BIOLNORGANIC CHEMISTRY 4,117-124
(1975)
The Chemical Principles of Chronotherapy from an in vitro Model of Circadian Concentration Rhythms MARJORIE
D. WALKER
Department of Chemistry, Fife, Scotland KY1 6 PST
and DAVID
Urziversity
117
as Established
R. WILLIAMS
of St. Andrews,
ABSTRACT A model reaction for investigating the effects of chemical parameters on circadian rhythms is suggested. Its main advantage is that oscillations occur on a minute scale rather than daily and so accelerate studies. Some factors were found to increase the period or amplitu.de of the oscillations, others decreased them. The chemical principres prevailing during such oscillations are itemized. The effects of adding poisons or drugs are also noted and a computer calculation has been used to show that desferrioxamine B treatment for serum iron removal could be 65% more effective if administered at the correct point in the circadian cycle-
INTRODUCTION The majority of in vivo reactions, both metabolic and genetic, occur in cycles with periodicities ranging from milliseconds to months [ 1,2] _ The daily variations in the concentrations of species distributed throughout the body (the diurnal or circadian rhythms) have pharmacological significance because such rhythms drastically influence the therapeutic and toxic effects of many drugs and other agents. Unfortunately, there are several factors involved in selecting the optimum pattern of chronotherapy, (for example, rates of absorption, metabolism, excretion, the amount of food in the stomach, etc.) and so there is a pressing need for in vitro models of these temporally oscillating phenomena in order that these factors may be characterized, quantized, and assessed. The temporal content of such phenomena suggests the possibility of computer models involving kinetic rate constants analogous to our equilibrium models involving formation constants [3]_ However, even the “simplest” of oscillating inorganic reactions has not yet been unambiguously resolved into k values and so models involving some 200 or more k, akin to the equilibrium models of plasma using more than 200 P values 141, are currently just futuristic thinking.
0 Am&can Elsevier Publishing Company, Inc., 1975
MARJORIE
118
D. WALKER AND DAVID R. WILLIAMS
8am
8am
FIG. 1. The circadian variation of serum iron for a healthy human subject, redrawnfrom [ 5 ] _
Nevertheless, although we are unable to decipher physiological reaction mechanisms, we can still list the general chemical principles’. Thus, we have seIected a chemical system which oscillates in a manner that mimics the endogenous circadian rhythms as closely as possible and investigated the parameters controlling the periodic& and amplitude of the oscillations because it must be recognized that all itz viva oscillations have a chemical explanation and that the nature of the rhythm is dictated solely by the biochemistry_ DESCRIPTION OF THE MODEL REACTION The diurnal variation in the concentration of ferrous ions in blood plasma is shown in Fig_ 1 [ 5]_ A literature search revealed that the Belousov-Zhabotinski reaction had a similar profue (Fig. 2) but that the period of oscillation was minutes rather than hours [6,7] _ Although this reaction has been studied for 15 years, the kinetic constants governing the mechanism have not, to date, been compietely resolved_ The chemistry involves the acid-catalyzed enolization of maionic acid. 3Br0a +- SCHa(COOH)a 4C02 -c-SH,O.
+- 3Hf
catalysis
3BRCH(COOH)z
+ 2HCOOH
-+ (1)
Catalysis is provided by one electron redox couples having a formal redox potential of about I V (eg., Ce4’/Ce3’, Mn3f/Mn2’, tris 1,I 0 phen Fe3+/tris I, 10 phen Fe**). The overall reaction is composed of four basic reactions BrOs f 2Br- •f-3CH,(COOH) BrO>t 4Fe2+ + CH2(COOH)+
+ 3H+--
3BrCH(COOH)*
+ SH+------tBrCH(COOH)2
+ 3Ha0,
(2)
+ 4Fe3* + 3H20,(3)
‘Just as scale models of estuaries display tidal and current patterns even though hydrodynamic constants and laws cannot, as yet, predict such effects.
MODEL FOR BIO-INORGANIC
119
CHRONOTHERAPY
5 mV 0 iv loo !c#cands
0
FIG. 3,. The Belousov-Zhabotinski reaction as followed using the equipment and concentrations given in the text.
