Debajyoti Bhaumik

Charged bosons and the coherent state

The coherent state for charged bosons is constructed, its properties are investigated and the corresponding classical model is discussed.

On the possibility of ‘Bose condensation’ in the excitation of coherent modes in biological systems

Abstract The phenomenon of Bose-Einstein condensation of phonons in biological structure, predicted by Frohlich on the basis of rate equations, is approached here from a microscopic point of view. Rough estimates are compared with the recent experimental evidence of the action of coherent millimeter electromagnetic radiation on biological systems.

Polar modes with elastic restoring forces, “bose condensation” and the possibility of a metastable “ferroelectric” state

Abstract The system consists of an electric polarisation field coupled on the one hand to an elastic field and on the other to a thermal reservoir. When the polarisation modes are pumped, Bose condensation in the lowest mode occurs, for energy inflow above a certain critical amount. It is shown that elastic forces, called into play to stabilise the excitation of the polar modes, lowers the threshold for Bose condensation. With further increase in the pumping rate the possibility exists for the softening of the polarisation oscillations leading, in the presence of quartic self-interaction of the polarisation field (inserted for stability), to a metastable ferroelectric state. The work represents an attempt to develop a microscopic approach to the Frohlich model for the dynamics of macromolecules (such as proteins and enzymes) of biological significance.

Classical limit of the hydrogen atom

A wave packet which travels on an elliptic trajectory is constructed for the hydrogen atom. This is achieved by mapping the Schrodinger equation for the hydrogen atom into the equation for a four-dimensional oscillator with a constraint. A set of coherent states for the constrained oscillator are then shown to have at high average energy the classical limit properties as obtained for planetary motion, to a good approximation.

The possible role of solitonic processes during A to B conformational changes in DNA

Among the conformations which the DNA molecule can adopt, the transition beween the A and B families, controlled by water content (relative humidity), seems to be implicated in the transcription process. Focusing on the main structural difference involved (tilting of base normals with respect to the helix axis), a model is constructed, solitary wave solutions of the resulting equation of motion are demonstrated and possible experimental implications indicated.

Coherent states for angular momentum

Angular momentum states analogous to the coherent states of the harmonic oscillator are defined and their properties discussed.

The “Van Der Waals interaction” between loose structures

Abstract Defining a “loose” structure as that possessed by a molecule requiring for configurational transformation to a metastable state, an energy less than or comparable to the energy of interaction with another such structure, we construct a model to study the peculiarities of the interaction of such objects, when attendent non-linear effects are taken into account. It is shown that the interaction potential possesses some rather intriguing features whose possible relevance to enzymatic and other processes involving biomolecules is indicated. Our work is along the line of certain speculations of Frohlich.

ELECTRIC FIELD DEPENDENCE OF PHASE TRANSITIONS IN BILAYER LIPID MEMBRANES AND POSSIBLE BIOLOGICAL IMPLICATIONS

Bilayer lipid membranes consist of an inner hydrocarbon tail region with the hydrophilic polar heads on either side. The order-disorder transition in the hydrocarbon tail reigon, from liquid crystalline (fluid) to gel state, is characterised in terms of a Landau-de Gennes description, in which the effect of an external electric field is incorporated through its description, in which the effect of an external electric field is incorporated through its interaction with the surface charges on the bilayer (placed as it is in an ionic medium) or with the polar heads. Biological implications of such a phase transition, for excitable membranes, resides in a model wherein ion channels (taken to be composed of protein bundles) are postulated to be surrounded by lipid molecules in the fluid phase when the membrane is in its resting state, while surface charges and/or the polar heads of the lipid molecules responding to an electric stimulus, if of adequate magnitude, induces a transition in the hydrocarbon tail region of the (boundary) lipid surrounding the ion channels from the liquid crystalline (fluid) to the crystalline (gel) phase which, in turn, through coupling with the relevant modes of the protein bundles, results in the opening of the ion channels, provinding thereby a mechanism for the desired response.

Effect of the intervening medium and of feeding of energy into polar modes on macro-molecular interactions

Abstract Macromolecules possess pliable structures and could be raised through interactions into metastable states with the excitation of giant dipolar modes (with zero wavenumber). This in turn would qualitatively alter the nature of the interaction between two such objects from the familiar Van der Waals form. The dispersive character of the intervening medium in the space between the interacting molecules gives The interaction between such “labile” molecules is amenable to profound influences due to the presence of external energy pumping into polar modes and leads to interesting possibilities of control at the molecular level and storage of energy in ordered states which may be of importance in biological processes.

Solitary waves and macromolecular systems

Macromolecules and their aggregates (such as protein bundles in biomembranes) possess polar modes which, when excited, tend to deform the system and call into play elastic restoring forces. A model of such systems, characterised typically by electric polarisation modes stabilised on the one hand by quartic self-interactions and on the other through coupling to the elastic deformations, admits the possibility of localised excitations (solitary waves) propagating with subsonic velocities, possessing the features of relative stability and efficient transport characteristics (associated with the collective nature of the phenomena), and at the same time provides a mechanism of control and variability which could be of considerable interest in biology.