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