6Fe3 ’
+ CH2(COOH)2 + 2H20_6Fe2t
+ HCOOH + 2C02 + SH+, (4)
4Fe3+ + BrCH(COOH)2 + 2H20 ___t
4Fe2+ +2CO, + 5H+ + Bi + HCOOH.(S)
For the purposes of this study, a set of standard concentrations were used; these comprised malonic acid (0.4 M), potassium bromate (0.1 M), sulfuric acid (0.2 M) and ferroin ( IO4 M). These initial reactant concentrations were kept as standard throughout all the experimental work (with the exception of the investigation shown in Table I)_
TABLE 1 Qualitative Observations on the Effects of Reactants and Period of the Standard Reaction Q
on the Amplitude
Oscillating
CH2(COOH)2 KBrO3
+
S S -
H2S04
+
S S S S
Ferroin Amplitude
Period 0 0
S
0
0
s
-
+?
+
+I-
s
-
S S S
S S
S
+
-
s
-
s
-
--
S
;
S -
f
i-
+
0
i-i-
-6
+
S S S
+
+
0 +
‘S = standard concentration as in text, + = increase, - = decrease.
Initiation
Period
+
0 -l-l-
+ 4-t i-i-
-
0 .
+
MARJORIE
120
D. WALKER
AND
DAVID
R. WILLIAMS
EXPERIMENTAL Reagents Potassium bromate, sulfuric acid (Fisons AR), malonic acid, and ferroin (BDS) were used without further purification. Stock solutions of potassium bromate (0.25 M), malonic acid (1 M) and sulfuric acid (5 AZ) were prepared using Elgastat deionised water. Ferroin solution X2.5 X 10m2 M) was used as supplied_
Electrodes
and Monitoring
Procedure
The oscillations in the Fe2+ /Fe3+ concentrations were monitored using a platinum bright spade electrode with a sodium sulfate calomel electrode as reference in conjunction with a Radiometer pH meter 26. The changes in potential were recorded using a Heath servo-recorder (Model EUW-20A). AlI potentiometric work was carried out at 25.0” under nitrogen in a thermostatted vessel.
Chemical Principles
Found to be Prevailing
During the Osciliations
(I)_ For sustained oscillations, a continuing decrease in the free energy of the system was necessary. For example, a clock requires a wound spring, the Belousov-Zhabotinski reaction needs a constant supply of malonic acid, and humans require nourishment_ A shortage or limitation imposed by these driving forces m=ust, of necessity, affect the oscillations (in accordance with the second law of thermodynamics). (2)_ The concentrations oscillated about nonequilibrium stationary states, ie., if the energy input is ceased, the equilibrium concentrations to which the oscillations eventually dwindle will, in all probability, not have values similar to those exhibited during the oscillations. Furthermore, the concentrations of BrO-a CH2(COOH)=, H’, and CO2 varied in a nonmonoton manner, whereas those of Bf, Fe3+, and Fe” oscillated_ The reaction commenced with an induction period during which BrCH(COOH)z accumulated and then oscillations began. The modes of synchronization between the oscillating concentrations and the non-monotonic ones are shown in Fig_ 3. This diagram closely resembles the in vivo situation because (a) the free energy of the system decreases continuously throughout the entire living process and (b) the oscillating reactions continue indefinitely provided a constant reservoir of reactants is provided (e.g., in vitro malonic acid or in vivo food)_ (3) Literature reports of kinetic relationships postulated for the model used [2] suggested that the amplitudes and periods of the concentration oscillations are dependent upon the initial (or total) concentrations of reactants_ The effects of changing the initial concentrations of each of the reagents in the standard reaction are shown in Table I_
MODEL FOR BIO-iNORGANIC
CHRONOTHERAPY
121
Time FIG_ 3. The temporal concentrationpatterns(a) varyingnonmonotonically,and (b) oscillating(see text).
