# Avoidance of Crystallization in Biological Systems

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## Aims

On completion of this TLP you should:

• Understand how nucleation and crystallization occur.
• Be aware of the reasons why crystallization in the cells of living systems is usually fatal.
• Appreciate the importance of sugars as solutes in the cellular liquid.
• Understand the ways in which some living systems avoid crystal formation.

## Before you start

Before beginning this TLP, you should:

## Introduction

Many plants and animals live in extreme climate zones, such as the polar regions or subtropical deserts. One of the major problems associated with living in such regions is that most biological systems are largely composed of water. Water is the universal solvent for biological processes, and most living organisms contain a large amount — humans, for example, are 50-75% water.

In the polar regions temperatures can fall to below –20°C. In deserts, the absence of water can lead to the dehydration of plants and animals. The organisms that live in these regions have become adapted to these conditions.

Plants that live in arctic regions must contend with the formation of ice crystals in their cells. This is fatal to living tissue for a variety of reasons, which are discussed in the next section. Plants and animals living in the desert have a similar problem; dehydration can cause salts and sugars to precipitate out of solution inside their cells.

In this TLP we will consider how biological adaptations to cells allow them to survive such conditions by preventing crystallization of ice or salts within cells. We will look at the basic theory behind nucleation and crystallization, and the details of the water-sucrose system that illustrate key features of the cellular liquid (the cytosol). We will then examine the specific ways in which some plants and animals avoid crystallization, through glass formation, extracellular crystallization (forming the crystals outside the cell) and the use of antifreeze proteins.

## Nucleation and crystallization

Living cells consist essentially of an aqueous solution contained within a cell membrane. Thus the soft tissues of many living systems can be described as structured water. The human body for instance, is 50-75 % water. This high proportion of water means that crystallization in the body occurs in two main ways:

• by dehydration, when minerals crystallize from a saturated solution.
• by freezing, when ice crystals are formed.

The formation of crystals in living cells is usually fatal. This is either due to a change in the ionic ratios in the cytosol or due to the bursting of the cell.

During dehydration, water is removed from the cell, leading to a supersaturated solution. Mineral or sugar crystals can then form, changing the ionic ratios in the cytosol.

Ice crystals can form in the cells of both plants and ectothermic (cold-blooded) animals. Since ice is essentially pure H2O, ice formation can increase the concentration of minerals in the remaining cytosol to a toxic level. The increased mineral concentration in the cytosol will cause water to be drawn in from the surrounding cells by osmosis, which can cause the cell to swell and burst.

In dehydration, the crystals that are formed can puncture the cell membrane causing the cells to burst, leading to death.

Both dehydration and ice formation involve the nucleation and growth of a new, solid phase from an aqueous solution. In the case of ice formation, the situation is effectively that of a solid crystallizing from a melt. In the case of the formation of mineral crystals, the case is that of precipitation from solution. Nucleation is the formation of a small cluster (or nucleus) of the new phase, and these nuclei arise spontaneously. Nuclei that are smaller than a certain size will simply disappear, but if a nucleus is greater than a certain size, it will spontaneously grow and will eventually form a grain. This critical size varies with temperature and the reasons for this are outlined below, using the example of ice forming in water.

Nucleation can occur either homogeneously (nucleation in a uniform phase in which there are no inhomogeneities on which nucleation can preferentially occur) or heterogeneously (in which the new phase nucleates on an inhomogeneity).

For the nucleation of ice in pure water, the transformation is a structural change only (there is no change in the chemical composition), and the change in free energy per unit volume on transformation is ΔGv. The interface between the ice and water phase has a free energy γ per unit area. Due to the random motion of the water molecules, nuclei of ice will continually form. Assuming that these nuclei are spherical with radius r, the work done in forming the nucleus is:

Work for nucleation = change in free energy of bulk phases + interface energy

or

$$W = {4 \over 3}\pi {r^3}\Delta {G_v} + 4\pi {r^2}\gamma$$

Since the interface between the water and liquid can be considered to be a defect, it contributes an excess energy to the system, and γ is positive. γ is approximately constant over the relevant range of temperatures. ΔGv varies with temperature (as described below), but if the transformation occurs spontaneously, (i.e. if the temperature is below the melting temperature of ice), then ΔGv is negative, and a graph of <W against r has the form:

