Discussion:
G2
Checkpoint
in
Frog
Cell
After
completing
the
exercise
on
the
G2
checkpoint
in
the
frog
cell,
the
students
had
a
lively
discussion
of
what
the
results
of
the
various
simulations
meant.
The
next
day,
I
requested
them
to
try
to
reproduce
their
ideas
of
the
previous
day
(plus
any
further
insights)
in
writing.
The
purpose
of
collecting
this
information
was
to
capture
the
in‐class
discussion,
as
best
I
could,
and
reproduce
it
for
future
reference.
I
have
used
the
answers
almost
verbatim.
When
presented
as
an
answer
from
more
than
one
student,
the
answer
represents
a
consensus
and
is
copied
from
the
easiest
answer
to
understand.
1. Using graphs of the model output:
a. What biological behaviors regarding the cell cycle in frog egg extracts are
reproduced by these simulations?
Victor: The biological behaviors regarding the cell cycle in the frog egg extracts
are entry of the cell into mitosis due to repeated increases and decreases of (MPhase promoting factor.)
Ilya/Hyuki/Adiba/Jesse/Samantha/Ziping/Fred/Elzara/Tamara: The
simulations show creation and destruction of cyclin and MPF regulate the cell
cycle at the G2 checkpoint, where MPF and pre-MPF regulate DNA synthesis
and mitosis in the frog cell.
Mate: We are seeing the concentrations of MPF, cyclin, and other molecules tjat
are responsible for pushing the cell cycle into mitosis, and the cycling of the
concentrations.
Jason: The amount of cyclin at a given point reacts with different enzymes, to
signal different stages in cell division.
Ann-Marie/Danny: The G2 checkpoint is the point at which the cell will make
sure DNA is accurately replicated before entering mitosis.
Elzara/Alex: It also shows the apc-cyclin feedback loop.
Alex: The APC peaks about when the cyclin (MPF & pre-MPF) reaches a
minimum (and vice versa).
b. In what order do the peaks in pre-MPF and MPF occur in each cell cycle?
All: pre-MPF first, then MPF
Jesse: Even though the cyclin and cdk combine to make MPF, the wee1 and
cdc25 feedback loops cause it to become pre-MPF and the pre-MPF peaks first.
Ilya: Thatʼs because at first Cdc25 and Wee1 are unphosphorylated and favor
the creation of pre-MPF over MPF. This switches as more of the enzymes
become phosphorylated.
c. What happens to the oscillations in MPF activity if you change the rate of
cyclin synthesis to 1? to 0.2? to 0.05?
Ziping/Truong/Hyukin/Jesse/Samantha/Victor/Alex/Tamara: The period of
MPF oscillation increases.
Nagy: The lower the cyclin synthesis rate, the more gap between the MPF peaks
(and therefore MPF activity). At 0.05, the rate is too low, and cycling never
happens.
Fred: Hereʼs a graph of the length of the cycles.
K1
1
0.5
.2
Time “length” of cycle
~50
~98
~208
Ann-Marie/Jason/Jesse/Ilya/Danny: So, if K1 (rate of cyclin synthesis) is
changed from 0.5 to k1=1 -> the frequency nearly doubles/amplitude is similar
K1=0.2-> the frequency is longer so a period is “slower”.
K1=0.05-> MPF activity no longer oscillates.
Jason: At .05 rate, the curve reaches a plateau around 9.00 concentration and
does not oscillate.
Ilya/Jesse: We found that oscillations occur of 0.082 < k1 < 2.9. Within this
range, a higher k1 increases frequency and lower k1 decreases frequency (wants
for MPF to reach threshold). If k1 > 2.9, cyclin never gets degraded faster than
created and if k1 < 0.082 it never gets created > degraded. Either way, the rates
donʼt switch and it doesnʼt cycle.
Adiba/Elzara: The peaks change as well, they get lower with lower cyclin
synthesis.
2. In 1990, Solomon et al. published a study in which extracts were treated with
cycloheximide (to block protein synthesis) and supplemented with fixed amounts
of a mutant, non-degradable form of cyclin B (Δcyclin B). Simulate this
experiment.
We set the parameters as follws:
k1 = V2’ = V2” = 0
Initial conditions: set all species = 0, except cyclin = 5, 10, 15, 20, …
b. What is the minimal threshold concentration of cyclin required to activate
MPF?
Consensus: 16.281
c. Why do you think this cyclin threshold exists? (The “purpose” answer or the
“mechanism” answer, or both)
By purpose:
Ziping: A switch of cell mitotic control
Tamara: Maintains mitotic cycle
Jesse: This threshold exists to provide the switch-like mechanism that allows or
prohibits the cell from entering mitosis.
Alex: I’m not sure, but I think this ensures that MPF is activated (and when
mitosis begins) only when enough cyclin is present.
Fred: The threshold exists to provide a clear signal that G2 checkpoint was
successful and mitosis should proceed. Sigmoid-shaped response curves make
good signal indicators and underlie bistable behavior.
Ilya: As to the purpose, it’s the build up of cyclin signals cells ready for M phase.
This threshold serves as an on/off switch for mitosis.
