On the applicability of Guldberg & Waage's law of mass action to metabolic open-chain reactions of irreversible character

Abstract

Our expositions suggest that there are objective grounds and possibilities for applying the law of mass action also to chains of open irreversible metabolic reactions, or foi' transference of molecules through a series of irreversible Chain reactions, provided the »transference equilibrium« is attained in the reactions concerned. The apiplication should hold good in ali cases where, in the transference equilibrium, constant "dynamic" concentrations of compounds are established — of zero-molecules transferend from one part and of molecules of the transferring substances from another part. 

The application is equally possible in transference systems in which the transfeiTing subtances possess beforehand complete and free molecules with constant "concentrations", as well as in the cases where molecules of the transferring substances are instanfaneously liberated and continuously transferred, with approx. equal velocity and without any constant "concentration levels" from the substances they are liberated from direct to the spot where they combine with zero-molecules.

When the transference is done by the free molecules of the transferring substances, the reacting mass can be expressed by their "concentration", while such an expression of reacting masses for the zero-molecules is only possible as regards the first compound of the transference, tor here both the transfer­ ring and the zero substances are possessed of free molecules. As regards the subsequent members of the transference, the reacting masses of zero-molecules can only be expressed by absolute quantities of the transport of the molecules concerned with reference to a unit of time. However, the method of expressing an active mass in two different ways has its drawback in the fact that specific velocities of syntheses are equal only to the reciprocal values of "concentrations" of free molecules of the transferring substances. Since these values can be different, this would be contradictory to the actual process of transference, for the combination quantity cannot be increased merely by an augmentation in the "concentration" of transferring, free molecules witout a simultaneous increase in the transference velocity of the zero-molecules, which is not bound to occur. This contradiction is obviated in the absence of free molecules of the transferring substance, i. e. when the latter are liberated directly before reacting with zero-molecules Seeing that the number of zero-molecules to be transferred is equal to that of molecules of the transfering sub­stance in the case of monomolecular reactions, it follows that for the formulation of the equation it is sufficient to know the transference quantity of the zero-molecules since the equivalent of the transferring substance is known ipso facto. As the transference quantity of the zero-molecules is equal for ali members of the transference along the entire reaction chain, it follows that the specific velocities of the syntheses of ali members of the trans­ference are co-equal, i. e. no specific individual velocities exist for the synthesis of a given compound; there exists only the collective velocity constant of the syntheses, vvhich is equal to the reciprocal value of the absolute transfer­ ence quantity of the zero-molecules. Two further conclusions can be drawn-from this, i. e.

(a) The syntheses of subseguent transference members in a given reaction chain do not depend upon "concentrations" of free molecules of the transferring substances concerned (in so far as they exceed the necessary minimum). The fact of the matter is that only a collective value of the specific velocity of the syntheses can be said to exist, which is determined by the transference velocity of the zero-molecules along the entire chain, independent of the previous state of the molcules of transferring substances of a later -transference stage, i. e. the rule holds good irrespecpective of the existence of free molecules of the transferring substances. To go and enter "concentrations" of free molecules of such transferring substances into the equations of sintheses would therefore be incorrect, for it is only the reacting quantities of mole­cules of this kind that actually take part in the equilib’riums of a chain; 

