BIOCHIMICA ET BIOPHYSICA ACTA 567

BBA 2 5 0 1 3

T H E I N F L U E N C E OF M A G N E S I U M A N D CALCIUM P Y R O P H O S P H A T E

C H E L A T E S , OF F R E E M A G N E S I U M IONS, F R E E CALCIUM IONS,

A N D F R E E P Y R O P H O S P H A T E IONS ON T H E D I S S O C I A T I O N OF

ACTOMYOSIN I N S O L U T I O N

DENISE GRXNICHER AND H I L D E G A R D P O R T Z E H L

Physiological Institute (Hallerianum) *, University of Berne, Berne (Switzerland)

(Received October 2 ist, 1963)

SUMMARY

I. The dependence of the actomyosin-dissociating effect of systems containing polyphosphate, Ca 2+ and Mg ~+, on the free polyphosphate ions, magnesium poly- phosphate chelates or calcium polyphosphate chelates has been investigated. In particular the effect of the MgPPt system on the viscosity of actomyosin in solution has been studied.

2. Only the chelate MgPPt has a dissociating effect while Mg2PPt, Mg ~+ and free PPt are not capable of causing any dissociation of actomyosin.

3. Some experiments seem to indicate the formation of a Mg(PPt) z chelate when the concentrations of the added PPt and Mg ~+ exceed a ratio of about IOO:I. This chelate is not effective in the dissociation of actomyosin.

4. Free Mg z+ and free PPt are not capable of producing an actomyosin dis- sociation. Mg ~+ at concentrations above I mM reduces the MgPPt concentration neces- sary to produce a given degree of actomyosin dissociation, while free PPI does not have such an effect.

5. In contrast to MgPPt the chelate CaPPt does not cause any dissociation of actomyosin in solution.

6. Calcium as CaPP~ plus Ca ~+ has a small enhancing effect on the MgPPt-induced dissociation of actomyosin when the total concentration of Ca 2+ is more than 30 % of the total concentration of added alkaline earth.

7. The results described in this paper are probably also valid for the other actomyosin-dissociating polyphosphates such as ATP, since the viscosity-decreasing effect of all polyphosphates depends on the presence of Mg ~+ to varying degrees.

INTRODUCTION

Since the classical papers of A. SZENT-GY6RGYI and F. B. STRAUB 1¢, it is well known tha t actomyosin in solution dissociates into actin and myosin in the presence of ATP. Furthermore, the investigations of the BARANY-group 1,z have shown that the "plas-

Abbreviat ions : MgPPt, [MgP.oO~] 3- + [MgHP20~- ; Mg2PPt, Mg~P20 ~ ; Mg(PPt)~, EMg(P20~)~ ~- + [,Mg(P~O~-HP~O~)]~- + [Mg(P~O~" H~P~O~)]4-; CaPPt, ECaP~O~]a- + [CaHP20~]-.

Director Professor A. voI~ MURALT.

Biochim. Biophys. Acla, 86 (1964) 567-578

568 D. GR~NICFIER, H. PORTZEHL

ticizing" effect of ATP on actomyosin gels and glycerol-extracted fibres is also based on a decreased interaction between actin and myosin filaments (see also H. H. WEBERlS). I t is an open question whether the dissociating effect depends on the presence of free ATP ions or of ATP chelates with Mg 2+ or Ca 2+.

The "plasticizing" effect of ATP does not depend on added Mg 2+ (refs. 6, 7)- However, in the presence of other nucleosidetriphosphates or orthopolyphosphates actomyosin dissociation occurs only if Mg 2+ is added, and the polyphosphates can be easily arranged in a sequence of decreasing Mg 2+ requirement 7. I t seems plausible therefore to assume t h a t ATP for its dissociating effect also requires Mg 2+ but in the extremely low concentrations present in the actomyosin preparations.

So far, the possibility that Ca 2+ may replace Mg ~+ in polyphosphate-induced actomyosin dissociation has not been examined.

The present report is concerned with the role of alkaline earth polyphosphates in actomyosin dissociation. Inorganic pyrophosphate has been chosen as a model substance, because PPI has the highest Mg 2+ requirement within the polyphosphate series and its Mg z+ and Ca ~+ chelating constants are rather well known. The dis- sociating effect* is measured as the decrease in viscosity of actomyosin solutions at neutral pH.

