Computational Analysis of the Control of Cell Cycle Entry

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Authors Everetts, Nicholas John

Publisher The University of Arizona.

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COMPUTATIONAL ANALYSIS OF THE CONTROL OF CELL CYCLE ENTRY

Approved b

Dr. Guang Y ao

By

NICHOLAS JOHN EVERETTS

A Thesis Submitted to The Honors College

In Partial Fulfillment of the Bachelors degree With Honors in

Biochemistry

THE UNIVERSITY OF ARIZONA

MAY2015

Department of Molecular & Cellular Biology

Abstract

The reactivation of quiescent cells (e.g. stem cells) into proliferation is a crucial process

for tissue repair and regeneration. The start of cell proliferation from quiescence is dependent on

a "bistable" Rb-E2F gene pathway. The bistable nature allows the Rb-E2F pathway, in response

to serum growth signals, to exist in two distinct states: an E2F-OFF/quiescence state and an E2F­

ON/proliferation state. In 2008, Y ao at al. derived a mathematical model that predicts the effects

of serum stimulation on the Rb-E2F pathway. The research described in this paper involved

altering the values of model parameters (corresponding to individual gene regulation events)

systematically to understand how cellular factors affect the serum threshold to activate the Rb-E2F

bistable switch. Many of the model parameters that displayed the highest sensitivity on the OFF­

to-ON serum threshold of the Rb-E2F model were involved with cyclin D activity. In addition, the

model was used to predict the time required for cell to reach the R-point under a variety of

stimulant conditions and gene mutations.

Introduction

Understanding a cell's decision to remain in quiescence or enter proliferation gives

valuable insight into diseases such as cancer. Critical to the study of quiescence and proliferation

is the R-point, which has been related to a number regulation activities for the mammalian cell

cycle (1, 6, 7, 8, 12). Previous research has shown that the start of cell proliferation from

quiescence is dependent on a bistable Rb-E2F gene network (9, 1 0). The bistable nature allows the

pathway to exist in two distinct states: An E2F-OFF state and an E2F-ON state. In the OFF state,

E2F activity is repressed and cells enter quiescence (non-proliferation). With enough serum

stimulation, cells enter the ON state, where E2F is active and cells proliferate. Furthermore, the

bistable Rb-E2F pathway is an ali-or-nothing response. Once a cell has passed the R-point in the

cell cycle, it will commit to proliferation even if growth-inducing stimulation is significantly

reduced.

The effect of serum stimulation on the Rb-E2F pathway has been explored in great detail,

with a simplified model for the pathway derived by Yao et al. in 2008 (Figure 1 ). This model

identifies the major biological species within the Rb-E2F pathway and their interactions with each

other. At the heart of this model is E2F, a family of genes that encode for cell growth and

replication (1 ). High E2F concentration and activity ultimately determined a cell's decision to enter

the cell cycle. The retinoblastoma tumor suppressor protein (Rb) is vital in its regulation of

inhibiting cell proliferation (2, 4, 5, 11 ). It accomplishes this regulation by binding to E2F

transcription factors, and as a result prevents the expression of genes on E2F responsible for the

G1 to S transition and DNA replication. Cyclin-dependent kinases (such as the cyclin D and cyclin

E complexes) are responsible for phosphorylating Rb in order to naturally stimulate cell replication

(8). Phosphorylation ofRb inactivates the protein, breaking up the Rb-E2F complex and inducing

E2F activity. Myc serves as a regulator gene that promotes entry into the cell cycle. Yao et al. also

provided a mathematical model of the Rb-E2F pathway in 2008 (9) (Figure Sl). This mathematical

model is composed of seven ordinary differential equations, which are defined by 24 parameters.

These parameters correspond to individual gene regulation events.

The experiments detailed in this paper involve systematically "mutating" (increasing or

decreasing) parameters for the purpose of understanding how they affect the following: 1) the

serum threshold required to promote the transition from the E2F-OFF state to the E2F-ON state

(the OFF-to-ON serum threshold), 2) the time required for a cell to reach the R-point in the cell

cycle under various serum stimulation conditions (the R-point time), and 3) the time required for

a cell to reach half-maximal E2F concentration (E2F half-activation) when given continuous serum

stimulation and given only sufficient serum stimulation to reach the R-point. In order to achieve

these goals, the computer program COP ASI was utilized (3), which allows for the concentration

of important biological species in a system to be monitored. COPAS! has two functions that were

invaluable in these experiments. The first, Parameter Scan, allows for multiple simulations to be

conducted where one input (such as serum concentration) is varying for each of the simulations.

This function enabled precise identification of the OFF-to-ON serum threshold and R-point time.

The second function, Time Course Scan, shows the concentration of biological species as they

change per unit time. This function facilitated the determination of E2F half-activation under a

variety of scenarios.

Experimental Methods

Determining the sensitivity of parameters in the Rb-E2F model

The computer program COP ASI was crucial in the sensitivity analysis of parameters in the

Rb-E2F model. The Rb-E2F mathematical model determined by Yao et al. in 2008 (9) (hereby

referred to as the base model) was entered into the program COPAS! (3). First, the OFF-to-ON

serum threshold of the base model was determined. A Parameter Scan was run, with serum

concentration ranging from 0 to 20% in intervals of 0.2%. For this scan, time was set to 1333

hours, the initial concentrations of all protein species were set to their E2F-OFF state

concentrations (as reported by Yao et al.), and all other settings in COPAS! remained at their

default values. The serum concentration at which E2F levels transitioned from the OFF to ON state

corresponded to the OFF-to-ON serum threshold.

