The Continuum Model: A Fresh View of Cell Cycle Control and its Application to Mathematical Analysis

1
The Continuum ModelA Fresh View of Cell Cycle
Controland its Application to Mathematical
Analysis
Stephen Cooper Department of Microbiology and
Immunology University of Michigan Medical
School Ann Arbor, MI
MBI-OSU September, 2003
2
Outline of talk

• Review current ideas on cell cycle regulation
• Present the Continuum Model
• Discuss why whole-culture synchronization does
  not work
• Present time-lapse experiments showing that
  whole-culture synchronization does not work
• Analyze Retinoblastoma phosphorylation during the
  division cycle
• Analyze microarray experiments
• Discuss the challenge of the Continuum Model for
  mathematics

3
Current view of the Mammalian Division Cycle

• Regulatory controls are in G1-phase
• Preparations for S phase occur in G1-phase
• Cells arrest in G1-phase
• Cells differentiate from G1-phase
• Cells die or apoptose (a-po-tose) from G1 phase
• Cells regulate division cycle length in G1 phase
• Specific biochemical events in G1 phase

4
Events in the Cell Cycle
5
Key Sources of G1-phase Control Model

• Variability of G1 phase invariance of S and G2
  phase lengths
• G1-arrest, or arrest with a G1-phase amount of
  DNA
• G1-arrest is believed to synchronize cells

6
G1-phase Variability

• G1-phase is most variable phase
• Long G1 phase associated with, or produced, slow
  growing cells
• Short G1 phase associated with, or produced, fast
  growing cells
• Was concluded that G1 phase controlled growth
  rate and interdivision time

7
Does G1-phase Determine Interdivision Time?
Classic Conclusion G1-phase controls IDT
8
Interdivision Time Determines G1-phase Length
Conclusion IDT determines G1-phase Length
9
Variation in Growth RateProduces G1-phase
Variation
G1 S G2
Interinitiation time
10
Cyclins and G1-phase length

• Adding cyclins to cells (using plasmids) shortens
  G1 phase
• Was concluded that cyclins were limiting for
  G1-phase passage
• Alternate (Continuum) conclusion Cyclins added
  to cells make cells grow faster, produce shorter
  interdivision time, and thus shorter G1-phase

11
No G1-phase Specific Syntheses
No unique G1-phase syntheses
12
Continuum Model Icon
Mass synthesis
S, G2/M
Division
Division is the end of a process, and the
beginning of none!
13
The Continuum Model

• Division is regulated by a to continuous,phase-in
  dependent, synthesis and accumulation of
  initiator
• G1-phase is what is left over when accumulation
  time is greater than SG2M
• Specific S- or G2-phase syntheses are not
  excluded
• No unique syntheses, specific to G1 phase occur
  in G1-phase

14
Analysis of Liskay/Prescott Experiment

• G1-less cells studied
• Mutants isolated with a G1 phase
• Length of G1-phase exactly equal to increase in
  interdivision time
• S and G2-phase constant
• The selection of mutants was one that would
  select slow-growing mutants

15
Continuum Analysis of G1-mutants

• Selection of slower cells produced G1-phase
• Mutants did not produce specific G1-phase events
• Published in Nature, 1979

16
Study of the Cell Cycle

• Synchronized cells
• Cells should reflect normal cell cycle of
  growing cells
• Method should not have artifacts
• Should synchronize cells
• Dominant synchronization method is Whole-culture
  synchronization

17
Whole Culture Synchronization Cannot Work

• Whole-culture Synchronization is most widely used
  approach to cell-cycle analysis
• Whole culture Synchronization cannot, in theory,
  produce synchronized cells
• Both cytoplasm and DNA amounts vary during
  division cycle
• Whole-culture synchronization methods cannot
  produce cells with both specific DNA content and
  narrow size distribution for a particular cell age

18
General Laws and Biology

• Biology is not used to laws that are general
  and theoretical--What is, is!
• Physics has conservation of energy and
  conservation of mass
• Law proposed here is that of Conservation of
  Cell Age Order which means one cannot alter, or
  narrow, age distribution by whole-culture
  treatments
• Let us examine the idea with Gedanken analysis

19
During Division Cycle BothMass and DNA Vary
DNA
Mass
Not synchronized
20
Steady-State Growth
21
Steady-State Growth
1.05
2.00
22
Cells must synthesize mass to a certain level to
initiate DNA replication

• All cells, prokaryotic and eukaryotic, require
  mass accumulation to initiate DNA replication.
• If initiations stopped, DNA replications that are
  started continue to completion
• In eukaryotes, cell division occurs as well when
  mass accumulation inhibited