DEPENDENCE OF ACTOMYOSIN DISSOCIATION ON P P 1 AND M g 2+ CONCENTRATIONS

In a neutral medium, solutions of Mg 2+ and PPI contain four different compounds ~* that might influence the actomyosin dissociation : free Mg ~+, free PPI, and the chelates MgPP~ and Mg2PP~. In solution containing Ca ~+ and PPt, only three compounds, namely free Ca ~+, free PPI, and CaPP~, can be identified at neutral reaction. The actual concentrations of all these compounds can be calculated from the amounts of Mg ~+, Ca e+, and PPI added (see MATERIALS, METHODS A N D CALCULATIONS).

Fig. I shows the changes in actomyosin dissociation as a function of added PPt and Mg ~+. Without added Mg ~+ no dissociation occurs, even at o.i M PP~ (Fig. I , Curve I). On addition of Mg 2+, PPI produces a drop in viscosity. This effect increases when the Mg 2+ concentration is increased from o.I mM to 3 mM (Curves 2-5), where the opt imum is obviously reached. Above 3 mM no further drop in viscosity is ob- served (Curve 5).

On the other hand, the concentration of PPt that produces a maximal decrease in viscosity is quite independent of the Mg °'+ concentration; it is found in all curves, each referring to different concentration of Mg ~+, at a PPI concentration of about o.oi M (see Fig. I ; 50 % of this maximal effect at about 0.8 raM). Surprisingly, vis- cosity increases again at PP~ concentrations above 0.03 M, whatever the Mg ~+ concen- tration may be (Fig. I).

The complete failure of PPI solutions to affect actomyosin dissociation in the absence of Mg ~+ shows that free PPI as such cannot act as an actomyosin-dissociating agent.

* The effect is expressed in tab les and d i a g r a m s as "degree of a ssoc ia t ion" of ac tomyos in . The degree of assoc ia t ion is zero a t comple te d issoc ia t ion and I oo ~o in t o t a l absence of d issocia t ion . I t corresponds to the t e r m "Viskositiitszuwachs" of HASSELBACH 4 and co-workers, see also MATERIALS, METHODS AND CALCULATIONS.

** The chela tes ~MgP2Ov~ ~- and [MgHP2Ov]- are considered as one compound . Since bo th are necessar i ly p resen t in nea r ly the same concent ra t ion , i t is no t possible to d i f ferent ia te the dis- soc ia t ing effect p roduced by one or the o the r of the two chelates . (The s a m e s i t ua t i on occurs for t he chela tes wi th Ca~+.) The ex is tence of a Mg(PPt)~ chela te is no t ye t proved, see p. 57 ~.

Biochim. Biophys. Acla, 86 (1964) 567-578

ACTOMYOSIN DISSOCIATION BY THE PYROPKOSPHATE SYSTEM 569

I t has been known for a long time that free Mg l+ without polyphosphates causes no dissociation of actomyosin (see Table I), and therefore it too cannot be a dis- sociating agent. Thus, of the four different compounds known to exist in solutions containing Mg ~+ and PPI, only MgPPi and Mg~PPI can be considered as dissociating factors.

100

.~ ,~ 'O ~o ~ 60

~ i ~0,

~ ~ I_

121

°t

o - - a ~ - - . , , ~ f l ~ o. ~ o - - ~ o o =~'-'~,=,~.----- ~ ------~_ x _ - 2 x ~ o - -

.

•

v ~ a ~ o j ~

10 "5 10"4 10-3 10-2 10-1

Added pyrophosphate concentration ( M )

Fig. I. Dependence of a c t o m y o s i n d issoc ia t ion on the concen t r a t i on of added PP i and Mg z+. Curve i ( O - - © ) , w i t h o u t added Mg~+; Curve 2 ( x - - × ) , w i t h add i t i on of o.I raM; Curve 3 ( & - - & ) , w i t h 0.5 mM, Curve 4 ( + - - + ) , w i t h I raM, a nd Curve 5 (~2), w i th 3 mM and (V) 5 mM

Mg z+. p H 6.8; o.o2 M p h o s p h a t e buffer; I 0. 5 (KC1); 20 °.

