Transcript Evidence that cells are critical

Are cells dynamically critical
Stuart A. Kauffman, iCore chair
[email protected]
Institute for Biocomplexity and Informatics, University of Calgary, Canada
Department of Physics & Astronomy of the University of Calgary, Canada
University of Calgary
2500 University Drive NW, T2N 1N4
CANADA
http://www.ibi.ucalgary.ca/
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Cancer Stem Cell Therapy
1. Cancer stem cells have been discovered in breast, prostate, skin, blood,
brain and other tumors.
2. Cancer stem cells are capable of persistent self renewal and differentiating
into other cells of limited proliferation potential in the tumor.
3. Recent evidence suggests that specific subsets of genes are abnormally
expressed in cancer stem cells.
4. Aim of cancer stem cell therapy is to kill, stop the proliferation of, or cause
differentiation of cancer stem cells.
5. IBI lab is focusing on high throughput and specific siRNA, small molecules,
and expression vector library screening.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Genetic Regulatory Networks
Transcriptome Yeast regulates 6500 genes
Transcriptome in Humans regulates about 25000 genes
Transcriptome plus Protein signaling network is a parallel
processing non linear stochastic dynamical system.
Systems Biology seeks the integrated behavior of this
system within and between cells.
Systems Biology also seeks possible general laws.
A possible general law is that cells are dynamically critical.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Boolean networks as models of GRN’s
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Boolean networks as models of GRN’s
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Boolean Networks basins of attraction
All basins of attraction belong to the same network realization
with K=2 and N=15.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Ordered, Critical and Chaotic Behaviour
Order
Stuart A. Kauffman
Critical
Chaos
Nature, Max Planck Dec. 2006
Derrida Curve and criticality
Normalized Hamming distance
(000) --- > (001)
dT=1/3
(100
dT+1=2/3
) --- > (100)
Derrida curves of RBN's with
k=1,2,3,4,5. Analytical results.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Reasons why cells “should” be critical
.Cells must bind reliable past discriminations to future
reliable actions.
. In the order regime convergence in state space forgets
past distinctions.
.In the chaotic regime small noise yields divergence in
state space trajectories precluding reliable action.
.Critical regime with near parallel flow optimizes capacity
to bind past and future.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Reasons why cells “should” be critical
Critical Cells maximize correlated behaviour of genes over time.
Hence can carry out most complex coordinated behaviour
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Reasons why cells “should” be critical
. Critical Boolean Networks maximize robustness to mutations.
. Numerical experiments: add random gene, connected at random, to
the existing network, with random logic.
.Hypothesis: Cell types correspond to attractors
.Results: critical networks maximize the probability that such mutations
leave all existing attractors intact and occasionally add new attractors.
. Thus, critical networks optimize robustness of cell types to mutations
and the capacity to evolve new cell types.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Capacity to evolve to criticality
Selection on Boolean Networks to play mismatch
and random games converged from chaotic and
ordered regimes to critical behaviour
Selection for capacity to coordinate classification
of time varying signal converged to critical regime.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Evidence that cells are critical
. Reka Albert Boolean model of early Drosophila development is
critical by derrida criteria.
. Elena Alvarez-Buylla model of floral development in Arabidopsis is
critical by derrida criteria.
.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Evidence that cells are critical
Known e Coli. Network is critical, with random
Boolean functions (1500 genes).
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Evidence that cells are critical
Known Yeast. Network is critical, with random
Boolean functions (3500 genes).
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Evidence that cells are critical
Hela 48 hourly time point
gene array data.
(Lempel-Ziv analysis)
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Evidence that cells are critical: Avalanche size distribution
n - avalanche size
250 Yeast deletion mutants and the
distribution of number of genes that
alter activity is a power law with slope
-1.5 (characteristic of critical
networks).
P(Z=n) - number of times avalanche size
was observed divided by the number of
observations.
Dotted line: power law with slope -1.5.
Solid line: data from Hughes et. al.
Logarithmic binning. A gene is considered
differentially expressed if its expression
has changed more than 4 fold.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Evidence that cells are critical: normalized
compression distance (NCD) analysis
A
Analysis of Toll-like
receptors by gene array
A : binary macrophage data.
