Simulating the Dynamic
Regulation of a Cell: relevance
to cellular reprogramming
Bradly Alicea and Steven Suhr
Cellular Reprogramming Laboratory (http://reprogramming.net)
Michigan State University
Translation Transcription
Mechanism Alteration
Cell Cycle
Arrest
Ribosome
Disintegration
Protein
Inhibition
RNA Fluctuations
Dynamic Reprogramming-like Representation
Mechanism Alteration Mechanism alteration: administer drug, treatment that will interfere with (e.g. knock-
out) specific function of the cell. Mimic cell reprogramming, transformation.
Q: how does mechanism alteration
affect transcription and translation?
* can we use this strategy to better
understand cellular regulation?
Actinomycin C: stops cell cycle,
leaves protein synthesis intact.
Mitomycin D: shuts down protein
synthesis.
Saporin: disintegrates ribosome.
Inspired by RNA ½ life studies:
administer drug, measure decay over 24h
interval (in our case, 4d).
AGGREGATION: compound
mechanism, increase in RNA over time.
DECAY: compound mechanism,
decrease in RNA over time.
* gene-dependent response, some genes
“decay” more than others.
* will translatome correspond to
transcriptome? Vice versa?
Mechanism Alteration
Can mechanism alteration be an indicator of
regulation?
Actinomycin D treatment, dynamic (1d-3d).
2nd-order polynomial represents trend only.
Above line, positive.
Below line, negative.
Normalized to control
measured at 0d.
Mechanism Alteration
Can mechanism alteration be an indicator of
regulation?
* gene-specific time-course expression
profiles
* variable w.r.t. specific mechanism being shut
down.
Actinomycin D treatment, dynamic (1d-3d).
2nd-order polynomial represents trend only.
Above line, positive.
Below line, negative.
Normalized to control
measured at 0d.
2d of Saporin treatment, translatome
(TLT) and transcriptome (TST)
CONTROL
(0d, no treatment) 2d POST-TREATMENT
Specific (COL, FB, FN)
and non-specific genes
(various functions)
Understanding regulation in the cell using
transcription and translation…
COURTESY: Reuveni, S. et.al
(2011). PLoS Computational Biology,
7(9), e1002127.
cellular dynamics
cellular dynamics
Candidate gene data: profiles of
senescent and non-senescent
fibroblasts.
Isolating translation RNA, associated protocols:
Journal of Biological Chemistry, 280(8), 6496-6503 (2005).
Cell, 135, 738–748 (2008).
Science, 324, 218-223 (2009).
Translatome: introduction Translation is a relatively unexplored area:
Translation (mRNA) Transcription (mRNA) Protein (peptide)
Sequence compression: DNA-RNA, RNA-RNA’, RNA’-PROTEIN
Post-transcriptional
modifications
Translation (tRNA
conversion)
Translatome: introduction
Polysome (A, B) precipitated from ribosome (C), mRNA in process of being
converted into a polypeptide chain (B, micrograph in D):
* loosely associated mRNA immediately pre-translation (200-400 nt).
Translation is a relatively unexplored area:
Protein (peptide)
Sequence compression: DNA-RNA, RNA-RNA’, RNA’-PROTEIN
Post-transcriptional
modifications
Translation (tRNA
conversion)
A B
C
D
Translation (mRNA) Transcription (mRNA)
RNA decay and Regulatory Control
H: physiological “control” can be inferred from mRNA. Based on RNA kinetics
(decay, transcription/translation rate, ½ life). Initial model:
Feedforward scenario Feedback with saturation scenario
Stimulus Stimulus Production at
ribosome
Presence of
mRNA
Presence of
mRNA
Decay rate
(1/d)
Decay rate
(1/d)
If above threshold, (-)
If below threshold, (+)
(+) (+) (+) (+)
Mechanism for differences observed
between TLT, TST within passage,
condition.
Mechanism for differences
observed across TLT, TST or
between passage, condition.
Rein control:
* two sources (TLT, TST) that
are independently regulating
(controlling) a common
process (cellular state).
Production at
ribosome
(+) (+)
INSETS: IEEE Spectrum, March 2011, 38-43
Control Model Based on Decay
TST TLT
Feedback with saturation model using drug
treatments (stripped-down version of RNA
regulation and decay in cell).
Theoretically:
* Actinomycin D disallows A.
* Mitomycin C disallows A, allows C and D.
* Saporin disallows B, C, and D.
A1
B
C D
A2
Control Model Based on Decay
TST TLT
TST FF
FB
D
Feedback with saturation model using drug
treatments (stripped-down version of RNA
regulation and decay in cell).
Theoretically:
* Actinomycin D disallows A.
* Mitomycin C disallows A, allows C and D.
* Saporin disallows B, C, and D.
A1
B
C D
TST TLT
TST TLT
Decay off example FB, FF off example
Control strategy: rein control (FB, FF drive state of TST over time)
with brake (saturation, characterized by decay).
