Free energy and water potential.

Introduction

Free energy and water potential

Free energy is defined as the maximum energy available (excluding temperature change) to do work. The free energy per mole is the chemical potential (μ). The water potential is the chemical potential of a water solution in a system minus the chemical potential of pure water at atmospheric pressure and at the same temperature. Water potential is a measure of the tendency of water to move from high free energy to lower free energy. The water potential of a system is also the ability to do work compared with the ability of the same quantity of pure water at atmospheric pressure and at the same temperature. Despite it may seem more logical to express water potential in terms of energy, pressure units (e.g. KPa and MPa) which are considered to be simpler to measure. Due to convention the water potential of water is set equal to zero. Therefore the water potential of an aqueous solution will be a negative number.

The components of water potential are pressure potential (ψp) and osmotic potential (ψs). At constant temperatures the water potential results from the combined opposing actions of pressure and osmotic potential:
ψ = ψp + ψs
It is these two factors which work against each other to determine the direction of net water movement into or out of cells.

Plasmolysis

When a plant tissue is placed in a hypertonic solution, having lower water potential than that of the cells, the net flow of water is from the solution to the cells, down a water potential gradient, through partially permeable membranes. Consequently the protoplasts of the plant cells pull way from the cell wall. This process is called plasmolysis. The turgor pressure of the cells decreases, causing the cells to become flaccid. The damage is irreversible when a cell becomes plasmolysed.

Incipient plasmolysis occurs in tissue in which about half of the cells are just beginning to plasmolyse, representing an internal pressure of 0. Therefore at this stage the osmotic potential of the solution is equivalent to the osmotic potential of the cells within the tissue, after they have become isotonic with the solution.

Cell membranes (e.g. plasma membrane and tonoplast)
Membranes exist in a wide variety, but osmosis will occur regardless of how the membrane functions, as long as solute movement is restricted compared to water movement. The membrane could consist of a layer of material in which the solvent is more soluble than the solute, which would allow more solvent molecules than solute molecules to pass through. All biological membranes are selectively permeable. The permeability of cell membranes is very much dependant on the following factors:
Intrinsic properties of the cell membrane itself, which include the presence or absence of particular carrier and transport proteins and the composition of the lipid bilayer in which they are embedded.

In 1972, S.J. Singer and G.N. Nicholson proposed the fluid mosaic model. The model indicates that some protein molecules are imbedded in various places within a fluid phospholipid bilayer such that “the proteins float in a lipid sea.”

Each phospholipid molecule is composed of two fatty acid tails, which are hydrophobic and a phosphate group, which is hydrophilic. In all membranes, the hydrophilic phosphate groups point outwards, dissolving in water at either surface, and the hydrophobic fatty acids repelled by water are pointed inwards
Although water is a polar molecule, it is still able to pass through the lipid bilayer (through the hydrophobic fatty acid tails) of the plasma membrane. This is due to the relatively small size of water molecules. Many hypotheses suggest that water penetrates through the phospholipid bilayer through other ways. It has been stated that water molecules may move through temporary faults that are created by flexing and bending movements of fluid hydrocarbon chains of phospholipids. At any instant in time, these faults might open narrow spaces in one bilayer half or the other, which allows water molecules to slip from the surface into the bilayer halves, or from one bilayer half to the other. However, at no time would these movements open a continuous channel through the bilayer.

Transmembrane proteins that form hydrophilic channels have been also stated to accelerate the process of the passage of water. It has been recently discovered that aquaporins facilitate the water flux between cells.

As filters of the cell, aquaporins prevent the loss of e.g. sugar molecules or ions. Despite this high degree of selectivity, aquaporins have a very high efficiency of up to three billion water molecules per second and channel. A membrane patch of 10x10 cm2 with embedded aquaporins could filter 1 litre of water in about 7 seconds. The classical aquaporins transport solute-free water across cell membranes. They seem to be exclusive water channels and do not allow ions or other small molecules to permeate through membranes.

Potatoes

Potatoes are well-known for being starchy, and a potato tuber consists of almost 100% starch storage parenchyma. The potato “skin” is a parenchymous bark, having very few tiny vascular bundles.

