Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems

Protocol for biomodel engineering of unilevel to multilevel biological models using colored Petri nets

Biological systems inherently span multiple levels, which can pose challenges in spatial representation for modelers. We present a protocol that utilizes colored Petri nets to construct and analyze biological models of systems, encompassing both unilevel and multilevel scenarios. We detail a modeling workflow exploiting the PetriNuts platform comprising a set of tools linked together via common file formats. We describe steps for modeling preparation, component-level modeling and analysis, followed by system-level modeling and analysis, and model use.

OPTIMIZATION OF PRE-HOSPITAL FIRST AID MANAGEMENT STRATEGIES FOR PATIENTS WITH INFECTIOUS DISEASES IN HUIZHOU CITY USING DEEP LEARNING ALGORITHM

The aim of the study was to optimize the pre-hospital first aid management strategy for patients with infectious diseases in Huizhou city, which is expected to provide a basis for the epidemic prevention and control, to save lives, and increase the pre-hospital first aid efficiency. At the Department of Emergency, Huizhou Third People's Hospital as the research subject, the common pre-hospital first aid procedure for infectious diseases was identified. The Petri net was used to model and determine the execution time of each link of the pre-hospital first aid process. The isomorphic Markov chain was used to optimize the pre-hospital first aid procedure for infectious diseases. In terms of the emergency path, deep learning was combined with the reinforcement learning model to construct the reinforcement learning model for ambulance path planning. Isomorphic Markov chain analysis revealed that the patient status when returning to the hospital, the time needed for the ambulance to come to designated location, and the on-site treatment were the main problems in the first aid process, and the time needed for the pre-hospital first aid process was reduced by 25.17% after optimization. In conclusion, Petri net and isomorphic Markov chain can optimize the pre-hospital first aid management strategies for patients with infectious diseases, and the use of deep learning algorithm can effectively plan the emergency path, achieving intelligent and informationalized pre-hospital transfer, which provides a basis for reducing the suffering, mortality, and disability rate of patients with infectious diseases.

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.

Analysis of Pattern Formation by Colored Petri Nets With Quantitative Regulation of Gene Expression Level

Modeling and simulation are becoming indispensable tools for studying multicellular events such as pattern formation during embryonic development. In this paper, we propose a new approach for analyzing multicellular biological phenomena by combining colored hybrid Petri nets (ColHPNs) with newly devised biological experiments that can control level of a gene quantitatively. With this approach, we analyzed patterning of the boundary cells in the Drosophila large intestine, where one-cell-wide domain of boundary cells differentiate through Delta-Notch signaling. Biological experiments regulating the level of Delta resulted in six distinct patterns of boundary cells correlating with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling. This approach can be easily adapted to address other similar pattern formation issues in the systems biology area.

Nets-within-nets for modeling emergent patterns in ontogenetic processes

Ontogenesis is the development of an organism from its earliest stage to maturity, including homeostasis maintenance throughout adulthood despite environmental perturbations. Almost all cells of a multicellular organism share the same genomic information. Nevertheless, phenotypic diversity and complex supra-cellular architectures emerge at every level, starting from tissues and organs. This is possible thanks to a robust and dynamic interplay of regulative mechanisms. To study ontogenesis, it is necessary to consider different levels of regulation, both genetic and epigenetic. Each cell undergoes a specific path across a landscape of possible regulative states affecting both its structure and its functions during development. This paper proposes using the Nets-Within-Nets formalism, which combines Petri Nets' simplicity with the capability to represent and simulate the interplay between different layers of regulation connected by non-trivial and context-dependent hierarchical relations. In particular, this work introduces a modeling strategy based on Nets-Within-Nets that can model several critical processes involved in ontogenesis. Moreover, it presents a case study focusing on the first phase of Vulval Precursor Cells specification in C.Elegans. The case study shows that the proposed model can simulate the emergent morphogenetic pattern corresponding to the observed developmental outcome of that phase, in both the physiological case and different mutations. The model presented in the results section is available online at https://github.com/sysbio-polito/NWN_CElegans_VPC_model/.

A Petri nets-based framework for whole-cell modeling

Whole-cell modeling aims to incorporate all main genes and processes, and their interactions of a cell in one model. Whole-cell modeling has been regarded as the central aim of systems biology but also as a grand challenge, which plays essential roles in current and future systems biology. In this paper, we analyze whole-cell modeling challenges and requirements and classify them into three aspects (or dimensions): heterogeneous biochemical networks, uncertainties in components, and representation of cell structure. We then explore how to use different Petri net classes to address different aspects of whole-cell modeling requirements. Based on these analyses, we present a Petri nets-based framework for whole-cell modeling, which not only addresses many whole-cell modeling requirements, but also offers a graphical, modular, and hierarchical modeling tool. We think this framework can offer a feasible modeling approach for whole-cell model construction.

