacodynamics (PK/PD) modeling to today's platform-based approach of quantitative systems pharmacology (QSP) modeling. Aimed at understanding the mechanism of action of investigational drugs, QSP models characterize systemic effects by incorporating information about cellular signaling networks, which is often represented by omics data. In this perspective, we share a few examples illustrating approaches for the integration of omics into mechanistic QSP modeling. We briefly overview how the evolution of PK/PD modeling into QSP has been accompanied by an increase in available data and the complexity of mathematical methods that integrate it. We discuss current gaps and challenges of integrating omics data into QSP models and propose several potential areas where integrated QSP and omics modeling may benefit drug development.

Integrating a dynamic central metabolism model of cancer cells with a hybrid 3D multiscale model for vascular hepatocellular carcinoma growth

We develop here a novel modelling approach with the aim of closing the conceptual gap between tumour-level metabolic processes and the metabolic processes occurring in individual cancer cells. In particular, the metabolism in hepatocellular carcinoma derived cell lines (HEPG2 cells) has been well characterized but implementations of multiscale models integrating this known metabolism have not been previously reported. We therefore extend a previously published multiscale model of vascular tumour growth, and integrate it with an experimentally verified network of central metabolism in HEPG2 cells. This resultant combined model links spatially heterogeneous vascular tumour growth with known metabolic networks within tumour cells and accounts for blood flow, angiogenesis, vascular remodelling and nutrient/growth factor transport within a growing tumour, as well as the movement of, and interactions between normal and cancer cells. Model simulations report for the first time, predictions of spatially resolved time courses of core metabolites in HEPG2 cells. These simulations can be performed at a sufficient scale to incorporate clinically relevant features of different tumour systems using reasonable computational resources. Our results predict larger than expected temporal and spatial heterogeneity in the intracellular concentrations of glucose, oxygen, lactate pyruvate, f16bp and Acetyl-CoA. The integrated multiscale model developed here provides an ideal quantitative framework in which to study the relationship between dosage, timing, and scheduling of anti-neoplastic agents and the physiological effects of tumour metabolism at the cellular level. Such models, therefore, have the potential to inform treatment decisions when drug response is dependent on the metabolic state of individual cancer cells.

Hybrid modelling of biological systems: current progress and future prospects

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

A Novel Hybrid Logic-ODE Modeling Approach to Overcome Knowledge Gaps

Mathematical modeling allows using different formalisms to describe, investigate, and understand biological processes. However, despite the advent of high-throughput experimental techniques, quantitative information is still a challenge when looking for data to calibrate model parameters. Furthermore, quantitative formalisms must cope with stiffness and tractability problems, more so if used to describe multicellular systems. On the other hand, qualitative models may lack the proper granularity to describe the underlying kinetic processes. We propose a hybrid modeling approach that integrates ordinary differential equations and logical formalism to describe distinct biological layers and their communication. We focused on a multicellular system as a case study by applying the hybrid formalism to the well-known Delta-Notch signaling pathway. We used a differential equation model to describe the intracellular pathways while the cell-cell interactions were defined by logic rules. The hybrid approach herein employed allows us to combine the pros of different modeling techniques by overcoming the lack of quantitative information with a qualitative description that discretizes activation and inhibition processes, thus avoiding complexity.

Connecting signaling and metabolic pathways in EGF receptor-mediated oncogenesis of glioblastoma

As malignant transformation requires synchronization of growth-driving signaling (S) and metabolic (M) pathways, defining cancer-specific S-M interconnected networks (SMINs) could lead to better understanding of oncogenic processes. In a systems-biology approach, we developed a mathematical model for SMINs in mutated EGF receptor (EGFRvIII) compared to wild-type EGF receptor (EGFRwt) expressing glioblastoma multiforme (GBM). Starting with experimentally validated human protein-protein interactome data for S-M pathways, and incorporating proteomic data for EGFRvIII and EGFRwt GBM cells and patient transcriptomic data, we designed a dynamic model for EGFR-driven GBM-specific information flow. Key nodes and paths identified by in silico perturbation were validated experimentally when inhibition of signaling pathway proteins altered expression of metabolic proteins as predicted by the model. This demonstrated capacity of the model to identify unknown connections between signaling and metabolic pathways, explain the robustness of oncogenic SMINs, predict drug escape, and assist identification of drug targets and the development of combination therapies.

Complex and highly dynamic interconnected networks allow cancer to take different routes and circumvent chemotherapy. Therefore, understanding these context-specific networks and their dynamics of molecular interactions driven by different oncogenic signaling and metabolic pathways is very much needed to predict drug targets and the effect of therapeutics. We incorporated high-throughput transcriptome and proteome data into mathematical models to deduce properties of cancer cells through systems biology approach. Here we report the development, testing and validation of an integrated systems biology model of information flow between signaling and metabolic pathways to understand the regulation of the interconnection between them in cancer. Our model efficiently identified unique connections and key nodes important in signaling-metabolic information flow. We predicted some potential novel targets before performing actual drug tests. We have successfully applied this model to identify the interconnections altered in the constitutive signaling of the mutated EGFR by comparing EGF-dependent and wild-type EGFR signaling in glioblastoma multiforme.

Using Systems Biology and Mathematical Modeling Approaches in the Discovery of Therapeutic Targets for Spinal Muscular Atrophy

Systems biology uses a combination of experimental and mathematical approaches to investigate the complex and dynamic interactions with a given system or biological process. Systems biology integrates genetics, signal transduction, biochemistry and cell biology with mathematical modeling. It can be used to identify novel pathways implicated in diseases as well as to understand the mechanisms by which a specific gene is regulated. This review describes the development of mathematical models for the regulation of an endogenous modifier gene, SMN2, in spinal muscular atrophy-an early-onset motor neuron disease that is a leading genetic cause of infant mortality worldwide-by cAMP signaling. These mathematical models not only can aid in understanding how SMN2 expression is regulated but they can also be used to examine the best ways to manipulate cAMP signaling to maximally increase SMN2 expression. These models will lead to the development of therapeutic strategies for treating SMA. This systems biology approach can also be applied to other neurological diseases, particularly those in which a disease-causing gene or a modifier gene has been identified.

