Osmotic or Solute Potential
    Solutes reduce the free energy of water, thus reducing the water potential.  This occurs primarily through the mixing of water and solutes, which increases dissorder in the solution, lowering the free energy.
    Solutes (1) reduce the vapor pressure above a solution
                (2) raise it's boiling point (hint: why put salt in water used to make spaghetti?)
                (3) lower the freezing point (why oceans don't freeze easily, along with your blood!)

    Van't Hoff determined the mathematical relationship between solutes and osmotic pressure (for which he later won the Nobel Prize in Chemistry, in 1901).  This is:
                                                            Y_s  =  -nRT/V

    where:    Ys is the solute potential
                    n is the moles of solutes
                    R is the gas constant (8.32 J mol^-1 K^-1)  (this is the same as 0.0083143 L MPa mol^-1 K^-1)
                    T is temperature in K, and
                    V is the volume of water (liters)
    The minus sign indicates that solutes lower the water potential below that of pure water.

Pressure Potential
    This term represents the hydrostatic pressure of a solution.  Positive pressures raise the water potential, and negative pressures lower it.  Pressure potentials, or turgor potentials, are measured as deviations from atmospheric pressure, so an open container of water would have no turgor pressure, but a turgid cell would.  However, don't forget that an open container of water has an absolute pressure exerted on it of 0.1 MPa, due to the weight of the air acting upon it.  But we relativize everything against this value, which is why it's turgor or pressure potential is 0 MPa.

Gravity
    Gravity forces water downwards unless an opposing force equal to or greater counteracts this movement.  The magnitude of the force (g) is 0.01 MPa (0.1 bar) per meter height of the water column.  So, a 10 meter tall tree would have a drop in water potential of 0.1 MPa (1.0 bar) at the top of the tree, and a 100 m tall tree would show a 1.0 MPa (10 bar) drop.  Actually, temperature and location on the earth also affect this value, since water density varies with temperature, and g varies with elevation and location on the earth.

Matric Potential
    Matric forces result when the free energy of water is lowered due to the interaction of water molecules with the surface of some solid, such as cell membranes or soil particles.  Charges on these surfaces can immobolize some water molecules, lowering their free energy, and the water potential of the solution as a whole.  For hydrated cells, we can ignore this potential, because only a tiny fraction of the cellular water is so affected, and the same in fully saturated soils.  But as soils dry out, matric forces become dominant.

Total Water Potential
    Total water potential is simply the sum of the osmotic and turgor potentials.  Where necessary (tall trees, for instance) the gravitational component can be added in:
                                                        Y_w  =  Y_o  +  Y_p  +  g
 

Apoplastic and Symplastic Water Fractions
    Apoplastic water is that water contained in the intercellular spaces, and cell walls.  Because it is not bounded by membranes, there can be no turgor potential (but see next paragraph).  Thus the water potential of the apoplast is determined solely by the osmotic component, and in most plants, this is very small.  Most apoplastic water is nearly pure, with an osmotic potential of around -01. to -0.05 MPa at most.
    One exception to the no turgor condition is in the xylem.  Remember, xylem cells are dead at maturity, and have no membranes, so technically, all the water in the xylem is apoplastic water.  As we will see in future lectures, this xylem water can be under substantial negative pressures.  Then the total water potential is a function primarily of the pressure potential, with only a minor component due to solute potential.  However, for some plants growing in saline environments, salt may accumulate in the xylem and apoplastic spaces, which would lower the water potential of this water in these plants.

    Symplastic water is the water contained within cell membranes.  Since it is bounded by a membrane, the water potential can be determined by both the osmotic and turgor potentials.

    When water leaves a cell as it dehydrates, the first water to evaporate is thought to come from the apoplast.  This lowers the water potential of the apoplast, and water in the symplast then moves down the water potential gradient to replace it.  This means that under most conditions, as a plant cell dehydrates, the symplastic water volume decreases, while the apoplastic water content changes very little, if at all.  Only at extremely dry conditions is it thought that the apoplastic water content starts to decrease.

Determining Water Potential Components as a Cell or Tissue Dries Down
    Since knowing the total water potential does not tell uswhat the turgor or osmotic potentials are in a cell, it is important to understand how these components change as a cell or tissue loses water.  If a plant has thick, stiff cell walls, then when water leaves the cell, turgor will quickly drop.   If water continues to exit the cell, turgor will drop to zero.  After this point, all water potential values are determined solely by osmotic potentials.  For plants with flexible, thin, walls, turgor will not drop as swiftly, because the walls will collapse inwards, exerting some pressure on the remaining water in the cell.