The cells of parenchyma are large, thin-walled, and usually have a large central vacuole. In potato cells they are often partially separated from each other, containing numerous colourless membrane-bound, starch-storage organelles called amyloplasts. Insoluble starch (amylopectin) is deposited in concentric layers within the amyloplasts. Unlike the long, coiled molecules of soluble starch (amylose), the molecules of amylopectin are much shorter, with only 40-60 glucose subunits. Amylopectin molecules consist of highly branched chains that do not coil. Potato tuber starches contain about 78% amylopectin and 22 % amylose.
Magnified view (400X) of several parenchyma cells of a potato tuber (Solanum tuberosum) showing the thin, transparent cell walls and clusters of amyloplasts (starch grains).

Water, mineral and sugar content of 100g potato:
Water- 75.9g
Calcium- 13mg
Iron- 0.99mg
Magnesium- 23mg
Phosphorous- 55mg
Potassium- 437mg
Sodium- 7mg
Zinc- 0.33mg
Manganese- 0.187mg
Total mineral content- 522.517mg
Glucose- 0.4g
Fructose- 0.4g
Sucrose- 0.2g
Other sugars- 0.7g
Total sugar content- 1.7g

Swede

Swede cells are large, thin-walled and isodiametric. They are devoid of starch. The cells appear in cobweb-like groups. However the cells are smaller and thicker-walled than those of potato.

Water, mineral and sugar content of 100g swede:

Water- 89.7 g
Calcium- 30mg
Iron- 0.3mg
Magnesium- 11mg
Phosphorous- 27mg
Potassium- 191mg
Sodium- 67mg
Zinc- 0.27mg
Manganese- 0.134mg
Total mineral content- 326.7mg
Glucose- 3.3g
Fructose- 1.4g
Sucrose- 0.8g
Total sugar content- 5.6g

Prediction (for main experiment)

I would expect that the overall trend of ...

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Swede

Swede cells are large, thin-walled and isodiametric. They are devoid of starch. The cells appear in cobweb-like groups. However the cells are smaller and thicker-walled than those of potato.

Water, mineral and sugar content of 100g swede:

I would expect that the overall trend of results for both the potato and swede cylinders would be similar.
It can be predicted that:
The percentage change in mass would be very great for those cylinders placed in hypotonic sucrose solutions where the concentration is extremely low (e.g. 0M, 2M).
The percentage decrease in mass would be expected extremely great for the cylinders placed in very hypertonic solutions where the sucrose concentration is extremely high (e.g. 0.8M, 1M).
However within the middle range of sucrose concentrations, the percentage change in mass for each of the cylinders would less extreme.

The highly positive values for the percentage change in cylinder mass for extremely low sucrose concentrations would be due to the considerable gain in mass of the cylinders in relation to their initial masses. At 0M the water potential the ‘solution’ occupies higher free energy than the other solutions, as the maximum energy available for conversion to work (at constant temperature and pressure) is high. Therefore the chemical potential, which is the free energy per gram molecular weight is high. The water potential is the chemical potential of water in a system compared to the chemical potential of pure water at atmospheric pressure and at the same temperature (in this case room temperature). Therefore as the chemical potential of pure water is arbitrarily set at zero, the water potential of the 0M ‘solution’ is also equal to 0.
The value for water potential also can be stated to be caused by the combining actions of pressure and osmotic potential:

As the osmotic potential is defined as the amount that solute molecules lower the water potential of a solution its value for 0M ‘solution’ (containing no solutes) is 0. The pressure potential of the 0M solution is also equal to 0 at atmospheric pressure. Hence the water potential is equal to 0 at atmospheric pressure.
The average solute potential of the tuber cells (of the cylinders) would be considered to be a negative value, due to the presence of solutes within the cells (especially in their vacuoles). However the pressure potential of the tuber cells would be expected to be a positive due to the pressure exerted by the cell walls on the cells’ contents. Since the value for pressure potential of the cells would be less than that of the osmotic cells (but opposite in sign), the overall water potential would be negative. The chemical potential of the solution within each cell would also be considered to be negative, less than the value of 0 for pure water.

Since the water potential of the tuber cylinders would be lower than that of the solutions in which it is placed, osmosis would undeniably occur. Therefore the net movement of water molecules from a hypotonic region of higher water potential to a region of lower water potential down a steep water potential gradient through a semi permeable membrane would be able to occur.

