Among others, the complement components have been associated with neurodegenerative disorders including Alzheimer and Parkinson diseases as well as multiple sclerosis ( Mastellos et al., 2019). We also show how the integration of multiscale modeling techniques can help for improving the predictive model, while also providing mechanistic information at the molecular level.Ĭomplement dysfunction is associated with several diseases. Here, we report on the development of systems biology predictive models, which describe the intricate biochemical networks and the crosstalk among other elements of the immune system. ![]() The complex network of proteins and other macromolecular entities composing the complement system represents an ideal case to build a systems biology workflow predicting the system's response in immunity against invading pathogens, and how under complement deficiencies this same system mediates different pathologies. Complement is composed of three pathways known as alternative, classical and lectin that work in concert to achieve its function ( Schatz-Jakobsen et al., 2016a). The multi-scale nature of systems biology calls for a multifaced description to bridge the system scale at the cellular level to the molecular scale of individual macromolecules.Īmong the important biological cascades responsible for severe diseases, we focus here on the complement system, which is an effector arm of the immune system that eliminates pathogens, helps in maintaining host homeostasis, and forms a bridge between innate and adaptive immunity ( Bennett et al., 2017 Reis et al., 2019). This knowledge can be used for translational research and application in biomedicine ( McGillivray et al., 2018). Understanding the network of interactions that mediate these systems is of the utmost importance for deciphering the mechanisms associated with multifactorial diseases, as well as to address fundamental biological questions. This is the case of fundamental pathophysiological networks, such as epidemiological responses with host and pathogens ( Hillmer, 2015). Systems biology is a multi-scale field, as it has no fixed scale in the context of a biological response or cascade, where an ensemble of proteins, cofactors and small molecules concertedly act to achieve function. Our results shed light on how path integrals can be used to conceptualize coarse-graining biochemical systems and are readily generalizable.Systems biology implements a variety of statistical, computational and mathematical techniques to understand how networks of biological systems work together to achieve a function ( Westerhoff and Palsson, 2004 Wolkenhauer, 2014). ![]() In particular, both approaches involve converting many sums into many integrals, and the difference between the two methods is essentially the difference between using the Euler-Maclaurin formula and using Riemann sums. We compare this approach to the path-integral equivalent of a large system size derivation and show that they are qualitatively different. In this work, we construct an original path-integral description of the CME and show how applying Gillespie's two conditions to it directly leads to a path-integral equivalent to the CLE. ![]() In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation (CME).
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