    A stiff cell wall means that for a given change in water volume, the pressure drop is large.  This ratio of change in pressure to water volume loss is known as the bulk modulus of elasticity (e):

                                                                  e = delta P/delta V/V

    The advantage of this condition is that a small change in water content drastically lowers total water potential.  Under conditions where maintenance of water flow into the plant is important, this will allow the plant to keep water flowing from the drying soil into the plant.  For plants with low e, they can maintain turgor as the soil dries, and continue to grow and expand their cells.  This may be important in habitats where competition with neighbors is critical.

    Remember that osmotic potential according to Van't Hoff is:  Y_o  =  -nRT/V

    If we invert this equation, then we get:                              1/Y_o  =  -V/nRT

    Assume that nRT is a constant, and call 1/nRT  =  K.  Then,     1/Y_o  = -K*V

        This is a linear equation.  What it means is that as the cell dries down and loses symplastic water, the osmotic potential becomes more negative (remember, you have re-invert the equation to get back to water potential units instead of their inverse).  This change is linear, that is, for any unit change in water volume, the change in osmotic potential is the same.  We can then plot this equation and use it to estimate osmotic potentials at full turgor, at the turgor loss point, and any other point along the water volume continuum.  This is called a pressure-volume curve (PV Curve), and is shown in Figure 1 below.  Note that the X-axis is plotted as relative water content, rather than absolute water volume (just an easier way to draw it).

    When turgor pressure is present, the equation is:   1/Y_o  = -K*V  +  1/Y_p

    _{If we re-express V as relative water content (see previous lecture notes) then the PV Curve can be used to estimate turgor potential at any point, the bulk modulus of elasticity, and the apoplastic water content.}

  _{Osmotic Potential at full turgor (RWC = 100%) - get a regression for the straight portion of the PV Curve, and then
                extrapolate back to RWC = 100%.  This point is the inverse of this parameter.  Simply get the inverse, and this
                is osmotic potential at full turgor.
  Osmotic Potential at other RWC's - after a regression equation has been fitted to the straight portion of the PV
                Curve, which represents total water potential after turgor has gone to zero (i.e., osmotic potential), you can simply
                solve the equation for any value of RWC to get what the osmotic potential is at that water content.
  Turgor Potential at full turgor - this has to be equal to the osmotic potential at full turgor, but opposite in sign, since at
                full turgor, by definition, total water potential is zero!
  Turgor Potential at other RWC's - the deviation of the curved line from the extrapolated regression equation, which is
                the osmotic potential line, represents the contribution of turgor potential to total water potential.  Estimate turgor
                potential by subtracting osmotic water potential from total water potential.
  Osmotic Potential at turgor loss point - this is the osmotic potential when turgor becomes zero.  Estimated from the point
                where the curved line intersects the straight line representing osmotic potential.  This intersection point is where
                the turgor becomes zero.  See Figure 2.
  RWC at turgor loss point - this is the RWC where it is estimated that turgor has dropped to zero (where the curved and
                straight lines intersect).
  Apoplastic Water Content - this is estimated by extrapolating the regression equation to the X-axis.  Where it intersects
is an estimate of the amount of water in the apoplastic spaces.}

_{How Does One Actually Get the Points to Construct a PV Curve?
    Although we haven't yet discussed how to measure water potentials in plants, suffice it to say at this point that one simply (1) cuts off a plant segment, i.e., leaves, or twig with leaves, and hydrates the sample to full turgor.  Or, one takes the sample
        at a time when you are sure the plant is at full turgor.
(2) Then you measure the water potential (will be explained at a later date) and then let the sample dry on a bench, to allow
        it to lose some water volume.
(3) Then, remeasure the water potential.  Keep repeating steps 2 and 3 until you have about 20 measurements.  At some point,
        the turgor will go to zero, after which any further losses of water will be quite linear (you can plot them as you go).
        Once this has happened, you are essentially done.
(4) In order to calculate RWC's, you have to get the dry weights of the leaves.  Then apply formula from previous lecture.
(5) Finally, plot inverse water potentials versus RWC's to get the PV Curve.  Estimate water potential components as
        described above.}