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Effect of lithium and sodium valproate ions on resting membrane potentials in neurons: an hypothesis
Journal of Affective Disorders 65 (2001) 95–99 www.elsevier.com / locate / jad
Special article
Effect of lithium and sodium valproate ions on resting membrane potentials in neurons: an hypothesis Alagu Thiruvengadam* Neo-Neuro-Research Laboratories, 11862 Farside Road, Ellicott City, MD 21042, USA Received 27 September 1999; accepted 2 March 2000
Abstract In an attempt to understand the therapeutic effects of lithium and sodium valproate in stabilizing the moods in manic depressive illness, the well-known Goldman–Hodgkin–Katz (G–H–K) equation is modified to include a fourth ion, such as a lithium ion or a sodium ion. The modified G–H–K equation is used to calculate the resting membrane potential in neurons. These calculations show that the resting membrane potential is depolarized depending upon the relative concentration of the lithium ion and upon its relative permeability. These calculations suggest that the resting membrane potential may be hyperpolarized in bipolar patients before treatment, and that the lithium ion perhaps depolarizes the resting membrane potential back to the normal level. They further support the prevailing hypothesis that manic-depressive illness may be caused by the hyperpolarization of the resting membrane potential, which, in turn, may be caused by the changes in ionic conductance (permeability) of the membranes. Sodium ions in sodium valproate do not significantly affect the resting membrane potential since they do not significantly change in the serum. 2001 Elsevier Science B.V. All rights reserved. Keywords: Manic depression; Lithium; Sodium valproate; Resting membrane potentials
1. Introduction Coppen et al. (1966) noticed abnormally increased intracellular sodium levels in manic patients, while the sodium levels in their blood plasma remained unchanged. Akagawa et al. (1980) measured the activity of erythrocyte Na,K-ATPase under mania and found a significant increase in Na,K-ATPase in manic patients as compared with controls. Hokin*Tel.: 11-301-596-1969. E-mail address: [email protected] (A. Thiruvengadam).
Neaverson and Jefferson (1989) established that the sodium–potassium pump activity was deficient in bipolar patients, and reached close to normal levels during lithium therapy. After a comprehensive review of literature (including 135 references), ElMallakh and Wyatt (1995) proposed a Na,K-ATPase hypothesis for bipolar illness. In this hypothesis, they suggested that the alterations in Na,K-ATPase can lead to bipolar illness. They further proposed that a study of membrane potentials and associated neurotransmitter release would be very useful. As a first step toward that goal, the resting
0165-0327 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0165-0327( 00 )00216-0
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
96
membrane potential is calculated using the Goldman–Hodgkin–Katz (G–H–K) equation (Goldman, 1943; Hodgkin and Katz, 1949). The G–H–K equation was modified to include a fourth ion, and was normalized with respect to the Na concentration and Na permeability of the membrane. These calculations show that the resting membrane potentials are depolarized at various values, depending on the lithium ion concentrations and permeabilities. This result provides additional support for the prevailing hypothesis for bipolar disorder.
3. Calculation of resting membrane potentials Eq. (3) may be used to calculate the new resting potential if we know the values of permeabilities and ion concentrations from experimental measurements. Such measurements are readily available for squid giant axons at 188C (Hodgkin and Huxley, 1952; McCormick, 1999), as follows: PK :PNa :PCl 5 1.00:0.04:0.45 K 1 :Na 1 :Cl 2 5 400:50:40 for inside values and
2. Modified Goldman–Hodgkin–Katz equation
K 1 :Na 1 :Cl 2 5 20:440:560 for outside values.
