Personal Summary of Interaction of Glycolysis and Mitochondrial Respiration in Metabolic Oscillations of Pancreatic Islets

Interaction of Glycolysis and Mitochondrial Respiration in Metabolic Oscillations of Pancreatic Islets

Personal Summary of:Interaction of Glycolysis and Mitochondrial Respiration in Metabolic Oscillations of Pancreatic Islets

Original Paper: Richard Bertram, Leslie S. Satin, Morten Gram Pedersen, Dan S. Luciani, and Arthur Sherman

Biophysical Journal (2007) Vol. 92 pp.15441555.

2011-10879

: 2011-10879

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Contents

Introduction

Biological oscillations

Glucose-stimulated insulin secretion from pancreatic beta cells

Competing hypotheses

Dual oscillator model

Models

The glycolytic model

The mitochondrial model

The electrical/calcium model

Results

Fast, slow, and compound bursting

Plasma membrane hyperpolarization

A mechanism for fast and slow mice

Limitations of the model

Conclusion

Further Research

References

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Biological oscillations

Theoretical models can tell many features of the biological oscillation

Molecular mechanisms

The conditions for oscillation

Physiological implications

Relations to other oscillatory phenomena

Goldbeter, Berridge, Biochemical Oscillations and Cellular Rhythms, Cambridge University Press, 1997

Our biosphere is teeming with oscillations. Oscillatory phenomena are present in every molecular, cellular, organismic, and ecological level of biological system, some of which are listed in the table above. While most biological phenomena does not lend itself for simple theoretical analysis, biological oscillations relatively tractable and have been the objects of theoretical analysis for many decades.

Theoretical model can provide test for proposed molecular mechanism of the oscillation, find appropriate conditions for stable oscillation, and reveal the relationship between different oscillatory phenomena. Finally, it may give us the understanding of why certain oscillations arise and persist while others do not.

Biological oscillations allow modelling into Boolean logics, difference equations, ordinary and partial differential equations, stochastic processes and many other forms. Among these, set of ordinary differential equations based on spatially homogeneous that is, each cellular compartment is assumed to be chemically homogeneous chemical kinetics is relatively simple and versatile tool for analysis.

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Glucose-stimulated insulin secretion from pancreatic beta cells

Conventional model of insulin secretion

The conventional model fails to capture the dynamic aspect of the insulin secretion

Oscillation in insulin secretion occurs in several time scale

Faster component (15 sec ~ 2 min)

Slower component (2~7 min)

Lost in type 2 diabetes patients

Bertram et al., Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion, Am J Physiol Endocrinol Metab 293: E890E900, 2007.

Pancreatic beta cells in islets of Langerhans are stimulated by elevated blood glucose level and secrete insulin to blood in order to prevent hyperglycemia.

Interestingly, glucose does not bind to any cell surface receptors, but affects beta cells cytoplasmic ATP/ADP ratio, which causes Ca2+ influx and release of insulin by exocytosis.

However, this conventional picture leaves out dynamic aspect of the insulin secretion by beta cells, that the rate of insulin secretion fluctuates in oscillatory manner. This oscillation is also not a simple periodic oscillation, but consists of several components of different period. Also, this oscillation was reproduced in an isolated islet or beta cell, which suggested that the oscillatory mechanism was contained within each beta cell.

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Competing hypotheses

Glycolysis-driven mechanism

Positive feedback of FBP on PFK-M

Oscillation in [ATP] and [ADP]

Oscillation in conductance of KATP channel

The role of Ca2+ is mediatory and/or nonessential

Ca2+-driven mechanism

Ca2+ influx depolarizes the membrane

Burst of Ca2+ influx is stopped by negative feedback

K(Ca) channel activation

decrease of [ATP]/[ADP] that will cause KATP channels to open

Ca2+ actively initiates the oscillation

Two competing hypotheses on the mechanism of pulsatile insulin secretion exist. One hypothesis is that inherent oscillation in cellular metabolism was the driving force of the oscillatory insulin secretion pattern. M-isoform of phosphofructokinase in beta cells can drive oscillation in metabolite levels by positive feedback of its product, fructose-1,6-bisphosphate, and mitochondrial respiration amplifies the oscillation. According to the alternate hypothesis, oscillation in membrane potential and intracellular Ca2+ level initiated by sudden influx of Ca2+ is the source of metabolic and secretory oscillation. Each claims that it has the support of experimental results. For example, some researchers reported that pulsatile insulin secretion was observed without intracellular oscillation of [Ca2+](Tornheim, 1997), while others maintained that constant level of intracellular Ca2+ prevented oscillation in glucose or oxygen consumption(Kennedy et al., 2002), which the authors regarded as proof that fluctuation in [Ca2+] preceded metabolic oscillation.