All 24 parameters within the base model were evaluated in order to determine if they

displayed any significant effect on the OFF-to-ON serum threshold. To begin, the first parameter

in the system was mutated twice. During the first mutation, the parameter was increased by a factor

of 10. During the second mutation, the parameter was decreased by a factor of 10. After each

mutation for the parameter, a Parameter Scan was run, with serum concentration ranging from 0%

to 20% in intervals of 0.2%. All settings in COPAS! were exactly the same as during the previous

base model Parameter Scan. The data for each Parameter Scan was analyzed to determine the

concentration of the OFF-to-ON serum threshold, or if the threshold could not be observed in the

tested serum range. These steps involving the 1 0-fold mutation of a single parameter were repeated

for all 24 parameters. Any parameters that did not eliminate the OFF-to-ON serum threshold in

the tested serum range were labeled as non-sensitive parameters, and were excluded from all future

experiments.

Each of the remaining parameters (labeled "sensitive parameters") were analyzed to

determine their relative sensitivity in affecting the base OFF-to-ON serum threshold. One

parameter at a time was mutated by unique factor changes. These factor changes were distinctive

for each parameter, since each parameter displayed different relative sensitivity. The Slide tool in

COPAS! was used to quickly determine factor changes that would detail the gradual effects of

parameter mutations on the OFF-to-ON serum threshold. After each mutation on a parameter, the

Parameter Scan function was implemented to determine the concentration of the OFF-to-ON

serum threshold. The time of each Parameter Scan was set to 1333 hours, but the serum range and

serum intervals varied in order to maximize the resolution of results. However, the serum range

never exceeded 20% serum concentration. All other settings and concentrations matched those of

the previous threshold Parameter Scans.

Calculation of the R-point time using a serum pulse

A slightly modified base model was used to determine the time required to reach the R­

point under specific serum conditions. This model (hereby referred to as the base pulse model),

also supplied by Y ao et al., allows for serum concentration during a simulation to be changed after

a set time point. In all other regards, this model is identical to the aforementioned base model. For

these experiments, the concentration of serum began at an initial, high concentration (the "hi"

value), and was dropped to a lower concentration (the "low" value) after a serum pulse time. First,

the R-point time ofthe base pulse model was determined for a variety of different hi and low serum

concentrations (Table S 1 ). With serum defined by the hi and low values, a Parameter Scan was

run with the pulse time ranging from 0 to 10 hours in intervals of0.01 hours. The overall time of

the simulation was set to be 13 3 3 hours, the initial concentrations of all protein species were set to

their E2F-OFF state concentrations, and all other settings in COPAS! remained at their default

values. The lowest pulse time that resulted in the E2F-ON state being maintained at the end of the

simulation corresponded to the R-point time for the base pulse model.

Twelve sensitive parameters were mutated in order to determine the effect that each

mutation had on the R-point time. One parameter at a time was mutated by an appropriate factor

change that resulted in the OFF-to-ON serum threshold becoming 3.2% serum concentration.

Afterwards, the hi value was set to 20% serum concentration while the low concentration varied

(Table Sl). A Parameter Scan was run with the pulse time ranging from 0 to 50 hours in intervals

of 0.05 hours. All settings in COP ASI were exactly the same as during the previous base pulse

model Parameter Scan. Once again, the lowest pulse time that resulted in the E2F -ON state being

maintained at the end of the simulation corresponded to the R-point time for the mutated model.

Subsequent Parameter Scans were run with a smaller pulse time range, allowing for higher

resolution of results. These steps involving the serum pulse were repeated for all twelve parameters

mutations.

Because the low value for these experiments must be sufficient to only maintain the E2F­

ON state in the model, it is beneficial to determine the ON-to-OFF serum threshold for the base

model as well as for the twelve mutated models. For the base model ON-to-OFF serum threshold,

a Parameter Scan was run with serum concentration ranging from 0 to 20% in intervals of 0.2%.

Time was set to 1333 hours, the initial concentrations of all protein species were set to their E2F­

OFF state concentrations, and all other settings in COP ASI remained at their default values. The

concentration of protein species at 20% serum concentration was recorded. A second Parameter

Scan was run with serum concentration ranging from 0 to 5% concentration in intervals of0.005%.

The initial concentrations of protein species in this scan were set at the recorded values from the

previous scan, while all other settings remained unchanged. The ON-to-OFF serum threshold was

determined from this second scan. These steps were repeated for each of the twelve R-point

mutations in order to determine the ON-to-OFF serum threshold for each model mutation.

Determination of E2F half-activation time with and without continuous stimulation

The half-activation time of E2F was determined through two different methods. In the first

method, the base model and the serum pulse mutation models are given a continuous, unchanging

serum stimulation of 20% serum concentration. For all models, the Time Course function in

COP ASI was used to monitor E2F concentration at intervals of 1 hour for 1000 hours. The point

at which E2F concentration was at half-maximum was calculated. Subsequent Time Course scans

with smaller time ranges and intervals enhanced the resolution of the results. This first method of

determining E2F half-activation time was referred to as T 112.

In the second method, the base model and mutated models were given a serum pulse based

on the results of the serum pulse Parameter Scans. The hi value of this pulse was 20% serum

concentration, whereas the low value varied (Table S1). The length of the pulse was equivalent to

the determined R-point time for the base pulse model and the twelve serum pulse mutations. For

all models, the Time Course function in COP ASI was used to monitor E2F concentration at

intervals of 1 hour for 1 000 hours. The point at which E2F concentration was at half-maximum

was calculated. Subsequent Time Course scans with smaller time ranges and intervals enhanced

the resolution of the results. This second method of determining E2F half-activation time was

referred to as T I/2-RPoint.

