lecture #8
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Lecture #8
Stoichiometric Structure
Outline
• Cofactors and carriers• Bi-linear nature of reactions• Pathways versus cofactors• Basics of high energy bond exchange• Prototypic pathway models
Cofactors and Carriers
Basic Cofactor/Carrier Molecules in Metabolism
Some examples
Vitamins
The Bi-linear Nature of Biochemical Reactions: transfer/exchange of properties
Donor (X)
Carrier (C)Property (A)
Acceptor (Y)
Motif:
transferred/exchanged moietytransferred/exchanged moiety
Many donors
ATP ADP
Many, many acceptors
Highly connectedcarriers:
t 1min≅
PATHWAY VS. KEY COFACTOR VIEW
Redox Trafficking in the Core Metabolic Pathways:
pathway view
classical viewpointclassical viewpoint
Redox Trafficking in the Core Metabolic Pathways:cofactor view
A tangle of cycles through pools
systems viewpoint
HIGH ENERGY PHOSPHATE GROUP EXCHANGE
The Basics of High-Energy Phosphate Bond Trafficking
1. Basic Equations
ATP ADPvform
vuse
AMP ADP
vdistr+ -
Input/Output~0.0
= 0
(+I/O)
Dynamic Response to a Load Perturbation
ATP ADP
AMP ADP
50% increase in kuse
dynamic phaseportrait of fluxes
Graphical Representation of Charge and Capacity
fast
slow
here, capacity is constant at 4.2 mM since there are no I/O on the carrier molecule
(Reich, J.G. and Sel’kov, E.E., Energy Metabolism of the CellAcademic Press, New York, 1981).
2. Buffer on Energy Storage
is creatine in mammalian tissues
buffermolecule
Dynamic Response
btot =10Kbuff =1kbuff =1000
total capacity with buffer
same change as before
3. Open System: AMP made and degraded
ATP ADP
AMP ADP
10
0.03 mM/min
dAMPdt
=vamp,form-vamp,drain+vdistr
≠ 0
form
drain
Dynamic Response to a Load Perturbation (kuse,ATP50%)
(flux phase portraits)
Occupancy2ATP+ADPp(t)=Px(t)
Dynamic Response:capacity and charge
Capacity(ATP+ADP+AMP)
fast response
slow response
Charge and Capacity: Both Dynamic
fast
slow
PROTOTYPIC METABOLIC PATHWAYS WITH COFACTORS
C) Energy bonds for charging < recoveryD) The basic structure of pathways: it takes P ($) to make P ($)
Open System:charging and discharging metabolites
enabling a load to be placed on a system
Dynamic Responses to a Load Perturbation
Fast Slow
Dynamic Response (con’t)(flux phase portrait)
Differences from the un-coupled module
• The pathway input flux is fixed – Thus the ADP->ATP will be fixed– System will return to the original steady
state
• The ATP rate of use is increased 50% as before
Summary• The bi-linear properties of biochemical reactions lead to complex patterns
of exchange of key chemical moieties and properties. • Many such simultaneous exchange processes lead to a `tangle of cycles' in
biochemical reaction networks.• Skeleton (or scaffold) dynamic models of biochemical processes can be
carried out using dynamic mass balances based on elementary reaction representations and mass action kinetics.
• Many dynamic properties are a result of the stoichiometric texture and do not result from intricate regulatory mechanisms or complex kinetic expressions.
• Complex kinetic models are built in a bottom-up fashion, adding more and more details in a step-wise fashion making sure that every new feature is consistently integrated.
• Once dynamic network models are formulated, the perturbations to which we simulate their responses are in fluxes, typically the exchange and demand fluxes.
• A recurring theme is the formation of pools and the state of those pools in terms of how their total concentration is distributed among its constituent members.
• The time scales are typically separated.
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