The G–H–K equation for the resting membrane potential is given by:
Using these values, Eq. (3) becomes:
2 PK K o1 1 PNa Na 1 o 1 PCl Cl 1 V 5 (RT /kF ) log 10 ]]]]]]]] PK K i1 1 PNa Na i1 1 PCl Cl o2
(1)
where V is the resting membrane potential, PK , PNa and PCl are permeabilities of the respective ions, and K 1 , Na 1 and Cl 2 are concentrations of the respective ions. Subscripts o and i stand for outside and inside the membrane, respectively. R is the gas constant, T is the absolute temperature, F is the Faraday’s equivalent and k is the conversion factor from ln to log 10 . If another ion is introduced into the system, then the G–H–K equation can be modified as 1 o 1 i
1 o 1 i
2 i 2 o
1 3.2 1 PI /PNa [I 1 o /Na o ] V 9 5 58 log 10 ]]]]]]] 37.2 1 PI /PNa [I i1 /Na o1 ]
We further make the following assumptions, as being reasonable: 1 I1 PI /PNa | 10 to 100 i /Na o < 1;
Then PI /PNa [I i1 /Na o1 ] | 1 Now, Eq. (4) becomes: 3.2 1 PI /PNa [I o1 /Na o1 ] V 9 5 58 log 10 ]]]]]]] 37.2
1 I o 1 I i
PK K 1 PNa Na 1 PCl Cl 1 P I V 9 5 58 log 10 ]]]]]]]]]] PK K 1 PNa Na 1 PCl Cl 1 P I (2) where V 9 is the new resting membrane potential, I 1 and PI are the new ion concentration and permeability, respectively, and 58 is the value of RT /kF at 188C, which is the temperature of squid. By dividing the numerator and the denominator by 1 PNa (Na )o , Eq. (2) becomes V 9 5 58 log 10 PK /PNa [K 1o /Na 1o ]1l1PCl /PNa [Cl 2i /Na 1o ]1PI /PNa [I 1o /Na 1o ] ]]]]]]]]]]]]]] PK /PNa [K i1 /Na 1o ]1[Na 1i /Na 1o ]1PCl /PNa [Cl 2o /Na 1o ]1PI /PNa [I 1i /Na o1 ]
(3)
(4)
(5)
Eq. (5) may be plotted as shown in Fig. 1. Similar calculations for mammalian membranes (cat motor neurons) are made from measured values of permeabilities and concentrations, as found in Kingsley (1996). The equation for the resting membrane potential for the mammalian neuron, V 0 is given by: 4.7 1 PI /PNa [I o1 /Na o1 ] V 0 5 62 log 10 ]]]]]]] 100
(6)
Eq. (6) is shown plotted in Fig. 2. The results shown in Figs. 1 and 2 indicate how resting membrane potentials vary with relative ion concentrations and relative permeabilities of the added ions.
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
97
4. Discussion
4.1. Depolarization of membranes
Fig. 1. The resting membrane potential (mV) depolarizes (decreases in magnitude of negative voltages) as a function of the 1 relative concentration of the added ion, I 1 o /Na o . As the relative permeability of the added ions increases, the resting membrane potential further depolarizes to a less negative value at a given relative ion concentration. These data correspond to a squid giant axon at a temperature of 188C. The therapeutic and toxic levels of lithium in humans are also indicated.
Figs. 1 and 2 show that the resting membrane potential gets depolarized depending upon the relative concentration of the added ion and its relative permeability. The therapeutic effects of lithium may be due to this depolarizing effect of lithium ions. This would indicate that the resting membrane potential in bipolar patients is hyperpolarized before the lithium treatment. El-Mallakh et al. (1996) measured the transmembrane potential (TMP) in mononuclear leukocytes from patients with bipolar disorder and compared it with values in control individuals. They found that the majority of manic and hypomanic patients had a significantly hyperpolarized lymphocyte TMP. These findings seem to agree with the present results. Hokin-Neaverson and Jefferson (1989) found that the sodium pump activity increased significantly during lithium therapy, to a level that was not much different from that of controls. This again provides additional support for the present results. Also shown in these figures are the ranges of therapeutic levels and toxic levels of lithium in humans, as given in Bowden (1995) and Ravel (1996). However, these results show that the permeabilities of lithium have to be at least an order of magnitude higher than those of sodium for any significant depolarization to occur at these levels of extracellular lithium.
