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05_-_Entropy - Quantitative Physiology I Molecular and...

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Quantitative Physiology I / Molecular and Cellular Systems; BMEN E4001x Notes: 05 – Entropy no text Here, we investigate a complementary phenomenon to diffusion, namely entropy. You’ve probably seen this in terms of the Gibbs free energy for a given reaction: G= H-T S but what the heck does this mean? From earlier encounters with this term, it should increase. Vaguely, entropy is disorder, and it is an appropriate statement, as it really has different implications in different fields, and from different approaches. It is, to be sure, a thermodynamic property, such as temperature and enthalpy, but a bit harder to get a hold on. Temperature, it turns out, is equally intangible, but we interact with it on a more day-to-day basis. Where will we see entropy in molecular biology? It is a force as equally important as diffusion in driving molecular recognition. In Biol 2005 and in subsequent places, you will see examples of proteins interfacing. This must happen quickly, and quite often, be reversible. Yes, covalent modifications are one route. But to take advantage of thermal fluctuations, the barriers to interaction must be much less than that associated with covalent binding. This is the realm of hydrogren binding, hydrophilic/hydrophobic forces, and entropy. Antibodies: Immunoglobulins. Proteins really important in the immune response. A major type of these proteins, IgG, has a Y-shape, with a very archetypical structure; two antigen binding sites (called Fab sites) and a constant region (Fc region). So why have two binding sites?
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Microstates We’ll be following a microstate treatment, namely a lattice model following our discussion of diffusion. Let’s look at diffusion in a slightly different manner. Consider random motion of particles in a container composed of two boxes. For simplicity, consider two particles. As diffusion is additive, we can have more than 1 particle in each box. At any given moment, how are the balls distributed? 2 particles occupying a 2-compartment box. Each has a certain energy. 1 2 There are 4 ways to put these balls in this box 1 1 1 1 2 2 2 2 These are designated as microstates of the system. Each of these are equally probable. Under our model of diffusion, there are a limited number of direct transitions between these situations, but in general, we stand an equal chance of observing any one of these at any given look. However, we tend to look not at microstates, but groups of them, configurations that describe
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