After completing this study, we investigated the effect of introducing other substances into the system such as metal ions which could compete with the iron, competing amino-acids, drugs such as EDTA, and poisons such as ethano1. The effects of adding these impurities to the standard reaction were as follows: both ethanol and EDTA caused reductions in period and amplitude: phenylalanine and manganous sulfate caused an increase in both period and amphtude but in the case of manganous sulfate these changes were more marked; soluble aspirin, Zinc sulfate, and aspartic acid caused the period to increase, but there was no change in amplitude; however, in the case of the soluble aspirin there was a noticeable broadening of the peaks; finally, introducing malic acid caused no change in either period or amplitude_ From these results, it was decided to undertake further systematic studies with EDTA, ethanol, and also with theobromine to ascertain what, if any, relationship exists between the amount of “impurity” in the system and the degree of change in either the period or the amplitude. The results are listed in Tables 2, 3, and 4. A particular reason for investigating theobromine was that in vivo studies had already been reported for the effects of this drug (viz. its influence upon the periodicity of phaseo2us mulriflorus leaf movements [8,9]) and our in vitro model studies parallel the period lengthening observed in viva. (4). At least one step in the mechanism must involve a feedback loop, i.e., the oscillating reaction is autocataiytic other than through mass balances. This feedback may have either an activation or an inhibition effect. In our model the Br- produced in reaction (5) encourages reaction (2) and so by reducing the [ BrO-d inhibits reaction (3). (5). In any closed system oscillating about a transient state, the oscillations are necessarily damped since the system is continuously approaching equihbrium. However, when some reagents (e.g., malonic acid) are introduced initially as a large excess and when the reaction rate is not too rapid, the oscillations can approach quite closely the oscillations observable in open systems such as in vivo, where a reagent (food) is being continuously supplied_ For example, initial concentrations of CHa(COOH)a and KBrOa are approx_ 0.1 M whereas during the period of an oscillation about 10S4 M of these disappears_ Hence the closed Belousov-Zhabotinski reaction is a reasonable model of open in viuo oscillations.
MARJORIE
122
D. WALKER AND DAVID R. WILLIAMS
TABLE 2 Percentage Changes in Amplitude and Period Caused by Adding Ethanol (to Give a Final % VoltVol Concentration as Listed) to the Standard Oscillating Reaction-4 % &HsOHl
Amplitude
0.04 0.08 0.12 0.16 0.20 0.24 0.28
-I 3.5 -24.0 -34.0 -40.7 -53.9 -70.4 -95.5
Period - 9.6 44.8
64.8 -61.0 -76.0 -58-4 -60.0
=+ = increase,- = decrease. TABLE 3 The Effect of EDTA on Amplitude and period [EDTA]= 9.24 x 1.25x 1.56 X 1.65 X 2.88 x 3-34 x 3.61 X 4.54 x 5.19 x 6.56 x 8.55 X
10-4 10-3 10-3 1O-3 10-3 10-3 1O-3 10-3 10-3 1o-3 lO-3
Amplitude
Period
-13.0 -30.4 -21.7 -24.0 -34.7
-35.3 -58.9 43.8 -37.5 -58-9 -56.0 64.5 -58.9 -64.5 -70.6 -76.5
45.8 -34.7 -64.0 -76.0 -96.0 -9 1.3
*Measuredin Moles.
As a fiial illustration of the importance of the concepts discussed, a COMPLOT computer model [ 10,111 was constructed for the removal of iron(D) from serum by desferrioxamine B (25 BM “Desferal Ciba”). The two iron concentrations chosen were the extremes shown in Fig. 1 [30 and I8 @f Fe(D)]_ The drug was found to sequester 65% more Fe(D) when administerd to coincide with the maximum circadian concentration in serum (30 w at pH 7.4).
MODEL FOR BIO-INORGANIC
123
CHRONOTHERAPY TABLE 4
The Effect of Theobromine [ Theobromine] p
on Amplitude and Period
Amplitude
Period +11.1
1.11
x 1o-4
-
2.48 3.55 5.71 6.66
X x x x
-10.7 -15.8 -47.2 -68.4
1O-4 1o-4 lOA 10-4
2.7
+19.1 +25_9 +38_5 t48.1
%easured in Moles.
DISCUSSION One may ponder why evolution introduced oscillations; there have been several suggestions, none of which have been fully investigated_ (a) The tremendous compiexity of biochemical control circuits and of the feedback mechanisms in vivo statistically render oscillations almost inevitable. (b) Biochemical chain reactions require the concentrations of metabolities involved to be regulated via a feedback mechanism_ For example, the pioduct of a chain diminishes the activity of an enzyme synthesizing some distant precursor of the inhibitory product [2] _ (c) Circadian rhythms may be a consequence of beat phenomena resuIting from the cooperation of shorter rhythms with different periods. (d) Climatic or environmental conditions may have set the original phases of circadian rhythms durin g the process of evolution, for example, the thermochemical effects of beach organisms being washed by tides or of species being illuminated by daylight. Whatever their origin, the correct cognizance of these circadian rhythms in therapy can be beneficial. The increase in drug tolerance and response achieved in viva, and in the percentages quoted in Tables 2, 3, and 4, is not a trivial one_ In the extreme it can represent the difference between the success and failure of a therapy. In physiological terms, the chemicals and concentrations used in our model are freakish. Future research must aim at better models especiahy those involving the biotrace elements (since they lend themselves well to ion-selective electrode monitoring for both in uiuo and in vitro comparative studies). Such models can pictures of the effects of drugs or poisons and suggest new provide “i&n&it” directions for pharmacology research.