Results and Discussion

As predicted by the Yao Rb-E2F model, mutations on a single sensitive parameter resulted

in at least one of two effects on the OFF -to-ON serum threshold. These two effects allow parameter

mutations to be classified as two different types. In the first type (Type I), the parameter mutations

increased the serum concentration of the OFF-to-ON threshold (Figure 3). As the magnitude of

the Type I mutations increased, so did the serum concentration of the OFF-to-ON threshold.

Because these mutations essentially raise the necessary stimulation required for cells to enter

proliferation, they can result in negative health conditions such as hindered tissue repair and

regeneration. In the second case (Type II), the parameter mutations decreased the serum

concentration of the OFF-to-ON threshold. The OFF-to-ON serum threshold decreased as the

magnitude of these mutations increased. The Type II mutations are opposite of the Type I

mutations; they lower the barrier required for cells to enter the cell cycle and proliferate. As a

result, Type II mutations are predicted to correspond to diseases such as cancer.

The results of all tested mutations on all sensitive parameters were summarized in a plot of

OFF-to-ON serum threshold concentration vs. parameter factor change (Figure 4). Since the base

values of all sensitive parameters vary greatly, factor change provides a uniform method of

comparing parameter mutations. All parameter curves intersect at the point (1, 0.8), as this point

matches the OFF-to-ON serum threshold (0.8%) of the base model (factor change of 1). Points

above 0. 8% serum concentration (approximately the upper half of the graph) correspond to specific

parameter mutations that increase the serum threshold, or Type I mutations. Certain parameters

show Type I mutations when increased (e.g. dCD, kDP), whereas other parameters show Type I

parameters when decreased (e.g. k:P, dCE). Points below 0.8% serum concentration

(approximately the bottom half of the graph) correspond to specific parameter mutations that

decrease the serum threshold. As with Type I mutations, Type II mutations occur when certain

parameters are increased only (e.g. kCD, kP) or when others are decreased only (kR, dCD).

The relative sensitivity of each of the sensitive parameters on the OFF-to-ON threshold can

be approximated by the slope of the corresponding curves. Steep curves imply that relatively small

factor changes result in relatively large changes in the OFF-to-ON serum threshold concentration.

Shallow curves, on the other hand, imply the opposite. Altogether, these results predict the

likelihood that mutated processes in the Rb-E2F system will cause deleterious effects on a cell.

The parameters dCD (the rate at which cyclin D degrades) and kP (the rate ofRb phosphorylation

by both cyclin D and E) display the highest sensitivity of all parameters both when increased and

when decreased. Thus, mutations that affect these rates by a seemingly minor degree are predicted

to have large effects on a cell's decision to enter proliferation. Mutations to less sensitive

parameters, such as dR (the rate at which Rb degrades), would need to be large in magnitude in

order to significantly skewing the OFF-to-ON serum threshold. In addition, understanding how

sensitive parameters may be associated with mutations in proliferative diseases can suggest

potential therapeutic targets.

The relative sensitivity of parameters on the OFF-to-ON threshold was displayed on the

simplified Rb-E2F model from Y ao et al. (9) (Figure 5). In this model, the relative sensitivity of a

single parameter is ranked based on how the 0 FF -to-ON serum threshold changes when that single

parameter is increased only. Most of the parameters that display high sensitivity when increased

involve cyclin D interactions. As a result, the Yao Rb-E2F mathematical model suggests cyclin D

as a relatively sensitive protein. Mutations that affect the concentration or interactions of the

protein tend to drastically change the OFF-to-ON serum threshold. Thus, proper cyclin D activity

is crucial for maintaining normal cells, and minor mutations that overstimulate cyclin D activity

can easily lead to cancerous cells.

As previously noted, a cell's decision to enter the cell cycle and proliferate is an ali-or­

nothing response (9). Once a cell is sufficiently stimulated and crosses the R-point, the cell

commits to proliferation even if the original stimulant is significantly decreased (Figure 2). The

Yao Rb-E2F mathematical model was used to analyze and determine the minimum time required

to reach the R -point under a variety of serum conditions (Table 1, Table S 1 ). For this process, the

model was pulsed with a high serum concentration, and then the serum concentration was lowered

after a specific period of time. Because it was necessary for the high pulse concentration to

stimulate the model into the E2F-ON state (proliferation), the initial pulse was required to be

greater than the OFF-to-ON serum threshold. The low concentration, on the contrary, had to be

sufficient to only maintain the E2F-ON state, but not high enough to alone transition the model

from the E2F-OFF to E2F-ON state. Thus, the low concentration had to be lower than the OFF­

to-ON serum threshold (i.e. not high enough to induce proliferation) but higher than the ON-to­

OFF serum threshold (i.e. sufficient to maintain proliferation once the R-point was crossed). With

this setup, there exists a minimum pulse time required for the Rb-E2F model to reach the E2F-ON

state. This minimum pulse time corresponds to the necessary time for cells to reach the R -point

under certain serum conditions. Under these conditions, it was observed in COP ASI simulations

that E2F concentration would increase over time during the serum pulse (Figure 7). Once the pulse

was lowered to the maintenance concentration, E2F concentration would initially decrease. If the

system had passed the R-point though, E2F concentration would rebound and reach E2F-ON state

levels.

For the base model, the R-point time decreased as the high pulse concentration and low

maintenance concentration were both increased (Table 1, Figure 8). Thus, R-point time is reliant

on both the high and low serum concentrations. Furthermore, twelve parameter mutations were

applied to the model to determine the effects on the R-point time. All of these mutations increased

the OFF-to-ON serum threshold to the same value (3.2% serum concentration), in order to remove

the OFF-to-ON serum threshold as a potential factor affecting R-point time. The high

concentration remained constant (20% serum concentration) while the low concentration was

tested at different concentrations. In all mutated models, increasing the maintenance concentration

decreased the R-point time (Figure 8). However, for most mutated models, the decreases in R­

point time showed diminishing returns. In other words, linearly increasing the maintenance

concentration did not linearly decrease the R-point time. In comparable serum conditions, mutated

models displayed higher R-point times than the base model. No trend between parameter

sensitivity and R-point time was discerned.