T A B L E I

Mg,+ C O N C E N T R A T I O N A N D A C T O M Y O S l N D I S S O C I A T I O N

M~ *+ conch. Degrec of Numt~er of (raM) association experiments

3 9 8 ~o I O IO0 ~

3 ° 92 3

DEPENDENCE OF ACTOMYOSIN DISSOCIATION ON THE EFFECTIVE CONCENTRATIONS

OF THE MgPP~ AND Mg~PPt CHELATES IN THE PRESENCE OF FREE Mg 2+

Fig. 2. allows a differentiation of the effects of pyrophosphate chelates. The molarity of MgPPt is represented on the abscissa, and the degree of actomyosin association, on the ordinate. In tkis Figure the values do not refer to the ionic concentrations added but to the actual ionic concentrations (see MATERIALS, METHODS AND CALCU- LATIONS) formed by the reactions of PPt with Mg 2+. The five dotted lines show the influence of MgPPI concentration at five different Mg2PPt concentrations (Curves ia-5a) . The four full lines show the influence of MgPPt concentration at four different concentrations of Mg ~+ (Curves 1-4). The latter curves show clearly that, at any given concentration of Mg 2+, the actomyosin dissociation increases when the concentration of MgPPI, is increased from o.oi mM to 3 raM. Fig. 2 (cf. Curves 1-4) shows further that dissociation depends not only on MgPPI but also on Mg 2+, which in concen- trations above I mM facilitates the dissociating action of MgPPt. At higher levels of Mg ~+ a smaller MgPP1 concentration is needed in order to produce a given degree of

Biochim. Biophys. Acta, 86 (1964) 567-578

57 ° I~. GR~NICHER, H. PORTZEHL

dissociation. I t must be concluded, then, that MgPPt is an actomyosin dissociator and that Mg ~+ in sufficiently high concentrations seems to enhance the dissociating effect of MgPPt. This finding is evidence that, in the terminology of BARANYL ~ and WEBER 18, Mg 2+ in concentrations above i mM is an "interaction inhibitor" if added to the actomyosin-dissociating MgPPI. This result obtained with actomyosin sols may correspond to recent findings of A. WEBER 1~,17 that show that the contraction-inhi- biting dissociating effect of ATP on actomyosin gels is facilitated by increasing Mg ~+ concentrations.

100' - t ~ - ~ ~,==~ , ~ . ~

~ ~ ~

~ ~ ~ .

~0 ~ ~' ~ ~. ',

' " "~ ~0

~ 40

~ ~0

20

I~

0

10-5 10 .4 10 -3

Concentration of Mg pyrophosphote (M)

Fig. 2. Influence of Mg 2+ (full lines) and of the Mg2PP l chelate (dotted lines) on the dissociating effect of the MgPPi chelate. Full lines: Curve I (A), wi th 0.43 mM and ([]) wi th 1.5 mM Mg2+; Curve 2 ( V - - V ) , wi th i2 mM Mg2+; Curve 3 ( O O) , wi th 22 mM MgZ+; and Curve 4 ( O - - O ) , wi th 42 mM Mg 2+. Dot ted lines: Curve i a ~vith O.Ol 4 mM, Curve 2a with o.i mM, Curve 3a with o.21 mM, Curve 4a wi th 0.45 raM, and Curve 5a with 1.5 mM MgzPPi. In all exper iments the

concentrat ion of free PPi is smaller t han i mM, the other conditions are the same as in Fig. i.

The Mg2PPI chelate seems to be neither a dissociator nor an interaction in- hibitor. The curves (Ia-5a) in Fig. 2, in which the Mg2PPt concentrations are kept constant, appear difficult to interprete, for the viscosity first increases and then decreases again with increasing MgPPI concentration. However, when interpreting these curves it should be kept in mind that at constant Mg~PPt concentrations, a decrease of the concentration of the dissociator (MgPPI) necessarily leads to a con- siderable increase in the concentration of Mg 2+. This effect may account for the observed decrease in actomyosin viscosity. In fact, Fig. 2 (dotted lines) shows that the viscosity values at a given Mg2PPI concentration are determined by the cor- responding concentration of Mg 2+. The viscosity values of the dotted curves correspond exactly to the values expected in the presence of the concentration of Mg 2+ calculated

Biochim. Biophys. Acta, 86 (1964) 567 578

ACTOMYOSIN DISSOCIATION BY THE PYROPHOSPHATE SYSTEM 571

for the various MgPPI concentrations at a given Mg~PPI concentration. This is shown by the fact that at the intersections of the dotted lines (Ia-5a) with the full lines (1-4) the concentrations of Mg ~+ and MgPPt in each pair of experiments are identical. The results of these experiments are consistent with the interpretation that MgPPt dissociates the actomyosin, a reaction which is modified by the Mg ~+ "inter- action inhibitor". I t is then quite unnecessary to assume an influence of Mg~PPt on the actomyosin dissociation.

