Lecture #10 Metabolic Pathways

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

GLYCOLYSIS: AN OPEN SYSTEM

Glycolysis as an Open System

Compounds: the nodes pathway intermediates cofactors carriers

Reactions: the links

THE STEADY STATE

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

Glycolysis: ‘annotated’ S matrix ES=0

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

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

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

Reactions: the links pseudo elementary rate constants distance from equilibrium

DYNAMIC SIMULATION Model defined and ready for:

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

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

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

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

Glycolysis: 0-10 mins Tiled Phase Portrait: concentrations

Glycolysis: 10-infinity mins Tiled Phase Portrait: concentrations

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

STRUCTURAL PROPERTIES Towards systems biology

Glycolysis: the system with symbolic representation

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

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

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

Pools: from structural properties

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

Energy Value of Intermediates

Phosphate Bond Trafficking Incorporation: Recycled: Recycle ratio:

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

Glycolysis: 0-10 mins Tiled Phase Portrait: pools

Glycolysis: 10-infinity mins Tiled Phase Portrait: pools

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

RATIOS Towards physiology

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

Property rations or charges and their dynamic responses

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.

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.

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