By mechanism:
Hyukin: Since the parameters K1=V21=V22=0, the reaction between MPF and
pre-MPF depends on the amount of cyclin and parameters kwee and k25. The
cell can control the activation or deactivation of MPF by having a threshold of
cyclin.
Jason/Danny: A minimum amount of cyclin is needed to stimulate the positive
feedback lap with cdk25, and also to counteract the negative feedback from the
wee enzyme.
Samantha/Ann-Marie: This cyclin threshold exists because the MPF tries to
sustain itself. It phosphorylates Cdc25 which in turn results in a positive
feedback sending MPF up. Also it phosphorylates Wee1 resulting in a negative
feedback which produces pre-MPF.
Elzara/Alex: We need the threshold to exist in order to ensure the process of the
positive feedback loop of cdc25 with MPF, in order for the K25 rate to be faster
than the rate of Kwee. It needs enough cyclin to activate the mechanism and
phosphorylate cdc25 enzyme.
Adiba: The forward and reverse reactions (MPF to pre-MPF and vice-versa)
have different rates depending on the amounts of Wee1 and Cdc25 present, and
in order to keep direction-specific reactions going, there needs to be a certain
amount of material. The cyclin threshold is the minimum needed to produce
enough MPF that will be activated and there is positive feedback.
Nagy: In order for MPF to be activated, there needs to be enough MPF
generated to counteract its own phosphorylation by Wee1. If Wee1 is not
phosphorylated, it will continue to phosphorylate MPF, and MPF will stay in preMPF form.
Ilya: The mechanism here is that enough MPF has to form (from cyclin) to
phosphorylate both Cdc25 and Wee1, which in turn favors MPF to pre-MPF,
causing a positive feedback loop (MPF favors more MPF).
Truong: I looked at the level of cyclin required to put MPF over the threshold.
d[MPF]/dt = k2[cyclin][Cdk] – k2[MPF]-kwee[MPF]-k25[pre-MPF] and d[preMPF]/dt = -k2[pre-MPF] + kwee[MPF] – k25[pre-MPF]. Since k2=0 to activate
MPF, d[MPF]/dt ≥ 0 implies d[MPF]/dt = k3[cyclin][Cdk] – d[pre-MPF] ≥ 0. We
know k3 and [Cdk] so substituting in to equation implies [cyclin] ≥ (1/3)d[preMPF]/dt.
d. What happens if you raise the concentration of cyclin incrementally just above
the activation threshold?
Jesse/Samantha: If the amount of cyclin is raised just above the activation
threshold, then the rate of MPF produced rises dramatically. That is, MPF is
activated just above the activation threshold. Below the threshold MPF levels
never spike up.
Ilya: Above the threshold, MPF and pre-MPF concentrations swap values,
because enzymatically, MPF is favored, which brings around more of it, which
makes it more favored and pre-MPF less favored.
Hyukin/Truoung/Adiba/Jason/Ann-Marie/Danny/Victor/Elzara/Alex/Tamara:
The lag-time to activate MPF becomes shorter and shorter.
Mate/Fred: The threshold level of MPF is reached sooner and at a quicker rate,
since there are more MPF being created from cyclin and cdk coupling.
Alex/Tamara: In addition, you see a slightly higher concentration of MPF after
activation (e.g.) 88% instead of 85%).
3. Solomon et al. measured a cyclin threshold for MPF activation. Now let’s use
the model to predict a new behavior: a cyclin threshold for MPF inactivation. As
in Exercise 2, set k1 = V2’ = V2” = 0, and set the following initial conditions: cyclin
= 0, pre-MPF = 0, Cdc25P = 1, Wee1P = 1, IEP = 0, APC = 0, MPF = 20, 15, 10,
… In this case, you are simulating an extract in which all the cyclin is initially in
the form of active MPF.
a. What is the cyclin threshold for MPF inactivation?
Concensus: 7.75-8
Jason: at 7.9, MPF will be all inactivated around 600 seconds. With lower
concentration, MPF will become inactive more quickly.
Alex/Elzara: The threshold exists when 7.5 < cyclin < 8.0. Below this point, MPF
is inactivated, reaching an asymptote that is less than 10% of its original amount.
Ann-Marie: It takes more cyclin to activate than to deactivate MPF.
Tamara: The lower deactivation threshold introduces the lag time between
activation and deactivation; so it takes some time to get rid of cyclin.
b. How does the lag-time for MPF inactivation depend on total cyclin
concentration?
Ziping/Hyukin/Adiba/Elzara/Alex: The lag-time increases as cyclin level rises.
After a certain point, it dynamically increases.
Jason: It increases until the concentration reaches 7.9. Beyond that, MPF does
not fully deactivate.
Alex/Elzara: Above the threshold the time lag is “infinite”, because inactivation
does not occur.
Jesse: The higher the concentration of cyclin, the higher the concentration of
MPF. The higher concentration of MPF, the faster it activates and deactivates
causing APC to tag cyclin for degredation. The amount of cyclin drives the
oscillation rate of the entire simulation.
Nagy: The greater the concentration of cyclin, the greater the lag to MPF
degradation, because there are more MPF to be degraded, and as degradation
starts, some MPF are still being created.
