Soliton-assisted unidirectional circulation in a biochemical cycle

Abstract

The unidirectional circulation of an enzyme round a working cycle can be understood in terms of the formation and decay of a soliton that acts as a ligand for the protein and for which the surrounding heat bath serves as a sink. An experimental confirmation of this interpretation is suggested in which the soliton is of the Davidqv type and is created by infrared photon absorption as in recent experiments on agetanilide.Enzymes work in a cycle characterized by a certain turnover number. An understanding of this and the reason why all enzymes should be proteins is a major problem of biophysical chemistry. In simple cases in which the macromolecule is near equilibrium in the Onsager regime a possible answer that has been suggested lies in the concurrent effects of spontaneous fluctuations (1). In more complex situations the problem has been answered in a formal and overall way by postulation of the allosteric model, in accordance with which the macromolecule exists in two or more ligand-linked conformational states (2). This model, which has its roots in studies of reversible binding of gaseous ligands by respiratory proteins, notably hemoglobin, has been used with great success, though often somewhat uncritically and without any clear distinction between a steady state and true equilibrium, to explain the cooperativity and regulation shown by functioning enzymes, ignoring the fact that in many cases the system is operating far from equilibrium, in a region where the Onsager approximation no longer holds. In view of this, a "kinetic" variant of the allosteric model has been proposed, applicable to a working enzyme under steady-state conditions (3, 4). This has been called the "Turning Wheel" and will be briefly reviewed in order to show how, in some cases at least, the unidirectional 'circulation of an enzyme round a closed path can be explained, physically, in terms of a soliton trapped in the protein matrix as a peculiar kind of ligand. The importance of such unidirectional circulation lies in the fact that it gives rise to what may be called kinetic linkage and the associated phenomenon of free energy transduction. The Turning WheelConsider a macromolecule that exists in several different conformations and states of ligation. Suppose that it acts as an enzyme for one or more of its ligands. Suppose further that it is present in an environment in which its substrates and their products are maintained at constant concentrations (activities), in general not at equilibrium. The system will be described by a set of simultaneous first-order linear differential equations whose solution shows a unique asymptotically stable critical point. This means that no matter what the starting point the system will always settle down to a unique steady state. The approach to this steady state will be described by a set of relaxation times whose number is one less than the total number of forms. These are given by the roots of the secular equation constructed from the matrix formed by the coefficients of the various forms of...

Unidirectional circulation in a prebiotic photochemical cycle

“…Assuming a typical value of 108 mold'sect for the diffusion-controlled enzymatic rate constant (9) and assuming only one substrate molecule to be included in the water droplet considered above, we obtain a figure of one such encounter per year. Recognizing that allowance of a factor of 100 at least must be made for the lower efficiency of the protoenzyme, we conclude that at the concentrations defined above the substrate is likely to meet the enzyme with the soliton already trapped in it, thus allowing the substrate-enzyme complex to evolve unidirectionally (2).We believe that the model calculation considered above displays several attractive features in the prebiotic scenario. First, this model mimics the present chlorophyll-assisted solar energy pathway, although it is much simpler because it requires only one photon to be absorbed and stored as a trapped soliton.…”

“…Assuming a typical value of 108 mold'sect for the diffusion-controlled enzymatic rate constant (9) and assuming only one substrate molecule to be included in the water droplet considered above, we obtain a figure of one such encounter per year. Recognizing that allowance of a factor of 100 at least must be made for the lower efficiency of the protoenzyme, we conclude that at the concentrations defined above the substrate is likely to meet the enzyme with the soliton already trapped in it, thus allowing the substrate-enzyme complex to evolve unidirectionally (2).…”

“…In the fully developed organism, this state of affairs, which provides for the transduction of energy (or free energy) from one chemical reaction to another, is made possible by a set of highly developed polyfunctional enzymes. It was to provide a mechanism for such one-way circulation that the concept of a trapped soliton as an energy packet, created at one point of the network and liquidated at another, was introduced in an earlier paper (2). For the special conditions of prebiotic life, before the development of chlorophyll (3), we suggest retention of a trapped soliton as the driving mechanism for maintaining the unidirectional circulation of a complex system round a closed network but suppose that the soliton results from the absorption of solar radiation, which replaces the chemical free energy that is supplied by the driving reaction under present, more complex conditions.…”

Why are proteins with glutamine- and asparagine-rich regions associated with protein misfolding diseases?

“…Davydov's assumption is that the first event after the hydrolysis of ATP is the storing of the energy released in the chemical reaction in the form of a vibrational mode of the peptide group, known as Amide I, which consists essentially of the stretching of the C=O bond and whose energy varies with secondary structure of the protein (Krimm and Bandekar, 1986). In the Davydov/Scott model the interaction of the Amide I mode with the vibrations of the associated hydrogen bonds leads to a localization of the Amide I excitation in a few peptide groups, a mechanism known as self-trapping, that leads to a state designated in the literature as the Davydov soliton (Scott, 1992 (Careri et al, 1984) which includes hydrogen bonded chains identical to those that stabilize the secondary structure of proteins and thus constitutes a possible model system in which to test the Davydov/Scott model. Careri and co-workers (Scott, 1992) found an anomalous line, 15 cm…”

“…ps in ACN (Wyman, 1975) is kept running by Amide I excitations (Careri and Wyman, 1984). In the present work, the effect of neighboring water molecules on the protein is considered.…”