In simulations where the Rb-E2F model transitioned from the E2F-OFF to E2F-ON state,

the time required for E2F to reach half of its maximal concentration was measured under a variety

of conditions (Table 1, Table S1). Two methods of measuring E2F half-activation time were

conducted. In the first method, the Rb-E2F model was given continuous, unchanging serum

stimulation equivalent to the high concentration used during the R-point simulations. The time to

E2F half-activation under these conditions was denoted as T 112. In the second method, the Rb-E2F

model was pulsed in the same manner as during the R-point simulations. The length of the high

concentration serum pulse was set to be the appropriate R-point time, given specific high and low

serum concentrations. The time to E2F half-activation under these conditions was denoted as T 112-

RPoint, and corresponds to the E2F half-activation time of the model when it is given only sufficient

stimulation to reach the R-point. Both of these half-activation values were calculated for the Yao

Rb-E2F base model and the twelve mutated models from the R-point time experiments.

Given continuous stimulation of20% serum concentration, the base model predicted a T112

of 5.9 hours (Table 2). As expected, decreasing the serum concentration resulted in the T112

decreasing as well, although not in a linear fashion. At high concentrations of serum, it is likely

that the model is almost fully stimulated. Raising the concentration of serum even further, as a

result, is suggested to have little effect in accelerating the transition to the E2F-ON state. This can

be considered analogous to Michaelis-Menten enzyme kinetics, where enzymatic velocity begins

to plateau as the enzyme becomes fully saturated by increasing substrate concentration. Comparing

the values of T 112 and T 112-RPuise for all models and serum concentrations, T 112 was always lower

than T 112-RPulse. This can be explained by considering the differences between T 112 and T 112-RPulse.

While Tt/2-RPuise is measured by giving the Rb-E2F model just enough stimulation to reach the R­

point, T 112 is measured by giving the model continuous, high stimulation, even when the model

has reached the R-point. Accordingly, it is unsurprising that continuous stimulation (T112)

accelerates the transition between the E2F-OFF and E2F-ON states.

For all of the models examined, as the maintenance concentration continued to increase

while the pulse time continued to decrease, all models showed increases in T I/2-RPulse. In most of

the models (e.g. mutated dCD, mutated dRE, and base models), this increase in T112-RPuise was

drastic. This suggests that while higher maintenance concentration does lower the time to E2F

half-activation, a more important factor is the time in which cells are incubated with a high

concentration of serum. Longer incubation time is likely to rapidly increase the concentrations of

other protein species that promote E2F activity, such as cyclin D and E. Once the serum

concentration is dropped to a maintenance level, the high concentrations of these E2F-promoting

proteins accelerates the E2F half-activation time. This acceleration, as predicted by the model, is

greater than if the cells were given less incubation time but a greater maintenance serum

concentration.

While extensive simulations were performed in studying the OFF-to-ON serum threshold,

only a few simulations were conducted to determine the ON-to-OFF serum threshold

(corresponding to cells exiting proliferation and entering quiescence). The ON-to-OFF serum was

determined for the Yao Rb-E2F base model, as well as for the twelve mutated models used in

examining R-point time (Table 1, Table Sl). Compared to the base model, all mutated models

displayed higher ON-to-OFF threshold. The exact value of the ON-to-OFF threshold varied by

mutation, and no trend could be linked to OFF-to-ON sensitivities of the parameters nor to the

determined R-point times. Further studies involving the Yao Rb-E2F model may include more

simulations involving the ON-to-OFF serum threshold, akin to those conducted for the OFF-to­

ON serum threshold.

References

1. Attwooll, C., Lazzerini Denchi, E. & Helin, K. The E2F family: specific functions and

overlapping interests. EMBO J 23,4709-4716 (2004).

2. Burke, Jason R.; Hura, Greg L.; and Rubin, Seth M. Structures of inactive retinoblastoma

protein reveal multiple mechanisms for cell cycle control. Genes & Development 26, 1156-

1166 (2012).

3. Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes,

P ., and Kummer, U. (2006). COPAS!- a COmplex PAthway Simulator. Bioinformatics

22,3067-74

4. Lee, Changwook; Chang, Jeong Ho; Lee, Hyun Sook; and Cho, Yunje. Structural basis for

the recognition of the E2F transactivation domain by the retinoblastoma tumor suppressor.

Genes & Development 16, 3199-3212 (2002).

5. Liu, Xin and Marmorstein, Ronen. Structure of the retinoblastoma protein bound to

adenovirus E1A reveals the molecular basis for viral oncoprotein inactivation of a tumor

suppressor. Genes & Development 21, 2711-2716 (2007).

6. Pardee, A. B. A restriction point for control of normal animal cell proliferation. Proc. Nat!

Acad. Sci. USA 71, 1286-1290 (1974).

7. Sears, R. C. & Nevins, J. R. Signaling networks that link cell proliferation and cell fate. J

Biol. Chern. 277, 11617-11620 (2002).

8. Sherr, C. J. & Roberts, J. M. CDK inhibitors: positive and negative regulators of G 1- phase

progression. Genes Dev. 13, 1501-1512 (1999).

9. Yao, G.; Lee, T.J.; Mori, S.; Nevins, J.R; & You, L. A bistable Rb-E2F switch underlies

the restriction point. Nat Cell Biol10, 476-482 (2008).

