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Dynamic heterogeneity for the physical oncologist. Liao D, Estévez-Salmerón L and Tlsty TD 2012 Conceptualizing a tool to optimize therapy based on dynamic heterogeneity * Phys. Biol. 9 (6) 065005 (doi:10.1088/1478-3975/9/6/065005 ) Liao D, Estévez-Salmerón L and Tlsty TD 2012 - PowerPoint PPT Presentation
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Dynamic heterogeneity for the physical oncologist
Liao D, Estévez-Salmerón L and Tlsty TD 2012Conceptualizing a tool to optimize therapy based on dynamic heterogeneity* Phys. Biol. 9(6) 065005(doi:10.1088/1478-3975/9/6/065005)
Liao D, Estévez-Salmerón L and Tlsty TD 2012Generalized principles of stochasticity can be used to control dynamic heterogeneity Phys. Biol. 9(6) 065006(doi:10.1088/1478-3975/9/6/065006)
* The authors dedicate this paper to Dr Barton Kamen who inspired its initiation and enthusiastically supported its pursuit.
Dynamic heterogeneity for the physical oncologist
𝑡2 30 1
Ø
Ø
Outcome vs. frequency
Interconversion
Seeming randomness
Timings of biochemical reactions can seem to display randomness
3
Timings of biochemical reactions can seem to display randomness
4
𝑡2 3 40 1
Timings of biochemical reactions can seem to display randomness
5
𝑡2 3 40 1
𝑡2 3 40 1
Timings of biochemical reactions can seem to display randomness
6
Messy variety of durations between events Unpredictability: Varied outcomes
no protein
𝑡2 30 1
Dynamic heterogeneity for the physical oncologist
Ø
Ø
Outcome vs. frequency
Interconversion
Seeming randomness
Phenotypes can be stochastic and interconvert
8
𝑡2 3 4 5 6 7 8 90 1 10
Prot
ein
in c
ell A
Prot
ein
in c
ell B
noproduct
Relatively resistant
Relatively sensitive
Use Markov models to approximate phenotypic transitions
9
Prot
ein
in c
ell
ti
ti + Dt
𝑡2 3 4 5 6 7 8 90 1 10
Use Markov models to approximate phenotypic transitions
10
Prot
ein
in c
ell
ti
ti + Dt
cR
cSrS
rRmS
mR Ø
Ø
𝑡2 3 4 5 6 7 8 90 1 10
𝑡2 30 1
Dynamic heterogeneity for the physical oncologist
Ø
Ø
Outcome vs. frequency
Interconversion
Seeming randomness
Cell kill (t = Dt)
Cell kill (t = 0)
Metronomogram
12
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
Cell kill
Cell kill
Dt
TCD
N(0+)
N(Dt+)
N(Dt-)
Ø
Ø
𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿
Cell kill (t = Dt)
Cell kill (t = 0)
Metronomogram
13
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
Cell kill
Cell kill
Dt
TCD
N(0+)
N(Dt+)
N(Dt-)
KilledØ
Ø
𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿
Cell kill (t = Dt)
Cell kill (t = 0)
Metronomogram
14
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿
Cell kill
Cell kill
Dt
TCD
N(0+)
N(Dt+)
N(Dt-)
Killed
Expansion
Ø
Ø
𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿
Cell kill (t = Dt)
Cell kill (t = 0)
Metronomogram
15
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿
Cell kill
Cell kill
Dt
TCD
N(0+)
N(Dt+)
N(Dt-)
𝑓 𝑆> 𝑓 𝑃
𝑓 𝑆< 𝑓 𝑃
𝑓 𝑆=𝑓 𝑃
1.0
0.8
0.6
0.4
0.2
0 0.2 0.4 0.6 0.8 1.0
Sens
itize
d fr
actio
n
Population expansion fraction
>Killed
Expansion
Ø
Ø
𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿
Cell kill (t = Dt)
Cell kill (t = 0)
Metronomogram
16
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿
Cell kill
Cell kill
Dt
TCD
N(0+)
N(Dt+)
N(Dt-)
𝑓 𝑆> 𝑓 𝑃
𝑓 𝑆< 𝑓 𝑃
𝑓 𝑆=𝑓 𝑃
1.0
0.8
0.6
0.4
0.2
0 0.2 0.4 0.6 0.8 1.0
Sens
itize
d fr
actio
n
Population expansion fraction
Ø
Ø
Metronomogram
17
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿
𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿
Dt
𝑓 𝑆> 𝑓 𝑃
𝑓 𝑆< 𝑓 𝑃
𝑓 𝑆=𝑓 𝑃
1.0
0.8
0.6
0.4
0.2
0 0.2 0.4 0.6 0.8 1.0
Sens
itize
d fr
actio
n
Population expansion fraction
S and R
R only
N(Dt+)
N(Dt-)S and R
R only
N(0+)
S and R
R only
Ø
Ø
Metronomogram
18
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿
𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿
Dt
𝑓 𝑆> 𝑓 𝑃
𝑓 𝑆< 𝑓 𝑃
𝑓 𝑆=𝑓 𝑃
1.0
0.8
0.6
0.4
0.2
0 0.2 0.4 0.6 0.8 1.0
Sens
itize
d fr
actio
n
Population expansion fraction
S and R
R only
N(Dt+)
N(Dt-)S and R
R only
N(0+)
S and R
R only
Ø
Ø
Metronomogram
19
Given:
Cannot directly kill “R”Illustrate: When can deplete S + R
𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿
𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿
Cell kill
Cell kill (t = 0)
Cell kill (t = Dt)
Cell kill
Expansion andinterconversion
Dt
TCD
N(0+)
N(Dt+)
N(Dt-)
𝑓 𝑆> 𝑓 𝑃
𝑓 𝑆< 𝑓 𝑃
𝑓 𝑆=𝑓 𝑃
1.0
0.8
0.6
0.4
0.2
0 0.2 0.4 0.6 0.8 1.0
Sens
itize
d fr
actio
n
Population expansion fraction
Ø
Ø
𝑡2 30 1
Dynamic heterogeneity for the physical oncologist
Ø
Ø
Outcome vs. frequency
Interconversion
Seeming randomness
Dynamic heterogeneity for the physical oncologist
Liao D, Estévez-Salmerón L and Tlsty TD 2012Conceptualizing a tool to optimize therapy based on dynamic heterogeneity* Phys. Biol. 9(6) 065005(doi:10.1088/1478-3975/9/6/065005)
Liao D, Estévez-Salmerón L and Tlsty TD 2012Generalized principles of stochasticity can be used to control dynamic heterogeneity Phys. Biol. 9(6) 065006(doi:10.1088/1478-3975/9/6/065006)
* The authors dedicate this paper to Dr Barton Kamen who inspired its initiation and enthusiastically supported its pursuit.