23
Arrest with G1-amount of DNADue to Inhibition of
Mass Synthesis
1.28
0.67
24
Synchronization by Arrest with G1-phase DNA
1.0
25
Arrest with G1-phase DNA,But No Synchronization
1.001
0.999
0.7
1.4
Starve
Arrest with G1-DNA
0.999
0.5
Refeed
26
Other Whole-Culture Methods

• Inhibition of DNA synthesis
• Inhibition of mitosis (nocodazole)
• Similar results No narrowing of size
  distribution, no synchrony

27
Results of Whole-culture Synchronization
Steady-State Growth
Inhibition of Mass
Inhibit DNA Synthesis
Inhibit Mitosis
28
Conservation of Cell Size Distribution

• A corollary to the Law of Conservation of Cell
  Age Order is the
• Law of Conservation of Cell Size Distribution
• No whole-culture treatment can narrow cell size
  distribution
• Whole culture treatment cannot produce cells with
  narrow age/size distribution
• Results that ignore the Conservation of Cell Age
  Order/Cell Size Distribution are suspect

29
Selection and Synchrony

• Can only synchronize cells, according to these
  two conservation laws, by Selecting cells of a
  given age, size, and physiological state from
  entire population

30
Criteria for Synchronization

• Cells should exhibit synchronized divisions!
• Cells should have proper DNA contents through
  sequential division cycles
• Cells should have narrower size distribution
  throughout synchronous growth
• Cells should be prepared by selective, not
  whole-culture, synchronization (not criterion,
  more of a fact)

31
Criteria for Synchronization
These criteria are rarely met by Synchronization
methods
32
Selection and Forcing Synchronization
Whole-Culture Synchronization
Selection Synchronization
33
Selective vs. Batch Methods

• Only selective methods can, in theory, produce a
  synchronized culture
• Whole-culture methods cannot, in theory, produce
  a synchronized culture
• Baby Machine (membrane-elution) is a selective
  method that synchronizes cells

34
The Baby Machine
35
Eukaryotic Baby Machine Cells!!!(developed by
Helmstetter)
CellSizes
G1 DNA
36
Synchronous Growth
37
(No Transcript)
38
(No Transcript)
39
Synchronization results(Whitfield, et al)
40
Synchronization Patterns (Stein lab)(van der
Meijden, et al)
Hela cells synchronized by thymidine block
followed by Aphidicolin block. Cells analyzed
by Affymetrix microarray
41
Experimental Analysis of Starvation
Synchrony(data of Di Matteo, et al)
42
Importance of Three Cycles of Synchronized
Divisions Produced by Membrane-elution

• Fits criteria for synchronization
• Synchronous division pattern similar to, or as
  good as, this have never been reported for other
  methods

43
Selection synchrony is only wayto get
synchronized cells

• Cannot synchronize cells by starvation/inhibition
• Only selection worksin practice and in theory
• Must distinguish between G1-phase arrest and
  arrest with G1-phase amount of DNA

44
Analysis of Synchronization usingTime-Lapse
Videography

• Difficult to measure doubling in cell numbers,
  particularly when cells must be scraped from
  plate
• Cell numbers are rarely measured in eukaryotic
  synchrony experiments
• Can measure cell division times with time-lapse
  videography

45
Time-Lapse System
46
Flask in Place
47
Flask and Thermocouple
48
Time-lapse videography of dividing cells
49
Cell Division of Normal Cells
50
Plotting Three Divisions
51
Plotting Exponential Growth
52
Patterns of Cell Division
53
Example of Dividing Cells
1
2
3
4
5
7
8
6
A
1
2
3
4
5
9
10
11
13
12
11
10
9
7
8
6
19
18
17
16
15
14
20
21
27
26
25
24
23
22
28
29
C
B
54
Exponential Growth, U937
55
Exponential Growth, MOLT-4
56
Exponential Growth, L1210
57
Lovastatin Treatment, L1210
58
Serum Starvation, L1210
59
Does Lovastatin Synchronize Cells?(data of
Keyomarsi, et al)
60
Conclusions fromTime-Lapse Videography

• Can determine division pattern of growing cells
• Synchronized cells do not appear synchronized
• Neither lovastatin nor serum starvation appear to
  synchronize cells

61
Mathematical Analysis of Resultsfrom
Synchronization Experiments

• Should be careful not to apply complex
  mathematical analysis to data derived from
  whole-culture synchronization
• Many results are derivative results or ideas and
  the original synchronization experiment is
  hidden from view
• This is a major problem

62
Current View of Rb control ofCell Cycle
C
y
c
l
i
n

D
C
D
K
4
/
6
G
e
n
e

E
2
F
T
r
a
n
s
c
r
i
p
t
i
o
n
R
b
E
2
F
R
b
p
G
1
S
G
2
63
Results on Rb phosphorylation

• Rb Phosphorylation and dephosphorylation are not
  necessary events
• Rb phosphorylation not related to cell cycle
• Growth state affects phosphorylation state
• Rb experiments can explain WHY it is believed
  that phosphorylation during G1-phase is a
  necessary and ubiquitous event

