QUANTITATIVE LAWS June 13 -June 24

1. Naama Brenner
Dept of Chemical Engineering
& Network Biology Research Lab
Technion
Exploratory Adaptation in Random Networks

2. Unforeseen challenges
A novel, stressful situation
Not previously encountered
No available response
?
Improvisation
Reorganization
Exploration
Gene regulation and expression is also capable of
“Cells, Embryos and Evolution”
J. Gerhart & M. Kirschner

3. Regulatory evolution
* Gene co-option
* Gene recruitment
Reorganization of regulatory modes
-> Creation of novel phenotype
B. Prud’homme et al. (2007)
Developmental genes are
highly conserved
Their control elements are
complex and divergent

4. his3GAL
promoter
* 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

5. Gene expression tunes to challenge
Stolovicki et al. (2006)

6. Non-repeatability of adaptation
at 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

7. Unforeseen challenges
A novel, stressful situation
Not previously encountered
No available response
?
Exploration
Reorganization
Adaptation
Learning
Random network model of gene regulation
That can adapt by exploratory dynamics

8. 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 dynamics
As stable cell types
Binary neural-network (spin-glass) models
Mutations and fitness in evolving network populations
Non-specific properties
Fixed points, Modularity, Robustness…

9. 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 & Kaneko
2006, 2013

10. 1. Properties of gene regulation that might support exploratory adaptation
- A large number of interacting degrees of freedom
Many possible bindings for each TF
Heterogeneous network of interactions
Guelzim et al. (2002)
Harbison et al. (2004)

11. 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)

12. 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

13. 1. Properties of gene regulation that might support exploratory adaptation
- Alternative Splicing of TFs
Several possibilities
Alternative structures
Different interactions
Common:
~2/3 of human genome
Est. average 7 AS forms per gene
Niklas et al. (2015)
Pan et al. (2008)

14. 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)

15. 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

16. - 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

17. Cellular network model
 1 2, ,... Nx x x x
r
Large number of microscopic variables
( )x W x x 
r r r& Nonlinear equation of motion
Interactions and relaxation
Sompolinsky et al. (1988)
Random Gaussian matrix: uniform circular spectrum
Transition to chaos at threshold interactions
More complex networks – just starting to be explored

18. -50
0
50
0 200 400 600 800
x
Time
Macroscopic phenotype
Cellular network model
 1 2, ,... Nx x x x
r
Large number of microscopic variables
y b x 
r r
( )x W x x 
r r r& Nonlinear equation of motion
Interactions and relaxation
Typically irregular dynamics
-20
0
20
y
𝑦*
y b x 
r r
*
y y
constraint
Schreier et al., 2016
(arXiv)

21. “The curse of dimensionality:
Random and independent changes in high-dimensional space
Convergence not a-priori guaranteed
Simplest attempt:
W is a full random matrix with Gaussian elements
-> no convergence observed in simulations
Sparse random matrix
-> no convergence
Main Results:
1. Possible convergence to stable state satisfying the constraint
2. Convergence non-universal, depends on network properties
3. Complex and interesting, not yet understood, search dynamics

29. 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.

30. 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.

31. Acknowledgements
Hallel Schreier, Technion
Yoav Soen, Weizmann Institute
Technion Network Biology Research Lab:
Erez Braun, Shimon Marom, Omri Barak, Ron Meir, Noam Ziv
Network Biology Research Lab