Exploratory Adaptation in Random Networks - Naama Brenner
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Transcript of Exploratory Adaptation in Random Networks - Naama Brenner
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Naama Brenner Dept of Chemical Engineering
& Network Biology Research LabTechnion
Exploratory Adaptation in Random Networks
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Unforeseen challengesA novel, stressful situation
Not previously encountered No available response
?
ImprovisationReorganization
Exploration
Gene regulation and expression is also capable of
“Cells, Embryos and Evolution”J. Gerhart & M. Kirschner
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Regulatory evolution
* Gene co-option * Gene recruitment
Reorganization of regulatory modes-> Creation of novel phenotype
B. Prud’homme et al. (2007)
Developmental genes arehighly conserved
Their control elements arecomplex and divergent
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his3GALpromoter
* HIS3 gene recruited under the GAL regulation network
…
…
Input: carbon source his3
Synthetic Gene Recruitment
Stolovicki et al. (2006); Stern et al. 2007; David et al. 2010; Katzir et al. 2012
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Gene expression tunes to challenge
Stolovicki et al. (2006)
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Non-repeatability of adaptationat the microscopic (gene) level
Biological replicates
-> A non-repeatable expression pattern; exploratory dynamics at the microscopic level?
Stern et al. (2007)
Same experiment, two time points
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Unforeseen challengesA novel, stressful situation
Not previously encountered No available response
?Exploration
ReorganizationAdaptationLearning
Random network model of gene regulationThat can adapt by exploratory dynamics
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Random networks as models of gene regulation
S. Kauffman “The origins of order” (1993)
A. Wagner “The origins of evolutionary innovation” (2011)
Boolean networks “N-K model”Fixed points of the dynamicsAs stable cell types
Binary neural-network (spin-glass) modelsMutations and fitness in evolving network populations
Non-specific properties
Fixed points, Modularity, Robustness…
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1. Properties of gene regulation that might support exploratory adaptation
2. An organizing principle to support convergence to new stable phenotypes
3. A theoretical model implementing this principle
Random networks as models of gene regulation
Non-specific properties within a single cell – exploratory adaptation
Furusawa & Kaneko2006, 2013
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1. Properties of gene regulation that might support exploratory adaptation
- A large number of interacting degrees of freedom
Many possible bindings for each TFHeterogeneous network of interactions
Guelzim et al. (2002)Harbison et al. (2004)
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1. Properties of gene regulation that might support exploratory adaptation
- Context-dependent binding of TFs
A large space of combinations in two tested familiar environments
Harbison et al. (2004)
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1. Properties of gene regulation that might support exploratory adaptation- Intrinsically Disordered Protein (IDP) domains: Protein that exists in a dynamic ensemble of conformations with no specific equilibrium structure.
~ 90% TFs have extended disordered regions ~40% of all proteins
P53: tumor suppressor signaling protein
cell-cycle progression, apoptosis induction, DNA repair, stress response
Fuxreiter et al. (2008)
Liu et al. (2006)Uversky & Dunker (2010)
Conformation and function depends on context – cellular environment
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1. Properties of gene regulation that might support exploratory adaptation
- Alternative Splicing of TFs
Several possibilities Alternative structuresDifferent interactions
Common:~2/3 of human genomeEst. average 7 AS forms per gene
Niklas et al. (2015)
Pan et al. (2008)
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1. Properties of gene regulation that might support exploratory adaptation- Post Translational Modification
Chromatin structure is affected by PTM of histone proteins
TFs are regulated by e.g. phosphorylation (more than other proteins)And also in their ID domains
- Degenerate mapping to phenotype: A phenotype can be realized by many different gene expression patterns
Niklas et al. (2015)
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2. An organizing principle to support convergence to new stable phenotypes
Drive Reduction: a primitive form of learning
- Stress induces a random exploration in the space of possible configurations
- As long as stress is high, keep exploring / searching
- When a stable configuration is encountered, stress is reduced, exploration too
Example in low-dimensional space: Bacterial chemotaxis
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- A large number of interacting microscopic variables
- A global, coarse-grained phenotype which is sensitive to external constraint
- Unforeseen, arbitrary challenge induces a stress
which drives a random search
- Stabilization by drive reduction principle - within a short timescale (lifetime of the organism) and without selection
3. A theoretical model implementing this principle
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Cellular network model 1 2, ,... Nx x x x
Large number of microscopic variables
( )x W x x Nonlinear equation of
motionInteractions and relaxation Sompolinsky et al. (1988)
Random Gaussian matrix: uniform circular spectrumTransition to chaos at threshold interactions
More complex networks – just starting to be explored
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0 200 400 600 800-50
0
50
Time
x
Macroscopic phenotype
Cellular network model 1 2, ,... Nx x x x
Large number of microscopic variables
y b x
( )x W x x Nonlinear equation of motion
Interactions and relaxationTypically irregular dynamics
-20-10
01020
y
𝑦*y b x
*y yconstraint
Schreier et al., 2016(arXiv)
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“The curse of dimensionality: Random and independent changes in high-dimensional spaceConvergence not a-priori guaranteed
Simplest attempt:W is a full random matrix with Gaussian elements-> no convergence observed in simulationsSparse random matrix-> no convergence
Main Results:1. Possible convergence to stable state satisfying the constraint2. Convergence non-universal, depends on network properties3. Complex and interesting, not yet understood, search dynamics
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Summary
- Exposing cells to unforeseen regulatory challenge reveals their ability to individually adapt in one or a few generations.
- Global dynamics of the gene regulatory network produces multiple non-repeatable expression patterns.
- A random network model of gene regulation, with a stress signal feeding back to the connection strengths, demonstrates the principle of exploratory adaptation.
- Convergence is possible but non-universal. A broad distribution of outgoing connections facilitates it.
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Conclusions & speculations
- Cellular adaptation can occur by temporal exploration and stabilize by “drive reduction”.
- This process can be viewed as a simple for of learning: modest learning task but no computation required.
- Demonstrates an organizing principle that guides exploratory adaptation and selects from the vast number of gene expression patterns.
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AcknowledgementsHallel Schreier, TechnionYoav Soen, Weizmann Institute
Technion Network Biology Research Lab: Erez Braun, Shimon Marom, Omri Barak, Ron Meir, Noam Ziv
Network Biology Research Lab