4.2. Effect of extracellular potassium on hyperpolarization In order to understand the possible causes of hyperpolarization in manic patients, further calculations were made using the published data for sodium and potassium, as found in Coppen et al. (1966) and Krupp et al. (1997). Without adding any extra ions to the neurons in humans, Eq. (3) reduces to Fig. 2. The calculated values of the resting membrane potentials from Eq. (6) using typical values for cat motor neurons are shown in this figure, thus confirming the results shown in Fig. 1 for squid giant axons. These data correspond to the cat’s body temperature of 378C.
1 PK /PNa (K 1 o /Na o ) 1 1 V 5 62 log 10 ]]]]]] 1 PK /PNa (K i /Na 1 o )
(7)
Since there are no published data on the permeabilities of potassium and sodium in human
98
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
Fig. 4. Hyperpolarization is plotted at various values of relative permeabilities, since their exact values in humans are not known. Hyperpolarization does not increase significantly with relative permeabilities in the range considered. Fig. 3. Hyperpolarization (increase in magnitude of negative voltages) varies significantly with extracellular potassium levels in humans. Three relative permeabilities were considered, since their exact values in humans are not known.
neurons, a range of relative permeabilities were used to calculate their effect on hyperpolarization. Fig. 3 shows such calculations to demonstrate how extracellular potassium level would affect the hyperpolarization of human neurons at three different relative potassium levels. Extracellular potassium level does have a significant effect on the hyperpolarization of the resting membrane potentials. In order to evaluate the variations caused by the relative potassium permeabilities, the resting membrane potentials were calculated and are shown in Fig. 4. The relative permeability does not have any appreciable effect on hyperpolarization based on these equations.
4.3. Effect of extracellular sodium on hyperpolarization Coppen et al. (1966) reported that sodium concentrations in blood plasma varied in the range of 130 to 150 mEq / l in manic phase as well as in ‘normal’ phase. In order to see if such variations in extracellular sodium have any effect on hyperpolarization, the data shown in Fig. 5 were calculated using Eq. (7). They indicate that small changes in extracellular sodium do not have any significant effect on hyperpolarization. Since extracellular sodium levels do not change much during sodium
valproate therapy, it is highly doubtful that the sodium ions in sodium valproate play any direct role in mediating mania. However, it is possible that the valproic acid may play a role in regulating potassium channels in addition to other possible mechanisms.
4.4. Further research needed Hodgkin and Huxley (1952) showed that the resting membrane potential is directly related to the membrane conductance. According to this relationship, the hyperpolarization is caused by a reduction in the conductance of the membrane. This is further supported by the Na,K-ATPase hypothesis, which was put forward by El-Mallakh and Wyatt (1995). Clinical research by Akagawa et al. (1980), HokinNeaverson and Jefferson (1989) and El-Mallakh et al. (1996) has been very useful in furthering the understanding of the mechanisms of ionic-exchange processes that take place in the membranes of the neurons. As suggested by El-Mallakh and Wyatt (1995), it would be very useful to understand how hyperpolarization and depolarization affect the excitability of the membrane and associated transmitter release. With this objective in mind, further analysis is under way to study the role of the electrical properties such as conductance (permeability), capacitance and inductance on the voltage response of the membranes, using the equivalent circuits suggested by Cole (1941) and Hodgkin and Huxley (1952). Such voltage responses may be correlated
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
99
Fig. 5. Small variation in extracellular sodium concentration does not affect the hyperpolarization of membranes significantly, even at different permeabilities.
with electroencephalographic (EEG) measurements. Hopefully, this approach would lead to a relationship between the vesicle release rate and the voltage response of the membranes. Animal research to determine the relative permeabilities and to study if sodium valproate affects the ion concentrations in mammalian membranes would be useful.
Acknowledgements The author is grateful to Dr. Raj Thiruvengadam and to S. Nathan M.D. for useful discussions. The comments and suggestions made by the Editor and the anonymous reviewers are thankfully acknowledged.
