Projects and Grants

We are embarking on a mix of projects, most combining experiments with theory, but some purely theoretical. Here are descriptions of a few:

Predicting the Effects of Cell-to-Cell Signaling Variability on Proliferation

While it is appreciated that genetically identical cells exposed to the same conditions can exhibit different phenotypes, the types of cell-to-cell heterogeneity driving such divergent behaviors are not well understood. Understanding how cell-to-cell heterogeneity can drive phenotypes is important for treatment of diseases such as cancer, where heterogeneity can play a role in both drug sensitivity and resistance. Our operational hypothesis is that interactions between multiple noisy factors within signaling networks give rise to phenotypic diversity within a genetically identical population. These factors include individual component features such as total levels, basal activities, fold-activations, dynamics and localizations, and also higher-order features such as network topology, isoform ratios, and covariance between components. We aim to test this hypothesis in the context of non-transformed breast epithelial cell proliferation, with a long-term goal of understanding differential decision making between normal and breast cancer cells at various stages of progression. We will perturb non-transformed breast epithelial cells, namely MCF10A cells, using various combinations of compounds that are relevant to breast cancer, and then measure the resultant proliferation and spatiotemporal signaling using single-cell methods that include live-cell imaging with FRET-based biosensors, flow cytometry, and quantitative immunofluorescence with automated image analysis.  Proliferation responses will be related to population-level signaling characteristics such as means, variances, covariances, and bimodality via regression modeling. While this will yield a predictive understanding of proliferation, such regression models require a large amount of input data to make these predictions. Therefore, we will next construct a differential equation model that describes how the various perturbations elicit the observed single-cell, spatiotemporal signaling responses. When this differential equation model is combined with the regression model, the data input requirements for predicting proliferation are significantly reduced. Quantitative, variance-based global sensitivity analysis of this combined, hybrid model will then yield experimentally-testable predictions for how combinations of noisy signaling factors can drive the diversity of proliferation responses in a population of genetically identical cells. These predictions will be tested by simultaneously measuring proliferation, signaling, and protein levels in single cells via live-cell imaging-based proliferation assays, FRET-based biosensors, and knockdown and fluorescent protein-tagged rescue. Thus, the final products of the proposed work will be (i) a hybrid model capable of predicting how various cancer-related perturbations affect the propensity of non-transformed breast epithelial cells to proliferate and (ii) an understanding of how various combinations of noisy signaling factors may drive proliferative diversity.

Derivative-based Parameter Estimation and Experimental Design

The generic ordinary differential equation (ODE) model of biological signaling, when cast in terms of elementary processes, takes a form that has time derivatives on the left-hand sides, and is linear in the parameters on the right-hand sides. Upon time integration, however, the parameters become complex non-linear functions of the model states. Since models of biological signaling typically comprise tens to hundreds of states and the same numbers of unknown parameters, solving non-linear parameter estimation problems and designing experiments for identification of signaling models is computationally difficult, if not impossible given current technology.

Traditional biological assays used for modeling purposes (e.g. western blot, ELISA, immunofluorescence, etc.) rely on fixed or lysed cells. As a result, obtaining high frequency measurements from such assays is not feasible, and likewise nor is obtaining accurate estimates of time derivatives. This forces researchers to estimate model parameters after time integration, giving a difficult, high-dimensional non-linear optimization problem. However, a host of Forster resonance energy transfer (FRET) probes for detecting biochemical activities in live cells have recently been developed which allow for high frequency measurements and therefore more accurate estimation of state time derivatives. Thus, modeling elementary processes based on FRET probe data allows one to perform parameter estimation and identifiability analysis without time integration, yielding problems that are linear in the parameters. Furthermore, by considering time derivatives as an available measurement, one obtains an experimental design problem that is also linear in the parameters.

This project will explore to what extent this possibility of using time-derivative data for doing parameter estimation, parameter identifiability analysis, and model-based experimental design is valuable, and derive theoretical frameworks to support the use of such derivative-based methodologies. In derivative-based analyses, measurement noise is an important consideration, as estimates of time derivatives are in general noisy, despite the high-frequency sampling that can be provided via FRET probes. Thus, our theoretical framework will from the beginning consider the effects of potentially large measurement noise on the performance of the various modeling procedures. We will furthermore attempt to capitalize on previous theory based on modulating function approaches for dealing with the problems associated with derivative-based estimation.

Experimental Cordoning for Practical Parameter Estimation and Model-based Experimental Design

In general, the computational cost of performing a model-based experimental design or parameter estimation for non-linear ODE models scales exponentially with the number of unknown parameters. Even for linear models, large numbers of unknown parameters can pose a serious computational burden. For experimental design, there is the added consideration that the number of decision variables, which tends to grow with the number of model states, and also causes exponential increases in computational cost. As stated above, typical biological signal transduction models have tens to hundreds of unknown parameters and model states, posing significant computational issues for current parameter estimation and experimental design methods.

To address these computational issues, we envision a methodology whereby the dimensionality of the parameter and decision variable space can be reduced significantly by breaking the entire signal transduction model into several modules, each containing manageable numbers of parameters and decision variables. Specifically, one seeks mathematically independent sets of states, which may not only exist within the current model structure, but might also be created via inhibition of signaling links. The inhibition of signaling links will correspond to reactions for which selective, small molecule inhibitors exist. This will make it easy to cordon off independent modules experimentally by applying these small molecule inhibitors to the system. Furthermore, if states in “upstream” modules can be decoupled from “downstream” modules, the parameters in isolated “upstream” modules can be determined, and then held fixed while parameters in “downstream” modules are determined. Because the proposed methodology involves using small molecule inhibitors to halt signals of interest from entering the module under consideration, we call the proposed methodology “experimental cordoning”. This is not unlike analyzing traditional chemical manufacturing processes by (1) operating without feedback and/or feedforward controls (i.e. in open loop) and (2) understanding upstream processes before moving to the downstream ones.

For this project we will first develop a theoretical framework that one can use to determine a set of independent signaling modules given a model structure and experimentally available inhibitors. To test the theory, we will use previously published models of EGF signaling developed by us and others. Upon using the newly derived theory to obtain a potential set of independent signaling modules, for each module we will then perform experimental design, implement the design using MCF10A and MCF10CA1 cells, and estimate unknown parameters. Not only will this project yield a generally applicable and practical method for developing signal transduction models, but will also result in improved, separate descriptions of EGF signaling in MCF10A and MCFCA1 cells, which will give insight into differential signaling and decision making between non-transformed and malignant breast epithelial cells.

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Marc Birtwistle PhD
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