Exemplary Model Plan

Table 1: State Variables

Variable	Description	Initial Value
R	Number of Free Surface Receptors	RT
C	Number of Receptor-Ligand Complexes	0
L	Extracellular Concentration of the Ligand	0.01 KD

Table 2: Independent Parameters

Variable	Description	EGFR Value	TfR Value	LDLR Value	VtgR Value
kon	Rate of formation of receptor-ligand complexes (/min)	0.097	0.0030	0.0028	5.4 E -5
koff	Rate of dissociation of or receptor-ligand complexes (/min)	0.24	0.09	0.04	0.07
ke	Rate of internalization of receptor-ligand complexes (/min)	0.15	0.6	0.195	0.108
kt	Rate of internalization of unbonded receptors (/min)	0.02	0.6	0.195	0.108
QR	Rate of creation of new receptors on the cell surface (nM/min)	4000	15600	390	2.2 E10
V	Extracellular volume (liters)	4 E-10	4 E-10	4 E-10	4 E-10
f[t]	Introduction of new ligand molecules to the control volume (nM/min)	varies

Table 3: Calculated Parameters

Variable	Formula	Description	EGFR Value	TfR Value	LDLR Value	VtgR Value
KD	koff/ kon	Dissociation constant (nM)	2.47	29.8	14.3	1300
RT	QR/ kt	Steady state receptor abundance	2 E 5	2.6 E 4	2 E 4	2 E 11
D	ke/ kt	Downregulation	7.5	1.0	1.0	1.0
β	ke/ koff	Partition coefficient	0.63	6.67	5.51	1.44
γ	(QR kt)/(V kt koff Nav)	Specific avididty	0.34	0.004	0.006	638.6

• • N_av = Avogadro's number

• Note: $\quad$ EGFR: epidermal growth factor receptor, LDLR: low-density lipoprotein receptor, TfR: transferrin receptor, and VtgR: vitellogenin receptor

Hypothesis: 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.

We will test this hypothesis in the same manner that the paper does. As seen in the formulas for the specific avidity, $\gamma$ , and the partition coefficient, $\beta$ , in Table 3, the two calculated parameters are independent of one another with regards to the parameters $k_e$, and volume. Changing $k_e$ will only change the partition coefficient, and changing volume will only change the specific avidity. Specific avidity is a measure of the avidity of the system, while the partition coefficient serves as a measure of consumption. By varying specific avidity and the partition coefficient independently and observing each systems' responses, we will be able to classify each system as avidity controlled, consumption controlled, or a combination of the two. The responses of the systems will be quantified using time plots of percentage internalized ligand.

As with the course syllabus, each bullet point listed under a date is a goal for that day and should be completed by the following class. Intermediate goals and additional calculations have been folded into this timetable.

• March 19th

• Background research for the Introduction

• March 21st

• Outline Introduction
• Write Introduction

• March 26th ( Introduction due )

• Convert the state variable equations to their dimensionless form using relations given in the paper
• Recreate figure 2a from the paper using Mathematica's NDSolve function

• March 28th

• Outline Model Description
• Write Model Description

• April 2nd ( Model Description due )

• Reproduce all of figure 2 by using the pulse function defined in chapter 7.
• Create the manipulate that allows users to control the forcing function f[t] and the downregulation, D
• Outline description of recreation of figure 2

• April 4th

• Reproduce figures 3 & 4 again utilizing ,NDSolve
• Create a manipulate that allows user to control the variation of the system in question and the downregulation, D.
• Outline description of recreation of figures 3&4

• April 9th

• Perform extension by varying parameters other than those already examined
• Outline and quantify results of extension

• April 11th

• Attempt recreation of efficiency and sensitivity gradient plots using the partial derivatives given in the Materials and Methods section of the original paper
• Write Results

• April 16th ( Results due )

• Comparatively analyze results using outside research sources

• April 18th

• Write Discussion

• April 23rd ( Discussion due )

• Read other student’s Discussions and make comments (EC)

• April 25th

• ( If confident in our work ) Present to the class (EC)
• Revise, edit, respond to comments for paper

• April 29th

• Submit final draft of paper