Membrane Transport: A Mathematical Investigation
It is known that the primary constituents of the membranes of cells are lipids. These lipids are arranged in two layers and the membrane is frequently called a bilipid layer. Recent low intensity scanning electron micrographs of the bilipid layer has revealed that the bilipid layer has revealed that the bilipid membrane layer also contains proteins. The proteins in the bilipid membrane layer pass from one side of the layer to the other and thus constitute a “hole” in the membrane layer. The structure of the proteins is such that an essentially void space exists surrounded by the molecular structures of the protein. The exact functioning of the proteins has not yet been determined. The thesis of this paper is that the proteins act as mediators for the transport of specific catabolites. The supporting arguments for the thesis are in the form of mathematical models for the catabolite — protein interactions, and the results of simulations based upon the mathematical models. Physical verifications of the results presented in this paper await physiological experimental data. However the results of this work indicate that modest changes in the membrane proteins result in a significant change in the amount of catabolite transported across the cell membrane. The mediation of the catabolite transport by the proteins has the pathological implications that long term post-disease states of the cells may be linked closely to the altered states of the membrane proteins: which may occur during the period of the disease state.
KeywordsBrownian Motion Potential Field Oxygen Transport Smoluchowski Equation Oxygen Density
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