So, if a nucleus is formed, which has r > r*, it will decrease its energy by increasing r, i.e. by growing. Any nuclei with r < r* will decrease in energy by decreasing r and by disappearing. The critical radius, r* occurs when dW/dr = 0, giving:

$$r* = - {{2\sigma } \over {\Delta {G_v}}}$$

and

$$W* = {{16\pi } \over 3}{{{\sigma ^3}} \over {\Delta G_v^2}}$$

We define ΔG to be the free energy difference between the solid and liquid phases, ΔG = ΔGice - ΔGwater. Similarly we define the differences in enthalpy ΔH and entropy ΔS. Since ΔG = ΔH - TΔS and at Tm, the melting point of ice, ΔG  = 0, then ΔH = TmΔS. If ΔH and ΔS are independent of temperature, then, at temperature T, ΔG = ΔS(Tm - T= ΔS ΔT, where ΔT is the supercooling (also known as undercooling). The critical radius and the work for nucleation therefore decrease with decreasing temperature below Tm, and the rate of nucleation would increase with temperature below Tm. This effect is limited by the decrease in atomic mobility at lower temperatures, and the actual variation of nucleation frequency with temperature is shown below:

However, this analysis assumes homogeneous nucleation, which occurs only rarely. Usually there are heterogeneities, such as mould walls or cell membranes, in the melt onto which nucleation preferentially occurs. These heterogeneities are points with high excess energy and so the energy required to form the interface between the existing phase and the new phase is not so significant. Removing heterogeneities is one effective way of decreasing the temperature at which ice forms, i.e. increasing the difficulty of freezing.

## The water-sucrose system

Key features of the cytosol of cells are represented in the binary water-sucrose system. In practice, of course, cytosol compositions are much more complex. The equilibrium phase diagram for this system is shown below:

Due to kinetic factors, the equilibrium states shown in this phase diagram are rarely reached. Nucleation of sugar crystals is difficult, since the complexity of the sucrose molecule and the viscosity of the liquid make getting a critical mass of molecules with the right orientation uncommon. At high concentrations of sucrose the system becomes sufficiently viscous to be considered (at lower temperatures) as a glass.

The practical phase diagram is:

## Avoidance of crystallization by glass formation

As previously discussed, a common biological problem is dehydration.

Crystal formation upon dehydration can be avoided by forming a glass. Glasses are amorphous, and form by a continuous process (no interface or solidification front is involved). Their structure is comparable to that of a liquid (some short-range order is observed, but no long-range order), but their properties are those of a solid.

In response to dehydration, some living systems alter the composition of the cytosol in order to favour glass formation, for example by hydrolysis of starch to sugar. As can be seen on the sucrose-water phase diagram, the higher the sugar content, the higher the temperature at which a glass can be formed. Using this mechanism, complete dehydration can be survived.

### Examples of living systems that exploit the formation of glass in order to preserve life

• Resurrection Plant
Various different species fall in the category of "resurrection plant", including the Rose of Jericho and Selaginella lepidophylla. When dry, they appear brown and lifeless, but after rain they become moist and green. This can be seen in the image below, which shows the Selaginella lepidophylla plant in both the moist and dry states.

Image reproduced with permission of Brad Fiero, Pima Community College, Tucson, Arizona

• Flatworms
Under the stress of dehydration, some species of simple flatworm are able to convert starch into sugars, which promotes the formation of glass.

• Seeds
Sucrose is the most abundant sugar within mature seeds, and its ability to form a glass in dry tissues greatly slows the chemical reactions within the seed that could lead to its degradation and hence contributes to the longevity of seeds. When seeds are planted after storage in the dry glassy state, they take up moisture from the ground and become rehydrated, and are then able to germinate.

