On the computational modeling of the innate immune system

Abstract

In recent years, there has been an increasing interest in the mathematical and computational modeling of the human immune system (HIS). Computational models of HIS dynamics may contribute to a better understanding of the relationship between complex phenomena and immune response; in addition, computational models will support the development of new drugs and therapies for different diseases. However, modeling the HIS is an extremely difficult task that demands a huge amount of work to be performed by multidisciplinary teams. In this study, our objective is to model the spatio-temporal dynamics of representative cells and molecules of the HIS during an immune response after the injection of lipopolysaccharide (LPS) into a section of tissue. LPS constitutes the cellular wall of Gram-negative bacteria, and it is a highly immunogenic molecule, which means that it has a remarkable capacity to elicit strong immune responses. We present a descriptive, mechanistic and deterministic model that is based on partial differential equations (PDE). Therefore, this model enables the understanding of how the different complex phenomena interact with structures and elements during an immune response. In addition, the model's parameters reflect physiological features of the system, which makes the model appropriate for general use.

On the Coupling of Two Models of the Human Immune Response to an Antigen

“…Almost all parameters used in the simulation were obtained in Marchuk [44] applying the necessary unit conversions and some fitting to the coupled model. The only exceptions are the diffusion coefficients D M R , D M A , and D F which were estimated by Pigozzo et al [42] and the diffusion coefficient of bacteria D A based on the work of Haessler and Brown [62]. …”

“…The model has been extended (a) to allow the use of a three-dimensional domain in order to better represent the site of infection and (b) to use parallel programming techniques to guarantee a reasonable simulation time [43]. This work extends our previous models [42, 43], enabling the innate IS to activate the adaptive one. The main contribution of this work is a mathematical model that reproduces the dynamics of both innate and adaptive IS, coupling for this purpose models of different nature and scales.…”

Computational Studies of the Intestinal Host-Microbiota Interactome

“…Computational studies of inflammation can be divided between acute and chronic inflammation, which both focus on, but consider different aspects of, the innate immune system [134][135][136][137][138][139][140][141]. Inflammation is a response by the immune system to injury or infection and involves three basic steps: (1) sensing of damage or threat; (2) containment and clearance of the threat; and (3) repair of the damaged tissue.…”

Complex Stability and an Irrevertible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity

“…Although from the perspective of understanding the immune response, innate immunity has already been proposed a while ago to be most suitable for systems biology studies (10), the number of mathematical models focusing on this innate immunity is still limited (22), yet the innate immune system plays an important role in effective host defense against bacterial and viral infections (23,24) and possibly in allergies and tumorigenesis, and there may already be sufficient information to construct explicit mechanism-based systems biology models. A comprehensive map of IgE-mediated mast cell activation (25) might be used to explore both the intracellular and population dynamical properties of the corresponding section of the immune system, and the experimental field is now reporting genomewide experimental data sets, which systems biology can integrate and help understand in terms of the emergence of function (10).…”

“…Mavroudis et al (30) showed how stochasticity can be taken into account, which they did essentially for the simpler four-variable model referred to above. Other authors extended these models to include spatial dimensions and multiscale aspects (22,31), the latter authors shifting to a Boolean approach.…”