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Dual oscillator model

Fast component: Ca2+ feedback onto channels and metabolism

Slow component: oscillation in glycolysis

Bertram et al., Interaction of Glycolysis and Mitochondrial Respiration in Metabolic Oscillations of Pancreatic Islets, Biophysical Journal Volume 92 March 2007 15441555.

The authors of the paper reconciled the two views by assigning different roles for different oscillations. Their hypothesis was that the two mechanisms are not exclusive and rather work cooperatively to produce complex patterns of oscillation.

Fast bursting of the beta cell activity is based on Ca2+-centered feedback process, which is modulated by relatively slow glycolytic oscillation, although glycolysis is able to sustain [Ca2+] oscillation by itself. Mitochondrial respiration is the venue for electrical oscillation to feedback on itself by participation into the cell metabolism.

Biochemical reactions were modeled according to the laws of chemical kinetics into a set of ordinary differential equations, assuming that each cellular compartment is chemically homogeneous.

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The glycolytic model

is the average rate of considering the cooperative activation/inhibition of PFK subunits (Smolen, 1995)

Bertram et alCalcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets, Biophysical Journal Volume 87 November 2004 30743087.

A simplified model of glycolysis that emphasizes product activation/inhibition. R refers to the flow of chemicals. A constant flow(JGK) of glucose-6-phosphate from the action of glucokinase is assumed. Also, glucose-6-phosphate and fructose-6-phosphate are assumed to be in equilibrium. The glycolytic pathway below phosphorylation of fructose-6-phosphate is summarized as a single reaction rate equation adapted from Tornheim(1979).

All times are in units of second, and all concentrations are in units of M.

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NADH is produced in pyruvate dehydrogenase and citric acid cycle, and then consumed in oxidative phosphorylation.

: O2 consumption at the electron transport chain

ADP is consumed and ATP is produced in mitochondria

General form of the flux equation (c: adjustable parameter)

The mitochondrial model used by the authors is a simplified version of the Magnus-Keizer model(Bertram et al., 2006). Explicit formulas for J(chemical flux)s are too complicated to reproduce in here.

NADH is produced in glycolysis and citric acid cycle, but the formers contribution is relatively small, so was ignored. Also, the rate of citric acid cycle was assumed to be proportional to the rate of pyruvate dehydrogenase complex, and therefore was not distinguished from latter.

JPDH depends on mitochondrial NADH/NAD ratio and mitochondrial Ca2+ level.

The oxygen consumption rate depends on mitochondrial NADH level and the inner membrane potential.

Nucleotide transport rate is determined by mitochondrial ATP/ADP ratio and the inner membrane potential.

JF1F0 is determined by the mitochondrial ATP level and the inner membrane potential.

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affects oxidative phosphorylation rate and ionic flow across the membrane

Ca2+ enters the mitochondria by Ca2+ uniporter and leaves through Na+/Ca2+ exchanger.

: The fraction of free Ca2+

The inner membrane potential influences the oxidative phosphorylation rate and ionic flows across the inner membrane. The potential was in units of mV.

The rate of H+ production from respiration equals three times of the ATP production rate of the ATP synthase.

The ionic flow rate is determined by mitochondrial and cytosolic Ca2+ concentrations. Dependence on Na+ was discarded during the simplification step. (Bertram et al., 2006)

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Plasma membrane potential determines the conductance of ions across the plasma membrane and vice versa

The ionic currents are in general given by

All potentials are in units of mV.

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n: activation variable for the delayed rectifying K+ channel

,

: The conductance across the KATP channel

gKATP was a rather complex function of cytosolic adenine nucleotide concentrations, so was not reproduced in here.

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The cytosolic adenine nucleotide concentrations and cytosolic Ca2+ concentrations are related

Basal ATP hydrolysis rate was dependent upon cytosolic Ca2+ concentration and was proportional to cytosolic ATP concentration.

The flux of Ca2+ across the plasma membrane was the sum of the contributions from the membrane Ca2+ pump and passive flow proportional to the ICa2+.

The flux into ER was proportional to the cytosolic Ca2+ concentration, and the leakage out of ER was proportional to the difference in Ca2+ concentration between the two compartments.

The total cytosolic adenine nucleotide(ATP, ADP) concentration was conserved. Cytosolic AMP concentration was separately fixed.

