Basic modeling approaches for biological systems -II. Mahesh Bule

Transcription

1 Basic modeling approaches for biological systems -II Mahesh Bule

2 Modeling Metabolism Metabolism is general term for two kind of reactions Catabolic reactions (breakdown of complex compounds to get energy and building blocks) Anabolic reactions (construction of complex compounds used in cellular function)

3 Illustration of metabolism and its role in bottom up modeling approach

4 Approaches for modeling metabolic process

5 Modeling relation to real living world

6 Scheme of metabolic model construction

7 Study of metabolism Generally metabolism is studies at three levels of abstraction: Enzyme kinetic investigates the dynamic properties of the individual reactions in isolation The network character of metabolism is studied with stoichiometric analysis considering the balance of compound production and degradation Metabolic control analysis quantifies the effect of perturbations in the network employing the individual dynamics of concentration changes and their integration in network

8 Example: Modeling glucose utilization Glycolysis pathway by microorganism

9 Metabolic Network Basic elements of a metabolic network model are Substances with their concentrations The reaction or transport processes changing the concentration of substance

10 Modeling network function Accuracy Metabolic PPI Scale Kinetic models Approx. kinetics Constraint-based models Conventional functional models Topological analysis Dynamical systems Requires kinetic constants (mostly unknown) Optimization theory Constrained space of possible, steady-state network behaviors Probabilistic models, discrete models, etc Graph theory Structural network properties: degree distribution, centrality, clusters, etc

11 Kinetic models for metabolism Dynamics of metabolic behavior over time Metabolite concentrations Enzyme concentrations Enzyme activity rate depends on enzyme concentrations and metabolite concentrations Solved using a set of differential equations Impossible to model large-scale networks Requires specific enzyme rates data Too complicated

12 Basic definition in modeling r 1 = vmax 1 S K m1 + S Low K m will be the path with the higher flux (all other factors being equal). Low K m also means a strong interaction between substrate and enzyme. r Low K m High K m [S] These two curves have the same v max, but their K m values differ by a factor of 2.

13 Basic definition in modeling Total flux : F tot = vmax 1 S + vmax 2 S K m1 + S K m2 + S Selectivity F 1 = vmax 1 S K m1 + S S F 2 vmax 2 S r r 1 2 vmax vmax 1 2 K K m2 m1 K m2 + S S S I P 1 P 2

14 Glucose Glucose 6-Phosphate Phosphogluconate 2-Keto-3-deoxy-6- phosphogluconate Fructose 6-Phosphate Fructose 1,6-Bisphosphate Glyceraldehyde 3-Phosphate Phosphoenolpyruvate Glyceraldehyde 3-Phosphate Glyceraldehyde 3-Phosphate + Pyruvate Lactate Pyruvate Acetaldehyde NADH Ethanol Acetate Acetyl CoA Oxaloacetate Citrate NADH Malate Isocitrate CO 2 +NADH Fumarate FADH 2 Succinate a-ketoglutarate GTP GDP+P i CO 2 +NADH

15 Simplified metabolism - upstream end of glycolysis ATP v1 ADP ATP v2 ADP Glucose Glucose 6-Phosphate v3 Fructose 6-Phosphate Additional reactions v4 ATP ADP v6 ATP ADP Fructose 1,6-Bisphosphate ATP v7 ADP v5 ATP + AMP v8 2 ADP Pyruvate

16 How do you model this? What information is needed? equations for each v initial concentrations of each metabolite

17 Mass balances v8 dt damp 2v8 v7 v6 v4 v2 v1 dt dadp v8 v7 v6 v4 v2 v1 dt datp v5 v4 dt dfruc1,6p2 v4 v3 dt dfruc6p v3 v2 v1 dt dgluc6p

18 Defining reaction rate equations v1 1 [ATP(t)] K ATP1 v max,1 [ATP(t)][Glucose] [Glucose] K Glucose1 [ATP(t)] K ATP1 [Glucose] K Glucose1 v2 k2[atp(t)][gluc6p] v4 v max,4 KFruc6P4 1 Fruc6P(t) ATP(t) AMP (t) 2 2 Fruc6P(t) 2 v5 k5[fruc1,6p2]

19 Defining reaction rate equations v6 = k 6 ADP(t) v7 = k 7 ATP(t) v8 = k 8f ATP(t). AMP(t) k 8r (ADP(t)) 2

20 Selected packages for kinetic analysis

21 Constraint Based Models for Metabolism Provides a steady-state description of metabolic behavior A single, constant flux rate for each reaction Ignores metabolite concentrations Independent of enzyme activity rates Assume a set of constraints on reaction fluxes Genome scale models Flux rate: μ-mol / (mg * h)

