Unit 2b. Proteins, Membranes, and Entropy

BIOCHEMISTRY FOR CITIZENS

How can complex structure arise spontaneously?

Suggested reading: Search the Web for the poem "Identity" by A.R. Ammons. (Today I found it here, but apparently without permission, so it might not stay there long.) Students in One Culture can request the poem by email.

Think about the poem as you read this unit.

Structural unit of spider silk. Helices are colored by their order in the continuous chain, first helix blue, last one red. Some spider silks contain many such units, linked by disordered regions, like beads on a string.

Cells make proteins by linking amino acids together in long chains. As the linking occurs, or afterwards, the protein spontaneously folds into its native state, which is held together by many weak non-covalent bonds. Although the protein appears spontaneously to become more ordered, it sets free many bound water molecules as it closes up, and the net result is an increase in the net disorder of the complete system: the protein and its associated water. This process of protein folding in water thus obeys the second law of thermodynamics, which states that all spontaneous chemical and physical transformations, from the burning of the sun to the folding of proteins in water, cause the entropy (disorder) of the universe to increase. If a change in a system causes the total entropy to increase, then that change can occur spontaneously—that is, without an input of energy.

What is entropy? It is a measure of the disorder of a physical system, such as a pile of blocks, or a protein and the water in which it is dissolved. Analyzing the entropy of a system helps scientists to know how systems can change, and whether a natural process is driven by energy input, or occurs spontaneously. A simple example of spontaneity is a ball rolling down a hill. No one has to give it more than a little kick, and down it goes. The ball would never spontaneously roll up the hill. Someone would have to carry it, expending energy to drive a non-spontaneous process.

For an everyday example of entropy, consider a child’s playroom, with parents who like to have a place for everything and everything in its place at the end of the day. First thing in the morning, the entropy of the room is very low, with orderly placement of all toys and games. As the day progresses and children toys and leave them around, the entropy of the room increases—the room becomes more and more disordered. At the end of the day, the parents spend energy to again lower the system’s entropy.

Another example is the difference between a forest and a tree farm. The forest contains many types of trees in random locations. The farm contains many trees of the same species, planted in even rows. To describe the forest in detail, you must name all trees and specify locations. To describe the farm, you need only name the tree type, and give the dimensions of rows and tree spacing. As a result, far less information is needed to fully describe the farm. Entropy is related to information content; the more information needed to describe a system, the higher its entropy.

The entropy of one part of the universe, such as a spontaneously folding protein, might decrease, but overall, when we take the increase in the entropy of the surrounding water into account, protein folding in water obeys the second law. This shows that the laws of thermodynamics allow for order to appear spontaneously (properly folded protein), as long as there is an entropy price paid by some part of the system in which order appears (disordered water). The spontaneous formation of cell membranes from disordered fats is another example (more later in this unit).

In the mid-twentieth century, scientists realized that systems through which energy can flow will spontaneously become ordered in some way. The flow of nutrients into, and wastes out of, the placenta drives the orderly development of the fetus in mammals. Entropy can be viewed as a driving force that produces local order at the expense of disorder in the surroundings.

Order in a heated liquid

Here is a popular teaching example of order arising in an energy-dissipating system. Imagine a shallow pan of water heated evenly from below. This requires a source of energy, like a stove burner, which heats either by combustion of natural gas or by electrical heating of a metal coil. At first, heating simply makes molecules of water move faster. Heat moves through the water, and escapes at the surface, either by the escape of fast-moving water molecules themselves as water vapor, or by their collisions with air molecules at the surface. This is an energy-dissipating system, and at first, the heat is simply increasing the disorder of water and air molecules.

But the water that loses its energy to air molecules at the surface, or that has not been in contact with the bottom surface, becomes cooler than the water below it, and cool water is more dense than warm water. So cooler water at the surface begins to sink back into the warmer water nearer the heater. In order for cooler water to sink, the warmer water below must rise, and the two must “move aside” to allow each other to pass. The result is called convection, and it frequently becomes very orderly. Warm water in a small, cylindrical area might be moving upward, while cold water is moving downward in the hollow cylindrical area surrounding the warm, rising water. And this two-layered cylinder, called a convection cell, is surrounded by others just like it.

Commonly, each convection cell is surrounded by six others, in an array like a honeycomb. Imagine a honey comb made of nothing but water, in which the cylindrical cells contain rising, warm water, and the bees-waxy walls consist of descending, cool water.

