In response to stress, intracellular signaling proteins activate gene expression programs that protect the cell, address the instigating stress, or result in programmed cell death. In many cases, information about the stimulus is encoded in the dynamics of the signal. Stress-induced signaling dynamics can therefore dictate the cellular response to stress. Recently, it was shown that these dynamics are affected by the resting state of the cell prior to stimulation. If this relationship between steady state and stimulus-induced dynamics was known, then we might predict the cellular response to a particular stimulus using steady state measurements, or engineer a stimulus to elicit a desired response. These are the foundations of diagnostic biomarkers and personalized medicine. To characterize the relationship between steady state and the cellular response, I developed a suite of computational methods and applied them to the p53, NF- [kappa]B, and cell death pathways. First, I developed a method to derive analytical expressions for the steady states of mass action models. By applying this method to a model of cell death, I show how the steady state concentrations of different signaling proteins can affect the tolerance to the death-inducing ligand, TRAIL. Next I extended this method to examine perturbations in the steady state that don't affect the steady state protein concentrations. Applying this method to the p53 and NF- [kappa]B stress-response pathways, I show that a protein turnover signaling motif controls the stimulus-sensitivity of these two different pathways. Finally, using a Monte Carlo method, I show how sampling of the steady state prior to simulation can identify steady state predictors of the response to TRAIL. Interestingly, kinetic features, rather than steady state concentrations, figured prominently among the best predictors. If true, this has severe consequences for clinical biomarker discovery, which is based on measurements of protein abundance and not kinetic features

The steady states of cells affect their response to perturbation. Indeed, diagnostic markers for predicting the response to therapeutic perturbation are often based on steady state measurements. In spite of this, no method exists to systematically characterize the relationship between steady state and response. Mathematical models are established tools for studying cellular responses, but characterizing their relationship to the steady state requires that it have a parametric, or analytical, expression. For some models, this expression can be derived by the King-Altman method. However, King-Altman requires that no substrate act as an enzyme, and is therefore not applicable to most models of signal transduction. For this reason we developed py-substitution, a simple but general method for deriving analytical expressions for the steady states of mass action models. Where the King-Altman method is applicable, we show that py-substitution yields an equivalent expression, and at comparable efficiency. We use py-substitution to study the relationship between steady state and sensitivity to the anti-cancer drug candidate, dulanermin (recombinant human TRAIL). First, we use py-substitution to derive an analytical expression for the steady state of a published model of TRAIL-induced apoptosis. Next, we show that the amount of TRAIL required for cell death is sensitive to the steady state concentrations of procaspase 8 and its negative regulator, Bar, but not the other procaspase molecules. This suggests that activation of caspase 8 is a critical point in the death decision process. Finally, we show that changes in the threshold at which TRAIL results in cell death is not always equivalent to changes in the time of death, as is commonly assumed. Our work demonstrates that an analytical expression is a powerful tool for identifying steady state determinants of the cellular response to perturbation. All code is available at http://signalingsystems.ucsd.edu/models-and-code/ or as supplementary material accompanying this paper.

Stimulus-induced perturbations from the steady state are a hallmark of signal transduction. In some signaling modules, the steady state is characterized by rapid synthesis and degradation of signaling proteins. Conspicuous among these are the p53 tumor suppressor, its negative regulator Mdm2, and the negative feedback regulator of NFκB, IκBα. We investigated the physiological importance of this turnover, or flux, using a computational method that allows flux to be systematically altered independently of the steady state protein abundances. Applying our method to a prototypical signaling module, we show that flux can precisely control the dynamic response to perturbation. Next, we applied our method to experimentally validated models of p53 and NFκB signaling. We find that high p53 flux is required for oscillations in response to a saturating dose of ionizing radiation (IR). In contrast, high flux of Mdm2 is not required for oscillations but preserves p53 sensitivity to sub-saturating doses of IR. In the NFκB system, degradation of NFκB-bound IκB by the IκB kinase (IKK) is required for activation in response to TNF, while high IKK-independent degradation prevents spurious activation in response to metabolic stress or low doses of TNF. Our work identifies flux pairs with opposing functional effects as a signaling motif that controls the stimulus-sensitivity of the p53 and NFκB stress-response pathways, and may constitute a general design principle in signaling pathways.