Glass formation is similarly exploited in dried foods such as pasta, drug storage for drugs such as insulin for inhalation, and organ preservation. In these cases, the glassy state is used to inhibit degradation.

## Avoidance of crystallization by freeze resistance

Many organisms exist in habitats where the temperatures fall below the freezing point of water. As previously explained, the formation of ice crystals in cells is lethal and many species have therefore evolved to prevent ice crystals forming in cells.

There are two different types of resistance to freezing temperatures: freeze avoidance and freeze toleration.

### Freeze avoidance

During freezing of water ice crystals nucleate and grow. For pure water, homogenous nucleation occurs at ~ 40 K beneath the thermodynamic freezing point. This is a substantial supercooling, but in most cases, freezing occurs above –40°C due to heterogeneous nucleation.

One way to avoid freezing is to discourage heterogeneous nucleation. Some frost-hardened woods achieve this by dispersing the water in cells, and by the lack of nucleation on the cell walls. As a result, the water in their cells does freeze at –40°C.

Fish, insects and some plants that live in arctic regions have evolved to produce antifreeze proteins, which inhibit the growth of ice crystals by adsorption to the ice surface. Adsorption of these antifreeze proteins prevents crystal growth on the primary growth directions, forcing growth to occur parallel to the secondary axes. This inhibits the formation of stable ice crystals and lowers the kinetic freezing temperature.

### Freeze toleration

An alternative to freeze avoidance is to promote the freezing of extracellular liquid. This protects the cells in two ways:

• By the release of latent heat into the cells, which prevents their temperature from decreasing.
• By drawing water out of the cells and decreasing the temperature at which ice forms. This depression of the liquidus line at higher sucrose concentrations can be seen in the sucrose-water phase diagram.
• Ultimately dehydration of the cells leads to glass formation.

Many biological systems promote heterogeneous nucleation by the presence of a variety of Ice Nucleating Agents (INAs). These INAs may either be adaptive or incidental. Adaptive INAs, which are discussed below, are present in order to promote heterogeneous nucleation, whereas incidental INAs (for example, features such as cell walls) promote heterogeneous nucleation only as a normally unwanted side effect.

Some organisms have evolved to produce adaptive INAs, which nucleate ice crystals between the cells. These INAs can reduce the nucleation supercooling to as little as 1°C. Examples of these are the giant rosette plant (lobelia telekii) which grows on Mount Kenya, and the northern wood frog (rana sylvatica) which lives in Canadian forests. The northern wood frog's body contains 35-45% ice during the winter months.

Adaptive INAs are generally large proteins with molecular weights of up to 30,000 atomic mass units. The amino acids within the proteins are ordered, forming a template for ice. Thus a thin layer of ice can always form on the surface of an INA. However, this will not lead to spontaneous ice growth unless the INA is of a certain critical size. If the INA is assumed to have a circular surface with radius R, then free ice growth will occur only when R is greater than or equal to r*. The critical radius, r*, is given by the equation:

$r* = - {{2\gamma } \over {\Delta {S_v}\Delta T}}$

where γ is the interfacial energy per unit area, and ΔSvΔT is the free energy of solidification per unit volume. Nucleation will occur when the supercooling ΔT satisfies the condition:

$\Delta T \ge - {{2\gamma } \over {\Delta {S_v}R}}$

A larger INA (greater R) therefore gives a smaller required supercooling and a higher nucleation temperature.

## Summary

In this TLP, you have learnt how the formation of crystals can occur inside cells by cooling or dehydration, and why this is usually fatal to them. The basic theory behind nucleation and crystallization has been introduced, and the water-sucrose system has been described as an approximation to the composition of cell cytosol.

You should appreciate that some plants and animals have adapted in order to avoid crystallization. The three main ways of achieving this are:

• through the formation of a glass.
• through extracellular crystallization (formation of the crystals outside the cell membrane).
• through the use of antifreeze proteins.

