Mechanistic Modeling of Renal Allograft Failure: From Molecular Networks to Patient Outcome

Renal allograft failure is a complex process involving several immune cell types. Acute rejection is at least partially mediated by aberrant growth factor or cytokine-induced signaling events leading to programmed cell death or graft invasion by inflammatory cells. Furthermore, invasion is perhaps partially mediated by the graft itself though paracrine/endocrine signaling mechanisms. Physiochemical models that describe system-level responses can prioritize experimental directions, generate testable hypothesis and perhaps identify/validate therapeutic targets. In this study, we developed a population of mechanistic mathematical models of the injury and signaling programs, which can be used to estimate critical markers associated with graft failure. Human model connectivity was assembled from databases; String, NetworKIN, Phosphosite, NetPath and TRANSFAC and literature data. The integrated model was analyzed using parameter dependent and independent schemes, to determine critical points of network failure and possible sources of synergy between the pathways involved. Signaling events were modeled using mass action kinetics within an ordinary differential equation (ODE) framework. The central challenge with physiochemical models is parameter identification; it is typically impossible to uniquely identify model parameters, even with extensive training data and perfect models. Model parameters were estimated by comparing simulations with experimental data. We identified a population of models, consistent with data, using a multi-objective optimization framework combined with cross-validation using Pareto Optimal Ensemble Techniques (POETs) algorithm. Model ensembles quantified simulation uncertainty and generated statistical predictions despite incomplete parameter information. We tested the ensembles first using leave-N-out cross-validation during identification and secondly by comparing knock-down simulations with siRNA knockdown experiments. Knock-down simulations allowed us to identify structural perturbations that altered phenotypic markers; these shifts represent testable hypothesis about the functional role of nodes in the renal network that will be verified by siRNA. Important nodes predicted (and validated by the siRNA experiments) will then be compared against existing qRT-PCR - transplant outcome data sets. This linkage shall allow us to estimate which markers/nodes are related to graft outcome. The current work is an initial step towards a fundamentally different paradigm in transplantation research, namely, physiochemical model based assessment of biomarker importance.

Figure: Model connectivity implicated in Renal Allograft Failure visualized using GraphViz. The key signaling cascades include fibroblast growth factor 2 signaling, transforming growth factor beta signaling, vascular endothelial growth factor signaling and bone morphogenetic protein 2/7 signaling cascades.