Convection cells in a heated liquid. Liquid is risingn the center of
each cell, and sinking at each periphery (or vice versa).
Image from http://www.meta-synthesis.com/webbook/24_complexity/complexity3.html

We have here another example, as Jacob Bronowski put it. of

The force that makes the winter grow 
Its feathered hexagons of snow, 
And drives the bee to match at home, 
Their calculated honeycomb ... (1)

Looking at the image of this process, you have to admit that the movement of the water is very orderly. This is one kind of order that can arise in dissipative systems: orderly motion. It turns out that all dissipative systems (systems, such as you and me, through which energy flows) spontaneously produce order of some kind. And conversely, systems that become more ordered spontaneously dissipate energy. It can be orderly motion, like convection, or orderly structure, like snowflakes or complicated molecules.

Proteins form themselves!

Proteins, once synthesized, fold spontaneously into their functional shape. Intermediate stages are illustrative only, and do not depict actually detected stages of folding, which are thought to be more compact.

[ There are several simulations of protein folding on the web. Soon I will add links to them here. ]

Against the absolutely relentless movement of the universe towards greater overall disorder, life produces life, and order is maintained. Systems that dissipate energy, such as a liquid heated in a shallow pan, or life itself, spontaneously produce order of some kind.

The DNA recipe for a protein specifies only the sequence of building blocks, but after the protein chain is made, it is competent to fold properly into its functional form, as shown above for cytochrome b5. Perusing through simulated stages of folding (left to right, top to bottom), you can see the number of ordered sections (red and yellow) increasing, until the molecule reaches its final compact form. Folding is driven entirely by interactions among the building blocks, and with the surrounding water.

Living organisms dissipate energy as they become highly ordered. The self-ordering and self-organizing aspects of life begin at the molecular level, with molecules that self-assemble.

Membranes: cell and organelle boundaries

Model showing the structure of a biological membrane, with a few layers of water molecules shown on top.
In a cell, the membrane is bounded on both sides by water.

Membranes are barriers that enclose cells and, in eucaryotic cells, enclose organelles within the cell. (Eucaryotic means “good nucleus”, and the nucleus is one such organelle.) A typical membrane is two molecules thick (called a bilayer), and each molecule consists of a water-loving (polar) head and a water-avoiding (non-polar) tail. Such molecules are called amphipathic, meaning, roughly, “experiencing both”. In the figure above, several layers of water (B&S) sit atop one water-loving face of such a bilayer, formed from molecules of the lipid lecithin (Unit 1). Amphipathic molecules spontaneously assemble into bilayers in which the polar heads face outward to water on both sides (colored groups), and the non-polar tails (white) form a water-free interior. This arrangement produces a barrier to water and water-soluble substances. Nuclei, mitochondria, and some types of viruses are bounded by bilayer membranes. Many types of proteins are embedded in cell and organelle membranes, including proteins that act as selective channels, gates, or pumps. These proteins allow certain substances to pass in or out. This passage can be passive (water moves at random through water channels), or active (nerve cells actively move [pump] sodium ions out and potassium ions in). Membrane proteins also transmit signals across membranes, binding to signal molecules such as hormones at the outside of a cell, then changing shape to release signal molecules within the cell.

Membranes are self-organizing. The same entropic forces that drive protein folding cause certain lipids to become ordered into low-entropy bilayers, with liberated high-entropy water molecules again paying the entropic price.

Rising from dissipation

A photosynthetic reaction center (PRC), which lives in the membranes of chloroplasts, the power plants of plant cells. This PRC is composed of three proteins (colored ribbons), and numerous pigments (B&S), such as cholorophyll, which absorb light and transform it into chemical energy.

Membranes composed of fats surround each cell and divide it into specialized components, which include distinct compartments (Unit 1). One compartment is the nucleus, where DNA harbors the recipes for all other cell parts. Following those recipes, cells produce proteins, the most versatile family of molecules. The role of photosynthetic reaction centers (PRCs) is just one of many roles played by proteins, including importing nutrients and molecular building blocks; exporting wastes; breaking down nutrients (catabolism) in a combustion-like manner, while conserving the heat of combustion in the form of chemical energy; using energy from catabolism or from PRCs to build complex molecules from imported building blocks (biosynthesis, which, combined with catabolism is called metabolism); responding to molecular signals from outside the cell; and defending the cell from harmful invaders like toxins or viruses.

Central to all these functions is obtaining useful energy from catabolism, and using that energy to power biosynthesis and other aspects of the cell’s work. In every step of such processes, some energy is lost to the surroundings, and this loss increases the disorder in the environment of the highly ordered cell.

Order from disorder

Any system through which energy flows can become more organized and complex, even as the universe as a whole becomes more disordered. Even a pan of water, sitting on a warm unit of the stove, will respond to the flow of heat—into it from below and out of it from its surface—by organizing itself into cylindrical convection cells that form hexagonal groups, the shape of the snowflake and the honeycomb. You and I are much more complex examples of self-ordering systems supported by the dissipation of energy—certainly a truth, but one that captures little of the richness of life at the molecular level, nor of course, of our personal experience.

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(1) Bronowski, Science and Human Values, New York: Harper and Row, 1956.