B
Boolean
Discretization
C
Ternary
Discretization
D
B : ternary macrophage data
C : RBNs with K = 1,2,3,4
D : ternary nets with
K = 1, 1.5, 2, 3, 4
Boolean Networks
Ternary Networks
(for ternary nets, K=1.5 is critical)
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Serra stuff
Chi-square distance between experimental
data and theoretical prediction, concerning
6 more frequent avalanches
Comparison between experimental data
and analytical calculus of 6 more frequent
avalanches (theta = 7, lambda = 6/7)
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
More Serra stuff
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
More Serra stuff
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Cancer Stem Cell Therapy
1. Cancer stem cells have been discovered in breast, prostate, skin, blood,
brain and other tumors.
2. Cancer stem cells are capable of persistent self renewal and differentiating
into other cells of limited proliferation potential in the tumor.
3. Recent evidence suggests that specific subsets of genes are abnormally
expressed in cancer stem cells.
4. Aim of cancer stem cell therapy is to kill, stop the proliferation of, or cause
differentiation of cancer stem cells.
5. IBI lab is focusing on high throughput and specific siRNA, small molecules,
and expression vector library screening.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
• Approaches to discovering structure and
logic of genetic regulatory nets.
1. ChIP-Chip.
2. Inference of transcription factor binding
sites.
3. Inference of structure and logic from time
series gene expression data.
4. Promoter bashing.
5. Data base integration.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Basins of attraction
A. Wuensche. Basins of attraction in network dynamics:A conceptual framework for biomolecular networks. In G. Schlosser and G.
Wagner, editors, Modularity in Development and Evolution. (in press) University of Chicago Press, Chicago, 2002.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
IADGRN
1) Generate network and Boolean functions
2) Generate a random initial state
3) Generate a path of states (affected by noise)
4) Infer the network with pairwise MI and DPI
5) Apply post-inference engine
6) Results Analysis
Memory requirements:
N (number genes), R (number runs), k (connectivity)
Path of States ~ O(N.R)
K functions ~ (N.2k)
Memory usage before inference engine ~ O(N2+N.R+N.2k)
Adjacency Matrix ~ O(N2)
Inference engine: O(2.S.N2+N2)
Limits:
50.000 genes,
20 inputs/gene.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Mutual Information Threshold
Pairwise Mutual Information distribution of
randomly generated binary time series
Increasing number of nodes,
100 experiments per data point.
.With N genes we will compute about N^2 pair wise mutual information's.
.Given M samples, we require an MI threshold (Bickel, Samuelsson and
Andrecut) such that on the order of 1 false positive will be found.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Mean Mutual Information
and Inference ability
MI distribution of all Boolean Functions as a function of k
Expected Pairwise Mutual Information of Random Boolean
Functions Given Different Input Distributions
1
0.6
1E-11
Regular
1E-22
Poisson
Exponential
0.5
1E-33
k1
k2
k3
k4
k5
k6
k7
k8
k9
1E-44
1E-55
0.4
1E-66
1E-77
0.3
1E-88
0.2
1E-110
1E-99
1E-121
1E-132
0.1
1E-143
1E-154
0
0
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Stuart A. Kauffman
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05 0.1 .15 0.2 .25 0.3 .35 0.4 .45
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0. 0.5 0. 0.6 0. 0.7 0. 0.8 0. 0.9
1
Nature, Max Planck Dec. 2006
Inferring from random Boolean networks time series with
random Boolean functions and monotonic functions,
for increasing connectivity
30.000 nodes Boolean networks, 1000 independent state transitions,
100 experiments per data point.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Inferring from random Boolean networks time series with
monotonic functions, for increasing experimental
noise in measuring genes expression level
30.000 nodes Boolean networks, 1000 independent state transitions,
100 experiments per data point.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Inferring from random Boolean networks continuous time series with
Monotonic and random functions, for increasing k
Boolean functions
were inferred at
90%, independent
of k.
30.000 nodes Boolean networks, 1000 continuous state transitions,
100 experiments per data point.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006
Predicting inferability
. Yeast Network, 3459 genes, exponential input distribution: Medusa
network.
. Using 600 independent state transitions and mutual information
threshold we predicted that we could infer 33% of the regulatory
connections and in fact predicted 34% with no false positives.
. Future: Inferring Stochastic Genetic Networks with array noise.
. Long term aim is to use gene expression time series from real cells
and be able to estimate inferability of network’s structure and logic.
. Inferring personalized structure and logic of cancer stem cell aberrant
circuitry for therapy.
Stuart A. Kauffman
Nature, Max Planck Dec. 2006