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May 26, 2018

Discrete Dynamical Modeling of

Inducible Cellular Phenotypes

Current Work (2010-2012) and Future Directions

Bradly Alicea

http://www.msu.edu/~aliceabr/

Dynamics: an Alternative to

Reductionism Reductionism:

1) study a single gene, look for causal relationship. Problem: not scalable to a

whole-genome context, no account of interactions, correlation causation.

2) look for smallest possible units of analysis. Problem: there are many

mechanisms at many scales (space and time).

* cannot observe dynamics, or big picture of a process.

Complexity:

1) networks, interactions: smallest possible units interact and can form networks.

* gene-gene interactions, complex pathways, synthetic effects, futile cycles.

2) chaos: time-series can exhibit highly variable behavior across many time-

scales (intervals). Yet order maintained (intrinsic randomness aggregation -

order).

* actin remodeling, local field potentials, embryonic patterning.

Comparison with first poster

Dynamics Days 2010 (Chicago)

Evolution of a project, or

two sides of the same coin?

2010: excitable, sliding

cellular automata (CA).

2012: CAs + genetic

algorithms (GA).

2010: a way to discover

changes related to

reprogramming,

2012: a way to model

potential reprogramming

scenarios.

Cellular Automata (CAs)

Cellular Automata: discrete dynamical simulation.

Cells have properties and interaction rules, behave in parallel.

Properties: internal state.

Interaction rules: if n > 2 neighbors are red, turn red.

Parallelism: all cells use same set of rules, have same

properties.

current pattern 111 110 101 100 011 010 001 000

new state for

center cell 0 0 0 1 1 1 1 0

Example: Wolframs Rule 30 (1-D lattice)

Rule 30 - model Rule 30 - nature

1 2 3 4 5 6 7 8

Below: 2-D von Neumann neighborhood, order 1

Genetic Algorithms (GAs) Genetic Algorithm (GA): set of instructions based on what happens in a

biological genome (during evolution, gene expression). Dynamical simulation.

* used to find adaptive, optimal solutions for problems in computer graphics,

product design, robotics.

001 101 110 011 000

011 111 110 011 010

String can be replicated,

mutated, recombined over

several iterations. Produces

offspring, adaptive output.

Properties:

* single binary (or continuous) string

= chromosome.

* population of individuals.

* operators (mutation,

recombination, selection).

* evolution can be optimal, or it can

produce constrained variation.

Far left: fitness landscape for genetic algorithm optimization.

Courtesy: Mathworks.

Left: genetic algorithmically-evolved robot morphology.

Courtesy: Dr. Josh Bongard, New Scientist..

Dynamical Approximation Poster

(DD2010) Spatial heterogeneity:

colonies, cultures not

uniform.

Dynamical Approximation Poster

(DD2010) Spatial heterogeneity:

colonies, cultures not

uniform.

Kinetics among cells

across culture, colonies

not uniform.

Dynamical Approximation Poster

(DD2010) Spatial heterogeneity:

colonies, cultures not

uniform.

Kinetics among cells

across culture, colonies

not uniform.

Two stimulus model of

reprogramming: virus

and feedbacks.

Dynamical Approximation Poster

(DD2010) Spatial heterogeneity:

colonies, cultures not

uniform.

Kinetics among cells

across culture, colonies

not uniform.

Two stimulus model of

reprogramming: virus

and feedbacks.

Contact inhibition and

other topological

features (higher-D).

Dynamical Approximation Poster

(DD2010) Spatial heterogeneity:

colonies, cultures not

uniform.

Kinetics among cells

across culture, colonies

not uniform.

Two stimulus model of

reprogramming: virus

and feedbacks.

Sliding neighborhood:

cells can merge (B) and

change neighborhood.

Contact inhibition and

other topological

features (higher-D).

Dynamical Approximation Poster

(DD2010) Series of constraints (infectability, contact

inhibition, substrate). Determine initial,

subsequent state.