64
Basic Support for G1-phasePhosphorylation Event
65
All Phases of L1210 Cells Have Only Rb-P
Conclusion No G1-phase phosphorylation Of Rb in
L1210 cells
66
Flow-Cytometric Analysis of Rb in NIH3T3 cells
Conclusion G1-phase phosphorylation of Rb
67
Newborn Cells (0-30 minutes of age) All Rb-P
Conclusion No Phosphorylation even in very
youngest cells in cycle
68
Overgrowth Dephosphorylates
Conclusion Overgrowth leads to
dephosphorylation
69
Rb in NIH3T3 grown at different densities
Conclusion Overgrowth leads to
dephosphorylation
Conclusion Dilute growth leads to Total
phosphorylation
70
Explanation of Data Supporting G1-phase Rb
Phosphorylation

• Growth state affects phosphorylation of Rb
• Poor growth dephosphorylates
• Unrestrained growth phosphorylates
• Combination gives apparent G1-phase
  phosphorylation of Rb

71
Model for Rb phosphorylation
72
Retinoblastoma Phosphorylationduring Cell Cycle

• Rb phosphorylation is cycle-independent
• Rb phosphorylation is regulated by growth
  conditions
• Explains two G1-phase bands of Rb
• Rb is an example of a G1-phase event that does
  not necessarily exist
• Perhaps we should be skeptical of other G1-phase
  events

73
Growth arrest, G1-phase arrestand Rb
phosphorylation

• Growth arrested cells stop growing
• Growth arrested cells have a G1-phase amount of
  DNA
• Growth arrested cells dephosphorylate Rb protein
  (independent of G1-ness of cells)
• Appears as if Rb dephosphorylation caused
  G1-phase amount of DNA

74
Microarray Analysis of Gene ExpressionDuring the
Cell Cycle
75
The Work to be Analyzed Cho, et al.
700 cycle specific genes
76
Gene Expression during the HeLa Cell
Cycle(Whitfield, et al, 2002)
850 cycle specific genes.
77
Gene Expression during the HeLa Cell Cycle(van
der Meijden, et al, 2002)
many cell-cycle genes out of 2,846 expressed
genes
78
Experimental approach for Cell-cycle Analysis
(Cho, et al)

• Cells synchronized by double-thymidine block
• Cells collected every 2 hours for 24 hours
• Two cell cycles analyzed
• RNA analyzed by microarrays
• Data fit to sine wave
• Two replicate experiments performed
• Determine PVE Proportion Variance Explained by
  a sine wave (our analysis)

79
Problems with Microarray Analysis of Gene
Expression during Cell Cycle

• Problem with statistical analysis of large amount
  of data
• Problem related to producing cells that do not
  reflect the normal division cycle
• Problems with synchronization

80
Statistical problem with large databasesThe ESP
Analogy (ESPExtra-Sensory-Perception)

• Deck with 25 cards, five different pictures
• Cards shuffled
• One person (tester) looks at cards in succession,
  another person (subject) guesses pictures
• Can subject read mind of tester?
• Expectation is 20 correct
• Greater than 20 guessing is ESP-ability(!??)
• But there is a distribution of correct guessing

81
Selecting high guessers
10,000 analyzed
Guess better than20 haveESP-ability?
500 selectedfor reanalysis
82
ESP Analysis

• Some guess better than 20, some worse
• Good guessers have ESP-ability
• Repeat testing
• Some repeat, some do not
• Eventually all fail

83
The ESP Fallacy

• In large population, some will do better than
  random expectation
• With large enough group, will get initial
  guessers to repeat
• Eventually all fail
• How do we eliminate this problem?
• Compare results with random expectation for total
  population

84
Comparison with Random Expectation

• To correct ESP fallacy, see whether total pattern
  of guessing is better than random
• If it is, ESP exists if not, it is merely random
  chance that cards are guessed correctly

85
Does total pattern fit random?
Randomexpectation
86
Comparing Observed and Random Valuesfor
Microarray Results

• Synchronize Cells
• Sample cells at different times and measure mRNA
  expression during cell cycle
• Prepare randomized set of expression patterns
  from normalized data points
• Compare observed and random values for cyclicity
  (using PVE)
• PVEProportion of Variance Explained by a sine
  wave (1.0perfect sine wave 0.0no sine-like
  character)

87
Original data set
88
Randomized in rows
89
Randomized, rows and columns
90
Randomizing cyclical results
Do not expect highly cyclical results to
giveequal cyclicity after randomization
91
Randomization of Random gives Random
No change if random results are randomized
92
Comparison Data and Random
93
Comparing Observed and Random

• For a given threshold
• Does random set have as many cyclicals as
  observed data?
• If yes, then results consistent with noise or
  random variations

