Proto-osmosis

Due to the viscous coupling between K and water molecules, there will be a flux of water and salt in the lumen. Whether a pressure gradient [p(0) —p(/)]// is generated by such a flux or it is imposed across the OC, it will in turn also bring about a flux of and generate a streaming potential difference AF. Furthermore, the protons in / h will also react to the flux of K due to pressure flow via AF. Therefore all the three fluxes, fK and the flux of water, are interlinked. 

To solve this, rather intricate problem a subdivision of is undertaken into an outer layer close to the surface r = a — e = ao, and an inner layer R j, with the radial extensions of and 

Neglecting the fluxes of Cl and K in I / due to AF, (which again acts maximally at and / h) the equations of the three fluxes are written 

Here Ap = p(0) — p(/), and A P includes the contributions both of the streaming potential and the diffusion potential difference across the OC. A P and the coupling constants oc and fi have now to be determined. 

The general solution for the velocity of a viscous fluid of viscosity t/ in a capillary of radius Oq is given by  

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The proton flux mediated electro-osmosis or in short proto-osmosis is the perimembrane and transfilament analog of Mitchell s (transmembrane) chemiosmotic theory and could be operating at the cellular and organismal levels in diverse dynamical processes (see Transport in Plants, Chapter 21 in this volume). If the phenomenon is experimentally verified in muscles and in other systems, the dynamic aspects of cell biology would become amenable to quantitative treatment using the principles of electrochemistry. 

Can the phenomenon of H" "-flux mediated electro-osmosis provide the biodynamic principle which we have been looking for It is clear that cellular transport processes such as axonal transport and cytoplasmic streaming could directly result from proto-osmosis if the ATPases inject protons into the filamentous systems. Ciliary movements could possibly result from a periodic proto-osmotic insurge of fluid in the cilia. A relative (contractile) movement of two sets of filaments could be caused by a proto-osmotic loop flow between the pairs of the filaments by means of the associated visous drag couple. But the question of the relevance of the effect can be solved only if it can be shown that the magnitude of the effect is sufficient, quantitatively, to explain at least one biodynamic phenomenon. The best-studied system in this context, from structural and biochemical aspects, is that of muscles. The necessary quantitative data for the comparision of theoretical result with experiments is available, but it has to be first confirmed that the conditions for the proposed electro-osmotic flow obtain in muscles. 

The solution to the great puzzle of the unexplained energy in terms of the H stored at the cross-bridges also helps to explain the fast response of a muscle. The continued movement of the cross-bridges in the overlap free zone and after the end of the contraction is explicable in terms of the inertial hydrodynamic flow associated with proto-osmosis. This approach also does not require any long duration contact of a cross-bridge with the actins. The dissociation of ADP and P can occur at any time after the actual contact is made. 

Writing Jh for the transference number of H+, [Th = gJigH + k)] and eliminating AV from Eqs. (9)-(H) the final equations for proto-osmosis are written as... 

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