10. Yao, G.; Tan, C.; West, M.; Nevins, J.R.; & You, L. Origin of bistability underlying

mammalian cell cycle entry. Mol Syst Bio/7 (2011).

11. Xiao, Bing; Spencer, James; Clements, Adrienne; Ali-Khan, Nadeem; Mittnacht, Sibylle;

Broceno, Cristina; Burghammer, Manfred; Perrakis, Anastassis; Marmorstein, Ronen; and

Gamblin, Steven J. Crystal structure of the retinoblastoma tumor suppressor protein bound

to E2F and the molecular basis of it regulation. PNASvol. 100, 5, 2363-2368 (2003).

12. Zetterberg, A. & Larsson, 0. Kinetic analysis of regulatory events in G 1 leading to

proliferation or quiescence of Swiss 3T3 cells. Proc. Nat! Acad Sci. USA 82, 5365-5369

(1985).

Growth Signals I

1 1 CycD '

-~ 1

1~ ........... CycE

1 ~ ~

DNA Replication

Figure 1. Simplified model ofthe bistable Rb-E2F pathway, reproduced from Yao et al. 2008 (9).

(A) 1.4

E2F-ON State 1.2

c 1 0

·.;::; ro

~ 0.8 QJ u § 0.6 u u..

[;j 0.4

0.2

E2F-OFF State 0

0 0.5 1 1.5 2 2.5

Serum Concentration

(B) 1.4

E2F-ON State 1.2

c 1.0 0

:;::; ro

~ 0.8 QJ u § 0.6 u LL.

[;j 0.4

I E2F-0.2 1

oFF State

0.0 0 0.5 1 1.5 2 2.5

Seru m Co ncentrat io n

Figure 2. (A) The transition from the E2F-OFF to E2F-ON state in the Rb-E2F system, as

simulated by COP AS I. Serum concentration is increasing, and the large jump in E2F concentration

represents the OFF-to-ON serum threshold. (B) The transition from the E2F-ON to E2F-OFF state

in the Rb-E2F system, as simulated by COPAS!. Serum concentration is decreasing, and the large

fall in E2F concentration represents the ON-to-OFF serum threshold. The difference between the

OFF-to-ON and ON-to-OFF thresholds cotTesponds to maintenance concentrations, levels of

serum that are not sufficient to stimulate the E2F -ON state but can maintain the state once it has

been reached.

1.4

1.2 r:: 0 1 . ., .. E o.8 " g 0.6 u :::; 0.4 w

0.2

0 0

Base Model {dCD = 1.5)

1.4

1.2

0.8

0.6

0.4

0.2

dCD x1.2 {dCD = 1.8)

r::

1.4

1.2

~ 1 I! E 0.8 " g 0.6 u fj 0.4

0.2

dCD x1.4 {dCD = 2.1)

0 .. ---.----.----,---,----, 0 --~-.---..---~---.----, 10 15 20 25 0 10 15 20 25 0 10 15 20 25

Serum Concentration Serum Concentration Serum Concentration

dCD x1.57 {dCD = 2.355) dCD x1 .59 {dCD = 2.385)

1.4 1.4

1.2 1.2 c: ~ 1 I!! E 0.8

" " ~ 0.8

g 0. 6 u

~ 0.6

~ 0.4 0.4

0.2 0.2

0 0 0 5 10 15 20 25 0 10 15 20 25

Serum Concentration Serum Concentration

Figure 3. COPAS! simulations that display how the OFF-to-ON serum threshold changes as the

parameter dCD in the Yao Rb-E2F model is mutated. The mutations shown only involve increasing

the value of dCD. Serum concentrations range from 0 to 20%.

...,._dCO -·(£ -·· -·· ~dRE

- kCD

- kCOS

- kC£

...,._ k.DP _ ., _ , - kPl

~k.Pl ---..

Figure 4. The overall results of the sensitivity analyses of sensitive parameters on the OFF-to-ON

serum threshold. Each of the sensitive parameters were systematically increased and decreased,

and the position of the OFF-to-ON serum threshold was recorded for each mutation. Steeper curves

suggest relatively high sensitivity parameters, whereas shallower curves suggest relatively low

sensitivity parameters. The axes of the plot, serum concentration of OFF-to-ON threshold vs.

factor change, are logarithmically scaled.

Growth Signals

1 ~ KS~j~kCDS t ./dCD

---.:.___. eyeD '

KCD '--~ ~1 ' kPl kE~ dR .. kDP

'y ~ kRE Rb

" '.jR KE

E~J~E \ ., dE / 1 0~~

kCE dCE

DNA Replication

Figure 5. The simplified Rb-E2F model from Figure 1, with model parameters included in

appropriate positions showing their effect on the system. Each parameter is represented by an

arrow or bar, corresponding to how increasing a parameter affects a specific process in the Rb-

E2F model. The thickness of the arrows and bars qualitatively reflects the sensitivity of the

matching parameter when that parameter is increased only (i.e. this Figure does not reflect the

sensitivity of parameters when they are decreased).

Cell ~ •

Quiescence

A-point

E2F-OFF State Proliferation

E2F-ON State Figure 6. Visual description of the R-point in relation to cell quiescence and proliferation,

reproduced from Yao et al. 2011 (9). In this description, cells exist in one oftwo states, quiescence

and proliferation, as represented by the two wells (cell apoptosis is ignored). For cells to transition

from quiescence to proliferation, serum stimulation must be sufficient overcome the R-point

banier.

