Discrete dynamic modeling of biological regulatory networks

Transcription

1 Discrete dynamic modeling of biological regulatory networks Réka Albert Department of Physics, Department of Biology and Huck Institutes for the Life Sciences Pennsylvania State University

2 Life at the cellular level Cellular functions rely on the coordinated action of interacting components. Proteins provide structure to cells and tissues work as molecular motors sense chemicals in the environment drive chemical reactions regulate gene expression Interconnections between components are the essence of a living process. receptor proteins, enzymes, ribosomes, DNA David Goodsell/ Science Photo Library

3 Many non-identical elements connected by diverse interactions GENOME gene regulation PROTEOME protein-protein interactions external signals signal transduction METABOLISM Bio-chemical reactions Citrate Cycle

4 Cellular networks Genome level ~30,000 nodes Statistical mechanics of networks Component level ~3 nodes Molecular biology Module level 30 nodes Functional modeling

5 Common features of biological systems functionally diverse elements time-varying abundances & activities for each element diverse interactions that form networks have functions that need to be performed sensitive to some changes, insensitive/adaptable to others evolvable, shaped by evolution and natural selection Network = backbone of process Node states + transfer functions functional state of system Hypothesis: the organization of the regulatory network is more important than the kinetic details of the individual interactions.

6 From dose-response curves to Boolean switches X mrna Y transcriptional activator If ν is large, the dose-response curve becomes a switch Hill function If Y>K Y dx/dt>0 mrna production If Y<K Y dx/dt<0 mrna decay If activation is below threshold, mrna can decay. Boolean simplification: X* = Y Activation: If Y=ON X*=ON Decay: If Y= OFF X*=OFF * denotes the next state

7 Implementing time in discrete models 1. Synchronous models The state of each node is updated simultaneously at multiples of a common time step. Underlying assumption: the timescales of all synthesis and decay processes are similar 2. Asynchronous models The state of each node is updated individually Implementation used here: At each time step randomly select a permutation of the nodes and update them in that order. Synchronous models have deterministic state transitions, asynchronicity introduces stochasticity (update order dependence) in the dynamics.

8 Modeling drought signaling in plants Phenomenon: abscisic acid induced closure of plant stomata Hypotheses: network inference from indirect information protein activity is switch-like Validation: reproduces known wild type and disrupted behavior. Explored: disruptions changes in initial conditions ABA changes in timing Insight: variability in timing and initial conditions does not matter 65% of perturbations have no negative effect identified critical perturbations S. Li, S. Assmann and R. Albert, PLoS Biology 4, e312 (2006).

9 Stomata and guard cells The exchange of O 2 and CO 2 in plants occurs through stomata. 90% of the water taken up by a plant is lost in transpiration. Stomatal sizes are determined by the turgor (fullness) of the guard cells. During drought conditions plants synthesize a hormone called abscisic acid (ABA) that initiates a signal transduction network to close stomata. How is this crucial process being orchestrated, and how is its sensitivity and reliability maintained? CO 2 H 2 O

10 Experimental observations mainly indirect Genetic & pharmacological perturbations of putative mediators Compare input - output (ABA- aperture change) relationships in normal and perturbed plants Scarce biochemical evidence for interaction NO, S1P, IP3 membrane depolarization Ca 2+ c increase K + efflux ABA Closure ABI1

11 Network construction from indirect evidence nodes: all proteins, molecules, ion channels implicated in the process compress biological information into activation or inhibition hypothesis: indirect causal relationships and processes correspond to paths ABA ion flow, ABA Sph kinase activity activating or inhibiting effects on processes represented as intersection of two paths SphK (ABA closure) Node A interaction Node/Process B species ABA promotes SphK Arabidopsis PLC promotes ABA closure Commelina communis SphK partially promotes ABA AnionEM Arabidopsis Need to determine the closest regulator and target of each node

12 Network reduction Find the most parsimonious (least redundant) network that incorporates all nodes and known processes. Introduce intermediary nodes Contract intermediary nodes Review and revise General algorithm: binary transitive reduction with critical edges, pseudovertex collapse, implemented as NET-SYNTHESIS R. Albert, B. DasGupta et al, Journ. Comp Biology 14, 927 (2007).

13 enzymes, signal transduction proteins, transport, small molecules intermediary nodes

14 Asynchronous Boolean model States: 1 = active/high/open, 0 = inactive/low/closed NOT (inhibitors), AND (conditional activation), OR (independent activation) Ca 2+ c* = (CaIM or CIS) and not Ca 2+ ATPase Closure* = (KOUT or KAP) and AnionEM and Actin and not Malate 10,000 replicate simulations with randomly selected initial condition (except for ABA), random update order at each timestep. Output: frequency of closure=1 state

15 Percentag e of Closure Percenta 100% 80% 60% 40% 20% 0% 40% 20% 0% Signal transduction is resilient to perturbations Time Steps Time Steps Normal response to ABA stimulus. ABI1 knockout mutants respond faster. Perturbations in Ca 2+ lead to slower response. Perturbations in ph lead to decreased sensitivity. Surprising prediction: Ca 2+ disruption has less severe effects than ph c disruption.

