Glycolysis.
T. V. Bronnikova & W. M. Schaffer
I. INTRODUCTION.
A. Biological systems oscillate over a broad range of frequencies: fractions of a second to several hours.
B. Two Principal Types of Oscillators in Living Systems.
1. Cytoplasmic Oscillators: Periodic phenomena generated by dynamical instability in a metabolic pathway.
2. Membrane Oscillators: Membrane potential rhythm generated at the membrane's surface. Examples include
a) systems in which oscillations arise from oscillatory changes in permeability;
b) systems in which potential oscillations result from the periodic activity of an electrogenic pump.
3. Calcium is common component to both groups.
a. Intracellular levels of Ca++ determined by processes in both the membrane and the cytosol.
b. Organization of the cell as functional unit is such that cytoplasmic and membrane oscillatory mechanisms can never be entirely independent of each other.
II. GLYCOLYSIS
A. Two major processes take place in cytoplasm.
1. Synthesis of new molecules;
2. Energy production.
B. Principal metabolic networks involved in energy production are glycolysis and the citric acid (Krebs) cycle.
C. Glycolysis a sequence of nine enzyme-catalyzed reactions (right) that convert sugars into pyruvate which is further degraded to
1. alcohol (yeast fermentation
2. lactic acid (in muscles)
under anaerobic conditions or
3. acetyl coenzyme A
under aerobic conditions, i.e., via citric acid cycle.
D. For each molecule of sugar, there is a net production of two molecules of adenosine triphosphate (ATP).
1. Under anaerobic conditions, this is a cell's major energy supply.
2. Several ways to enter the glycolytic pathway:
a. Various sugars including glucose.
b. Glycogen.
3. Input pathways converge at the level of fructose-6-phosphate (F6P) which marks the beginning of the universal part of the reaction sequence.
III. GLYCOLYTIC OSCILLATIONS.
A. Glycolysis turns out to be a classic system for studying cytoplasmic (metabolic) oscillators.
1. Both damped and sustained oscillations (right) have been observed.
a. Damped oscillations first reported by Duysens & Amesz (1957).
b. Sustained oscillations in yeast cell free extracts observed when glucose-6-phosphate (G6P), fructose-6-phosphate (F6P) (Hess, et al., 1969) or trehalose (Pye, 1971) used as substrates.
2. Other experimental observations:
a. Yeast suspension (Chance, Schoener ∓ Elsaesser, 1964),
b. Ehrlich ascites tumor cells (Ibsen & Schiller, 1967),
c. Cardiac muscle (Frenkel, 1968),
d. Skeletal muscle (Tornheim & Lowenstein, 1974),
e. Blowflies Phormia terraenovae (Collatz & Horning, 1990),
f. Pancreatic b-cells (Chou et al., 1992)
g. Heart cells (O'Rourke et al., 1994) and
h. Intact myocytes (Hess, 1997).
B. Oscillations in yeast cells appear to be coupled to the plasma membrane potential (Hess, 1997).
C. Essential Properties of Glycolytic Oscillations
1. Sustained oscillatory behavior only observed over a limited range of substrate injection rates.
2. The period is of the order of several minutes and diminishes as the substrate injection rate increases (Hess et al., 1969; Hess & Boiteux, 1973).
3. Early on, phosphofructokinase (PFK) identified as source of oscillations (Ghosh & Chance, 1964; Hess & Boiteux, 1968; 1971).
D. Main Features of Glycolysis.
1. Phosphofructokinase is the key enzyme.
2. PFK activity is sensitive (Krebs 1972; Krebs and Beavo, 1979) to allosteric control by various components of the overall pathway.
a. Activated by its substrate, F6P, and also by reaction products, AMP and ADP (Ghosh & Chance,1964).
b. Inhibited by end product, ATP.
c. Note:
1. Activation of an enzyme by its product is rare.
2. Inhibition of an enzyme by end product of its pathway much more common (Cohen, 1983)
3. Changes in PFK activity can
a. Induce phase shifts;
b. Modulate period and amplitude;
c. Suppress oscillations (Hess, 1968).