A2
Dynamic FB Using Control Model
Baseline (BL) provides input to TST
(1d), state of TST is FF to TLT (1d),
state of TLT is FB to TST (2d)
Box A: FB off scenario (FB < FF)
Box B: decay off scenario (D < FB, FF)
Box C: FF off scenario (FF < FB)
TST FF
FB
D D
TLT BL
TST/TLT
Dynamic FB Using Control Model
10 4
0
2
5 3
0
Baseline (BL) provides input to TST
(1d), state of TST is FF to TLT (1d),
state of TLT is FB to TST (2d)
Box A: FB off scenario (FB < FF)
Box B: decay off scenario (D < FB, FF)
Box C: FF off scenario (FF < FB)
3
2
0
All scenarios a.u., based on Normalized Ct values
4
6
0
8
3
8
0
5
n days
n + 1 days
0 days
5/8
12/6
5/8
A
B C
Semi-discrete Dynamical System:
n days
TST FF
FB
D D
TLT BL
Numbers in boxes are measured quantities,
numbers on pathways are inferred values.
TST/TLT
Dynamic FB Using Control Model Transition rules: 1) for t1, difference between input and TST
2) for tn > 1, difference between TSTtn
and TSTtn+1 or TLTtn and TLTtn+1
3) if TST > TLT, then x > 0.
4) if Bt-1> Bt, then FB is x > 0.
Dynamic FB Using Control Model
0
0
1.24
24.06 0
2.811
12.799
0
27.89
3.34
1d
2d
21.25073 FF
FB
D D
31.235 20.0104/
28.4165
26.46 0
5.74 2.313
30.21
0
3d
0d
TST TLT
Transition rules: 1) for t1, difference between input and TST
2) for tn > 1, difference between TSTtn
and TSTtn+1 or TLTtn and TLTtn+1
Example model run using data from COL qPCR in L10A fibroblasts under
Actinomycin D treatment, 3d.
3) if TST > TLT, then x > 0.
4) if Bt-1> Bt, then FB is x > 0.
Control System Components
Left: Actinomycin D
treatment, 1-3d.
* large gain in TST on day 3
across genes.
* FB more robust than FF for
most genes across most days.
Right: Mitomycin C
treatment, 1-3d.
* large gain in TLT across
time-series (compared to
TST).
* FF and FB are similar, but
pattern is gene-specific (and
affects different genes).
Ch
an
ge
in C
t v
alu
e o
ver
tim
e
Genes tested
Ch
an
ge
in C
t v
alu
e o
ver
tim
e
Genes tested
Delay Differential Equations as a source of error
2d POST-SAPORIN TREATMENT CONTROL
Putting it All
Together…
2d POST-SAPORIN TREATMENT CONTROL
FIRST-ORDER FEEDBACK CONTROL MODEL
Putting it All
Together…
2d POST-SAPORIN TREATMENT CONTROL
FIRST-ORDER FEEDBACK CONTROL MODEL
OUTPUTS FOR DIFFERENT COMPONENTS OF
CONTROL MODEL (A-D and DECAY).
Putting it All
Together…
1d
2d
Interpreted in terms of discrete
dynamical equations (DDEs)
First-order DDE model, general case:
For applications to biology, see:
Orosz, G., Moehlis, J., and Murray, R.M. Controlling biological networks by time-delayed signals. Philosophical Transactions of the Royal Society A, 368, 439–454 (2010). MacDonald, N. Biological Delay Systems: Linear Stability Theory. Cambridge University Press, Cambridge, UK (1989).
Aggregation, nonlinear decay are second-order (e.g.
polynomial) effects
Interpreted in terms of discrete
dynamical equations (DDEs) Which process is being delayed:
translation or transcription? First-order DDE model, general case:
For applications to biology, see:
Orosz, G., Moehlis, J., and Murray, R.M. Controlling biological networks by time-delayed signals. Philosophical Transactions of the Royal Society A, 368, 439–454 (2010). MacDonald, N. Biological Delay Systems: Linear Stability Theory. Cambridge University Press, Cambridge, UK (1989).
Aggregation, nonlinear decay are second-order (e.g.
polynomial) effects LINEAR (NO DELAY)
AGGREGATION (DELAY
TRANSLATION)
LINEAR (NO DELAY)
NONLINEAR (DELAY TRANSCRIPTION)
AGGREGATION (DELAY
TRANSLATION)
AGGREGATION (DELAY
TRANSLATION)
A Model of Dynamic Transformation Touring the converted cell “zoo”
Valley (fibroblast) to peaks (neuron, induced
pluripotent stem – iPS -- cell)
Phase space (left) and bistability
(below) models of reprogramming.
“Energy barriers” or “peak climbing”
characterizes process of phenotypic,
functional conversion.
