Are cells dynamically critical

1. Are cells dynamically critical Stuart A. Kauffman, iCore chair Skauffman@ucalgary.ca 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/

2. 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.

3. Boolean networks as models of GRN’s

4. Boolean networks as models of GRN’s

5. Boolean Networks basins of attraction All basins of attraction belong to the same network realization with K=2 and N=15.

6. Ordered, Critical and Chaotic Behaviour Ordered Critical Chaotic

7. Derrida Curve and criticality Normalized Hamming distance (000) --- > (001) dT=1/3 dT+1=2/3 (100 ) --- > (100) Derrida curves of RBN's with k=1,2,4. N = 1024. 2000 initial pairs of states averaged.

8. 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.

9. Reasons why cells “should” be critical Critical Cells maximize correlated behaviour of genes over time. Hence can carry out most complex coordinated behaviour

10. 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.

11. 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.

12. 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. .

13. Evidence that cells are critical Known e Coli. Network is critical, with random Boolean functions (1500 genes).

14. Evidence that cells are critical Known Yeast. Network is critical, with random Boolean functions (3500 genes).

15. Evidence that cells are critical Hela 48 hourly time point gene array data. (Lempel-Ziv analysis)

16. Evidence that cells are critical: Avalanche size distribution 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). n - avalanche size 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.

17. Evidence that cells are critical: normalized compression distance (NCD) analysis Analysis of Toll-like receptors by gene array A : binary macrophage data. B : ternary macrophage data C : RBNs with K = 1,2,3,4 D : ternary nets with K = 1, 1.5, 2, 3, 4 (for ternary nets, K=1.5 is critical)

18. 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)

19. More Serra stuff

20. More Serra stuff

21. 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.

22. 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.

23. 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.

24. 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.

25. 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.

26. Mean Mutual Information and Inference ability

27. 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.

28. 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.

29. 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.

30. 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.