Single-Cell Transcriptome Analysis of Pluripotent Stem Cells
Pluripotent stem cell -...
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( ) Branching and Oscillations Abstract Existing mathematical models of gene interaction cannot fully characterize the temporal transformation of the epigenetic landscape because of fixed parameters and limited number of state variables. Here we present a high-dimensional model of gene interaction with time-varying asymmetric repression between gene regulatory factors. This model can predict the sequential branching in cell-fate determination and the oscillations that activate suppressed genes. Significance • Provide insights into the possible mechanisms of cell differentiation and associated diseases (e.g., cancer) • Contribute in devising strategies for cellular reprogramming (e.g., dedifferentiation back to pluripotency) Equilibrium points and sustained oscillations (determinisitc) are contained in Degenerate case (infinitely many equilibrium points) can arise if . , , , 2 2 2 2 2 1 1 1 1 1 n n n n n g g g g g g 1 ij i c c for all i,j. References: [1] C. H. Waddington, The Strategy of the Genes, George Allen & Unwin, 1957. [2] O. Cinquin, J. Demongeot, J. Theor. Biol. 233 (2005), 391-411. [3] B. D. Aguda, A. Friedman, Models of Cellular Regulation, Oxford U Press, 2008. [4] S. Yamanaka, Nature 460 (2009), 49-52. [5] J. F. Rabajante, PeerJ Pre-Prints (2014), e382v1. The Dynamic System Model ,...,n 2 , 1 i dW G σ dt g X β X u 1 γ X K X α dX i i i i i i j ij c j 2 i ij i c i i i c i i i strength of the gene regulatory factor (GRF) involved in expressing the gene of the i-th phenotype evolving parameter representing the time-varying strength of repression between the i-th and j-th GRFs dW δ dt u ) ( t) ε ( exp du i i i i kinetics growth A gene regulatory network that characterizes multi-stable cell-fate determination [2,3]. The X 1 , X 2 , and X 3 represent the strengths of gene regulatory factors (GRFs), such as transcription factors. Cells can undergo transdifferentiation and dedifferentiation [4]. This network can be regulated (e.g., via noise, oscillation, and temporary or permanent parameter modification) [2,5]. 2014 School on Hands-on Research in Complex Systems, Trieste Italy Branching and Oscillations in Cell-Fate Determination Jomar Fajardo Rabajante 1,2,3 , Ariel Lagdameo Babierra 1 , Cherryl Ortega Talaue 3 1 Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Philippines 2 Graduate School of Science and Technology, Shizuoka University, Japan 3 Institute of Mathematics, University of the Philippines Diliman, Philippines The canal is chosen by the differentiating cell based on the landscape’s potential such that the steeper pathway and deeper basin are preferred. Background about epigenetic landscape Waddington’s epigenetic landscape [1]. Branching canals depict various cell lineages towards different cell fates (phenotypes). Cell fates Daughter cells Pluripotent stem cell Gene regulation Pluripotent stem cell Daughter cells Gene Regulatory Network Acknowledgement: Partly funded by PCIEERD, DOST and by the University of the Philippines (JFRabajante MSc Thesis fellowship). Baltazar D. Aguda for the useful discussions about models of cellular regulation. Five branch endpoints Cell developmental pathways. We quantify Waddington’s branching canals, which illustrate the sequential multi-lineage differentiation at different timescales. → Sweeping rates control the number of endpoints. Aberrant network structure and dynamics lead to disease. Two branch endpoints Three branch endpoints Gradient-based optimization with sweeping Sweeping represents maturation Genetic Oscillator. Repressilator-type network can activate suppressed genes by generating an attracting limit cycle. → Evolving repression links drive dedifferentiation to pluripotency (equal phenotype probabilities) or to transdifferentiation. → Conjecture: aberrant oscillations describe mutator phenotype and abnormal plasticity in cancer stem cells. Dedifferentiation back to pluripotency Reversal of dominant phenotype; oscillation- driven transdifferentiation Phenotype probability Absolute value of quasi-potential Time Time GRF 2, 4 and 5 were initially suppressed cartilage bones pluripotent fats auto- activation repression Note: the number of nodes are arbitrary, usually high-dimensional
Transcript of Pluripotent stem cell -...