We thank Professor E. KGYis and Dr. D. Gzlvert for discussions and advice, and the University of St. Andrews for a maintenance grant.
MARJORIE
124
D. WALKER
AND
DAVID
R. WILLIAMS
REFERENCES 1. F. Halberg et aL,Experientfa 29,909 (1973) 2; E_ K&c%, in An Znfroduction&JBio-inorganicChemistry (D. R. Wiiams, Ed.), Charles C_ Thomas, Springfield, IlL in press. 3. D. R_ Wii, in An Lntraductionto Bio-inorganicChemisZry(D. R. Williams, Ed.), Charles C. Thomas, Springfield, Ill., in press; A. M_ Carrie, M. L. D. Touche, and D. R. WiIJiams.J_C%enr_Soe Dalton. 2561, (1973). 4. 5. 5_ Perrin and R. P. Agaanval.in lrietal Ions in BiologicalSysrems, Vol. 2 (H. Sigel, Ed), Marcel Dekker, New York (1973). p. 168. 5. J. C_ S. Paterson, 5. hfarrack, and H. S- Wiggins, Chin.Sci 11,417 (1953). 6_ R. M_ Noyes, R. 3. Field, and E. K&es, J. Amer. Chem. Sot. 95,1394 (1972) 7. B_ P_ Belousov, Sir. Ref: Radrizrs Med., 1958. Medgiz, Moscow, 1 (1969) 8. E. Bunning, The PhysiologicalClock, 2nd ed., Springer Verlag, New York (1967). 9. S. Keller, 2. Bof. 48,32 (1960) 10. D. D. Perrin and I. G. Sayce- Tabnta 14,833 (1967). 11. A. C. Baxter and D. R. Wihiams,J. Chem Sot Dafton. 1.117 (1974). Received Au--t
8. 19 74
(1975)
The Chemical Principles of Chronotherapy from an in vitro Model of Circadian Concentration Rhythms MARJORIE
D. WALKER
Department of Chemistry, Fife, Scotland KY1 6 PST
and DAVID
Urziversity
117
as Established
R. WILLIAMS
of St. Andrews,
ABSTRACT A model reaction for investigating the effects of chemical parameters on circadian rhythms is suggested. Its main advantage is that oscillations occur on a minute scale rather than daily and so accelerate studies. Some factors were found to increase the period or amplitu.de of the oscillations, others decreased them. The chemical principres prevailing during such oscillations are itemized. The effects of adding poisons or drugs are also noted and a computer calculation has been used to show that desferrioxamine B treatment for serum iron removal could be 65% more effective if administered at the correct point in the circadian cycle-
INTRODUCTION The majority of in vivo reactions, both metabolic and genetic, occur in cycles with periodicities ranging from milliseconds to months [ 1,2] _ The daily variations in the concentrations of species distributed throughout the body (the diurnal or circadian rhythms) have pharmacological significance because such rhythms drastically influence the therapeutic and toxic effects of many drugs and other agents. Unfortunately, there are several factors involved in selecting the optimum pattern of chronotherapy, (for example, rates of absorption, metabolism, excretion, the amount of food in the stomach, etc.) and so there is a pressing need for in vitro models of these temporally oscillating phenomena in order that these factors may be characterized, quantized, and assessed. The temporal content of such phenomena suggests the possibility of computer models involving kinetic rate constants analogous to our equilibrium models involving formation constants [3]_ However, even the “simplest” of oscillating inorganic reactions has not yet been unambiguously resolved into k values and so models involving some 200 or more k, akin to the equilibrium models of plasma using more than 200 P values 141, are currently just futuristic thinking.
