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The concept of water potential in plants tries (and succeeds) to explain various movement and transports in plants. I have learnt that it can be though of being composed of various components like the solute (osmotic) potential, Matric potential, gravitational potential and the pressure potential. I know how to quantitatively determine the osmotic pressure and have worked with the chemical potential of water in solution and pure state. Can someone help me develop an intuitive understanding of all these components quantitatively? I am comfortable with basic thermodynamic treatments of chemical potential and already have an intuition of the osmotic component. Here is the basic definition regarding water potential. (Since this pdf is quite old, I am not sure whether the same definitions operate or rather are used now.)

EDIT:- As an example, we can derive the lowering of chemical potential of pure water on addition of solute and for the ideal case, the lowering turns out to be $RTln(X_a)$ (where $x_a$ is the mole-fraction of solute, $R$ is the gas constant and $T$ the absolute temperature) and this is defined as the osmotic potential or the solute potential. Next, the gravimetric component. We can intuitively understand that the water must flow from higher gravitational potential to lower and hence flow downwards. But I want to understand how can we assign a quantitative basis to our arguments in terms of chemical potential for differenf heights. Same way, how can we ascribe a mathematical (or chemical) basis to all the components of water potential including the turgor pressure and the matric components.

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sadly this paper is behind a paywall - any other references? –  shigeta Jul 30 '13 at 4:42
I have a copy but I dont think we can share without uploading. Nevertheless, (en.wikipedia.org/wiki/Water_potential) wikipedia provides some minimal non rigorous definitions. See if that helps provide some quanlitative clarification of this concept. –  Satwik Pasani Jul 30 '13 at 5:52
could you add a couple of questions or issues you have - what sort of phenomenon or math puzzles you about water potential? again there's several ways to go here. –  shigeta Jul 30 '13 at 12:41
Added in the edit –  Satwik Pasani Jul 30 '13 at 15:35
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Ok let me try to tackle this one - still could be off - let me know.

The book Chapter from UCDavis that is linked from your wikipedia page is a good reference I think. Overall the term 'water potential' will try to estimate an energy function that describes the behavior of water in a chemo-mechanical sense.

$\Psi_{total} = \Psi_{reference} + \Psi_{solute} + \Psi_{pressure} + \Psi_{gravitational} + \Psi_{humidity} + \Psi_{matrix}$

It looks a lot like a Hamiltonian expression of total energy that tries to see the water as a fluid. The water potential is not the same as an energy equation for fluid dynamics which tries to understand the motion of a body of liquid and does not typically take into consideration chemical changes like solute in the behavior.

So first we are looking at a set of behaviors that the fluid experiences. some of them treat the fluid as a body ( pressure, gravitational) others look at the potential for evaporation or diffusion (solute and humidity to some degree). wetting of surfaces and surface tension (matrix).

The water potential is an equation broken down into a set of measurable or approximately measurable energy terms. But like a lot of Energy equations, when you are looking at a biological system, it is more often qualitative than a quantitated entity. The general observation that surface tension decreases when temperature goes up, or when the solutes have higher concentration is used to make arguments of the mechanism of say physiology

Generally speaking looking at the magnitudes of the various terms you can see how influential they are and then try to focus the hypothesis into a test that can make a distinction about the mechanism with specific measurements. The actual overall measurement of a water potential or any total energy is almost always intractable. The difference in energy is what you might be able to measure, but in the case of the water potential, the measurement will usually be an observation, with some uncertainty that water is moving from point A to B and not elsewhere.

Take a look at this paper describing Drought Stress in Arabidopsis. The water potential is cited as a critical element of drought response - and of course it should be. But all this work here, with all the proteins acting to change the physiology of the cell, adjust the chemical potential (and therefore the osmotic potential) of the cell membrane, its hard to imagine how measuring a root system at all points would be possible.

Physical properties of the cell wall play a crucial role in the response of plants to water deficit (Bacon, 1999). Transcriptome analysis of pDr showed the repression of many expansin genes (Bray, 2004), while mild osmotic stress revealed the induction of expansin genes (Skirycz et al., 2010). Cell expansion in response to drought was characterized in the maize (Zea mays) root system as an adaptation to low water potential (Wu and Cosgrove, 2000).

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