References Akagawa, K., Wakanabe, M., Tsukada, Y., 1980. Activity of erythrocyte Na, K-ATPase in manic patients. J. Neurochem. 35, 258–260. Bowden, C.L., 1995. Predictors of response to divalproex and lithium. J. Clin. Psychiatry 56 (Suppl.), 25–30. Cole, K.S., 1941. Rectification and inductance in the squid giant axon. J. Gen. Physiol. 25, 29–51.
Coppen, A., Shaw, D.M., Malleson, A., Costain, R., 1966. Mineral metabolism in mania. Br. Med. J. 1, 71–75. El-Mallakh, R.S., Wyatt, R.J., 1995. The Na, K-ATPase hypothesis for bipolar illness. Biol. Psychiatry 37, 235–244. El-Mallakh, R.S., Li, R., Worth, C.A., Peiper, S.C., 1996. Leukocyte transmembrane potential in bipolar illness. J. Affect. Disord. 41, 33–37. Goldman, D.F., 1943. Potential, impedance and rectification in membranes. J. Gen. Physiol. (Lond.) 27, 37–60. Hodgkin, A.L., Huxley, A.F., 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.) 117, 500–544. Hodgkin, A.L., Katz, B., 1949. The effect of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. (Lond.) 108, 37–77. Hokin-Neaverson, M., Jefferson, J.W., 1989. Deficient erythrocyte Na, K-ATPase in different affective states in bipolar affective disorder and normalization by lithium therapy. Neuropsychobiology 22, 18–25. Kingsley, R.F., 1996. In: Concise Text of Neuroscience. Williams and Wilkins, Baltimore, MD, p. 81. Krupp, M.A., Sweet, N.J. et al., 1997. Physicians Handbook. Lange Medical Publications, Los Altos, CA. McCormick, D.A., 1999. Membrane potential and action potential. In: Zigmond, M.J. (Ed.), Fundamental Neuroscience. Academic Press, New York, NY, pp. 129–154. Ravel, R., 1996. Clinical Laboratory Medicine. Year Book Medical Publications, Inc, Chicago, IL.
Special article
Effect of lithium and sodium valproate ions on resting membrane potentials in neurons: an hypothesis Alagu Thiruvengadam* Neo-Neuro-Research Laboratories, 11862 Farside Road, Ellicott City, MD 21042, USA Received 27 September 1999; accepted 2 March 2000
Abstract In an attempt to understand the therapeutic effects of lithium and sodium valproate in stabilizing the moods in manic depressive illness, the well-known Goldman–Hodgkin–Katz (G–H–K) equation is modified to include a fourth ion, such as a lithium ion or a sodium ion. The modified G–H–K equation is used to calculate the resting membrane potential in neurons. These calculations show that the resting membrane potential is depolarized depending upon the relative concentration of the lithium ion and upon its relative permeability. These calculations suggest that the resting membrane potential may be hyperpolarized in bipolar patients before treatment, and that the lithium ion perhaps depolarizes the resting membrane potential back to the normal level. They further support the prevailing hypothesis that manic-depressive illness may be caused by the hyperpolarization of the resting membrane potential, which, in turn, may be caused by the changes in ionic conductance (permeability) of the membranes. Sodium ions in sodium valproate do not significantly affect the resting membrane potential since they do not significantly change in the serum. 2001 Elsevier Science B.V. All rights reserved. Keywords: Manic depression; Lithium; Sodium valproate; Resting membrane potentials
1. Introduction Coppen et al. (1966) noticed abnormally increased intracellular sodium levels in manic patients, while the sodium levels in their blood plasma remained unchanged. Akagawa et al. (1980) measured the activity of erythrocyte Na,K-ATPase under mania and found a significant increase in Na,K-ATPase in manic patients as compared with controls. Hokin*Tel.: 11-301-596-1969. E-mail address: [email protected] (A. Thiruvengadam).