E. Adenylate Charge Control (Atkinson, 1968, 1977)
1. Metabolic regulation as whole can be comprehended in terms of "Adenylate Energy Charge."
a. Ratio of concentrations
 |
a measure of the energetic resources of the cell.
b. Varies on [0,1] depending on relative amounts of AMP, ADP and ATP.
2. Enzymes that consume ATP active at high values of adenylate charge, i.e. activated by ATP and inhibited by an excess of ADP and AMP.
3. Enzymes that regenerate ATP active at low values of adenylate charge i.e. are inhibited by ATP and activated by an excess of ADP and AMP.
4. PFK is unique, because it both utilizes and produces ATP - i.e.,
a. ATP consumed when F6P converts to fructose diphosphate (FDP).
b. ATP produced by two "downstream reactions:"
1. When 1,3 phosphoglycerate (1,3 PGA) converts to 3 phosphoglycerate (3 PGA).
2. When phosphoenolpyruvate (PEP) converts to pyruvate.
5. Note that because
a. ADP activates PFK (as noted above) and
b. PFK catalyzes degradation of ATP to ADP (in course of converting F6P to FDP),
PFK is activated by its own reaction product.
A. Key Enzyme is PFK.
1. Activation of PFK by its substrate, F6P, leads to increased level of FDP thereby providing
a. Substrate to the rest of the cycle
b. Production of ATP (as noted above).
2.Increase of ATP occurs at the expense of ADP and AMP.
3. As ADP, AMP and F6P fall, activation of PFK declines.
4. Additionally PFK is inhibited by increase in ATP.
5. Switching off PFK leads to
a. Decreasing concentrations of FDP and ATP.
b. Associated accumulation of F6P and AMP/ADP.
6. With accumulation of F6P and AMP/ADP, PFK switches back on, and the cycle repeats.
B. Assumption of a single control point at PFK provides good explanation for oscillations in extracts from muscle and beef heart (Frenkel, 1968; Tornheim & Lowenstein, 1975).
C. For yeast cells, additional control point at PK (pyruvate kinase) must be taken into account (Boiteux & Hess, 1974).
V. MODELS OF GLYCOLYSIS
A. All models based on same reaction scheme.
B. Different models principally reflect different simplifying.
C. First model proposed by Higgins (1964).
1. Based on the activation of PFK by FDP.
2. Induces unstable oscillations of the Lotka-Volterra type.
D. Second model (Sel'kov, 1968; 1972) also relies on the activation of PFK.
1. But by ADP.
2. Includes a trimolecular step
3. Allosteric nature of enzyme kinetics not considered explicitly.
4. Behavior:
a. Induces limit cycles.
b. Does not account for existence of a bounded parameter range (rates of substrate input) corresponding to sustained oscillations.
E. Allosteric Model..
1. Closely related to Sel'kov model.
2. Developed by Goldbeter and associates (Goldbeter & Lefever, 1972; Goldbeter, 1974; Goldbeter & Nicolis, 1976.)
3. Explicitly considers allosteric nature of PFK.
4. Assumed differences in roles of substrates:
a. ATP and F6P which are transformed into ADP vs. FDP.
b. ATP/ADP pair plays more important role:
1. Addition of ADP gives phase shift of oscillations immediately;
2. Effect of FDP is much weaker (Hess & Boiteux, 1968; Pye, 1969).
c. Regulation principally by ADP.
F. In reality, PFK is regulated by many positive and negative effectors. This is achieved
1. Principally through allosteric control (Hess & Boiteux, 1968; Mansour, 1972);
2. But also via phosphorylation (Kitajima et al., 1983).
VI. THE ALLOSTERIC MODEL
A. Assumes monosubstrate, product-activated allosteric enzyme reaction as shown at right.
1. Assumes enzyme consists of two subunits.
2. Special case of n-subunit enzyme (see Goldbeter, 1996, for details).
B. Additional hypotheses as follows:
1. As in experiments with yeast extracts, substrate (S) is injected at constant rate, vi.
2. Each subunit, or promotor, can exist in two states, R (active) and T (inactive), which differ with regard to
a. Substrate affinity (K effect)
b. Catalytic activity (V effect)
3. In the absence of ligands, subunits undergo "concerted," i.e., correlated, transitions between the states with the proportion, p = [R]/([R]+[T]), of enzyme in the R state, close to 0.