94
Random results
ObsRan
Random
Observed
Observed Results Due to Chance
95
Observed greater than chance
Random
Observed
Results Not Due to Chance
96
Large Number of Genes Analyzed

• Over 6000 genes analyzed
• Expect some cyclicity from random chance
• Example 10 coins tossed 6000 times would be
  expected, upon occasion, to give all 10 heads at
  once

97
Observed vs. Random Cyclicities
Comparison of Two Experiments of Cho, et al.
1000 genes analyzed
Same results obtained with total 6000 genes
98
Conclusion from Observed-Random Plot

• Results in two microarray experiments are
  explainable by random noise or chance variations
• Cyclicity in observed not better than random
  noise generating results

99
Analysis of Reproducibility of Results

• Two replicate experiments performed
• Is cyclicity reproducible?
• Is phase location reproducible?

100
Cyclicity compared in two replicate experiments
Cyclicity not reproducible
Results similar for all genes
101
Phase Location Determination

• Peak of gene expression determined by moving
  sine-wave analysis
• Values from -1 to 1 indicate peaks are more
  cosine-like or sine-like

102
Phase location compared in tworeplicate
experiments
Peak location is not reproducible
103
Conclusions

• Cyclicity is not reproducible
• Phase location is not reproducible
• Data compatible with random values

104
Results published in PNAS
Kerby Shedden, Department of Statistics
105
A separate questionAre cells synchronized?

• If synchronized, then peak values for gene
  expression should decay
• Synchrony decays due to entropic considerations
• Compare first peak to second peak
• Second should be less than first

106
Plot of First Peak minus Second Peak
Peak values do not decay over two cycles Cells
do not appear synchronized
107
Cells do not appear synchronized

• Peak values do not decay
• Just as likely for second peak to be above as
  below first peak
• Cells do not appear to be synchronized
• Fits with random noise giving results

108
The Continuum Model View of the G1-phase

• G1 phase does not control the division cycle
• Evidence for G1 phase specific events is
  questionable
• Cells do not arrest in G1 phase
• What happens in G1 phase also happens in other
  phases
• G1-phase biochemistry does not change when S
  phase begins

109
Other published applications ofthe Continuum
Model

• Explains G1-phase DNA content of differentiated
  cells
• Explains cell division in zygotes
• Eliminates restriction point and G0 phase
• Explains cell size determination
• Unifies growth control logic of eukaryotes and
  prokaryotes

110
Important Take-Home Messages

• Vast majority of experiments on cell-cycle events
  use cells synchronized by growth arrest
• Whole-culture synchronization does not work
• Be skeptical of work on cell cycle using cells
  synchronized by growth arrest
• Thus, be skeptical of a lot of work on cell cycle

111
Experiments and Mathematical Analysis

• Pure mathematics can be true independent of
  physical reality
• But to understand biological reality the
  mathematics should be applied to correct
  experimental data
• Just because a mathematical analysis is true
  does not mean that the data underlying the
  analysis is true

112
What mathematicians and other theoreticians
should think about

• What is the experimental support for the data
  that I am analyzing?
• What methods were used for cell-cycle analysis?
• Does the data have another biological explanation
  (e.g., the Continuum Model)?

113
Control of Cell Cycle by Environment
114
Bacterial Cell Cycle
8
6
0
3
0
1
0
0
8
1
9
0
6
0
3
0
1
0
0
1
9
0
6
0
4
0
2
0
1
0
0
6
0
1
5
0
4
0
2
0
1
0
0
2
5
0
4
0
3
0
2
0
1
0
0
2
4
0
3
5
2
5
2
0
1
0
0
2
3
5
3
0
2
0
1
5
5
0
2
3
0
2
5
2
0
1
5
1
0
0
2
5
4
2
0
1
5
1
0
5
0
2
0
4
115
Additional support and information

• Web page for papers at www.umich.edu/cooper

116
The Continuum Icon
117
The End

• Thank You

118
(No Transcript)
119
(No Transcript)
120
(No Transcript)
121
Inspiration
122
Yeast Analysis in Nucleic Acids Research
123
On Fitting ALL the Facts
The failure on the part of my colleagues to
discover the alpha-helix made a deep impression
on Jim Watson and me. Because of it I argued
that it was important not to place too much
reliance on any single piece of evidence. It
might turn out to be misleading, as the 5.1Å
reflection undoubtedly was. Jim was a little
more brash, arguing that no good model ever
accounted for all the facts since some data was
bound to be misleading if not plain wrong. A
theory that did fit all the data would have been
carpentered to do this and would thus be open
to suspicion. Francis Crick, 1988
124
Cyclin B Analysis during Division Cycle (Western
Blot)
125
Cyclin B Protein duringDivision Cycle
126
Newborn Cells are Small