Naama Brenner Dept of Chemical Engineering
& Network Biology Research LabTechnion
Exploratory Adaptation in Random Networks
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
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
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
Gene expression tunes to challenge
Stolovicki et al. (2006)
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
Unforeseen challengesA novel, stressful situation
Not previously encountered No available response
?Exploration
ReorganizationAdaptationLearning
Random network model of gene regulationThat can adapt by exploratory dynamics
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…
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
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)
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)
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
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)
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)
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
- 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
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
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)
“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
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.
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.
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