FREE ]~PI IONS DO NOT INFLUENCE THE ACTOMYOSIN DISSOCIATION

I t is certain that free PPI, just as Mg ~+, is unable to dissociate actomyosin by itself. In contrast to Mg ~+ the free PPt does not influence the dissociating effect of MgPPI.

If the degree of actomyosin association at four different MgPPt concentrations is plotted against the concentrations of free PP~ (Fig. 3) no dependence of viscosity on the concentration of free PPt is found when the concentration of free PPI is neither too high nor too low.

IO(0

_~ ~ oo

,n '~ ~o .~

~ ~,o ~_

o 20

q l o ~0

~ o o

o" oo

. , , . ,

~0 "5 10 4 10 .3

o f ¢ - - ' o o 2 o o

v Y

o / 3 o / ° ~ " S

4 v__ v v _ ~ v

~ ~

10 -2 tO-1

Con.centration of free pyrophosphate-ions (M)

Fig. 3. Dependence of ac tomyosin dissociation produced by MgPP l on the concentrat ion of free PPv Curve i ( ~ - - ~ ) wi th approx. 0.o 5 mM, Curve 2 (~2- - [ ] ) wi th approx, o.2 mM, Curve 3 ( O - O ) wi th approx, i mM, and Curve 4 ( V - - V ) wi th approx. 2.4 mM MgPPI. The full symbols of Curve 2 correspond to the same full symbols in Fig. 2 of Curves 4, 2 and i according to the Mg z+ concentrat ions of approx. 43 raM, 15 raM, and 1.5 mM. In all the other exper iments the concentrat ions of Mg =+ are below the threshold. The other condit ions are the same as in Fig. i.

The change in viscosity, however, at very high or very small concentrations of free PPt is not induced by the free PPt. The viscosity decrease in Curve 2 in the presence of about 0.o05 mM free PPI may be due to the increase of the Mg ~+ which must be expected if the concentration of MgPP1 is to be maintained in the face of this low concentration of free PPI. In fact, the viscosity at a concentration of free PPI of about 0.005 mM can be quantitatively accounted for by the given concen- trations of MgPPI and the calculated concentrations of Mg ~+. These viscosity values (full symbols) correspond to those obtained by the concentrations of MgPPt and of calculated Mg ~+ in Fig. 2, representing the viscosity dependence on MgPPI concen- tration (cf. full symbols of Fig. 2 and Fig. 3).

The increase of viscosity (or decrease of dissociation) in presence of high concen- trations of free PP~ could be due to a large excess of PPt over Mg ~+ resulting in

Biochim. Biophys. Acta, 86 (1964) 567-578

5 7 2 D. GR,~NICHER, H. PORTZEHL

the formation of a Mg(PPI)~ chelate and a corresponding decrease in MgPPI. The existence of a Mg(PPi)z chelate has already been postulated ~, but not yet proved.

T H E DISSOCIATION OF ACTOMYOSIN IN T H E P R E S E N C E

OF C a P P I C H E L A T E AND F R E E CA 2+

If Ca 2+ is added to PPt-containing actomyosin solutions no dissociation can be ob- served even at concentrations up to the limit of solubility of CaPPI. Hence the CaPPI chelate, in contrast to the MgPPI chelate (Table II) is not an actomyosin dissociator.

Even the partial dissociation of actomyosin induced by a given concentration of MgPPland Mg 2+ is not markedly modified by the presence of Ca z+ and CaPPt, as long as the total concentration of Ca ~+ is not higher than 20 % of the total concert-

T A B L E I I

C O M P A R I S O N O F T H E D I S S O C I A T I N G E F F E C T O F M g P P l A N D C a P P i

Degree of association in 4dded conch, of the presence of

Alkaline earths Mg~+ Ca2+ PPI (raM) (raM)

5 - - 97 97 5 o . I 88 97 5 0.5 51 92 5 I.O 3 ° 92

T A B L E I I I

THE ACTOMYOSIN DISSOCIATION PRODUCED BY M g P P i IN THE PRESENCE OF Ca 2+ AND 0.02 M TRIS-MALEINATE BUFFER

I a b o u t o .5; p H a b o u t 6 .9; t e m p . 2o °.