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Only intermediate value of promote glycolytic oscillation in this model

Only fast oscillation is observed when is high

Increase in Ca2+ level rapidly turns off itself by activating K(Ca) channel, KATP channel, and ER Ca2+ ATPase


In this model, only the intermediate values of JGK promote glycolytic oscillation, and the system shows supercritical Hopf bifurcation at the high and low limits. This behavior will be revisited during the analysis of fast and slow mice.

When glycolytic oscillation is stalled, the system shows small fast oscillation by fluctuation of the plasma membranes ionic conductance. The increase in cytosolic Ca2+ level causes depolarization of mitochondrial membrane and promotes respiration but discourages oxidative phosphorylation. ATP is also consumed in pumping Ca2+ into the ER. Decline of cytosolic ATP level in turn opens the ATP-sensitive K+ channels and together with the Ca2+-activated K+ channels, ends the short burst.

Cytosolic ATP level also affects PFK rate, but now the fluctuation has been dampened and the affect on glycolysis is minimal, which is consistent with prior conclusion.

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Both components are superimposed when has intermediate value

Cellular O2 consumption rate is in phase with Ca2+ level and therefore with insulin secretion


If JGK is decreased to intermediate level, slow, large glycolytic oscillation is superimposed on the fast bursting of Ca2+. Glycolysis provides fuel(NADH) to the mitochondria, so mitochondrial activity oscillates in phase with fructose-1,6-bisphosphate level. High ATP/ADP ratio inhibits ATP-sensitive K+ channels from opening and hyperpolarizing the membrane, thus the gentle rise and fall of cytosolic Ca2+ level.

The O2 consumption is characterized with slow oscillations with fast teeth superimposed, which was verified in experiments. (Jung et al., 2000). Also, the in the slow oscillation, mitochondrial inner membrane potential is in phase with Ca2+, which was also experimentally observed. (Kindmark et al., 2001)

Although the authors did not make any explicit claim about this, it seems plausible to say that the dominant slow glycolytic oscillation causes NADH level to fall from the peak, which combined with the persistently high Ca2+ level, depresses ATP production, and at some point, the cell is unable to replenish ATP fast enough during the interval between short bursts, and the fast oscillation dies out until the Ca2+ level abates.

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When membrane Ca2+ oscillation is terminated by setting the fraction of open K(ATP) channel 1, all metabolic oscillation is terminated


When the effect of diazoxide(Dz) was simulated by reducing the plasma membrane Ca2+ channel conductance by 10-fold, both fast and slow metabolic oscillations were terminated. This is consistent with the experimental results. (Kennedy et al., 2002)

The key determining factor for whether or not the termination occurs is the PFKs affinity for inhibitor ATP. When the affinity is low enough, then glycolytic oscillations may persist even when the membrane is hyperpolarized, as was in the authors previous paper(Bertram et al., 2004).

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Experiments showed that metabolic oscillations pause when the cell membrane is hyperpolarized by diazoxide

However, this is not necessarily a case against glycolytic mechanism for slow oscillations

When membrane is hyperpolarized, cytosolic ATP level increases enough to stall glycolysis


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A mechanism for fast and slow mice

Individual mice differs in the oscillation period of pancreatic beta cell

The differences in glycolytic oscillation threshold comes from differences in PFK isoform composition

M-isoform is oscillatory, while C-isoform is not oscillatory


Insulin oscillations in some mice are primarily fast, whereas in other mice they are primarily slow. (Nunemaker et al., 2005) Since large variation in average blood glucose level or glucokinase activity is unlikely, the authors suggest that the glycolytic oscillation threshold is different between slow mice and fast mice. The slow mice have JGK outside the oscillatory parameter regime, while the fast mice have JGK inside the oscillatory parameter regime. The similar JGK can be inside or outside the oscillatory regime because different composition of PFK isoform gives different values of the lower and upper threshold. Only the M-isoform of PFK is oscillatory, so if there is not enough M-isoform, then the glycolytic oscillation cannot be sustained at any level of JGK. Therefore, the authors hypothesize that changes in glucose concentration can cause the beta cells of the slow mice to enter and exit oscillatory region, while no glucose concentration can accommodate glycolytic oscillation in the fast mice.