22 Constraint Based Models for Metabolism Find a steady-state flux distribution through all biochemical reactions Under the constraints: Mass balance: metabolite production and consumption rates are equal Thermodynamic: irreversibility of reactions Enzymatic capacity: bounds on enzyme rates Availability of nutrients

23 Additional Constraints Transcriptional regulatory constraints Boolean representation of regulatory network Energy balance analysis Loops are not feasible according to thermodynamic principles Reaction directionality Depending on metabolite concentrations FBA solution space Meaningful solutions

24 Mathematical Representation of Constraint Based models Stoichiometric matrix network topology with stoichiometry of biochemical reactions Glucose + ATP Glucokinase Glucose-6-Phosphate + ADP Glucose -1 ATP -1 G-6-P +1 ADP +1 Glucokinase Mass balance S v = 0 Subspace of R n Thermodynamic v i > 0 Convex cone Capacity v i < v max Bounded convex cone 24

25 Constraint-based modeling applications Phenotype predictions: Growth rates across media Knockout lethality Nutrient uptake/secretion rates Intracellular fluxes Growth rate following adaptive evolution Bioengineering: Strain design overproduce desired compounds Biomedical: Predict drug targets for metabolic disorders Studying an array of questions regarding: Dispensability of metabolic genes Robustness and evolution of metabolic networks

26 Phenotype Predictions: Flux Predictions Predict metabolic fluxes following gene knockouts Search for short alternative pathways to adapt for gene knockouts (Regulatory On/Off Minimization- ROOM)

27 Strain design: maximizing metabolite production rate Identify a set of gene whose knockout increases the production rate of some metabolite The knockout of reaction v3 increases the production rate of metabolite F

28 Altering Phenotypic Potential: Gene Knockouts Minimization Of Metabolic Adjustment (MOMA) The flux distribution after a knockout is close to the wildtype s state under the Euclidian norm Regulatory On/Off Minimization (ROOM) Minimize the number of Boolean flux changes from the wild-type s state

29 ROOM vs. MOMA ROOM predicts metabolic steady-state after adaptation Provides accurate flux predictions Preserved flux linearity Finds alternative pathways Predicts steady-state growth rates MOMA predicts transient metabolic states following the knockout Provides more accurate transient growth rates

30 Altering Phenotypic Potential Explaining gene dispensability Only 32% of yeast genes contribute to biomass production in rich media Considered one arbitrary optimal growth solution OptKnock Identify gene deletions that generate desired phenotype OptStrain Identify strains which can generate desired phenotypes by adding/deleting genes

31 Modeling Gene Knockouts Gene knockout Enzyme knockout Reaction knockout

32 Regulatory On/Off Minimization (ROOM) Predicts the metabolic steady-state following the adaptation to the knockout Assumes the organism adapts by minimizing the set of regulatory changes Boolean Regulatory Change Boolean Flux Change Finds flux distribution with minimal number of Boolean flux changes

33 Example of network

34 Flux Balance Analysis (FBA) Finds flux distribution with maximal growth rate Biomass production rate represents growth rate Solver need to be used is Linear Programming (LP) Max v gro, s.t S v = 0, v min v v max - maximize growth - mass balance constraints - capacity constraints

35 Topological Methods Network based pathways: Extreme Pathways Elementary Flux Modes Decomposing flux distribution into extreme pathways Extreme pathways defining phenotypic phase planes Uniform random sampling

36 Extreme Pathways and Elementary Flux Modes Unique set of vectors that spans a solution space Consists of minimum number of reactions Extreme Pathways are systematically independent (convex basis vectors)

37 Flux Balance Analysis-Example Setp (I) : defination Vertex - substrate/metabolite concentration. Edge - flux (conversion mediated by enzymes of one substrate into the other) Internal flux edge External flux edge

38 Flux Balance Analysis Step (II)- Dynamic mass balance Concentration vector dx dt Stoichiometry Matrix S v Flux vector

39 Flux Balance Analysis Step (III)- Assumption of steady state Concentration vector dx dt Stoichiometry Matrix S v Flux vector 0 Sv 0 0 0

40 Minimal model of glycolysis

41 Structural kinetic modeling

42 Proposed flow for structural kinetic modeling