0 Am&can Elsevier Publishing Company, Inc., 1975
MARJORIE
118
D. WALKER AND DAVID R. WILLIAMS
8am
8am
FIG. 1. The circadian variation of serum iron for a healthy human subject, redrawnfrom [ 5 ] _
Nevertheless, although we are unable to decipher physiological reaction mechanisms, we can still list the general chemical principles’. Thus, we have seIected a chemical system which oscillates in a manner that mimics the endogenous circadian rhythms as closely as possible and investigated the parameters controlling the periodic& and amplitude of the oscillations because it must be recognized that all itz viva oscillations have a chemical explanation and that the nature of the rhythm is dictated solely by the biochemistry_ DESCRIPTION OF THE MODEL REACTION The diurnal variation in the concentration of ferrous ions in blood plasma is shown in Fig_ 1 [ 5]_ A literature search revealed that the Belousov-Zhabotinski reaction had a similar profue (Fig. 2) but that the period of oscillation was minutes rather than hours [6,7] _ Although this reaction has been studied for 15 years, the kinetic constants governing the mechanism have not, to date, been compietely resolved_ The chemistry involves the acid-catalyzed enolization of maionic acid. 3Br0a +- SCHa(COOH)a 4C02 -c-SH,O.
+- 3Hf
catalysis
3BRCH(COOH)z
+ 2HCOOH
-+ (1)
Catalysis is provided by one electron redox couples having a formal redox potential of about I V (eg., Ce4’/Ce3’, Mn3f/Mn2’, tris 1,I 0 phen Fe3+/tris I, 10 phen Fe**). The overall reaction is composed of four basic reactions BrOs f 2Br- •f-3CH,(COOH) BrO>t 4Fe2+ + CH2(COOH)+
+ 3H+--
3BrCH(COOH)*
+ SH+------tBrCH(COOH)2
+ 3Ha0,
(2)
+ 4Fe3* + 3H20,(3)
‘Just as scale models of estuaries display tidal and current patterns even though hydrodynamic constants and laws cannot, as yet, predict such effects.
MODEL FOR BIO-INORGANIC
119
CHRONOTHERAPY
5 mV 0 iv loo !c#cands
0
FIG. 3,. The Belousov-Zhabotinski reaction as followed using the equipment and concentrations given in the text.
6Fe3 ’
+ CH2(COOH)2 + 2H20_6Fe2t
+ HCOOH + 2C02 + SH+, (4)
4Fe3+ + BrCH(COOH)2 + 2H20 ___t
4Fe2+ +2CO, + 5H+ + Bi + HCOOH.(S)
For the purposes of this study, a set of standard concentrations were used; these comprised malonic acid (0.4 M), potassium bromate (0.1 M), sulfuric acid (0.2 M) and ferroin ( IO4 M). These initial reactant concentrations were kept as standard throughout all the experimental work (with the exception of the investigation shown in Table I)_
TABLE 1 Qualitative Observations on the Effects of Reactants and Period of the Standard Reaction Q
on the Amplitude
Oscillating
CH2(COOH)2 KBrO3
+
S S -
H2S04
+
S S S S
Ferroin Amplitude
Period 0 0
S
0
0
s
-
+?
+
+I-
s
-
S S S
S S
S
+
-
s
-
s
-
--
S
;
S -
f
i-
+
0
i-i-
-6
+
S S S
+
+
0 +
‘S = standard concentration as in text, + = increase, - = decrease.
Initiation
Period
+
0 -l-l-
+ 4-t i-i-
-
0 .
+
MARJORIE
120
D. WALKER
AND
DAVID
R. WILLIAMS
EXPERIMENTAL Reagents Potassium bromate, sulfuric acid (Fisons AR), malonic acid, and ferroin (BDS) were used without further purification. Stock solutions of potassium bromate (0.25 M), malonic acid (1 M) and sulfuric acid (5 AZ) were prepared using Elgastat deionised water. Ferroin solution X2.5 X 10m2 M) was used as supplied_
Electrodes
and Monitoring
Procedure
The oscillations in the Fe2+ /Fe3+ concentrations were monitored using a platinum bright spade electrode with a sodium sulfate calomel electrode as reference in conjunction with a Radiometer pH meter 26. The changes in potential were recorded using a Heath servo-recorder (Model EUW-20A). AlI potentiometric work was carried out at 25.0” under nitrogen in a thermostatted vessel.