Concentrations of Degree of Ca

MgPP~ M~ ~+ CaPP~ Ca 2+ association Mg + Ca (raM) (raM) (raM) (raM)

- - " Z O O *

0.89 0.8 o o 4 o 0.84 0.75 0.028 0.072 I I 6

0.07 4.0 o o 75 o 0 .069 4.0 0.003 0.52 72 I I

o .2 I 0.45 o o 29 o o.18 0.38 O.Ol 4 0 .o86 33 15

o. I o 0.34 o o 57 o 0.o85 0.26 o .o i 0 .o86 55 22

o.13 o. I o o o 61 o 0-033 0-063 55 3o o. I o o.24 48 58 o.16 0.37 48 69

~ Ca = t h e t o t a l c o n c e n t r a t i o n of Ca 2+ ; Mg + Ca = t h e t o t a l c o n c e n t r a t i o n s of Ca 2+ p lus Mg ~+.

B i o c h i m . B i o p h y s . Ac ta , 86 / I964) 5 6 7 - 5 7 8

ACTOMYOSIN DISSOCIATION BY THE PYROPHOSPHATE SYSTEM 573

tration of the alkaline earth (Ca 2+ plus Mg ~+, see Table I I I and Fig. 4). If the total concentration of Ca 2+ becomes 30-60 % the actomyosin dissociation is a little in- creased (Table III).

Since added Ca 2+ shows no effect, the degree of actomyosin dissociation decreases considerably if the added Mg ~+ is partially replaced by Ca ~+. A less pronounced de- crease in dissociation is also observed when Ca ~+ is simply added to a Mg 2+ and PPl-containing actomyosin solution because the efficient actomyosin dissociator MgPPI is partially transformed into the ineffective CaPP~. These observations in the actomyosin sol seem to be qualitatively consistent with the findings of A. WEBER 16, 17,

who was able to show that the dissociating effect of ATP on actomyosin gel is inhibited by Ca ~+. However, the mechanism of the inhibition may be quite different in the two cases, since the affinities of the two alkaline earths for ATP and for PPt are very different.

100' ~'a~

-~ 90 ~ x

~ N ~X 'i

g ~o ~ ~ ~ ~ " ~ ~ ~ k ~ ~ eo .~~/ ~ ~ ~

g~ • • /

~ ~ ~

x ~0 ~ ~

"- ~ ~

~

~ ff

i0 "5 107 ~ 10 "3

Concent~tion of Mg pyPophosphote (M)

~]g. + ~]ssoc]~t]on o[ ~ctom~os]~ ]~ the p~e~e~ce o[ o.o~ ~ phosphate ~ f i e~ (Curve z) o~ o.oz ~ ~ ] s - ~ ] e ] ~ t e bu~e~ (C~ve 2). ~ the experiments s~mbofise~ by ~ , C~ s+ ~s ~ d e d ~o th~L the t o t ~ co~ce~t~t~o~ o~ C~s+ is z z ~ o[ the tot~l co~ce~t~t~o~ o~ C~ s+ plus ~ s ~ . [~ the two c~ves

the concent~L]o~ o[ ~gs+ ~ e ~ ~om 3.8 to ~.8 ~ ; ~ 0.5; ~o ~.

Fig. 4 shows that actomyosin dissociation depends not only on MgPPI concen- tration but also on the buffer employed. At a given MgPPt concentration the acto- myosin dissociation is higher in the Tris-maleinate buffer than in the phosphate buffer. Since the formation of the MgHPO 4 chelate is taken into account in the calcu- lated concentrations, the actual concentrations of Mg z+ and MgPPI are equalin both buffers. Therefore the increase in actomyosin dissociation at a given MgPPt concen- tration is probably because the Tris-maleinate is itself an "interaction inhibitor" similar to Mg 2+.