1.2

1

0.8

0.6

0.4

0.2

0

0 20 40 60 80 100 120 140 h

Figure 7. Concentration ofE2F over time when the Rb-E2F system is given a semm pulse that is

only sufficient for the system to overcome the R-point, as simulated in COPAS!. After the pulse

time R, serum concentration is lowered to a maintenance value (only sufficient to maintain the

E2F-ON state once the R-point has been passed). E2F concentration increases over the time of the

pulse. Once the pulse is ended and semm concentration is lowered, E2F concentration initially

decreased but eventually recuperates and rises to E2F-ON state levels.

.2! 2 <Q z 0 .<:: "' .S "' 2 .8 Q)

"' :; 0.. ~ E ;:)

:::> 0 Q; E. If)

0 Q)

E i= E ;:)

E ·c: 2 Q)

;; cr'

35

lO

15

20

l5 --=---..

10

05 1.5

Maintenance Serum Concentration

2.5

--+- cKO

~dRE

~ t;co

>COS

......... ---"'1 ......... -a-UlE

--+- K5

-a- St.-.dard (Hi"' I)

~ Sta1dard {Ht:olO)

-, StJndard (Hiz20)

Figure 8. Plot of the R-point time (lu:) vs. the maintenance serum concentration(%). In all ofthe

mutated models, the serum concentration of the pulse is 20%. For the base model (denoted as

"Standard"), the serum concentration of the pulse is either 1%, 10%, or 20%, as noted in the legend.

For all cases, as maintenance serum concentration is decreased, the R-point time decreases as well.

Minimum T1me of Serum Pulse{R) to E2FHalf·

ElF Half· Reach and Actlvatlon Time

Orictnaf Parameter Value Off.to-ON Serum ON-tcKlFF Serum Adivationnme Maintain E2f.ON with Serum Pulse Parameter Parameter Value Factor ChanR:e xF.C. Threshold Threshold h<l Pulse HI Value Pulse low Value Statelh<l h<l dCD 1.5 1.416 2.124 3.2 0.357 14.85 20 0.5 15.06 26.75

1.5 1.416 2.124 3.2 0.357 14.85 20 0.7 13.675 23.5 1.5 1.416 2.114 3.2 0.357 14.85 20 12.9 28.8

1.5 1.416 2.124 3.2 0.357 14.85 20 1.4 12.225 33 15 1416 2114 32 0 357 14 85 20 15 12 05 3871

dRE 0.03 4.538 0.13614 3.2 0.516 8.69 20 0.5 N/A N/A 0.03 4.538 0.13614 3.2 0.516 8.69 20 0.7 7.625 30 0.03 4.518 0.13614 3.2 0.516 8.69 20 1 5.85 25.64

0.03 4.538 0.13614 3.2 0.516 8.69 20 1.4 4.6 24.59

0.03 4.538 0.13614 3.2 0.516 8.69 20 1.5 4.325 35.35 Standard 0.79 0.2425 21.95 0.3 21.325 33.6

0.79 0.2425 21.95 0.5 19.425 33.43 0.79 0.2425 21.95 0.7 13.15 103.7

0.79 0.2425 6.11 10 0.3 6.87 22.71 0.79 0.2425 6.11 10 0.5 3.9 22.95 0.79 0.2425 6.11 10 0.7 2.18 103.1

0.79 0.2425 5.9 20 0.3 6.73 22.4 0.79 0.2425 5.9 20 0.5 3.72 31.09

0.79 0.2425 5.9 20 0.7 2.05 103.7

Table 1. Portion of the overall serum pulse results (full table: Table Sl). This table shows three of

the examined models, the base model and models were dCD and dRE are mutated. For the mutated

models, the mutated parameter was adjusted so that the OFF -to-ON serum threshold was 3 .2%.

The serum concentrations of the pulses are given as the "Pulse Hi Value," whereas the maintenance

serum concentrations are given as the "Pulse Low Value." The values for the R-point times, T112,

and TI/2-RPulse are shown, determined by COPAS! simulations.

E2F Half-Mutated Activation Time Parameter (hr) dCD 14.85

dRE 8.69

KCD 18.65

kCDS 16.21

kDP 20.98

kE 16.58

KE 25.9

kP1 15.84

kP 22.23

kRE 18.45

KS 6.59

kR 30.54

Standard (S = 1) 21.95

Standard (S = 10) 6.11

Standard (S = 20) 5.9 Table 2. Table relating the base model and each of the mutated models (listed by the parameter

that was mutated) with the appropriate measured E2F half-activation time (T 112), given continuous

serum stimulation. The concentration of serum stimulation was 20% for all mutated models. For

the base model, T 112 was measured when serum stimulation was 1%, 10%, and 20%.

Supplementary Materials

d([M]· Vcompartment)

dt ( kM·[S)) - +V .

- compartment KS + [S]

- V compartment · ( dM · [M])

d (CE] · V compartment) d t = - V compartment · C dE· [E])

+V ·(kE·~·_j.§__+ kb·[M]) compartment KM+[M] KE+[E] KM+[M]

+V • +--~~~~ (

kPl·[CD] ·[RE] kP2 ·[CE] ·[RE]) compartment KCD + [RE] KCE + [RE]

- V compartment ·(kRE ·[R] ·[E))

d([CD]·Vcompartment) = +V .,kCDS·[S)) d t compartment KS + [S]

- V compartment·( dCD ·[CD])

+V ·( kCD·[M]) compartment KM + [M]

d (CCE] · V compartment) d t = - V compartment·( dCE '[CE])

+V ·(kCE·[E)) compartment KE + [E]

d (CR] · V compartment) = -V compartment·( dR ·[R])

dt

+Vcompartment '(kR)

- V compartment ·(kRE·[R] ·[E))

_ V ·( kPl '[CD] ·(R] + kP2 ·[CE] ·[R]) compartment KCD + [R] KCE + [R]