Chemical Principles
Found to be Prevailing
During the Osciliations
(I)_ For sustained oscillations, a continuing decrease in the free energy of the system was necessary. For example, a clock requires a wound spring, the Belousov-Zhabotinski reaction needs a constant supply of malonic acid, and humans require nourishment_ A shortage or limitation imposed by these driving forces m=ust, of necessity, affect the oscillations (in accordance with the second law of thermodynamics). (2)_ The concentrations oscillated about nonequilibrium stationary states, ie., if the energy input is ceased, the equilibrium concentrations to which the oscillations eventually dwindle will, in all probability, not have values similar to those exhibited during the oscillations. Furthermore, the concentrations of BrO-a CH2(COOH)=, H’, and CO2 varied in a nonmonoton manner, whereas those of Bf, Fe3+, and Fe” oscillated_ The reaction commenced with an induction period during which BrCH(COOH)z accumulated and then oscillations began. The modes of synchronization between the oscillating concentrations and the non-monotonic ones are shown in Fig_ 3. This diagram closely resembles the in vivo situation because (a) the free energy of the system decreases continuously throughout the entire living process and (b) the oscillating reactions continue indefinitely provided a constant reservoir of reactants is provided (e.g., in vitro malonic acid or in vivo food)_ (3) Literature reports of kinetic relationships postulated for the model used [2] suggested that the amplitudes and periods of the concentration oscillations are dependent upon the initial (or total) concentrations of reactants_ The effects of changing the initial concentrations of each of the reagents in the standard reaction are shown in Table I_
MODEL FOR BIO-iNORGANIC
CHRONOTHERAPY
121
Time FIG_ 3. The temporal concentrationpatterns(a) varyingnonmonotonically,and (b) oscillating(see text).
After completing this study, we investigated the effect of introducing other substances into the system such as metal ions which could compete with the iron, competing amino-acids, drugs such as EDTA, and poisons such as ethano1. The effects of adding these impurities to the standard reaction were as follows: both ethanol and EDTA caused reductions in period and amplitude: phenylalanine and manganous sulfate caused an increase in both period and amphtude but in the case of manganous sulfate these changes were more marked; soluble aspirin, Zinc sulfate, and aspartic acid caused the period to increase, but there was no change in amplitude; however, in the case of the soluble aspirin there was a noticeable broadening of the peaks; finally, introducing malic acid caused no change in either period or amplitude_ From these results, it was decided to undertake further systematic studies with EDTA, ethanol, and also with theobromine to ascertain what, if any, relationship exists between the amount of “impurity” in the system and the degree of change in either the period or the amplitude. The results are listed in Tables 2, 3, and 4. A particular reason for investigating theobromine was that in vivo studies had already been reported for the effects of this drug (viz. its influence upon the periodicity of phaseo2us mulriflorus leaf movements [8,9]) and our in vitro model studies parallel the period lengthening observed in viva. (4). At least one step in the mechanism must involve a feedback loop, i.e., the oscillating reaction is autocataiytic other than through mass balances. This feedback may have either an activation or an inhibition effect. In our model the Br- produced in reaction (5) encourages reaction (2) and so by reducing the [ BrO-d inhibits reaction (3). (5). In any closed system oscillating about a transient state, the oscillations are necessarily damped since the system is continuously approaching equihbrium. However, when some reagents (e.g., malonic acid) are introduced initially as a large excess and when the reaction rate is not too rapid, the oscillations can approach quite closely the oscillations observable in open systems such as in vivo, where a reagent (food) is being continuously supplied_ For example, initial concentrations of CHa(COOH)a and KBrOa are approx_ 0.1 M whereas during the period of an oscillation about 10S4 M of these disappears_ Hence the closed Belousov-Zhabotinski reaction is a reasonable model of open in viuo oscillations.
MARJORIE
122
D. WALKER AND DAVID R. WILLIAMS
TABLE 2 Percentage Changes in Amplitude and Period Caused by Adding Ethanol (to Give a Final % VoltVol Concentration as Listed) to the Standard Oscillating Reaction-4 % &HsOHl
Amplitude
0.04 0.08 0.12 0.16 0.20 0.24 0.28
-I 3.5 -24.0 -34.0 -40.7 -53.9 -70.4 -95.5
Period - 9.6 44.8
64.8 -61.0 -76.0 -58-4 -60.0
=+ = increase,- = decrease. TABLE 3 The Effect of EDTA on Amplitude and period [EDTA]= 9.24 x 1.25x 1.56 X 1.65 X 2.88 x 3-34 x 3.61 X 4.54 x 5.19 x 6.56 x 8.55 X
10-4 10-3 10-3 1O-3 10-3 10-3 1O-3 10-3 10-3 1o-3 lO-3
Amplitude
Period
-13.0 -30.4 -21.7 -24.0 -34.7
-35.3 -58.9 43.8 -37.5 -58-9 -56.0 64.5 -58.9 -64.5 -70.6 -76.5
45.8 -34.7 -64.0 -76.0 -96.0 -9 1.3
*Measuredin Moles.