16 Experimental validation Normal: open and closed state distinguishable Percentage Ca 2+ disrupted: open and closed state distinguishable ph c disrupted: open and closed state indistinguishable Aperture in µm

17 Discrete model of T cell survival Phenomenon: survival of cytotoxic T cells in T-LGL leukemia Constructed: survival signaling network inside T- LGL cells Hypotheses: discrete states, switch-like state changes Validation: reproduces known deregulations and known key mediators Predicts: minimal initial condition necessary for T-LGL state manipulations that ensure apoptosis of T-LGL cells additional deregulations Predictions were validated experimentally Implications: identifying therapeutic targets for T-LGL leukemia tumor and cancer vaccine development J. R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, T. P. Loughran, PNAS 105, (2008).

18 CTL activation induced cell death and LGL leukemia cytotoxic T lymphocytes (CTL) eliminate infected cells and tumor cells The majority of activated CTL undergo activation induced cell death (AICD), mainly through Fas-induced apoptosis T-LGL: abnormal clonal expansion of antigen primed mature CTL Activation of multiple survival pathways (MAPK; JAK-STAT) Insensitive to Fas-induced apoptosis No known curative therapy Erika L. Pearce & Hao Shen, 2006, Immunological Reviews Thierry Lamy & Thomas P. Loughran, Jr, 1998, Cancer Control

19 General CTL activation AICD network (extracted from literature) Known deregulated components in T LGL and related pathways NET SYNTHESIS (a signaling network inference and simplification tool) Augmented T LGL CTL survival network Strategy Discrete dynamic model T LGL CTL survival network Reveal possible causes of the pathway abnormalities Identify key survival mediators

20 T-LGL survival signaling network Rectangle: intracellular; ellipse: extracellular; diamond: receptor. Upregulated, downregulated, deregulated node; Activation, inhibition edge

21 Asynchronous Boolean model Aims: reproduce an LGL-like state determine minimal cause of an LGL-like state determine minimal intervention that reverses LGL-like state Rules for state transitions: Timestep: a round of updating during which all nodes are updated in a randomly selected order Simulation ends when apoptosis = 1 (cell death) is reached Multiple (>300) simulations for each initial condition, 20~40 timesteps Output of the model: the frequency of node activation; representative of cells that are still alive

22 Determined the causal hierarchy within the known deregulations Upregulated, downregulated in LGL Positive, negative causal effect Overexpression of IL15 and PDGF can cause all known deregulations.

23 Reproduce a T-LGL-like state Apoptosis stabilizes at OFF in a subset of simulations, JAK upregulated, IL-2 and proliferation downregulated. C Minimum condition: IL-15 constantly ON, PDGF intermittently ON, Stimuli initially ON. Suggestive of inflammation during infection Provision of IL-15 and PDGF may generate long-lived CTL for the virus and cancer vaccines.

24 Identify key mediators of T-LGL survival Identify nodes that stabilize when a T-LGL-like state is achieved Alter the node state and track the change of apoptosis frequency Key mediator: altering its state causes total apoptosis. Identified: SPHK1, NFκB, S1P, SOCS, GAP, BID and IL2RB Validation: NFκB constitutively active in T-LGL Model: NFκB stabilizes at ON, setting it OFF causes total apoptosis Validation: NFκB inhibition induces apoptosis in T- LGL

25 Identify additional deregulations Model: T-bet needs to be constitutively activated concurrently with NFκB activation to reproduce the low IL-2 production phenotype in leukemic T-LGL Experimental validation: T-bet overexpressed and highly active in T-LGL

26 Lessons learned Network allows the logical organization of disparate information into a coherent whole Network-based discrete dynamic model enables ranking of most important components and interactions has predictive value - corrections to conventional wisdom allows discovery of new strategies Methodology can be refined iteratively with experiments The topology of the network of interactions plays a determinant role in the system's behavior

27 Acknowledgements Song Li Ranran Zhang Juilee Thakar Assieh Saadatpour Moghaddam Colin Campbell Zhongyao Sun Ruisheng Wang Suann Yang Collaborators: Sarah Assmann (PSU Biology) Eric Harvill (PSU Vet. Sci.) and his group Thomas Loughran (HMC) and his group Bhaskar DasGupta Alfred P. Sloan Foundation NSF, NIH US Dept. of Agriculture