(b) Total transference velocity along the entire chain is governed by the
quantities of the reacting masses, i. e. by the existing "concentrations" of zero-molecules as well as those of the transferring substance that is at the head of the entire chain, the substance that actually starts the chain of the binding tcgether of the zero-molecules. Seeing that — according to Piitter, Jost, Gurney & Bertalamffy (13, 9, 7, 3) — in a chainlike reaction series, the total velocity of the chain is determined by the velocity of the slowest physical or Chemical process, it follows by inference — according to our formulae — that the slowest process is to be found in the first member of the chain. This conclusion, unexpected though it may seem, unavoidably follows from an analysis of our equations. We should. find this quite logical in the case of phosphoric acid transmission, where the first reaction is started by sucrose-combinations which, in the exothermic way, provide the phosphoric acid with the energy required for its further exothermic transmission. However, we are unaware whether ali reaction chains are started iby a similar reaction, i. e. the one that makes ava'ilable a given amount of free reacting energy to the entire chain. As long as the rate of inflow of transferring molecules, in successive series of transference, remains adequate for the reception of ali the zero-molecules introduced into the chain by the first transferring substance, the latter molecules will have no direct influence upon the chain equilibrium. However, should the rate of molecular inflow from any of the fransferring substances belonging to a later transference stage (i. e. a substance that enters the chain lateraily) become inadequate for the reception of the entire supply of zero-molecules, then a definite disturbance of transfer-ence equilibrium would be bound to follow. This again would be reflected in the fali in the »dynamic-concentration« rate of synthetic binding of the transferring substance the inflow of which is insufficient, as well as in the number of members that have to be provided with zero-molecules by the stage of insufficiency. Yet a reduced inflow should also be reflected in a higher "concentration" rate in the binding together of the transferring and the zero-mole­ cules at a previous stage (or several earlier stages) of transference directly before the blocking up of the reaction series. The conclusion therefore should be as follows: The lateral transferring substances, as distinct from the frontal one, can act upon the equilibrium of the chain only by the minimum of their influx, and not by the maximum of molecules available to the chain for the transference of the zero-molecules. In the case of molecular deficiency in a transferring substance, the change of equilibrium is characterised by an altogether different feature: its proportions have to be changed.

Eguations for specific velocities of decompositions, as distinct from those
of sintheses, have identical formulations for the two states of transferring substances, i. e. the equation obtained by transposing free transferring molecules is identical to the one deduced when the molecules do not exist in a free state.

This is because into its formulation therei enters besides a flowing-concentration compound of the zero and transferring molecules, the absolute transference quantity of the zero-molecules only (without that of the transferring molecules). Accordingly, in the achieved equilibrium of transference the proportions of stationary, or "flowing" "concentrations", combinations in successive stages of a reaction series are governed exclusively by the values of specific decomposition velocities, since the transference quantities of zero-molecules are equal foi' ali transference members. The formulae disclose that in this case the stationary concentrations are in inverse proportion to only the specific velocities of decomposition, for the same transference-quantity is divided by various magnitudes of decomposition constants. An amount of a substance in an organism, which we call "concentration", represents no static value when seen in the light of metabolism, but rather a stationary manifestation of an established dynamic steady state, i.e. an equilibrium between a contributed share of a substance and. its conversion and decomposition in course of its circulation (through syntheses or decompositions, its introduction into and its exit from the cells, etc.).

The content of the "concentration" concept is determined by the dynamics of the movement of subtances in the direction of a synthesis as well as de­composition, or by the differences in speed of the two processes. Metabolic chains of transference show analogy with a river and. its course; here, the stationary level of flowing water does not represent a basis that conditions objectively the dynamics of movement of the water mass; in fact, the reverse is true: the corresponding stationary level in a water mass is a reflexion of the established equilibriuirf betvveen the respective rates of speed of the filling up of a river with new masses of water coming from the direction of its source, on one side, and of the rate of outflow of its water mass-towards its mouth, on the other side.

Viewing biochemistry and metabolism from this standpoint, we would
suggest that there is little that can be said in support of E. Baldwin’s (1)
assumption to the effect that, in a living organism, "statics" is the basis of dynamics. On the contrary, according to L. Bertalamfy (3) ali living organism are balanced flowing systems having a series of characteristic features: maintenance of constants under conditions of a permanent flow through of matter and energy, of automation and autoregulation on the principle of excessive compensation, etc. Likewise, according to Schoenheimer, Borsook (21, 22, 5, 6) and others, it is contended that "statics" does not exist at ali in a living organism because the living structure itself is destroyed only to be recomposed. "Statics" comes about by the act of our analysis (e. g. by our taking and preserving of samples for analysis, etc.). In an organism there are only movements of substances in their course toward uninterrupted decomposition and repeated regenerating syntheses; there are also dynamic or "flowing" equilibriums between the two processes that are apt to impress usi as being "static" — also because we forcibly change them into such by interrupting their life cycle (for we find it more convenient, for the purpose of our analytical methods, to use them in a static state). It would be more to the point, in our opinion, to suggest that the correct understanding of "statics" or a "flowing balance" with refer­