Simulating an Infection Growth Model in Certain Healthy Metabolic Pathways of Homo sapiens for Highlighting Their Role in Type I Diabetes mellitus Using Fire-Spread Strategy, Feedbacks and Sensitivities

Feedbacks and Sensitivities. PLoS ONE 8(9): e69724. doi:10.1371/journal.pone.0069724 Simulating an Infection Growth Model in Certain Healthy Metabolic Pathways of Homo sapiens for Highlighting Their Role in Type I Diabetes mellitus Using Fire-Spread Strategy, Feedbacks and Sensitivities Somnath Tagore 0 Rajat K. De 0 Dipshikha Chakravortty, Indian Institute of Science, India 0 1 Department of Biotechnology and Bioinformatics, Padmashree Dr. D. Y. Patil University , Navi Mumbai , India , 2 Machine Intelligence Unit, Indian Statistical Institute , Kolkata , India Disease Systems Biology is an area of life sciences, which is not very well understood to date. Analyzing infections and their spread in healthy metabolite networks can be one of the focussed areas in this regard. We have proposed a theory based on the classical forest fire model for analyzing the path of infection spread in healthy metabolic pathways. The theory suggests that when fire erupts in a forest, it spreads, and the surrounding trees also catch fire. Similarly, when we consider a metabolic network, the infection caused in the metabolites of the network spreads like a fire. We have constructed a simulation model which is used to study the infection caused in the metabolic networks from the start of infection, to spread and ultimately combating it. For implementation, we have used two approaches, first, based on quantitative strategies using ordinary differential equations and second, using graph-theory based properties. Furthermore, we are using certain probabilistic scores to complete this task and for interpreting the harm caused in the network, given by a 'critical value' to check whether the infection can be cured or not. We have tested our simulation model on metabolic pathways involved in Type I Diabetes mellitus in Homo sapiens. For validating our results biologically, we have used sensitivity analysis, both local and global, as well as for identifying the role of feedbacks in spreading infection in metabolic pathways. Moreover, information in literature has also been used to validate the results. The metabolic network datasets have been collected from the Kyoto Encyclopedia of Genes and Genomes (KEGG). - An important aspect of metabolic pathway analysis is studying the impact of infections or disease spread in healthy metabolic pathways. Tackling the growth of infection in a healthy metabolic pathway as well as curing it simultaneously is rather complex. Let us consider a scenario, wherein, a metabolite in a healthy metabolic network becomes infected due to some mutation or external perturbation. Moreover, a metabolite is said to be infected if its formation, in a metabolic pathway, is somehow impaired. The major problem lies in tracking the progress of this infection to other non-infected neighboring metabolites and understand the nature of this spread [1]. The result of such an infection may further give rise to in improper production of certain metabolites leading to improper functioning of the entire metabolic pathway. In case of a healthy metabolic network, tracking this path is very difficult. The reason is that prior probability of a healthy metabolite to be infected is difficult to predict. Moreover, once the metabolite is infected, it can infect its neighbors with an infection rate, and can also be cured with a curing rate. Once cured or healthy, the metabolite is again prone to the infection. However, both infection and curing process may occur independently [2]. In this study we have implemented the forest fire strategy for analyzing the infection spread in a healthy metabolic pathway. The classical forest fire algorithm suggests that when fire erupts in a forest, it spreads to its surrounding trees, resulting in their further burning. At each step of this process, the burning trees have a probability of staying on fire and burning out, whereas the surrounding trees also have a probability of ignition [3]. This fundamental idea can be taken into consideration for studying the spread of infection in metabolic networks that are represented as directed graph format. Infection can be caused in the healthy metabolites via an infected metabolite, which can spread further and hence can be used to study the harm caused to the overall metabolic network [4]. In such cases, there is a possibility that either the metabolites are infected, safe or cured. Also, infections can be caused either by its nearest neighbors or its next-nearest neighbors. We have constructed a simulation model which can be used to study the infection caused in a network from infection initiation, to spread and ultimately combating it. Moreover, we have used certain probabilistic scores to complete this task that results in interpreting the harm caused in a healthy metabolic network, given by certain critical value for checking whether the infection can be cured or not [5]. Thus, any harm caused to any metabolite in the pathway can provide a clear picture of the overall infection spread. But, the difference between a metabolic pathway and forest is that in the former, there are no direct contact links, wherein contacts are linked as reaction links. Also, there are many other factors involved, such as, feedback links, presence of topological units, to name a few, which must be considered for predicting the cause and nature of the path of infection spread. We have used strategies such as feedback link prediction, sensitivity approaches for handling such instances (discussed in details later). Recent literature shows that some basic disease models have been developed to analyze the spread of certain diseases in realworld networks. These models describe the susceptibility, infection scenario and recovery rates of populations from a particular disease. In all these models information related to infection progress is not taken into account because of the differences in response among individuals in a specific population. Moreover, based on the epidemiological studies of individuals, two standard models, namely, susceptible-infectious-recovered (SIR) and susceptible-infectious-susceptible (SIS), have been proposed (discussed in section Methodology) for analyzing the study of disease spread in populations [6]. These models work on determining the source of infection and then linking each infected individual to one another, as well as to a variable number of others to whom they transmitted the disease. It generated a network of individuals consisting of all the links through which infection spreads in course of a single disease outbreak. Furthermore, some contact-tracing approaches were also developed to identify all potential transmission contacts from a source individual. These approaches identified a new set of individuals who might have the tendency to get infected from some already infected individuals. It has been applied in cases of sexually transmitted diseases (STDs) where a contact is most easily defined. But, all (...truncated)