+V ·( kDP·[RP] ) compartment KRP+[RP]

d([RP]· vcompartment) d t = - V compartment · ( dRP · [RP])

+ v . +--=--=-~..::. (

kPl·[CD] ·[RE] kP2 ·[CE] ·[RE]) compartment KCD +[RE] KCE + [RE]

+V . + (

kPl·[CD) ·[R) _kP_2-=.·[C_E..::..) ·-=-[R...::.)) compartment KCD+[R] KCE+[R]

( kDP ·[RP] )

-Vcompartment' KRP+[RP]

d (CRE] · v compartment) d t = - V compartment·( dRE '[RE])

_ V ·( kPl'[CD] ·[RE] + kP2 ·[CE] ·[RE]) compartment KCD + [RE] KCE + [RE]

+V compartment ·(kRE·[R]·[E])

Figure Sl. The Yao Rb-E2F mathematical model (9).

dRE

KCD

kOP

kE

KE

kP1

kP

kRE

KS

Standard

1.5

1.5

1.5

15

0.03

0.03

0.03 0.03

0.03

0.92 0.92

0.92

0.92

092

0.45

0.45

0.45

0.45

0.45

3.6 3.6 3.6 3.6

36 0.4

0.4

0.4

0.4 0.4

0.4

0.4

0.4 0.15

0.15

0.15

0.15

015

18

18

18

18

18

18

18

18

18

18

180 180

180 180 180 0.5

0.5

0.5

0.5

05

0.18

0.18 0.18

0.18

0.18

1.416

1.416 1.416

1416

4.538 4.538

4.538

4.538

4.538

1.7658

1.7658

1.7658

1.7658 17658

0.689451111

0.689451111

0.689451111

0.689451111

0.689451111

1.5586

1.5586

1.5586 1.5586 15586

0.3398

0.3398

0.3398

0.3398

0.3398

0.3398

0.3398

0.3398

2.6695 2.6695 2.6695

2.6695

2 6695

0.7093

0.7093

0.7093

0.7093

0.7093

0.7265

0.7265 0.7265 0.7265

07265 3.403

3.403

3.403

3.403

3.403

4.0908

4.0908

4,0908

4.0908

40908

9.43 9.43

9.43

9.43

9.43

2.124

2.124

2.124

2.124

0.13614

0.13614

0.13614 0.13614

0.13614

1.624536

1.624536

1.624536 1.624536

16245:16

0.310253

0.310253

0.310253

0.310253 0.310253

5.61096

5.61096

5.61096 5.61096

5.61096

0.13592

0.13592

0.13592

0.13592

0.13592

0.13592

0.13592

0.13592

0.400425

0.400425

0.400425

0.400425

0400425

12.7674

12.7674

12.7614

127674

12.7674

13.077

13.077

13.077

13.077

13077

612.54

612.54

612.54

612.54 612.54

2.0454

2.0454

2.0454 2.0454

20454

1.6974

1.6974

1.6974

1.6974

1.6974

3.2

3.2

3.2

32

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

32

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

32

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

32

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

32

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

3.2

32

3.2

3.2

3.2

3.2

3.2

0.79

0.79

0.79 0.79

0.79

0.79

0.79

0.79

0.79

0.357

0.357

0.357

0 357

0.516

0.516

0.516 0.516

0.516

0.297

0.297 0.197

0.297 0 297

0.339

0.339

0.339

0.339 0.339

0.927

0.927

0.927

0.927

0927

1.638 1.638

1.638

1.638

1.638 1.638

1.638

1.638 0.717

0.717

0.717

0.717

0717 0.354

0.354

0.354

0.354

0.354

0.66 0.66

0.66

0.66

066

0.282 0.282

0.282

0.282

0.282

0.936

0.936

0.936

0.936 0936

0.699 0.699

0.699

0.699

0.699

0.2425

0.2425

0.2425

0.2425 0.2425

0.2425

0.2425

0.2425

0.2425

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

1

10

10 10

20

20

20

0.7

1.4

15

0.5

0.7

1.4 1.5

0.5

0.7

1.4

15

0.5

0.7

1.4

1.5

0.5

0.7

1.4

15

0.5

0.7

1.4

1.5

1.7

2.4

0.5

0.7

1.4

15

0.5

0.7

1.4

1.5

0.5

0.7

1.4

15

0.5

0.7

1.4 1.5

0.5

0.7

1.4

15

0.5

0.7

1.4

1.5

0.3

0.5 0.7

0.3 0.5

0.7

0.3 0.5

0.7

12.9

12.125

12 05

N/A 7.625

5.85

4.6

4.325

17.9

17.05

16.4

15.6 15 3

15.9

14.775 14.075

13.375

13.175

N/A N/A

23.825

19.275

18 8

N/A N/A N/A N/A N/A 33.2

19.8

12.55

N/A

N/A 27.21

23.45 227

15.75

14.45

13.725

13.05 1285

N/A 26.7

21.125 19.775

1945

17.725 16.925

16.425 15.95

15.8

N/A N/A 11.9

6.05

5 625

N/A 47.65

29.73

27.36

26.7

21.325

19.425

13.15

6.87

3.9

2.18

6.73

3.72 2.05

1.0366

1.08536

1.11836

1.1239

N/A 0.601865

0.71121

0.794011 0.805869

0.988337

1.04691

1.09203

1.12281

112505

0.976806

1.03933

1.08713

1.11958

1.12505

N/A N/A

0.911707

0.985412

0 996887

N/A N/A N/A

N/A N/A

0.155106

0.168815

0.191788

N/A N/A

0.812121

0.846443

0779487

0.9735

1.0374

1.08605 1.11898

1.12453

N/A 0.923011

1.00487

1.05546

0 795234

1.02677

1.08305

1.12616

1.15544

1.16035

N/A

N/A 0.845503

0.950668

0.968431

N/A 0.905116

0.994

1.0668

0.655833

0.913455

1.03583

0.44893

0.913455

1.03582

0.607185 0.913455

1.03583

0.448448

Table Sl. Table displaying all results of the serum pulse simulations.