Biochim. Biophys. Acta, 86 (1964) 567-578

574 D. GR.~NICFIER, H. PORTZEHL

MATERIAL, METHODS, AND CALCULATIONS

Actomyosin was isolated according to PORTZEHL, SCHRAMM AND WEBER 11 and purified by four precipitations by dilution. The actomyosin solutions contained about 0. 7- I.O % protein. For the experiments, the stock solutions were diluted to about o.15 % protein. The ionic strength was 0.5 and the pH was adjusted to about 7.0 with a 0.02 M phosphate or Tris-maleinate buffer. These solutions were used for 2 days only (cf. JAISLES), whereas the stock solutions were stored at 2 ° for up to a fortnight.

Viscosity measurements were carried out at 2o ° in viscosimeters of Schachmann type with an internal capillary diameter of about 0. 9 mm, a total length of 63 cm and an average outflow time of 20 sec for 2 ml of water; under this condition the Hagenbach corrections become unnecessary. The viscosimeters were calibrated for the flowtime of 2- 4 ml of buffer. In a typical experiment for determining the degree of association, the viscosity of undissociated actomyosin was measured first; then the viscosity of actomyosin partially dissociated by Mg 2+ and PPI was determined and finally ATP was added in order to measure the viscosity of fully dissociated actomyosin. Because of the thixotropy of actomyosin solutions, runs were repeated until at least three consecutive measurements gave identical values.

The "increase of viscosity" or "the degree of association" was computed from the viscosity numbers according to the formula:

Zr/ppi - - Z~/ATp • ioo (~)

Z~ -- Z~A~,

where Z~vpi is the viscosity number of actomyosin in the presence of PPI, Mg 2+,

and Ca~+; Z~AWl " is the viscosity number of fully dissociated actomyosin" Z~/ is

the viscosity number of undissociated actomyosin. The viscosity number can be calculated according to PORTZEHL, SCHRAMM AND

WEBER 11 ; 2.31og rlrel

2 7 - (2) c

where c is the protein concentration in g/1. All values of "degree of association" given in curves and tables axe averages from 3- Io experiments.

I t is useful to describe in detail the ways in which the concentrations of the dif- ferent compounds are calculated when pyrophosphate, alkaline earths, and phosphate are present in the same solution.

The association constants used in calculations of the interactions of H +, Mg ~+, and Ca ~+ with the ligands are given in Table IV, together with the abbreviations used for them. In the calculations of the association constants for the ionic strength of o.5 only binding by the forms of ligand with two negative charges, in the case of phosphate, and three and four negative charges in the case of pyrophosphate, as well as binding of two Mg ~+ by one PPI have been considered.

The transformation of the association constants found in the literature into the constants for the ionic strength of o.5 was made according to the Formulae 3a and

• According to WATTERS AND L A M B E R T ls , in solutions containing Ca ~+ and PPi no Ca2PP i chelate was detectable at concentrat ions up to the limit solubility of Ca ~+ plus PPI.

Biochim. Biophys. dcta, 86 (1964) 567-578

ACTOMYOSIN DISSOCIATION BY THE PYROPHOSPHATE SYSTEM

T A B L E I V

THE TRUE ( ~ ) AND THE APPARENT (K') ASSOCIATION CONSTANTS OF THE LIGANDS PHOSPHATE AND PYROPHOSPHATE (20 °)

575

tog K Calculated ]3r 1 0.5 ( KCI) Abbreg iation Compler of log K" or K used

cation + ligand E~timated Numerical log K ~ in ~alue plt 7,o pH 6.7

a. Phos pha t e

H + + L z- o . I M KC1 11.7I (ref. 3) 11-37 - - - - - -

H + + H L ~- o . I M KC1 6.77 (ref. 3) 6 .56 - - - - K~

H + + H ~ L - o . I M KC1 1.6o (ref. 3) 1-53 - - - - - -

M g z+ + H L z- o . I M KC1 1.77 (ref. 5) 1.18 1.o45 0.943 K~tg~rvoa

Ca ~+ + H L ~- 0.2 M KC1 1.5o (ref. 5) 1.13 0.988 0.893 - -

b. P y r o p h o s p h a t e

I-I + + L ~- o . i M KC1 8.45 (ref. 13) 8 . 2 i - - - - K 1 o . I M (CHz)aNC1 9 . I1 (ref. IO)

H + + H L ~- o . I M KC1 6.08 (ref. 13) 5 .84 - - ~ K~ o . I M (CH:~)~NC1 6.36 (ref. IO)

H + + H z L ~ - o . I M KC1 2.52 (ref. 13) 1.92 - - - - K~ o . I M (CHz)aNC1 2.22 (ref. IO)

