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About this book

Is it not sheer foolishness to try to apply the methods of theoretical physics to biological structures? Physics flowered because it limited itself to the study of very simple systems; on the other hand, the essence of "living things" seems to have to do with the extreme intricacy of their structure. Is it a hopeless endeavour to attempt to bring the two together, or should one try nevertheless? Most of my colleagues in theoretical physics feel one should not waste one's time and stick to "the good old hydrogen atom", but some of them feel one should try anyhow. This minority point of view was shared by Bohr in the thirties, Schrödinger in the fourties, Delbrück in the fifties and sixties, PurceIl in the seventies, etc. The theory of chemoreception represents only a very small part of this immense scientific question. Its study was started by Delbriick and others in the fifties. I was introduced to these problems by Charles DeLisi, during a visit to the National Institutes of Health in the summer of 1980. During the following decade I had the pleasure to collaborate with George Bell, Byron Goldstein, Alan Perelson and others at the Los Alamos National Laboratory. We studied a wide variety of questions, some of them relevant to the theory of chemoreception. I am grateful to them, both for the pleasure which our joint research always gives to me, as weIl as for their friendship and hospitality.

Table of Contents

Frontmatter

I. General Considerations

Abstract
From the point of view of the physical sciences a living organism is a material system of staggering complexity. As a material object it must conform to all the laws of physics, yet its actual behaviour usually follows patterns which seem altogether alien to the world of physics. So, at the present stage of scientific sophistication one should study those living systems that are as simple as possible, and try to understand the physical principles which are involved in their behavior which is generally known as chemoreception (examples will be discussed shortly).
Frederik W. Wiegel

II. Spatial Diffusion

Abstract
The calculation of the translational diffusion coefficient DT of proteins and other ligands in the intercellular fluid forms the subject of a vast literature; some of the classical papers are those by Chandrasekhar [1] and Einstein [2].
Frederik W. Wiegel

III. Ligand Current into a Single Receptor

Abstract
If no ligands are created or annihalated in the intercellular medium ligand conservation is expressed by the equation
$$ \frac{{\partial c}}{{\partial t}} = - div\vec j.$$
(1.1)
Frederik W. Wiegel

IV. Theory of One-Stage Chemoreception

Abstract
Once the ligand current into a single receptor is known, the next task is to develop a general theory for the rate of absorption of ligands by a cell of any shape that carries a large number of identical receptors in its cell membrane (cf. section 1.4 (d)). In this chapter we address this problem, using the effective boundary condition method of DeLisi and Wiegel [1] and Wiegel [2], which can in principle be applied to cells of any shape, with an arbitrary distribution of receptors in the cell membrane. We shall include cases in which there are forces acting between the ligands and the cell and a flow field is present too.
Frederik W. Wiegel

V. Ligand Capture by a System of Many Cells

Abstract
In the present chapter we turn to problems which are related to a system of many cells, as well as to the time-dependence of ligand capture by such a system. The rough model calculations which follow are inspired by the fact that in the tissues of a living organism the cells which are involved in chemoreception will often not occur in isolation but in great numbers. This leads us to consider chemoreception by identical cells which are distributed in space with some number density (r⃗,t) which can be a function of space and time.
Frederik W. Wiegel

VI. Diffusion and Flow in the Cell

Abstract
In chapters II-V we developed the theory of one-stage chemoreception, in which a ligand can only be absorbed by a cell by a direct hit on the binding site of the receptor molecule. In chapter VIII the theory will be extended to incorporate two-stage capture processes in which the ligand is first incorporated in the cell membrane and then diffuses laterally in the plane of the membrane till it hits a binding site. Actually, two-stage chemoreception is only one of a variety of processes which occur at the surface of the living cell and in which the lateral translational - or rotational diffusion of proteins plays an essential role. It is for this reason that the experimental determination of the relevant diffusion coefficients has been pursued vigorously during the last decade [37–44]. Experimental values of the the lateral translational diffusion coefficient (DT’) range from 10-8 to 10-11 cm2 s-1. For the rotational diffusion coefficient (DR’) of proteins embedded in the cell membrane one measures values in the range from 105 to 103 s-1.
Frederik W. Wiegel

VII. Excluded Volume Effects in the Diffusion of Membrane Proteins

Abstract
In section II.3 we developed a theory which enables one to calculate the effects of excluded volume on the equilibrium distribution of cell membrane proteins. In various situations (like photobleaching recovery experiments) the kinetics plays a role. It is the aim of the present chapter to describe a theory which enables one to analyze the effects of excluded volume on the kinetics of proteins which diffuse laterally in the cell membrane, and to apply this theory to some experiments of current interest. We shall also study the case of diffusion in a three dimensional space.
Frederik W. Wiegel

VIII. Theory of Two-Stage Chemoreception

Abstract
The central theme of the previous two chapters was the diffusion of proteins in the cell membrane. In this chapter we are going to use some of that work to study two-stage chemoreception, which is related to the ability of most cells to bind certain ligands nonspecifically, i.e. many ligands can bind weakly to the nonreceptor portion of the cell surface as well as specifically to appropriate receptors. Consequently, ligands may bind nonspecifically and then diffuse in the plane of the membrane until they encounter a receptor molecule. Such binding paths are often referred to as non-specific. These paths will be in competition with specific paths that involve binding directly from solution; in general both types of paths will contribute to the rate with which the cell captures ligands. In this short chapter we develop the theory of two-stage chemoreception for the standard model of chapter IV, following some work by Wiegel and DeLisi [1].
Frederik W. Wiegel

IX. Chemoreception by a Swimming Cell

Abstract
In many cases of biological interest the cell which is involved in chemoreception is in a state of uniform motion with respect to the surrounding extracellular fluid. This situation would describe a swimming bacterium, for example. If the cell is described by the standard spherical model with N binding sites, as discussed in section IV.2, one can ask for the effect of swimming on the rate of ligand capture. Up till now this question has not been studied theoretically in a fully satisfactory way. It is the aim of this short chapter to formulate the problem as far as possible, to identify the dimensionless parameters which occur in it, and to solve it in some limiting cases.
Frederik W. Wiegel
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