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Lecture #10 Metabolic Pathways

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Outline Glycolysis; a central metabolic pathway Fundamental structure (m x n = 20 x 21) Co-factor coupling (NAD, ATP, P i ) The stoichiometric matrix –Its null spaces Setting up a simulation model –Steady state Interpreting the results from simulation –Concentrations, fluxes, pools, ratios

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GLYCOLYSIS: AN OPEN SYSTEM

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Glycolysis as an Open System

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Compounds: the nodes pathway intermediates cofactors carriers

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Reactions: the links

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THE STEADY STATE

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The Stoichiometric Matrix mxn=20x21, Rank(S)=18 dim(Null)=21-18=3 dim(Left Null)=20-18=2 3 pathways 2 conserved moieties

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Glycolysis: ‘annotated’ S matrix ES=0

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Glycolysis: Pathways in Null(S) Selected basis based on biochemical intuition ~P synthesisredox couplinginventory of AMP

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The Steady State Fluxes (mM/hr): fluxes have to balance the network upper glycolysis lower glycolysis exchange & demand fluxes AMP

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The Steady State Concentrations (mM); determined by flux map and kinetic constants

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Reactions: the links pseudo elementary rate constants distance from equilibrium

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DYNAMIC SIMULATION Model defined and ready for:

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Simulation: 50% increase in k ATP : dynamic responses of the concentrations ADPATP load=k[ATP] 50% increase at t=0 Key Concepts 1. Time constants 2. Pools 3. Transitions

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Glycolysis: 0-10 mins Tiled Phase Portrait: fluxes of interest

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Glycolysis: 10-infinity mins Tiled Phase Portrait: fluxes of interest

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drain accumulation Dymamic Responses of the Fluxes drainaccumulation Secretion > stst Secretion

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Glycolysis: 0-10 mins Tiled Phase Portrait: concentrations

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Glycolysis: 10-infinity mins Tiled Phase Portrait: concentrations

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Simulation: 50% increase in kATP: dynamic responses of the concentrations fastintermediateslow ADPATP load=k[ATP] 50% et=0 Key Concepts 1.Time constants 2.Pools 3.Transitions

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STRUCTURAL PROPERTIES Towards systems biology

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Glycolysis: the system with symbolic representation

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Structural Properties: redox trafficking in glycolysis (#): Redox value #: Flux value

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Structural Properties: high-energy bond trafficking in glycolysis (#): High-energy bond “value” x: Flux value

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Structural Properties: The Trafficking of Phosphate Groups in Glycolysis “through” “cycle”

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Pools: from structural properties

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Redox Value of Intermediates reduce glycolytic intermediates oxydized glycolytic intermediates metabolites carrier

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Energy Value of Intermediates

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Phosphate Bond Trafficking Incorporation: Recycled: Recycle ratio:

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Pool Map: shows their interconnections and steady state concentrations by area of square

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Glycolysis: 0-10 mins Tiled Phase Portrait: pools

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Glycolysis: 10-infinity mins Tiled Phase Portrait: pools

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Dynamic Responses of the Pools 2(ATP+ADP+AMP) 2ATP+ADP PiPi ~P i capacity occupancy GP + and GP -

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RATIOS Towards physiology

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Dynamic Responses of the ratios Adenosine E.C Glycolytic E.C Phosphate recycle ratio

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Property rations or charges and their dynamic responses

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Summary First draft dynamic models can be obtained from using measured concentration values, elementary reactions, and associated mass action kinetics. This first draft can be used as a scaffold to build more complicated models that include regulatory effects and interactions with other pathways. Dynamic simulation can be performed for perturbation in environmental parameters and the responses examined in terms of the concentrations and the fluxes. A metabolic map can be analyzed for its stoichiometric texture to assess the co-factor coupling Such breakdown of the biochemistry helps define pools that are physiologically meaningful from a metabolic perspective, and are context dependent.

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Summary The raw output of the simulation can be post processed with a pooling matrix that allows the pools and their ratios to be graphed to obtain a deeper interpretation of dynamic responses. Some of the responses are built into the topological features of a network and require no regulatory action. The identification of the reactions that move the key pools is possible by the use of the stoichiometric matrix.

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Projects: perform same analysis Simulate response to NADH load Add R-L Shunt for 2,3 DPG in RBCs Add pentose pathway Add AMPK as a global regulator Add HK, PFK, PK as regulators of glycolysis

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