Undoubtedly the plasma membrane and the tonoplast are partially permeable, whilst the cell wall is freely permeable. In the process of osmosis water therefore firstly diffuses through the cell wall, followed by the plasma membrane and then through the tonoplast. Polar water molecules are able to pass through the phospholipid bilayer (passing the hydrophobic fatty acid tails) of the plasma membrane and the tonoplast due to their small. Some water molecules are permeated by the exergonic facilitated diffusion of transport proteins called aquaporins.

Eventually the tuber cells would develop a higher pressure, which will increase until the water potential of each tuber cell is equal to 0. Therefore the water potential of the tuber cells would be equal to that of the solution (i.e. reaching the state of being isotonic.) The is the stage where the turgor pressure (solute potential) equals the osmotic potential The cells become turgid due to the build up of the large positive internal turgor pressure. The turgor pressure increasingly becomes exerted against the cell wall by the cells’ contents.

Consequently due to the process of osmosis occurring (where the ‘solution’ is 0M) there is a volume and mass increase of the tuber cylinders.

The highly negative values for the percentage change in cylinder mass for extremely high sucrose concentrations would be due to the significant loss in mass of the cylinders in relation to their initial masses. At 1M the sucrose solution occupies considerably less free energy than the other solutions, due to the maximum energy available for conversion to work (at constant temperature and pressure) being rather low. Therefore the chemical potential would be expected to be very low. Consequently the water potential value of the sucrose solution would be expected to be rather low (i.e. very negative). Theoretically the osmotic potential is due to the presence of solute particles and the addition of a solute causes the water potential of the solution to decrease becoming more negative. Therefore the osmotic potential of the 1M sucrose solution should be considerably negative. The pressure potential of the 1M solution is equal to 0 at atmospheric pressure. Hence the water potential is negative at atmospheric pressure.

Undeniably the overall water potential of the tuber cells would be expected to be negative. Therefore the chemical potential of the solution within each cell would also be considered to be negative. However it is assumed that the average water potential of the tuber cells would less negative than that of the 1M sucrose solution

Osmosis would occur due to the presence of a water potential gradient. The water potential of the tuber cylinders would be higher than that of the 1M solutions in which they are placed. Therefore the net movement of water molecules would be from hypotonic tuber cells (of higher water potential) to the hypertonic surroundings (of lower water potential), down the steep water potential gradient, through a semi permeable membrane. This movement of water out of the cells results in an overall decrease in volume and mass of the tuber cylinders. The flow of water also results in the protoplasts of the cells shrinking until no pressure is exerted at all on the cell wall. At this point as the pressure potential is equal to zero, the water potential is equal to the solute potential. The decrease in turgor pressure results in the flaccidity of the cells. Consequently the tuber cylinders lose their rigidity. The process of plasmolysis occurs as the protoplasts shrink to an extent that they begin to pull away from the cell wall. The cells therefore become plasmolysed. With the progression of osmosis the sap solution inside the protoplasts becomes more concentrated, developing a more negative osmotic potential. Hence the water potential of the cells decreases. Meanwhile the concentration of the sucrose solution decreases, increasing the osmotic potential and therefore also the water potential. These notable changes in water potential occur until the cells are isotonic with the sucrose solution. At this point there will be no net flow of water by osmosis as there would be no apparent water potential gradient.

At a concentration between 0M and 1M there would be expected to only slight or no net flow of water by osmosis between the tuber cells and the sucrose solution down a water potential gradient. If the sap in the tuber tissue is in osmotic equilibrium (i.e. isotonic) with the outside surrounding sucrose solution and no pressure or tension existed within the tissue, then the osmotic potential of the sap would be equal to the osmotic potential of the surrounding solution. The problem with such a measurement is to obtain zero pressure within the tissue without changing other osmotic properties any more than necessary. This is the method of measuring osmotic potential by incipient plasmolysis. Incipient plasmolysis is the stage when half of the cells of a tissue are just beginning to plasmolyse (i.e. when protoplasts are just beginning to pull away from the cell wall). This represents an internal pressure of zero. Providing that this assumption is true the osmotic potential of the solution producing incipient plasmolysis is equivalent to the osmotic potential of the cells within the tissue, after they have come to equilibrium with the solution. Since the pressure potential is equal to zero at this stage, the osmotic potential is equal to the water potential.
Providing that the range of concentrations is wide enough, I would expect the graph of percentage mass change against concentration of sucrose to look like this:

At higher concentrations the gradient of the graph would be expected to decrease (i.e. the curve would flatten). This is mainly due to the state of the tissue being unable to progress from full plasmolysis beyond a particular sucrose concentration .