Dynamical Approximation Poster

(DD2010) Series of constraints (infectability, contact

inhibition, substrate). Determine initial,

subsequent state.

Infectability: excitable media approach.

Excitability in neurons and slime molds

(physical, electrical potentials).

Infection creates a potential in each cell

(cells interact, potential of magnitude can

convert cell).

Dynamical Approximation Poster

(DD2010) Series of constraints (infectability, contact

inhibition, substrate). Determine initial,

subsequent state.

Autonomous factors: infectability +

feedback = internal state, then external state.

* what is secondary stimulus? Intercellular

signaling?

Infectability: excitable media approach.

Excitability in neurons and slime molds

(physical, electrical potentials).

Infection creates a potential in each cell

(cells interact, potential of magnitude can

convert cell).

Dynamical Cellular Encodings

(DD2012)

Encoding: turn cell and

cell population behavior

into a computational

model.

Dynamical Cellular Encodings

(DD2012)

Hybrid Model: CA and

GA work in tandem.

Mapped to infectibility,

reprogramming process.

Encoding: turn cell and

cell population behavior

into a computational

model.

Dynamical Cellular Encodings

(DD2012)

Hybrid Model: CA and

GA work in tandem.

Mapped to infectability,

reprogramming process.

Encoding: turn cell and

cell population behavior

into a computational

model.

Population of cells are

infected. Fraction of

cells become carriers.

Trigger for additional

changes (focus on

intercellular factors).

Dynamical Cellular Encodings

(DD2012)

Design of each cells genome (basic

functional units). Initial switch (epigenetic

state), segments are expressed in

combination, at different intensities.

Dynamical Cellular Encodings

(DD2012)

Design of each cells genome (basic

functional units). Initial switch (epigenetic

state), segments are expressed in

combination, at different intensities.

More complex ruleset than 2010

poster. Rules for influencing

conversion of neighbors based on rate

of leaderless protein exchange, etc.

Leaderless Proteins Role in

Inducing Cellular Phenotype Intercellular signaling is done by leaderless proteins:

In leaderless mRNAs, 3 end is cleaved,

modifies sites of action (Cell, 147(1),

147-157 2011).

Interleukin 1- secretory protein lacking a signal

peptide (special route to transport). Mol Bio. Cell,

10(5), 1463-1475 (1999).

Figure 6 Figure 1

Leaderless Proteins Role in

Inducing Cellular Phenotype Intercellular signaling is done by leaderless proteins:

Occupy x,y,z,t? Shoaling fish?

What does it mean to be leaderless? In leaderless mRNAs, 3 end is cleaved,

modifies sites of action (Cell, 147(1),

147-157 2011).

Interleukin 1- secretory protein lacking a signal

peptide (special route to transport). Mol Bio. Cell,

10(5), 1463-1475 (1999).

Figure 6 Figure 1

Leaderless: not embedded in a hierarchy.

Leaderless molecules do not follow the leader (but

not necessarily random behavior).

* under certain conditions, leaderless activity

(shoaling fish?) may lead to order, patterned

behavior.

See also: Intracellular signaling proteins as

"smart" agents in parallel distributed processes.

BioSystems, 50, 159-171 (1999).

Future Work and Directions

Reconcile models presented

in 2010 (top) and 2012

(bottom).

Systems process model vs.

algorithmic model.

More explicit kinetics, stochastic

components?

Future Work and Directions

An excitable model focused on the activities of leaderless proteins:

Leaderless

proteins

Epigenetic

state Infected

Cell

Gene

regulation

Combinatorial

action

Inducement to a pluripotent state is still a two-stage process (positive for

virus, positive for pluripotency.

Needs more explicit stochastic mechanism within each cell (CA is

stochastic at the spatial (macro) scale.

Determines local cellular state

Collectively determine

neighborhood state

Focus on alternative intercellular

signaling molecules (take an alternate

pathway to action, more likely to

have a collective effect).

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