Neaverson and Jefferson (1989) established that the sodium–potassium pump activity was deficient in bipolar patients, and reached close to normal levels during lithium therapy. After a comprehensive review of literature (including 135 references), ElMallakh and Wyatt (1995) proposed a Na,K-ATPase hypothesis for bipolar illness. In this hypothesis, they suggested that the alterations in Na,K-ATPase can lead to bipolar illness. They further proposed that a study of membrane potentials and associated neurotransmitter release would be very useful. As a first step toward that goal, the resting
0165-0327 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0165-0327( 00 )00216-0
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
96
membrane potential is calculated using the Goldman–Hodgkin–Katz (G–H–K) equation (Goldman, 1943; Hodgkin and Katz, 1949). The G–H–K equation was modified to include a fourth ion, and was normalized with respect to the Na concentration and Na permeability of the membrane. These calculations show that the resting membrane potentials are depolarized at various values, depending on the lithium ion concentrations and permeabilities. This result provides additional support for the prevailing hypothesis for bipolar disorder.
3. Calculation of resting membrane potentials Eq. (3) may be used to calculate the new resting potential if we know the values of permeabilities and ion concentrations from experimental measurements. Such measurements are readily available for squid giant axons at 188C (Hodgkin and Huxley, 1952; McCormick, 1999), as follows: PK :PNa :PCl 5 1.00:0.04:0.45 K 1 :Na 1 :Cl 2 5 400:50:40 for inside values and
2. Modified Goldman–Hodgkin–Katz equation
K 1 :Na 1 :Cl 2 5 20:440:560 for outside values.
The G–H–K equation for the resting membrane potential is given by:
Using these values, Eq. (3) becomes:
2 PK K o1 1 PNa Na 1 o 1 PCl Cl 1 V 5 (RT /kF ) log 10 ]]]]]]]] PK K i1 1 PNa Na i1 1 PCl Cl o2
(1)
where V is the resting membrane potential, PK , PNa and PCl are permeabilities of the respective ions, and K 1 , Na 1 and Cl 2 are concentrations of the respective ions. Subscripts o and i stand for outside and inside the membrane, respectively. R is the gas constant, T is the absolute temperature, F is the Faraday’s equivalent and k is the conversion factor from ln to log 10 . If another ion is introduced into the system, then the G–H–K equation can be modified as 1 o 1 i
1 o 1 i
2 i 2 o
1 3.2 1 PI /PNa [I 1 o /Na o ] V 9 5 58 log 10 ]]]]]]] 37.2 1 PI /PNa [I i1 /Na o1 ]
We further make the following assumptions, as being reasonable: 1 I1 PI /PNa | 10 to 100 i /Na o < 1;
Then PI /PNa [I i1 /Na o1 ] | 1 Now, Eq. (4) becomes: 3.2 1 PI /PNa [I o1 /Na o1 ] V 9 5 58 log 10 ]]]]]]] 37.2
1 I o 1 I i
PK K 1 PNa Na 1 PCl Cl 1 P I V 9 5 58 log 10 ]]]]]]]]]] PK K 1 PNa Na 1 PCl Cl 1 P I (2) where V 9 is the new resting membrane potential, I 1 and PI are the new ion concentration and permeability, respectively, and 58 is the value of RT /kF at 188C, which is the temperature of squid. By dividing the numerator and the denominator by 1 PNa (Na )o , Eq. (2) becomes V 9 5 58 log 10 PK /PNa [K 1o /Na 1o ]1l1PCl /PNa [Cl 2i /Na 1o ]1PI /PNa [I 1o /Na 1o ] ]]]]]]]]]]]]]] PK /PNa [K i1 /Na 1o ]1[Na 1i /Na 1o ]1PCl /PNa [Cl 2o /Na 1o ]1PI /PNa [I 1i /Na o1 ]
(3)
(4)
(5)
Eq. (5) may be plotted as shown in Fig. 1. Similar calculations for mammalian membranes (cat motor neurons) are made from measured values of permeabilities and concentrations, as found in Kingsley (1996). The equation for the resting membrane potential for the mammalian neuron, V 0 is given by: 4.7 1 PI /PNa [I o1 /Na o1 ] V 0 5 62 log 10 ]]]]]]] 100
(6)
Eq. (6) is shown plotted in Fig. 2. The results shown in Figs. 1 and 2 indicate how resting membrane potentials vary with relative ion concentrations and relative permeabilities of the added ions.