( )
Branching and Oscillations
Abstract Existing mathematical models of gene interaction cannot fully characterize the temporal transformation of the epigenetic landscape because of fixed parameters and limited number of state variables. Here we present a high-dimensional model of gene interaction with time-varying asymmetric repression between gene regulatory factors. This model can predict the sequential branching in cell-fate determination and the oscillations that activate suppressed genes.
Significance • Provide insights into the possible mechanisms of cell
differentiation and associated diseases (e.g., cancer) • Contribute in devising strategies for cellular reprogramming (e.g.,
dedifferentiation back to pluripotency)
Equilibrium points and sustained oscillations (determinisitc) are contained in Degenerate case (infinitely many equilibrium points) can arise if
.,,,2
22
2
2
1
11
1
1
n
nn
n
n gggggg
1 iji cc for all i,j.
References: [1] C. H. Waddington, The Strategy of the Genes, George Allen & Unwin, 1957. [2] O. Cinquin, J. Demongeot, J. Theor. Biol. 233 (2005), 391-411. [3] B. D. Aguda, A. Friedman, Models of Cellular Regulation, Oxford U Press, 2008. [4] S. Yamanaka, Nature 460 (2009), 49-52. [5] J. F. Rabajante, PeerJ Pre-Prints (2014), e382v1.
The Dynamic System Model
,...,n2,1i
dWGσdtgXβ
Xu1
γXK
XαdX iiiii
ij
ijc
j2
i
ijic
ii
ic
iii
strength of the gene regulatory factor (GRF) involved in expressing the gene of the i-th phenotype
evolving parameter representing the time-varying strength of repression between the i-th and j-th GRFs
dWδdtu
)(t)ε(expdu i
i
ii
kinetics growth
A gene regulatory network that characterizes multi-stable cell-fate determination [2,3]. The X1, X2, and X3 represent the strengths of gene regulatory factors (GRFs), such as transcription factors. Cells can undergo transdifferentiation and dedifferentiation [4].
This network can be regulated (e.g., via noise, oscillation, and temporary or permanent parameter modification) [2,5].
2014 School on Hands-on Research in Complex Systems, Trieste Italy
Branching and Oscillations in Cell-Fate Determination Jomar Fajardo Rabajante1,2,3, Ariel Lagdameo Babierra1, Cherryl Ortega Talaue3
1Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Philippines 2Graduate School of Science and Technology, Shizuoka University, Japan
3Institute of Mathematics, University of the Philippines Diliman, Philippines
The canal is chosen by the differentiating cell based on the landscape’s potential such that the steeper pathway and deeper basin are preferred.
Background about epigenetic landscape
Waddington’s epigenetic landscape [1]. Branching canals depict various cell lineages towards different cell fates (phenotypes). Cell fates
Daughter cells
Pluripotent stem cell
Gene regulation
Pluripotent
stem cell
Daughter cells
Gene Regulatory Network
Acknowledgement: Partly funded by PCIEERD, DOST and by the University of the Philippines (JFRabajante MSc Thesis fellowship).
Baltazar D. Aguda for the useful discussions about models of cellular regulation.
Five branch
endpoints
Cell developmental pathways. We quantify Waddington’s branching canals, which illustrate the sequential multi-lineage differentiation at different timescales.
→ Sweeping rates control the number of endpoints. Aberrant network structure and dynamics lead to disease.
Two branch
endpoints
Three branch
endpoints
Gradient-based optimization with sweeping Sweeping represents maturation
Genetic Oscillator. Repressilator-type network can activate suppressed genes by generating an attracting limit cycle.
→ Evolving repression links drive dedifferentiation to pluripotency (equal phenotype probabilities) or to transdifferentiation.
→ Conjecture: aberrant oscillations describe mutator phenotype and abnormal plasticity in cancer stem cells.
Dedifferentiation
back to pluripotency
Reversal of dominant
phenotype; oscillation-
driven transdifferentiation
Phenoty
pe p
robabili
ty
Absolute value of quasi-potential
Time Time
GRF 2, 4 and 5 were initially suppressed
cartilage
bones
pluripotent
fats
auto- activation
repression
Note: the number of nodes are arbitrary, usually high-dimensional