As a fiial illustration of the importance of the concepts discussed, a COMPLOT computer model [ 10,111 was constructed for the removal of iron(D) from serum by desferrioxamine B (25 BM “Desferal Ciba”). The two iron concentrations chosen were the extremes shown in Fig. 1 [30 and I8 @f Fe(D)]_ The drug was found to sequester 65% more Fe(D) when administerd to coincide with the maximum circadian concentration in serum (30 w at pH 7.4).
MODEL FOR BIO-INORGANIC
123
CHRONOTHERAPY TABLE 4
The Effect of Theobromine [ Theobromine] p
on Amplitude and Period
Amplitude
Period +11.1
1.11
x 1o-4
-
2.48 3.55 5.71 6.66
X x x x
-10.7 -15.8 -47.2 -68.4
1O-4 1o-4 lOA 10-4
2.7
+19.1 +25_9 +38_5 t48.1
%easured in Moles.
DISCUSSION One may ponder why evolution introduced oscillations; there have been several suggestions, none of which have been fully investigated_ (a) The tremendous compiexity of biochemical control circuits and of the feedback mechanisms in vivo statistically render oscillations almost inevitable. (b) Biochemical chain reactions require the concentrations of metabolities involved to be regulated via a feedback mechanism_ For example, the pioduct of a chain diminishes the activity of an enzyme synthesizing some distant precursor of the inhibitory product [2] _ (c) Circadian rhythms may be a consequence of beat phenomena resuIting from the cooperation of shorter rhythms with different periods. (d) Climatic or environmental conditions may have set the original phases of circadian rhythms durin g the process of evolution, for example, the thermochemical effects of beach organisms being washed by tides or of species being illuminated by daylight. Whatever their origin, the correct cognizance of these circadian rhythms in therapy can be beneficial. The increase in drug tolerance and response achieved in viva, and in the percentages quoted in Tables 2, 3, and 4, is not a trivial one_ In the extreme it can represent the difference between the success and failure of a therapy. In physiological terms, the chemicals and concentrations used in our model are freakish. Future research must aim at better models especiahy those involving the biotrace elements (since they lend themselves well to ion-selective electrode monitoring for both in uiuo and in vitro comparative studies). Such models can pictures of the effects of drugs or poisons and suggest new provide “i&n&it” directions for pharmacology research.
We thank Professor E. KGYis and Dr. D. Gzlvert for discussions and advice, and the University of St. Andrews for a maintenance grant.
MARJORIE
124
D. WALKER
AND
DAVID
R. WILLIAMS
REFERENCES 1. F. Halberg et aL,Experientfa 29,909 (1973) 2; E_ K&c%, in An Znfroduction&JBio-inorganicChemistry (D. R. Wiiams, Ed.), Charles C_ Thomas, Springfield, IlL in press. 3. D. R_ Wii, in An Lntraductionto Bio-inorganicChemisZry(D. R. Williams, Ed.), Charles C. Thomas, Springfield, Ill., in press; A. M_ Carrie, M. L. D. Touche, and D. R. WiIJiams.J_C%enr_Soe Dalton. 2561, (1973). 4. 5. 5_ Perrin and R. P. Agaanval.in lrietal Ions in BiologicalSysrems, Vol. 2 (H. Sigel, Ed), Marcel Dekker, New York (1973). p. 168. 5. J. C_ S. Paterson, 5. hfarrack, and H. S- Wiggins, Chin.Sci 11,417 (1953). 6_ R. M_ Noyes, R. 3. Field, and E. K&es, J. Amer. Chem. Sot. 95,1394 (1972) 7. B_ P_ Belousov, Sir. Ref: Radrizrs Med., 1958. Medgiz, Moscow, 1 (1969) 8. E. Bunning, The PhysiologicalClock, 2nd ed., Springer Verlag, New York (1967). 9. S. Keller, 2. Bof. 48,32 (1960) 10. D. D. Perrin and I. G. Sayce- Tabnta 14,833 (1967). 11. A. C. Baxter and D. R. Wihiams,J. Chem Sot Dafton. 1.117 (1974). Received Au--t
8. 19 74