Fred: As total cyclin concentration falls below the threshold, the lag time
decreases, eg, total cyclin conc. 7.8 => lag-time around 208 units (point of
inflection).
4. Using the original set of parameter values, plot MPF vs. total cyclin. What is
the interpretation of the oval-shaped curve you will see?
Mate/Samantha: The oval shows how the total cyclin and the MPF relate. The
oval shows that there is a delay between cyclin degradation and creation and
MPF degradation and creation (if there was not, then the relationship would be
linear and we would have a single line, with points running up and down it).
Danny: As we increase the total cyclin, the amount of MPF increases,
decreases, and increases again.
Ilya: Drew the following graph to describe the 3 different modes in the relation of
MPF to total cyclin, over the cycle of synthesis.
Adiba: It shows the self-degradation of MPF when it reaches high levels after
total cyclin threshold is passed.
Jason: As k1 increases, cyclin production increases, until it levels off and
decreases (as does MPF).
Ziping: The oval graph collapses time – we should think of a third axis, the time
axis, extending into the board, and picture a spiral rather than an oval.
Elzara/Alex: The oval is a parametric representation of the cyclin-MPF
relationship, with the time component in it, which shows the progression of MPF
activation and deactivation.
a. Compare this oval to your graph of steady states in Exercise 3b.
Jesse: The oval shape demonstrates the strong relationship between cyclin
levels and MPF levels as they cycle.
Hyukin: Like the graph for 3b, the concentration of MPF increases as Total cyclin
increases.
Adiba: They re-enforce each other since 3b shows that when have high amounts
of cyclin, you get to the MPF self-degradation (inactivation) rather quickly (lower
lag time).
Jason: The peak production with k1=.2 is the same as the threshold amount of
cyclin needed to activate MPF.
Mate: The graph had a steep increase at roughly concentration of 16 and
reached minimum at around concentration 7.5 (both concentration of total nondegradable cyclin). Threshold values differ with degradable cyclin from steady
states be cause there are more interactions involved.
b. How are MPF oscillations related to the activation and inactivation thresholds
investigated in Exercises 2 and 3?
Hyukin/Victor/Tamara: As cyclin increases and decreases, it activates and
deactivates the MPF.
Jason: The oscillations in MPF are triggered and controlled by the initial amount
of cyclin and regulated by the catalyzation rates.
Samantha: MPF oscillations act like switches. When it is on/active it enables the
progression of mitosis, when it is off/inactive it waits for the cyclin to build up in
order to proceed to the IE.
Mate: When the activation threshold is reached, the cycle starts to shoot up in
MPF concentration until the APC is activated and starts to decrease MPF
concentration and cyclin concentration. When the cyclin concentration drops
below the inactivation threshold, we reach the minimum of the cycle, and it has to
start to build up again. That is why we have the cyclin in the first place. If we
didn’t have it inactivated we would stay above the threshold values forever.
Jesse: There is a strong correlation even down due to drift in the oscillations
over time.
Adiba: The cyclin first accumulates past a certain threshold that is enough to
activate MPF. Though the high amounts of MPF turns the APC on which causes
its self-degradation and both MPF and cyclin levels drop which causes the
inactivation of MPF. Once the MPF levels are low enough, APC is turned off
which allows the cyclin levels to increase again which repeats the whole process,
producing the oscillations in the graph.
Ilya: As [cyclin] increases, MPF also increases at a lower rate until the activation
threshold (AT) is reached. Now, MPF causes itʼs own increase in concentration,
so it increases at a faster rate. We expected the mirror of this to be true ([MPF]
decreases until deactivation [cyclin] threshold is reached, and then it goes faster),
but this does not happen. This possibly hints at the relative influence of APC
degradation of MPF and enzymatic inactivation of MPF (Cdc25 and Wee1 get
unphosphorylated as [MPF] decreases). Our model also allowed for APC
degredation of pre-MPF. Which may have nullified the effect of inactivation in
favor of degredation of MPF.
c. What advantages does bistability confer to the physiology of mitosis?
Truong: Bistability is a decision-making process in cell cycle progression.
Danny: The ability to delay the G2 checkpoint.
Hyukin: It allows cell to decide to go to the mitosis stage or not, ex. If it is peak,
go. If it is valley delay.
Fred: Clearly defined states, unidirectionality of reactions, clock-like mechanism
Jason: The oscillations trigger the stages in mitosis. The differential between
different rates, insure that mitosis will move “forward”.
Tamara: Levels of cyclin impact the proper function of cell division. Bistability
improves the ability to control, monitor and measure.
Mate: Bistability enables the cell to reach MPF concentration that causes APC to
degrade cyclin in order for the inactivation threshold to be reached. This means
that the cell must go through the cycle, it has no chance of backing out of it.
Once started, without other effects to the concentrations, the cycle will have to
run its course indefinitely.
Adiba/Elzara: The cell cycle is irreversible. Only at certain checkpoints, the cycle
is prolonged a bit to fix anything that went wrong. Once the cell enters mitosis
phase, it cannot go back, an advantage of the bistability.