I would expect to find that swede tissue has lower water potential than potato tuber tissue. Swede and potato tissue are mainly composed upon parenchyma cells. Potato tuber consists of almost 100% starch storage parenchyma. Parenchyma cells are large and thin walled with a large central vacuole.

Potato cells contain numerous colourless membrane-bound amyloplasts, which are starch storage organelles. These amyloplasts are found within the stroma of chloroplasts. Two types of starch are found within the plastids, amylose and amylopectin, both of which are composed of α glucose molecules connected by α-1-4 glycosidic bonds. Amylopectin is insoluble and consists of branched molecules. α-1-6 glycosidic bonds are found where the branches occur. Amylose, which is more soluble, is composed of long coiled molecules. As potato tuber starches contain about 78% amylopectin and 22% amylose, most of the starch is insoluble.

Swede cells are isodiametric, appearing in cobweb-like groups. In comparison to potato tuber they are considerably devoid of starch. However according to nutritional analyses swede has a very high total soluble sugar content of 5.6g per 100g. However potato has a very low sugar content in comparison to swede, of only 1.7g per 100g. Potato only contains only 30% of the sugar of swede. Therefore it would be expected that the concentration of swede cell sap would be higher than that of potato cell sap. Hence the solute potential a water potential of swede would be lower (i.e. more negative. The high starch content of the potato cells is likely to not affect the solute potential and water potential very much due to the insolubility of the amylopectin.
Undeniably the tuber water and mineral content are also factors among many others, which should be taken into consideration. The water content of 100g potato is 75.9g whilst that of swede is 89.7g. Therefore potato contains 85% of the water of swede. The total mineral content of 100g potato is 537mg, whilst that of swede is 327mg. Therefore swede contains 61% of the minerals of potato. Despite the a higher water content would be expected to increase the water potential (i.e. of swede) and a higher mineral content would be expected to decrease the water potential (i.e. of potato), the sugar content values would be expected to have considerably greater influence upon the water potential. This is mainly due to the exceptionally large difference between the sugar content values for swede and potato.

Preliminary experiment

Before carrying out the main experiment a preliminary experiment will be carried out to determine the water potential of carrot cells using sodium chloride solutions.

Method

Cut cylinders of carrot from the tap root using a cork borer.
Use a razor blade on a white tile to cut 6 cylinders which are 3cm in length.
Blot the cylinders on paper towel and weigh them on a balance to the nearest 0.01g. Record the masses of the cylinders and the concentrations of the solutions in which they will be immersed in a table.
Use a 10 ml graduated pipette and pipette filler to measure and transfer the necessary volumes of water and 1M sodium chloride solution into each of the six test tubes. The following concentrations (moles/Litre) of sodium chloride solution should be used: 1, 0.8, 0.6, 0.4, 0.2 and 0.0.
Place the cylinders in their test tubes and leave for 24 hours.
Remove the cylinders from their test tubes, blot them dry with paper towel and weigh them. Record their mass in the table.
Calculate the percentage change in mass using the following equation:

[Final mass – (Original mass / original mass)] x 100

Plot a graph (% change in mass against concentration of sodium chloride

solution).

Conclusions and evaluation for preliminary experiment

According to the results, only the carrot cylinder placed in 0M sodium chloride solution gained mass. In this case the net flow of water was from the hypotonic solution to the cylinder (i.e. from higher to lower water potential) down a water potential gradient through semi-permeable membranes. However the carrot cylinders immersed in solutions of 0.2M to 1M lost mass. The net flow of water was from the cylinders to the hypertonic sodium chloride solution again down a water potential gradient through partially permeable membranes.

According to the graph when the sodium chloride solution is approximately 0.11M it is isotonic with the carrot cells since at this point the mass of the cylinder remains constant. Using a graph showing the relationship between solute potential and sodium chloride concentration, it can be deduced that the mean water potential of the carrot cells is approximately –0.475 MPa.

However as indicated by the presence of two anomalous results, it is expected that the value determined for the water potential of carrot must be inaccurate. These inaccuracies of the results could be due to the following flaws involved in the experimental procedures:

Inconsistent blotting of the cylinders may have caused the final masses recorded to be higher or lower than expected.
Cylinders originating from different carrots.
Cylinders originating from different regions of the carrot – e.g. whilst some cylinders consisted of the inner core of the carrot, other cylinders consisted of the outer region (having different water potential).
Concentration intervals of 0.2M may have been slightly too large to produce a reliable graph.
No repetition of the experiment led to an unreliable graph being produced.