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
97
4. Discussion
4.1. Depolarization of membranes
Fig. 1. The resting membrane potential (mV) depolarizes (decreases in magnitude of negative voltages) as a function of the 1 relative concentration of the added ion, I 1 o /Na o . As the relative permeability of the added ions increases, the resting membrane potential further depolarizes to a less negative value at a given relative ion concentration. These data correspond to a squid giant axon at a temperature of 188C. The therapeutic and toxic levels of lithium in humans are also indicated.
Figs. 1 and 2 show that the resting membrane potential gets depolarized depending upon the relative concentration of the added ion and its relative permeability. The therapeutic effects of lithium may be due to this depolarizing effect of lithium ions. This would indicate that the resting membrane potential in bipolar patients is hyperpolarized before the lithium treatment. El-Mallakh et al. (1996) measured the transmembrane potential (TMP) in mononuclear leukocytes from patients with bipolar disorder and compared it with values in control individuals. They found that the majority of manic and hypomanic patients had a significantly hyperpolarized lymphocyte TMP. These findings seem to agree with the present results. Hokin-Neaverson and Jefferson (1989) found that the sodium pump activity increased significantly during lithium therapy, to a level that was not much different from that of controls. This again provides additional support for the present results. Also shown in these figures are the ranges of therapeutic levels and toxic levels of lithium in humans, as given in Bowden (1995) and Ravel (1996). However, these results show that the permeabilities of lithium have to be at least an order of magnitude higher than those of sodium for any significant depolarization to occur at these levels of extracellular lithium.
4.2. Effect of extracellular potassium on hyperpolarization In order to understand the possible causes of hyperpolarization in manic patients, further calculations were made using the published data for sodium and potassium, as found in Coppen et al. (1966) and Krupp et al. (1997). Without adding any extra ions to the neurons in humans, Eq. (3) reduces to Fig. 2. The calculated values of the resting membrane potentials from Eq. (6) using typical values for cat motor neurons are shown in this figure, thus confirming the results shown in Fig. 1 for squid giant axons. These data correspond to the cat’s body temperature of 378C.
1 PK /PNa (K 1 o /Na o ) 1 1 V 5 62 log 10 ]]]]]] 1 PK /PNa (K i /Na 1 o )
(7)
Since there are no published data on the permeabilities of potassium and sodium in human
98
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
Fig. 4. Hyperpolarization is plotted at various values of relative permeabilities, since their exact values in humans are not known. Hyperpolarization does not increase significantly with relative permeabilities in the range considered. Fig. 3. Hyperpolarization (increase in magnitude of negative voltages) varies significantly with extracellular potassium levels in humans. Three relative permeabilities were considered, since their exact values in humans are not known.
neurons, a range of relative permeabilities were used to calculate their effect on hyperpolarization. Fig. 3 shows such calculations to demonstrate how extracellular potassium level would affect the hyperpolarization of human neurons at three different relative potassium levels. Extracellular potassium level does have a significant effect on the hyperpolarization of the resting membrane potentials. In order to evaluate the variations caused by the relative potassium permeabilities, the resting membrane potentials were calculated and are shown in Fig. 4. The relative permeability does not have any appreciable effect on hyperpolarization based on these equations.
4.3. Effect of extracellular sodium on hyperpolarization Coppen et al. (1966) reported that sodium concentrations in blood plasma varied in the range of 130 to 150 mEq / l in manic phase as well as in ‘normal’ phase. In order to see if such variations in extracellular sodium have any effect on hyperpolarization, the data shown in Fig. 5 were calculated using Eq. (7). They indicate that small changes in extracellular sodium do not have any significant effect on hyperpolarization. Since extracellular sodium levels do not change much during sodium
valproate therapy, it is highly doubtful that the sodium ions in sodium valproate play any direct role in mediating mania. However, it is possible that the valproic acid may play a role in regulating potassium channels in addition to other possible mechanisms.
