Exemplary Term Paper Proposal 1

Alan Long

Biology 300

3/2/2013

Project Proposal

Peter and I intend to recreate the model presented in Cell Surface Receptors for Signal Transduction and Ligand Transport: A Design Principles Study by Harish Shankaran, Haluk Resat, and H. Steven Wiley. The paper focuses on the functional modules of cell signaling in an attempt to “facilitate the task of obtaining a systems-level understanding of cell function” (986). Four unique signaling modules/receptor systems are selected for study. They are EGFR, epidermal growth factor receptor, LDLR, low-density lipoprotein receptor, TfR, transferrin receptor, and VtgR, vitellogenin receptor. The same mathematical model is used for all four systems, but each receives its own unique set of initial parameter values based on previous scientific research. The paper hypothesizes that, through parameter manipulation, the selected receptor systems may be classified as avidity, describing the system’s ability to form receptor –ligand complexes, controlled, consumption, describing the system’s ability to internalize receptor-ligand complexes, controlled, or a combination of the two, and hence partially, if not completely, distinguish the receptor systems from one another.

The differential model used relates three state variables: R, the number of free surface receptors, C, the number of receptor-ligand complexes, and L, the extracellular concentration of the ligand. In addition to the state variables, there are six independent parameters: k_on, the rate that the ligand bonds to free surface receptors, k_off, the rate that the receptor-ligand complexes dissociate, k_t, the rate that free receptors are internalized, k_e, the rate that receptor-ligand complexes are internalized, R_T, the steady state receptor abundance, and V, the extracellular control volume. Also, the function f[t] represents the introduction of new ligand molecules to the control volume. The initial model is then nondimensionalized to create the working model used for analysis within the paper. R* ,C* , and L* are the nondimensionalized state variables that are now related by parameters α, β , and γ which are functions of the original independent parameters. Of particular interest for classification of the system are β, the partition coefficient, which “quantifies the probability that a captured ligand molecule will be internalized before it dissociates,” and γ , the measure of specific avidity, which characterizes “how efficiently a receptor system can capture and extracellular ligand” (992). In order to simplify their analysis the authors of this model restricted analysis to the cell-surface receptor complexes and neglected processes after internalization such as the recycling of receptors. Additionally, they ignored nonuniformities such as uneven spacing of the receptors or the extracellular concentration gradients caused by internalization of the ligands at the cell surface.

To begin our reconstruction, we will first focus on the effect of endocytic downregulation, or loss of receptors due to bonding with ligands, on the accuracy that the system processes information. This effect will first be studied with respect to the EGFR system. Various magnitudes of downregulation will be applied along with altering the introduction of new ligands through manipulation of the function f[t]. Our work will be checked for correctness by comparing our results with Figure 2 of the paper. After establishing correctness, we intend to create a manipulate function within Mathematica that will allow the user to vary the magnitude of downregulation at will in addition to varying f[t]. Next, the other three selected systems will be analyzed for responsiveness to changes in downregulation which will be checked for correctness with Figure 3 from the article. Then we will analyze the four systems for sensitivity to volume changes, checking our work by comparing with Figure 4. Again, manipulates will be created to allow user control. Finally, we hope to extend the analysis presented within the paper by examining the effects of other functions for ligand introduction, f[t], and probing the model for predicted sensitivities to alteration of other parameters that would allow for greater ability to distinguish one system from the others based solely on its parameter sensitivities. If time permits, we will venture into the creation of the level curve plots used to show efficiency and sensitivity gradients with respect to the coordinate location to each of the receptor systems based on nondimensionalized parameter values, Figures 5 and 6.