M g ~+ + L ~- o M NaC1 7.20 (ref. 19) 4.33 3.07 2.75 K[~tgp~o~]~-* i . o M (CHz)aNC1 5.41 (ref. 9)

Mg ~+ + H L z- i , o M (CHz)aNC1 3 .06 (ref. 9) 2 .86 2.81 2.80 K[~gHPaOT]- *

2 M g a+ + L ~- i . o M (CH~)INC1 7.75 (ref. 9) 6 .34 5.08 4.76 K~ga~p l

Ca ~+ + L ~- o M NaC1 6.80 (ref. 19) 4 .00 2.74 2.42 K[c~P~OT],-* I.O M (CHa)aNC1 4.95 (ref. I5)

Ca z+ + H L z- i . o M (CHz)INC1 2.30 (ref. 15) 2 .2o 2.15 2 . i 4 K[C&HP~0?]-*

* S ince i n t h e e q u a t i o n s for b o t h K ' t h e d e n o m i n a t o r s a r e t h e s a m e o n e m a y c a l c u l a t e KtMgpp i = K'[~gP~O7] ~- + /~'[~tgaP~OT]- a n d g ' c ~ P P l = K'[o~P~OT] ~- + K'[c~itP~OT]-, i.e. log K'~tgPPl = 3.26 a t p H 7.o a n d 3.o8 a t p H 6.7; log K ' c a P e l = 2-84 resp . 2.6o.

3b in which as example the transformation of one ionic strength into an other is given for the binding of alkaline earth (Me 2+) by the ligand with four negative charges (L 4-):

b- ~,~- log KMeI~ + log12÷.f4 - -- log/l;~el~ + log 1~'÷'/4"- (3a)

o r

1 2 - I ~ - l o g KMeI , = l o g / ~ e L - - l o g ~ + l o g l~÷.lg~ (3b)

where K~tel~ is the constant which shall be calculated at I = a; K~teL is the known constant at I = b; in the equilibrium

[ M e L 2 - ] - - K "

EMe 2+] [ L 4-]

f~_, f~+, and fa_ respectively f2-, f2+, and f4 - are the act ivi ty factors of the ions in- volved at I ---- b respectively I = a.

B i o c h i m . B i o p h y s . d c ta , 86 (1964) 5 6 7 - 5 7 8

576 D. GR.~NICHER, H. PORTZEHL

The activity factors were calculated according to the extended formula of Debye-Hiickel (cf. ref. 20):

0.5 z2~/~ - - l o g / _ = - - l o g [+ = (4 a)

I + o .33 . IOS a ~ / ~ -

o r

0.5 z2~/~ --log/_ = --log/+ = (4b)

i + 0.33. lO 8 aX~/~

in which z is the charge of the ion and a is the radius of the ion in solution. The radius of H + was assumed to be 9.1o-* cm and the radius for other ions was 5-1o-* cm. Formula 4a was employed in the transformation of all association constants deter- mined in alkaline chloride into the association constants at I 0.5.

If the association constants of the literature were estimated in I M (CH~)4NC1 solution, Formula 4b was used for the calculation of the thermodynamic association constants (at an I of about o). In the Formula 4 b x is an empirical factor necessary to obtain the same thermodynamic constant as that calculated from the association constant determined in i M (CH~)4NC1 or in alkaline chloride solution. From this calculation of the thermodynamic association constants values of x--~ 25 for the ligand with four negative charges and x ~-- 8 for the ligand with three negative charges were found.

In the cases where the association constants were determined only in I M (CH~)4NC1 solution (of. Table IVb), the thermodynamic association constants were first calculated according to Formula 4 b, and following from it the association con- stants at I 0.5 were obtained according to Formula 4 a.

The association constants at I 0.5 obtained in this way may correspond more closely to the real association constants at 1 0. 5. However, the early assumptions that MgPPt chelate is the dissociator of actomyosin and that Mg ~+ is an interaction in- hibitor were valid as shown in Fig. 5, even if the concentrations of the different com- pounds were calculated by association constants which strongly differed from each other. Moreover Fig. 5 also shows that the same augmentation of the association constants (MgPPI 5 ×, Mg2PPt 14 ×, and MgHPO4 1. 7 x) shifts the curves to smaller concentrations of MgPP1, if the concentration of Mg s+ is high (cf. Curve 2 with Curve 2a) or to higher MgPP~ concentrations, if the concentration of Mg 2+ is small (cf. Curve I with Curve Ia). Therefore an alteration of the association constants only produces a change in the absolute value of the concentrations of MgPP~ and Mg 2+ without affecting qualitatively their effects on actomyosin.