## Questions

### Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

1. Crystallization is usually fatal to cells because:

 Yes No a Crystals can puncture cell walls Yes No b The formation of crystals changes the ionic ratios in the cytosol Yes No c Crystallization speeds up the cell reactions Yes No d Ice formation causes water to be drawn into the cell by osmosis causing the cell to swell and burst Yes No e Nucleation of the crystals requires large amounts of energy

2. Ice formation in cells can be limited by:

 Yes No a The presence of antifreeze proteins Yes No b The dispersion of water in the cellular structure, which limits heterogeneous nucleation Yes No c The formation of starch from sugar Yes No d The introduction of Ice Nucleating Agents (INAs) into the cells Yes No e The freezing of extracellular water

3. Crystallization of minerals in the cells can be limited by:

 Yes No a The presence of anti-freeze proteins Yes No b The hydrolysis of starch to sugar Yes No c The preferential formation of a glass Yes No d The increased activity of the Golgi Apparatus

4. In some alpine plants, extracellular ice formation occurs at around –2°C. What is the critical radius for ice nucleation at this temperature?

In these plants, the extracellular ice forms on ice nucleating agents. If an ice nucleating agent is a circular disc and is a perfect template for ice, what size must it be for nucleation to occur at –2°C?

(For the ice-water interface, the interfacial energy γ = 0.028 J m-2; the latent heat of freezing of ice is ΔHv = -3.34 x 108 J m-3.)

## Going further

### Books

• Fletcher, Chemical Physics of Ice, CUP,1970.
• Franks F, Biophysics and Biochemistry at Low Temperatures, CUP, 1985.
• Greenwood G W, Greer A L, Herlach D M, & Kelton K F, Nucleation Control, Phil. Trans. Royal Society (A 361, no 1804, 15 Mar 2003), pp. 403-633.

### Websites

• Cryobiology - A Short Course
An online course in cryobiology from the University of Calgary. Particularly useful are: chapter 1, which describes biological cells; chapter 6, on freezing as a crystallisation process; and chapter 12, on animal strategies for surviving in cold climates.
• Ice Formation in Higher-Plant Cells
A page describing freeze avoidance in plants on the Physiology Online website.
• Resurrection Plant
This page on the Union County College website describes the Selaginella lepidophylla resurrection plant.
• Nucleation in Metals and Alloys
This section from the online manual for the MATTER project's Materials Science on CD-ROM, gives more in-depth information about nucleation. The page refers to the nucleation of metals, but the same applies for nucleation of ice or minerals in cells.
• Rana sylvatica (wood frog)
This page on the Animal Diversity website of the University of Michigan Museum of Zoology describes the freezing capabilities of the Northern Wood Frog.

## Osmosis

Osmosis involves the movement of water molecules down a concentration gradient from an area of high concentration to an area of low concentration, through a semi-permeable membrane.

Cell membranes are semi-permeable, so allow small molecules such as water, oxygen, carbon dioxide and glucose to pass through, but prevent larger molecules such as sucrose and starch from passing through.

When a cell is placed into a liquid containing water, one of three possible situations will arise:

• If the cell has a lower water concentration than its environment, water will diffuse into the cell by osmosis, and the cell will swell. Although water molecules can diffuse both ways across the cell membrane, more water will enter the cell than leave it. Animal cells do not have cell walls, so they may eventually burst. In contrast, plant cells are prevented from bursting by the presence of their cell walls: the cells will become turgid (swollen and hard), and the pressure inside the cells rises until eventually no more water can enter them.
• If the cell has a higher concentration of water than its environment, more water will diffuse out of the cell than into it, and the cell will shrivel.
• If the cell has exactly the same water concentration as its environment, there will be no net movement of water across the cell membrane and the cell will stay the same size.

Academic consultant: Lindsay Greer (University of Cambridge)
Content development: Jessica Gwynne, Sarah Parker and Stuart Fraser
Photography and video: Brian Barber and Carol Best
Web development: Dave Hudson

This TLP was prepared when DoITPoMS was funded by the Higher Education Funding Council for England (HEFCE) and the Department for Employment and Learning (DEL) under the Fund for the Development of Teaching and Learning (FDTL).

Additional support for the development of this TLP came from the UK Centre for Materials Education.