The Genome-Scale Integrated Networks in Microorganisms

The genome-scale cellular network has become a necessary tool in the systematic analysis of microbes. In a cell, there are several layers (i.e., types) of the molecular networks, for example, genome-scale metabolic network (GMN), transcriptional regulatory network (TRN), and signal transduction network (STN). It has been realized that the limitation and inaccuracy of the prediction exist just using only a single-layer network. Therefore, the integrated network constructed based on the networks of the three types attracts more interests. The function of a biological process in living cells is usually performed by the interaction of biological components. Therefore, it is necessary to integrate and analyze all the related components at the systems level for the comprehensively and correctly realizing the physiological function in living organisms. In this review, we discussed three representative genome-scale cellular networks: GMN, TRN, and STN, representing different levels (i.e., metabolism, gene regulation, and cellular signaling) of a cell’s activities. Furthermore, we discussed the integration of the networks of the three types. With more understanding on the complexity of microbial cells, the development of integrated network has become an inevitable trend in analyzing genome-scale cellular networks of microorganisms.

Biosystem models, generated from a complex rule/reaction/influence network and from two functionality prototypes

In this work we have further developed the Direct Computer Mapping (DCM) based modelling and simulation methodology. A unified, transition-based representation of complex rule, reaction and influence networks has been introduced and two prototypes (one general state- and another general transition-prototype) have been developed for the unified functional modelling of the state and transition nodes. Starting from the network and from the functional prototypes, an automatic generation method of the graphically editable and extensible GraphML description of biosystem models has been elaborated. The new developments have been implemented in the improved kernel of DCM models. The applied knowledge representation makes possible the unified generation and execution of the balance-based quantitative and influence- or rule-based qualitative, as well as optionally time-driven, multiscale biosystem models. Application of the developed methodology has been illustrated by the improved implementation of the formerly studied and upgraded example biosystem model for combining the detailed, quantitative p53/miR34a signalling system with the pathological model through an extended rule-based coupling model.

Advances and challenges in logical modeling of cell cycle regulation: perspective for multi-scale, integrative yeast cell models

The eukaryotic cell cycle is robustly designed, with interacting molecules organized within a definite topology that ensures temporal precision of its phase transitions. Its underlying dynamics are regulated by molecular switches, for which remarkable insights have been provided by genetic and molecular biology efforts. In a number of cases, this information has been made predictive, through computational models. These models have allowed for the identification of novel molecular mechanisms, later validated experimentally. Logical modeling represents one of the youngest approaches to address cell cycle regulation. We summarize the advances that this type of modeling has achieved to reproduce and predict cell cycle dynamics. Furthermore, we present the challenge that this type of modeling is now ready to tackle: its integration with intracellular networks, and its formalisms, to understand crosstalks underlying systems level properties, ultimate aim of multi-scale models. Specifically, we discuss and illustrate how such an integration may be realized, by integrating a minimal logical model of the cell cycle with a metabolic network.

Metabolomics in epidemiology: from metabolite concentrations to integrative reaction networks

Metabolomics is becoming feasible for population-scale studies of human disease. In this review, we survey epidemiological studies that leverage metabolomics and multi-omics to gain insight into disease mechanisms. We outline key practical, technological and analytical limitations while also highlighting recent successes in integrating these data. The use of multi-omics to infer reaction rates is discussed as a potential future direction for metabolomics research, as a means of identifying biomarkers as well as inferring causality. Furthermore, we highlight established analysis approaches as well as simulation-based methods currently used in single- and multi-cell levels in systems biology.

Constraint Based Modeling Going Multicellular

Constraint based modeling has seen applications in many microorganisms. For example, there are now established methods to determine potential genetic modifications and external interventions to increase the efficiency of microbial strains in chemical production pipelines. In addition, multiple models of multicellular organisms have been created including plants and humans. While initially the focus here was on modeling individual cell types of the multicellular organism, this focus recently started to switch. Models of microbial communities, as well as multi-tissue models of higher organisms have been constructed. These models thereby can include different parts of a plant, like root, stem, or different tissue types in the same organ. Such models can elucidate details of the interplay between symbiotic organisms, as well as the concerted efforts of multiple tissues and can be applied to analyse the effects of drugs or mutations on a more systemic level. In this review we give an overview of the recent development of multi-tissue models using constraint based techniques and the methods employed when investigating these models. We further highlight advances in combining constraint based models with dynamic and regulatory information and give an overview of these types of hybrid or multi-level approaches.

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.

Data- and knowledge-based modeling of gene regulatory networks: an update

Gene regulatory network inference is a systems biology approach which predicts interactions between genes with the help of high-throughput data. In this review, we present current and updated network inference methods focusing on novel techniques for data acquisition, network inference assessment, network inference for interacting species and the integration of prior knowledge. After the advance of Next-Generation-Sequencing of cDNAs derived from RNA samples (RNA-Seq) we discuss in detail its application to network inference. Furthermore, we present progress for large-scale or even full-genomic network inference as well as for small-scale condensed network inference and review advances in the evaluation of network inference methods by crowdsourcing. Finally, we reflect the current availability of data and prior knowledge sources and give an outlook for the inference of gene regulatory networks that reflect interacting species, in particular pathogen-host interactions.

Quantitative and logic modelling of molecular and gene networks

Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms.