The immune response is incredibly complex. At the cellular level, individual cells move, react, and interact in response to chemokines, cytokines, and other environmental signals, creating a chain of events that ultimately results in cellular and humoral immunity. Despite this complexity, there has been a great deal of success in using computer models to study immune responses to infectious diseases (Bernaschi & Castiglione, 2002; Castiglione
et al., 2004; Segovia-Juarez et al., 2004; Beauchemin, 2006). In this thesis, I have described the development and calibration of a computer model ofLeishmania majorinfection, the identification of correlates of escape mutant success in a computer model of a viral infec- tion, and statistical software to aid in the analysis and calibration of computer models.
5.1 Host-pathogen interactions and emergent behavior in intracellular infections
The emergent behavior of a system, by definition, can only be understood through consideration of how system components interact. In this thesis, analysis of two computer models reveal insight into immune and pathogen behavior not obvious unless interactions between individual components or pathogen and immune parameters are considered.
In the agent-based model of L. majorinfection, growth rate has the largest effect on the first macrophagetime point, despite the fact that growth rate is a pathogen parameter. This happens because increasing growth rate causes infected macrophages to reach carry-
ing capacity sooner, which spreads the infection to additional cells. Infected macrophages release chemokine, which boosts macrophage recruitment. Increasing growth rate can also favor or suppress pathogen loads, depending on the stage of the infection and the ability of the pathogen to avoid detection. This is because a pathogen that proliferates rapidly risks being quickly detected and eliminated by the immune response. As a result, higher growth rates lead to higher peak pathogen loads but shorter infection lengths.
In in silicoexperiments involving the injection of escape mutants, a key finding is that loss of infectivity in humoral escape mutants benefits the virus, despite the fact that less infectious escape mutants would generally be considered less fitin vitro. This is because the strength of the cellular response depends on the infectiousness of the virus (Arnaout & Nowak, 2000), and decreasing infectivity weakens the cellular response. We also find that simultaneous escape from both cellular and humoral responses is substantially more success- ful than escape from either response alone. This is because of the multiplicative effect of be- ing able to infect more cells (humoral escape) and producing more virus (cellular escape). In general, this finding highlights the importance of both immune responses in control- ling infection, and supports the need for vaccination strategies that induce both responses (Wanget al., 2008).
5.2 Future work
In the future, I plan on extending the computer models and the statistical software presented in this thesis. InL. major infection, low levels of pathogen persist following reso- lution of the infection, a stage of the infection that the current model cannot capture. It is known that natural regulatory T cells (Tregs) are required to maintain pathogen persistence (Belkaidet al., 2003). However, the antigen-specificity of Tregs is not entirely clear. Sen- sitivity analysis could reveal implications of alternative models of Treg antigen-specificity.
The computer model could also be used to quantitatively compare alternative models. Equine infectious anemia virus (EIAV) is a close relative of HIV that causes persis- tent infection in horses with disease characterized by acute, chronic, and asymptomatic stages (Lerouxet al., 2004). Interestingly, evolution of the protein Rev, which facilitates nu- clear export of incompletely spliced viral RNA, correlates with the clinical stage of the dis- ease and Rev activity is highest during the chronic stage (Belshanet al., 2001). Our modi- fied version of C-IMMSIM will be extended and calibrated to simulate EIAV infection, and will then be used to characterize the fitness advantage achieved through increased Rev ac- tivity.
Finally, a limitation of current Gaussian process (GP) predictors is the assumption that the computer model is eitherdeterministic or has constant variance (i.e., is home- oscedastic). There is therefore a need for statistical methods that accurately predict het- eroscedastic computer model output. The R packagemlegp, which allows the user to specify a diagonal nugget matrix up to a multiplicative constant, is a first step in this direction. In future versions of the package, I will allow forhierarchicalGP models that use one GP to predict computer model variance and a second GP that predicts computer model output, conditional on the predicted computer model variance of known runs. For heterescedastic computer models, a hierarchical GP model will minimize bias in GP predictions, improve posterior predictions in calibration, and could also be adapted for use in computer model optimization (Joneset al., 2004) and adaptive sampling (Gramacy, 2005).
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