The concentrations of the different forms of the ligand such as L a- and L ~- of pyrophosphate, vary with the pH. The association constants at I 0.5 (K in Table IV) were therefore transformed into apparent association constants (K' in Table IV) corresponding to the experimental pH (7.0 or 6.7) according to SCHWARZENBACH 12.

The equations by which the concentrations of the different compounds can be calculated from the added concentrations of PPI, Mg e+, and Pl or PPI, Mg 2+, and Ca 2+ are equations of higher order, only solved by an approximate method. Therefore the calculations were carried out by a computer of the firm Bull. The divergence of the results from the real values was smaller than o.ooi %, i.e. the divergence was much smaller than the experimental error.

The pH of the actomyosin solutions, between 6. 7 and 7.1, was controlled with

Biochim. Biophys. Acta, 86 (t964) 567-578

ACTOMYOSIN DISSOCIATION BY THE PYROPHOSPHATE SYSTEM 577

a Metrom precision compensator E 322 using a glass electrode. Protein nitrogen content was determined by the semi-micro Kjeldahl method.

Merck analytical grade sodium pyrophosphate (Na4P20 ~. ioH20 ) was used. The stock solutions were prepared weekly and stored at 4 ° . The dissociation curve of PPI was determined (glass electrode) in order to detect possible degradation into P l .

MgC12- 6H~O and CaCI~ (siccum) were also Merck analytical grade. Ca ~+ concentrations were controlled by titration.

The ATP was obtained from Pabst, Milwaukee; a l l the other chemical products employed were Merck analytical grade preparations.

~0o

- ~ ' ~ ~ ~

~ "-,.,~ ~ x ,~ ~ \ \ '°

- ,,-,\ \ ~ , \ \ ,o

"" : Z ° .~ 60 ~

~ ~ ' , , / ~ g0

,,,. X ~ ~ ~ ~

~ ~

~ ~ X ~,

~ X X X

~ x

~ . ~ ~ ~ ~ ~. ~o

~0 "5 I0 "~ ~0 -~

Concenteotion ot M~ oyroo~o$ohote (M)

F ig . 5. D e p e n d e n c e of a c t o m y o s i n d i s s o c i a t i o n o n t h e c o n c e n t r a t i o n of NgPP~ , if t h e c o m p o u n d s a r e c a l c u l a t e d w i t h t w o d i ~ e r e n t s e t s of a s s o c i a t i o n c o n s t a n t s . C u r v e s ~ a n d e : N '~g~ppl 1.2. I o ~, ~ g P P I 1 .8" IO ~, ~ ¢ ~ P O ~ I I ; C u r v e s I a a n d 2 a : ~ ¢ ~ g ~ P P t o . i ~ . i o g, ~ g P P I 8 . 9 " I °~ , ~ g N P o ~ I 9 . C o n c e n t r a t i o n of Mg~+: i n C u r v e ~, o.e m ~ ( ~ ) a n d o. 4 m M ( V ) ; in C u r v e ~a, o.~5 m N ( ~ ) a n d

o.36 m ~ ( ~ ) ; in C u r v e ~, 4 ~ m M ; i n C u r v e ea, 4 o mM.

A C K N O W L E D G E M E N T S

We are part iculary indebted to Professor H. H. WEBER for helpful discussions and wish to thank Mr. A. GRIEDER and Mr. R. Mf3LLER for valuable technical assistance as well as Mr. BLAU and Mr. RAGATZ of the Inst i tut ftir Angewandte Mathematik of the university Berne, who were kind enough to program and run the computer calcu- lations. We are also very grateful to Professor Lf3SCHER and Priv. Doz. Dr. Dr. ROEGG for supervising the translation of this report into English. This article is dedicated to Professor von MURALT on his sixtieth birthday.

This research was supported by grants of the Swiss National Research Council.

Biochim. Biophys. Acta, 86 (1964) 567 578

578 D. GR_~NICHER, H. PORTZEHL

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Biochim. Biophys. Acta, 86 (1964) 567-578