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Limitations of the model

The model omitted large part of the glycolysis and citric acid cycle

The model does not preserve stoichiometry of the aerobic respiration

The far from ~6

The parameter values of the calculations used in the paper gives the JO/JGK between ~53 and 84, which is very different from 6, which is expected from simple aerobic respiration equation. This was probably because many reaction pathways were omitted from the model. Nevertheless, the actual ratio in beta cells can vary from 6 and should be determined empirically. (Bertram et al., 2008)

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Conclusion

A mathematical model of the beta cell that can account for fast(15 sec ~ 2 min) and slow(2~7 min) oscillations in insulin was demonstrated

The glycolytic component produces slow oscillation and the electrical/calcium component generates fast oscillation, and the two communicate through the action of mitochondria (and ER)

Plasma membrane hyperpolarization can terminate metabolic oscillation, but it is not an evidence against glycolytic oscillations

The differences between individual mices insulin oscillation period was ascribed to differences in the isoform composition of PFK, which will be a possible experimental test for this model

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Further studies

Experimental and few theoretical investigations on the function of different molecular components

Affect of the different SERCA isoforms using islets from SERCA3(relatively low Ca2+ affinity) knockout mice (Bertram & Arceo II, 2008)

Modulation of oscillation by phosphofructo-2-kinase and fructose-2,6-bisphosphate (Merrins et al., 2012)

The role of Ca2+ oscillations (Merrins et al., 2010; Pedersen et al., 2013)

The role of KATP conductance in compound bursting (Watts et al., 2011; Ren et al., 2013)

Interislet synchronization (Zhang et al., 2008)

The further studies on this model was done on two directions. Many efforts were invested in experimentally determining the function of each molecular components of the system and interpreting the results using the double oscillator model. On the other hand, Zhang et al.(2008) attempted to use the model in analyzing the experimental result on interislet synchronization.

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References

Bertram et al., Calcium and glycolysis mediate multiple bursting modes in pancreatic islets, Biophys. J. (2004) Vol. 87, pp. 3074-3087.

Bertram et al., A simplified model for mitochondrial ATP production, J. Theor. Biol. (2006) Vol. 243, pp. 575-586.

Bertram et al., Interaction of Glycolysis and Mitochondrial Respiration in Metabolic Oscillations of Pancreatic Islets, Biophys. J. (2007) Vol. 92 pp. 15441555.

Bertram et al., Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion, Am J Physiol Endocrinol Metab (2007) Vol. 293, pp. E890E900.

Bertram, Arceo II, A mathematical study of the differential effects of two SERCA Isoforms on Ca2+ oscillations in pancreatic islets, Bull. Math. Biol. (2008) Vol. 70, pp. 12511271.

Bertram et al., Response to the comment by F. Diederichs, Biophys. J. (2008) Vol. 94, pp. 5080.

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References

Goldbeter, Berridge, Biochemical Oscillations and Cellular Rhythms, Cambridge University Press, 1997.

Jung et al., Correlated oscillations in glucose consumption, oxygen consumption, and intracellular free Ca2+ in single islets of Langerhans, J. Biol. Chem. (2000) Vol. 275 pp. 66426650.

Kennedy et al., Metabolic oscillations in -cells, Diabetes (2002) Vol. 51, Supplement 1, pp. S152-S161.

Kindmark et al., Glucose-induced oscillations in cytoplasmic free Ca2+ concentration precede oscillations in mitochondrial membrane potential in the pancreatic cell, J. Biol. Chem. (2001) Vol. 276, pp. 3453034536.

Merrins et al., Metabolic oscillations in pancreatic islets depend on the intracellular Ca2+ level but not Ca2+ oscillations, Biophys. J. (2010) Vol. 99, pp. 76-84.

Merrins et al., Phosphofructo-2-kinase/fructose-2,6-bisphosphatase modulates oscillations of pancreatic islet metabolism, PLoS ONE (2012) Vol. 7, No. 4, e34036.

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References

Nunemaker et al., Individual mice can be distinguished by the period of their islet calcium oscillations: Is there an intrinsic islet period that is imprinted in vivo?, Diabetes (2005) Vol. 54 pp. 35173522.

Pedersen et al., Complex patterns of metabolic and Ca2+ entrainment in pancreatic islets by oscillatory glucose, Biophys. J. (2013) Vol. 105, pp. 29-39.

Ren et al., Slow oscillations of KATP conductance in mouse pancreatic islets provide support for electrical bursting driven by metabolic oscillations, Am. J. Physiol. Endocrinol. Metab. (2013) Vol. 305, pp.E805-E817.

Tornheim, Are metabolic oscillations responsible for normal oscillatory insulin secretion?, Diabetes (1997) Vol. 46, pp. 1375-1380.

Watts et al., Mathematical modeling demonstrates how multiple slow processes can provide adjustable control of islet bursting, Islets (2011) Vol. 3, pp. 320-326.

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References

Zhang et al., Long lasting synchronization of calcium oscillations by cholinergic stimulation in isolated pancreatic islets, Biophys. J. (2008) Vol. 95, pp. 4676-4688.

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Personal Summary of Interaction of Glycolysis and Mitochondrial Respiration in Metabolic Oscillations of Pancreatic Islets