Modeling and Analyzing Transmission of Infectious Diseases Using Generalized Stochastic Petri Nets

Some infectious diseases such as COVID-19 have the characteristics of long incubation period, high infectivity during the incubation period, and carriers with mild or no symptoms which are more likely to cause negligence. Global researchers are working to find out more about the transmission of infectious diseases. Modeling plays a crucial role in understanding the transmission of the new virus and helps show the evolution of the epidemic in stages. In this paper, we propose a new general transmission model of infectious diseases based on the generalized stochastic Petri net (GSPN). First, we qualitatively analyze the transmission mode of each stage of infectious diseases such as COVID-19 and explain the factors that affect the spread of the epidemic. Second, the GSPN model is built to simulate the evolution of the epidemic. Based on this model’s isomorphic Markov chain, the equilibrium state of the system and its changing laws under different influencing factors are analyzed. Our paper demonstrates that the proposed GSPN model is a compelling tool for representing and analyzing the transmission of infectious diseases from system-level understanding, and thus contributes to providing decision support for effective surveillance and response to epidemic development.

Extended Robust Boolean Network of Budding Yeast Cell Cycle

Background:

How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling.

Methods:

We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable.

Results:

Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved.

Conclusion:

The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.

A mathematical modelling approach for treatment and control of Echinococcus multilocularis

Alveolar echinococcosis (AE) is a zoonotic parasitic diseases caused by a cestode parasite known as Echinococcus multilocularis. The parasite has a wildlife cycle with definitive hosts (foxes) and small mammals as intermediate hosts (rodents) while humans are the accidental hosts. Parasite infection pressure relation to time of the year and age dependent infection pressure for parasite abundance also depend on the urbanization. The aim of current work is forecasting the thresholds via the computational analysis of the disease spread which is a useful approach since it can help to design the experimental settings with better planning and efficiency. Network analysis when interlinked with the computational techniques provides better insight into the spatial and temporal heterogeneities. In the present study, a mathematical framework that describes the transmission dynamics and control measures of E. multilocularis in foxes is documented. We used treatment of foxes with baits for the prevention of the E. multilocularis infection. A novel approach of networking, called Petri net (PN), based on density dependent differential equations, is utilized during this research. The accurate description of the transmission of the parasite and the effect of drug on it is provided to the readers in this article. The transitions, which are difficult to analyse theoretically, are presented with the aid of the discrete approach of networking. A discrete mathematical framework can prove to be an accurate and robust tool to analyse and control the parasite dynamics.

Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

BACKGROUND

Quorum sensing drives biofilm formation in bacteria in order to ensure that biofilm formation only occurs when colonies are of a sufficient size and density. This spatial behaviour is achieved by the broadcast communication of an autoinducer in a diffusion scenario. This is of interest, for example, when considering the role of gut microbiota in gut health. This behaviour occurs within the context of the four phases of bacterial growth, specifically in the exponential stage (phase 2) for autoinducer production and the stationary stage (phase 3) for biofilm formation.

RESULTS

We have used coloured hybrid Petri nets to step-wise develop a flexible computational model for E.coli biofilm formation driven by Autoinducer 2 (AI-2) which is easy to configure for different notions of space. The model describes the essential components of gene transcription, signal transduction, extra and intra cellular transport, as well as the two-phase nature of the system. We build on a previously published non-spatial stochastic Petri net model of AI-2 production, keeping the assumptions of a limited nutritional environment, and our spatial hybrid Petri net model of biofilm formation, first presented at the NETTAB 2017 workshop. First we consider the two models separately without space, and then combined, and finally we add space. We describe in detail our step-wise model development and validation. Our simulation results support the expected behaviour that biofilm formation is increased in areas of higher bacterial colony size and density. Our analysis techniques include behaviour checking based on linear time temporal logic.

CONCLUSIONS

The advantages of our modelling and analysis approach are the description of quorum sensing and associated biofilm formation over two phases of bacterial growth, taking into account bacterial spatial distribution using a flexible and easy to maintain computational model. All computational results are reproducible.

BioModelKit - An Integrative Framework for Multi-Scale Biomodel-Engineering

While high-throughput technology, advanced techniques in biochemistry and molecular biology have become increasingly powerful, the coherent interpretation of experimental results in an integrative context is still a challenge. BioModelKit (BMK) approaches this challenge by offering an integrative and versatile framework for biomodel-engineering based on a modular modelling concept with the purpose: (i) to represent knowledge about molecular mechanisms by consistent executable sub-models (modules) given as Petri nets equipped with defined interfaces facilitating their reuse and recombination; (ii) to compose complex and integrative models from an ad hoc chosen set of modules including different omic and abstraction levels with the option to integrate spatial aspects; (iii) to promote the construction of alternative models by either the exchange of competing module versions or the algorithmic mutation of the composed model; and (iv) to offer concepts for (omic) data integration and integration of existing resources, and thus facilitate their reuse. BMK is accessible through a public web interface (www.biomodelkit.org), where users can interact with the modules stored in a database, and make use of the model composition features. BMK facilitates and encourages multi-scale model-driven predictions and hypotheses supporting experimental research in a multilateral exchange.