Stochastic approximation to the T cell mediated specific response of the immune system

Figueroa-Morales, Nuris; León, Kalet; Mulet, Roberto

doi:10.1016/j.jtbi.2011.11.003

Cited by 4 publications

(4 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In an infinite system, these oscillations die out, but the stochasticity due to the finite size of the system acts as a white noise, see equation ( 4), that interacts with the proper frequency of the system producing a resonance-like effect. This characteristic frequency is connected with the presence of an imaginary part in the eigenvalues of the system of differential equations and is a phenomena that has been very well characterized before in other models, see for example, [22][23][24][25][26]. In our specific case it is easy to show (see the appendix A), that the frequency of the oscillations only depends on the effective activation rate of p53 ( − k k 2…”

Section: Basal Responsesupporting

confidence: 62%

“…Moreover, to understand the role of the parameters of the model it is important to have at least approximate solutions to the problem. Here, we use the Linear Noise Approximation (LNA) [21], that was first proposed in the context of chemical kinetics and have gain considerable attention in the last few years for modeling intracellular processes, [22][23][24], but also in more general contexts [25,26]. In addition we compare the results of this approximation with experimental data from the literature.…”

Section: The P53-mdm2 Model and Mathematical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

On the role of intrinsic noise on the response of the p53-Mdm2 module

Cruz-Rodríguez¹,

Figueroa-Morales²,

Mulet³

2015

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

Background: The protein p53 has a well established role in protecting genomic integrity in human cells. When DNA is damaged p53 induces the cell cycle arrest to prevent the transmission of the damage to cell progeny, triggers the production of proteins for DNA repair and ultimately calls for apoptosis. In particular, the p53-Mdm2 feedback loop seems to be the key circuit in this response of cells to damage. For many years, based on measurements over populations of cells it was believed that the p53-Mdm2 feedback loop was the responsible for the existence of damped oscillations in the levels of p53 and Mdm2 after DNA damage. However, recent measurements in individual human cells have shown that p53 and its regulator Mdm2 develop sustained oscillations over long periods of time even in the absence of stress. These results have attracted a lot of interest, first because they open a new experimental framework to study the p53 and its interactions and second because they challenge years of mathematical models with new and accurate data on single cells. Inspired by these experiments standard models of the p53-Mdm2 circuit were modified introducing ad-hoc some biologically motivated noise that becomes responsible for the stability of the oscillations. Here, we follow an alternative approach proposing that the noise that stabilizes the fluctuations is the intrinsic noise due to the finite nature of the populations of p53 and Mdm2 in a single cell. Results: We study three stochastic models of the p53-Mdm2 circuit. The models capture the response of the p53-Mdm2 circuit in its basal state, in the presence of DNA damage, and under oncogenic signals. They are studied using Gillespie's simulations, mean field methods and analytical predictions within the context of the Linear Noise Approximation. For the first two models our results compare quantitatively well with existing experimental data in single cells. The study of the response of the p53-Mdm2 circuit under oncogenic signals is process for which we do not have single cell measurements, but can be modeled waiting for experimental verifiable results. While we can not discard that other sources of noise in the cells may also be important, our results strongly support the relevance of the intrinsic noise in these systems. Conclusions: We suggest that the noise induced by the finite size of the populations is responsible for the existence of sustained oscillations in the response of the p53-Mdm2 circuit. This noise alone can explain most of the experimental results obtained studying the dynamics of the p53-Mdm2 circuit in individual cells.

show abstract

Section: Basal Responsesupporting

confidence: 62%

Section: The P53-mdm2 Model and Mathematical Backgroundmentioning

confidence: 99%

On the role of intrinsic noise on the response of the p53-Mdm2 module

Cruz-Rodríguez¹,

Figueroa-Morales²,

Mulet³

2015

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Other mathematical and computational models described the probabilistic interactions between the antigen-presenting cells and regulatory and effector CD4 T cells inside the LN, in the context of immunity as well as autoimmunity and immunological self-tolerance (Figueroa-Morales et al. 2012 ; Celli et al. 2012 ).…”

Section: Models For Cellular-scale Immune Dynamicsmentioning

confidence: 99%

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

2016

View full text Add to dashboard Cite

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

show abstract

“…Another potential approach wherein the total number of required agents may be reduced, would be the recruitment of other cell types, besides idle cells, e.g., in the CRM, an activated regulator cell may be able to recruit an effector cell. However, the outcome of this scenario needs to be explored further, particularly in stochastic simulations with fewer agents, where the discrepancies with the mean field model predictions can be not only quantitative (as in the case of the parameter regime studied here) but even qualitative [16]. Also worth exploration is the impact of random perturbations to the number of agents representing the T-cells or the entities representing APCs, as stochastic perturbations could drive anomalous behaviours akin to relapsing autoimmunity [17].…”

Section: Discussionmentioning

confidence: 99%

Clonal Expansion without Self-replicating Entities

Tarapore

Christensen

Lima

et al. 2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

The vertebrate immune system is a complex distributed system capable of learning to tolerate the organisms' tissues, to assimilate a diverse commensal microflora, and to mount specific responses to invading pathogens. These intricate functions are performed almost flawlessly by a self-organised collective of cells. The robust mechanisms of distributed control in the immune system could potentially be deployed to design multiagent systems. However, the essence of the immune system is clonal expansion by cell proliferation, which is difficult to envisage in most artificial multiagent systems. In this paper, we investigate under which conditions proliferation can be approximated by recruitment in fixed-sized agent populations. Our study is the first step towards bringing many of the desirable properties of the adaptive immune system to systems made of agents which are incapable of self-replication. We adopt the crossregulation model of the adaptive immune system. We develop ordinary differential equation models of proliferation-based and recruitment-based systems, and we compare the predictions of these analytical models with results obtained by a stochastic simulation. Our results define the operational parameter regime wherein growth by recruitment retains all the properties a cell proliferation model. We conclude that rich immunological behaviour can be fully recapitulated in sufficiently large multiagent systems based on growth by recruitment.

show abstract

Stochastic approximation to the T cell mediated specific response of the immune system

Cited by 4 publications

References 25 publications

On the role of intrinsic noise on the response of the p53-Mdm2 module

On the role of intrinsic noise on the response of the p53-Mdm2 module

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

Clonal Expansion without Self-replicating Entities

Contact Info

Product

Resources

About