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Give Us a Hand

Saturday 4th Apr 2015, 12.15pm

What links drugs, shells, springs and vines? It's something called 'chirality' and mathematics can help us understand it. But how? And why does it matter?

What is Chirality?

The word ‘chiral’ comes from the greek word, kheir, which means ‘hand’. An object is said to be chiral if it cannot be superimposed on its mirror image. For instance, your hands are chiral, if you place your right hand over your left hand, it doesn’t fit – the thumbs stick out in opposite directions, and when you turn your hands to point them in the same direction the palm of your hand still looks different to the back of your hand. Chiral objects are classed as either right-handed or left-handed. By contrast, achiral objects can be superimposed on their mirror image (think for instance a cube or a sphere).

The convention of referring to chiral structures as being right- and left-handed was established by the 19th century Scientists James B. Clerck Maxwell and used the common cork-screw as an example (and stunningly as the main definition) of what is right-handed. A helical structure is said to be right-handed if it has the same thread direction than a regular cork-screw (screws are right-handed because most people are right-handed and use their right hand to operate a screw-driver).

One of the most important applications of this idea is found in DNA. The typical form of the DNA is right-handed as the grooves wind up exactly like the thread of a screw. DNA is typically found as right-handed (but a form of DNA exists, referred to as Z-DNA, that is left-handed). Interestingly, the human brain is not very good at determining handedness and many illustrations show DNA with the wrong handedness! A nice example is the 100 Argentinian Pesos.  As you can see the helical thread goes up and to the left, that is the opposite of a common screw.

The easiest chiral objects to spot are those that are spiralled, so shells, horns, springs, spiral staircases, vines and so on. Some chemicals are chiral too, such as DNA, sucrose and carvone.

Many illustrations show DNA with the wrong handedness!

What can maths tell us about how shells form?

Mathematical models describe objects, shapes, and structures through the idealisation and abstraction of mathematics. For example, the growth of a seashell can be described using formulae that describe growth rate, angles of shell formation relative to previous formations, and so on. Assigning rules from the biology of cell division allows us to predict the overall shape of the seashells and the many beautiful patterns that are found on the seashells themselves. Ultimately, mathematics allows us to explain and understand how shape emerge and how the laws of physics and biology produce these structure as well as their function. Beyond the particular case of seashells, through mathematical modelling, we can form and test hypotheses in many different scientific fields, including physics, chemistry and beyond.

Why do different chiral forms of the same chemical have different effects on the human body?

The shape of a protein dictates what the function of that protein is and how it interacts with other molecules. For example, receptors are proteins that receive and respond to chemical signals. To do this they are shaped to recognise only certain chemicals, but typically will fail to recognise their mirror images. Amino acids, the building blocks of proteins, are themselves chiral. Additionally, if a chemical comes in different chiral forms, then only one of these chiral forms, known as enantiomers, will fit into the receptor. The receptor will only respond to the form that fits. The same goes for enzymes. Overall the situation is similar to a lock and a key – a lock will only be opened by a key with the correct shape to fit the lock and the mirror image of a key would fail to open the lock.

This distinction is really important when producing chemicals as medicines. Many medicines target receptors and enzymes. When you produce a medicine, both chiral forms are created, but only one form will have the desired effect in the body. The other, non-functional, form can either dilute the effect of the functional form, or even worse can have negative effects. An infamous example is thalidomide. The drug was given to pregnant women to help relieve morning sickness. They didn’t realise that whilst one chiral form of the drug would help with morning sickness, the other form led to children being born with malformed limbs. There has also been a case where a skier was banned from competition for having tested positive for a banned substance which turned out to have come from a chiral form of that substance found in a well-known menthol vapour rub that the athlete had used.

Nicer examples of how different chiral structures interact differently with the body are those that have an odour or taste. You can smell and taste things because you have receptors that pick up the smelly or tasty chemicals. The classical (and historically first) example of how different chiral forms interact via smell was carvone. One enantiomer smells of caraway seed whilst the other enantiomer smells of spearmint. Another example is limonene; right-handed limonene has an orange aroma whereas left-handed limonene smells like lemon.  

The best example where taste is concerned is the umami taste (our fifth taste), which is related to our ability to detect MSG (monosodium glutamate, extracted from seaweed). The mirror image of MSG has no taste.

Is there a mirror image Earth out there somewhere?

One surprising aspect of chirality is that all of the naturally occurring amino acids found in organisms on Earth are only left-handed. You might expect there to be a 50/50 split between right- and left-handed amino acids. There are a couple of different theories about why we exclusively use just the one chiral form. One theory is that both chiral forms of amino acids existed on early Earth but only one type survived, perhaps because radiation from space had more of a damaging effect on one chiral form over the other. This may be because the radiation itself may become ‘circularly polarised’, travelling through space in a screw-like spiral fashion, meaning the radiation itself could have been chiral. If amino acids on another planet were subjected to a different form of ‘chiral radiation’ then it’s entirely possible that the opposite chiral form of amino acids would be the basis of any life that may develop on that planet.

The other theory is about the fundamental forces of physics themselves. In particular the weak nuclear force, which plays a role in radioactive decay, may be asymmetric in some way. This would mean that the bias in amino acid chiral forms found in life may be down to a predisposition for it to exist in one form over another, and that this comes about because of effects at the most fundamental level of matter. Because the laws of physics are the same across our universe, if this were the case then it’s unlikely that there would be a ‘mirror-image’ Earth.

All of the naturally occurring amino acids found in organisms on Earth are only left-handed. You might expect there to be a 50/50 split between right- and left-handed amino acids.


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