The following improvements could be made when carrying out the main experiment to determine the water potential of swede and potato:

Cut the cylinders to a longer length with smaller radius – this would increase the tendency of the cylinders to have a greater percentage change and the overall trend would be more significant.
Repeat each experiment at least twice.
Dry the cylinders consistently (e.g. by rolling them 5 times on paper towel for 5 seconds).
Aim to cut all cylinders from the same tuber in order to ensure that the cells are identical genetically (increasing the possibility of the all the cells have very similar water potentials).
Aim to cut cylinders from the same region of the tuber- using a tuber large in size should make this less difficult.
Ensure that the solutions are prepared accurately by improving pipette use – e.g. allow solution to drain naturally, touch the surface of the drained solution with the jet to allow correct retention of the last drop etc.
The concentration intervals should be reduced (e.g. by carrying out the experiment with solution concentrations of 0.1M, 0.2M, 0.3M, 0.4M … 1M. This would mean that overall 42 test tubes would have to be handled if the concentration intervals were 0.1M – this would considerably increase the amount of complications within the experimental procedures, increasing the likelihood of the method going wrong and numerous anomalous results being produced.

Independent variables

Concentration of sucrose solution
Type of tuber

Dependant variables

Percentage mass change of tuber cylinders
Water potential of tubers

The following measurements will be made in the main experiment:
Volume of 1M sucrose solution
Volume of distilled water
Length of cylinders
Initial mass of the cylinders
Final mass of the cylinders

Accuracy

Further accuracy will be ensured, by carrying out the following procedures:
The surface area of the cylinders will be kept consistent by using a cork borer to cut them. The cork borer will ensure that the cylinders are of the same diameter. The surface area would also be kept uniform by cutting the cylinders to the same length.

A balance which reads to 2 decimal places would be used to weigh the cylinders.

Safety

The following precautions will be taken in order to ensure optimum safety in carrying out the main experiment:

Wear safety goggles throughout the experiment
Avoid skin contact with the sucrose solution, as it can be an irritant (especially at higher concentrations)
Handle scalpel with great care
Clear up any spillages or breakages

Apparatus
24 test tubes
Cork borer
Scalpel
2 white tiles
3 test tube racks
Weighing balance
10 ml graduated pipette (with pipette filler)
Distilled water (100 cm3)
1M sucrose solution (100 cm3)
1 large potato
1 large swede

Method

1) A cork borer on a white tile will be used to cut numerous cylinders from peeled potato and swede.
2) A scalpel will be used on a white tile (as shown in the diagram) to cut 12 cylinders of exactly 5cm length from the potato cylinders. The same procedure will be repeated with the swede cylinders.

3) Each of the cylinders will be lightly rolled twice on paper towel for 2 seconds.
Then they will be weighed individually on a weighing balance to the nearest 0.01g. The masses of the cylinders, as well as the concentrations of the solution in which they will be placed will be recorded in a table. 2 potato cylinders and 2 swede cylinders will be placed in each of the concentrations of sucrose solution.

4) The 10 ml graduated pipette and pipette filler will be used to measure and transfer the necessary volumes of water and 1M sucrose solution into the test tubes. The following concentrations (moles/Litre) of sucrose solution will be used: 1, 0.8, 0.6, 0.4, 0.2 and 0.0. Each of these concentrations of sucrose solution will be contained in 4 test tubes (i.e. 2 test tubes which will each contain a potato cylinder and 2 test tubes which will each contain a swede cylinder.)

5) The table (on the next page) shows the amounts of sucrose solution and water to use for each concentration. Each of the prepared solution samples would have an overall volume of 10 cm3.

6) The cylinders will then be placed into their test tubes and left overnight (for approximately 24 hours).

7) The cylinders will be removed from their test tubes. Each cylinder will then be dried on paper towel by being lightly rolled 5 times for 5 seconds. Their final masses will be determined by weighing to the nearest 0.01g. These masses will then be recorded in the table.

8) The % change in mass for each cylinder will be calculated by using the following equation:
[Final mass – (Original mass / original mass)] x 100

Diagram

Results

Potato

1st experiment

2nd experiment

Averages

Swede

1st experiment

2nd experiment