1.0366

1.08536 1.11835

1.1239

N/A 0.601799

0.721192 0.794003

0.80586

0.988334 1.04691 1.09203

1.1218

111799 0.976802

1.03933

1.08713

1.11958

1.12503

N/A N/A

0.911631

0.985351

0996774

N/A N/A

N/A N/A N/A

0.176652

0.192069

0.204425

N/A N/A

0.812075

0.854845 0 861759

0.973495

1.03739

1.08605 1.11898

1.12452

N/A 0.922971

1.00486

1.0554 106357

1.02677

1.08305

1.12616

1.15543

1.16036

N/A N/A

0.845496

0.950665

0.968428

N/A 0.905842

0.993996

1.04738

1.05595

0.913452

1.03582

1.09032

0,913453

1.03582

1.09032

0.913453

1.03582 1.09032

23.5 28.8

33

38 71

N/A 30

25.64

24.59

35.35

27.5 23.8

28.8

33

38 69

27.4

24.01

23.53

41.07

60.18

N/A N/A

52.02

56.7

65 7

N/A N/A N/A N/A N/A

191.4

176.55

174.55

N/A

N/A 64

88.6

97 85

27.17

25.32

24.36

31.49

53.45

N/A 47.71

37.8

63.91

102 28

26.9

23.49 22.6

49.7

62.89

N/A N/A 27,5

19.65

184

N/A 74.88

60.03

98.75

104.39

33.6

33.43 103.7

22.11 22.95

103.1 22.4

31.09

103.7

14.85 14.85

14.85

14 85

8.69 8.69 8.69

8.69 8.69

18.65

18.65

18.65 18.65 1865 16.21

16.21

16.21

16.21

16.21

20.98

20.98

20.98

20.98

2098

16.58

16.58

16.58

16.58

16.58

16.58

16.58 16.58

25.9

25.9

25.9

25.9

259

15.84 15.&4

15.84

15.84

15.84

22.23 22.23

22.23

22.23

22 23

18.45

18.45 18.45

18.45

18.45

6.59

6.59 6.59

6.59

6 59 30.54

30.54 30.54

30.54

30.54

21.95 21.95

21.95

6.11 6.11

6.11

5.9

5.9 5.9

1.19701 1.19701

119701

0.955993

0.955993

0.955993 0.955993 0.955993

1.19697

1.19697

1.19697

L19697

119697

1.19721

1.19721

1.19721 1.19721

1.19721

1.12898

1.12898

1.12898

1.12898

112898

0.24754

0.24754

0.24754

0.24754

0.24754

0.24754

0.24754 0.24754

0.947634

0.947634 0.947634

0.947634

0 947634

1.19749

1.19749

1.19749

1.19749

1,19749

1.16445 1.16445

1.16445 1.16445

116445 1.22539 1.22539 1.22539

1.22539 1.21539

1.121321

1.121321

1.121321

1.121321

1121321 1.16075

1.16075

1.16075 1.16075

1.16075

1.13229

1.13229

1.13229

1.22417 1.22417 1.22417

1.22.944

1.22944

1.22944

Par3met~r BasecValu~btYaoRb- Description 'EZFMoilel

kE 0.4 11Mihr Synthesis rate ofE2F by Myc and E2F autocatalysis kM 1.0 !lMihr Synthesis rate of Myc by growth factors kCD 0.03 !lMihr Synthesis rate of Cyclin D by Myc kCDS 0.45 11Mihr Synthesis rate of Cyclin D by growth factors

kR 0.18l1M/hr Constitutive synthesis mte of Rb

kRE 180 11M/hr Synthesis rate of the Rb-E2F complex from interactions between Rb and E2F

kb 0.003 f.!M/hr Basal synthesis rate of E2F by Myc

kCE 0.35 !lMihr Synthesis rate of Cyclin E by E2F

dM 0.7/hr Degradation rate ofMyc

dE 0.25/hr Degradation rate of E2F

dCD 1.5 /hr Degradation rate of Cyclin D

dCE 1.5 /hr Degradation rate of Cyclin E

dR 0.06 /hr Degradation rate ofRb

dRP 0.06 /hr Degradation rate of phosphorylated Rb

dRE 0.03 /hr Degradation rate ofRb-E2F Complex

kP1 18 /hr Phosphorylation rate ofRb by Cyclin D

kP2 18/hr Phosphorylation rate ofRb by Cyclin E

kP 18 /hr Composite of both kP1 and kP2

kDP 3.6 !lMihr Dephosphorylation rate ofRb

KM 0.15 11M Half-occupation constant of Myc

KE 0.15 pM Half-occupation constant ofE2F

KCD 0.92 11M Half-occupation constant of Cyclin D

KCE 0.92 11M Half-occupation constant of Cyclin E

KRP 0.01 11M Half-occupation constant of phosphorylated Rb

KS 0.5 !lMihr Half-occupation constant of growth factors Variable·. Initial Concentr.ation Description

M 011M Myc

E 011M E2F

CD 011M CyclinD

CE 011M Cyclin E

R 011M Retinoblastoma protein (Rb)

RP 011M Phosphorylated Rb

RE 0.55 11M Rb-E2F Complex

Table S2. Base values and descriptions of all parameters in the Yao Rb-E2F mathematical model (9).