Gradients and Biological Work.

Living organisms maintain large differentials (or gradients) between their internal and the external environment, and between different compartments of the internal system. Many of these gradients must be maintained actively (they require ATP) and some of them actively contribute to generation of ATP. In fact, all biological work ultimately depends upon such gradients.

Some examples of the functions to which gradients can be put:

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Blood flow.

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Movement of sap in plants.

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Heat flow in thermoregulation.

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Air flow in lungs.

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Excretion of nitrogenous waste.

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Generation of ATP in mitochondrion; Carbon fixation in chloroplast.

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Generation of action potentials.

All of these examples involve flow processes. This may be bulk flow as in the case of movement of sap in plants or flow of blood in vertebrates, or it may be particle flow as in processes used to generate ATP in mitochondrion or electrochemical gradients key to produce action potentials. Thermoregulation involves heat flow by conduction as well as bulk flow by convection, and still other systems may be best described as charge flow, or electrical current. Whatever the system involved, the basic mathematical models underlying them are similar; the flow process is driven by a gradient ( $\Delta P/\Delta x$) (in pressure, temperature, concentration, charge, etc.) multiplied by a resistance factor (A): $\mbox{Flux} = A (\Delta P/\Delta x).$ The resistance factor subsumes a lot of biology as well as geometry (for example, flow occurs across an area).