4. The reaction product binds exclusively to a regulatory site of the enzyme in the R (active) state. This binding stabilizes the R state and allows p to increase.
5. The reaction product leaves the system at a rate proportional to its concentration.
C. The autocatalytic regulation of PFK is thus introduced by assuming that the product binds to a regulatory site that is accessible only when enzyme is in the active (R) state which is stabilized thereby.
D. Because binding of the product to the regulatory site in the R state is assumed to stabilize that state, the overall reaction rate is consequently enhanced.
E. Model assumption a spatially homogenous system corresponding to experiments subject to continuous stirring.
1. E.g., Yeast extract experiments
2. In the absence of such stirring, diffusion may lead to the formation of spatial or spatiotemporal structures in the form of propagating waves (Goldbeter & Lefever, 1972; Goldbeter, 1973; Goldbeter & Nicolis, 1976).
F. Equations.
1. Fast-slow time scale approximation permits reduction to two-variable system:
 |
 |
where a and g are dimensionless concentrations of substrate and product, and
 |
gives the desired sigmoid kinetics.
2. For additional details, see Goldbeter (1996).
G. Allosteric model reproduces the following experimental observations:
1. Sustained oscillations with period and amplitude observed in yeast extract experiments (Hess et al., 1969).
2. Dependence of enzymic activity on substrate injection rate.
3. Existence of a restricted range of substrate injection rates for which sustained oscillations observed.
4. Experimentally observed dependence of period and amplitude on injection rate (Hess & Boiteux, 1973).
5. Effect of enzyme concentration which is similar to that of substrate input rate (Frenkel, 1968).
6. Phase shifts induced by addition of ADP.
a. Experimentally, it is observed that ADP addition induces phase shift if [ADP] near minimum but not if [ADP] near maximum.
b. Model gives an explanation in terms of allosteric nature of the oscillatory enzyme.
VII. SUMMING UP.
A. Molecular Mechanism of Oscillations.
1. Starting with a low concentration of product, the latter slowly increases owing to the small amount of enzyme present in the R conformation - i.e., most enzyme in T state.
2. Product production rate increases as substrate accumulates.
3. With increasing concentration of product, increasing amounts of enzyme are stabilized in the active (R) state.
a. Results in enhanced rate of reaction.
b. Depletes concentration of substrate.
4. With reduced concentration of substrate and product degredation, product concentration drops.
5. Permits return of the enzyme to the less active T state and repetition of cycle.
6. Thus the mechanism of glycolysis can be considered as periodic alternation of the allosteric enzyme between its two conformational states driven by the constant substrate input and by the autocatalytic regulation of the enzyme by its reaction product.
B. Model can also reproduce experimental observations of entrainment and chaos resulting from periodic variation in rate of substrate input.
C. More complicated models.
1. Single allosteric enzyme but with additional "down-stream" enzymes modelled explicitly (Sel'kov, 1968; Schellenberger et al., 1978; Reich & Sel'kov, 1981; Termonia & Ross, 1981; Markus & Hess, 1984; Hocker et al., 1994).
2. Models with two allosteric enzymes both modelled as above for PFK (Decroly, 1987; Decroly & Goldbeter
1982)
a. Results in 3rd order systems.
b. Induce complex dynamics, including bursting oscillations, spiral chaos, etc., in absence of periodic forcing.
VIII. FUNCTIONAL SIGNIFICANCE.
A. Glycolytic oscillations may
1. Underlie circadian rhythms (Chance et al., 1964).
2. Facilitate alternation between biochemical pathways (Boiteux, Hess & Sel'kov, 1980; Reich & Sel'kov, 1981).
3. Increase efficiency of glycolysis cycle itself by 5-10% due to oscillations as argued by Ross and associates (Reich & Ross, 1980).
4. Drive pulsatile secretion of insulin in pancreatic beta-cells (Lipkin, Teller &
de Haen, 1983).
5. Cause certain forms of arrhythmia in cardiac cells (O'Rourke, et al., 1994).
B. Alternatively, glycolytic oscillations may be a metabolic "accident" that necessarily results from autocatalytic regulatory properties of PFK (Goldbeter, 1996).
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