4.4. Further research needed Hodgkin and Huxley (1952) showed that the resting membrane potential is directly related to the membrane conductance. According to this relationship, the hyperpolarization is caused by a reduction in the conductance of the membrane. This is further supported by the Na,K-ATPase hypothesis, which was put forward by El-Mallakh and Wyatt (1995). Clinical research by Akagawa et al. (1980), HokinNeaverson and Jefferson (1989) and El-Mallakh et al. (1996) has been very useful in furthering the understanding of the mechanisms of ionic-exchange processes that take place in the membranes of the neurons. As suggested by El-Mallakh and Wyatt (1995), it would be very useful to understand how hyperpolarization and depolarization affect the excitability of the membrane and associated transmitter release. With this objective in mind, further analysis is under way to study the role of the electrical properties such as conductance (permeability), capacitance and inductance on the voltage response of the membranes, using the equivalent circuits suggested by Cole (1941) and Hodgkin and Huxley (1952). Such voltage responses may be correlated
A. Thiruvengadam / Journal of Affective Disorders 65 (2001) 95 – 99
99
Fig. 5. Small variation in extracellular sodium concentration does not affect the hyperpolarization of membranes significantly, even at different permeabilities.
with electroencephalographic (EEG) measurements. Hopefully, this approach would lead to a relationship between the vesicle release rate and the voltage response of the membranes. Animal research to determine the relative permeabilities and to study if sodium valproate affects the ion concentrations in mammalian membranes would be useful.
Acknowledgements The author is grateful to Dr. Raj Thiruvengadam and to S. Nathan M.D. for useful discussions. The comments and suggestions made by the Editor and the anonymous reviewers are thankfully acknowledged.
References Akagawa, K., Wakanabe, M., Tsukada, Y., 1980. Activity of erythrocyte Na, K-ATPase in manic patients. J. Neurochem. 35, 258–260. Bowden, C.L., 1995. Predictors of response to divalproex and lithium. J. Clin. Psychiatry 56 (Suppl.), 25–30. Cole, K.S., 1941. Rectification and inductance in the squid giant axon. J. Gen. Physiol. 25, 29–51.
Coppen, A., Shaw, D.M., Malleson, A., Costain, R., 1966. Mineral metabolism in mania. Br. Med. J. 1, 71–75. El-Mallakh, R.S., Wyatt, R.J., 1995. The Na, K-ATPase hypothesis for bipolar illness. Biol. Psychiatry 37, 235–244. El-Mallakh, R.S., Li, R., Worth, C.A., Peiper, S.C., 1996. Leukocyte transmembrane potential in bipolar illness. J. Affect. Disord. 41, 33–37. Goldman, D.F., 1943. Potential, impedance and rectification in membranes. J. Gen. Physiol. (Lond.) 27, 37–60. Hodgkin, A.L., Huxley, A.F., 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.) 117, 500–544. Hodgkin, A.L., Katz, B., 1949. The effect of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. (Lond.) 108, 37–77. Hokin-Neaverson, M., Jefferson, J.W., 1989. Deficient erythrocyte Na, K-ATPase in different affective states in bipolar affective disorder and normalization by lithium therapy. Neuropsychobiology 22, 18–25. Kingsley, R.F., 1996. In: Concise Text of Neuroscience. Williams and Wilkins, Baltimore, MD, p. 81. Krupp, M.A., Sweet, N.J. et al., 1997. Physicians Handbook. Lange Medical Publications, Los Altos, CA. McCormick, D.A., 1999. Membrane potential and action potential. In: Zigmond, M.J. (Ed.), Fundamental Neuroscience. Academic Press, New York, NY, pp. 129–154. Ravel, R., 1996. Clinical Laboratory Medicine. Year Book Medical Publications, Inc, Chicago, IL.