How do we show molecules and how they move?

Publiceret Juli 2014

Biological macromolecules are extremely complex and have adapted over billions of years of evolution to ensure incredibly sophisticated functions of structure, catalysis, storage, transport and signalling in cell biology. Their biochemical and biophysical properties at the atomic and molecular level define life and this is what we would like to understand and convey through so-called "structural biology". However, this visualization challenges our minds since our consciousness and logical frameworks are trained and limited by the processing of sensual inputs of the macroscopic world.

We smell, taste, feel, hear and see things and put them in frameworks of physical objects, symbols and emotions. The way we see things for example is defined by the optical properties of (then) visible light with a wavelength in the 400-700 nm range, i.e. orders of magnitude larger than atoms and chemical bonds, so how can we gain detailed insight and understand the nature of molecules? Many methods exist. Electron microscopy and nuclear magnetic resonance spectroscopy, for example, but not least X-ray crystallography.

Crystallography exploits the optical properties of X-rays with a wavelength at scale with atoms and chemical bonds (about 0.1 nm = 1 Å). It is the most important method to obtain detailed information of molecular structure. X-rays are electromagnetic waves and are scattered by the electrons of atoms. The sample is a crystal, i.e. a material where billions of molecules are arranged in a regular pattern and where every single molecule is related to all others through explicit, mathematical operations. The scattering of X-rays from a single molecule is therefore amplified in specific directions from the entire crystal (full-filling so-called Bragg angles) yielding a characteristic crystal diffraction pattern of reflections. The individual intensities of these can be measured with X-ray sensitive detectors and through Fourier operations we can derive the electronic structure that gave rise to the measured diffraction.

The electronic structure is a three-­dimensional contour map, similar to a topographical map, and represents the average distribution of electrons throughout the molecule of the crystal. High contours mean many electrons in that region and pinpoint the position of atoms in the molecule. At high resolution such maps show spherical structures for individual atoms and also detailed features of chemical bonds that provide very accurate information on the chemical structure. The attainable resolution is ultimately defined by the order through which the molecules actually obey the mathematical relations in the crystal and is directly observed by the maximal diffraction angle of ­reflections.

From the electron density maps we can build an atomic models that fits the map (Figure 1), and using this model we can calculate theoretical diffraction properties of the crystal, so a minimization of the discrepancies between experimental and calculated diffraction patterns leads to an optimized structure. As for all scientific data, there are both strengths and limitations to such refined structures. Very detailed and accurate information on the "typical" structure is obtained that no other methods can yield, but then as an average structure of billions of molecules arranged in a crystal. Therefore a crystal structure gives only limited information on the dynamics of the molecule as they are revealed from the more smeared features in the electron density map. A crystal structure more appropriately should be considered a sampling of minimum in a dynamical equilibrium of many, slightly different structures.

Figure 1. Molecular representations (larger version)

Left: the blue mesh is a section of an electron density map derived from a crystallographic experiment on a protein molecule. It is shown at a contour level that exceeds the noise level and reveals the positions of atoms. An atomic model represents the map and is show by lines connecting bonded atomic positions. Isolated spheres of density are water molecules associated with the surface of the protein and represented by red dots.

Right: A combined atomic and schematic representation of insulin, a very small protein molecule that acts as a hormone to regulate sugar levels in the body. Insulin is made up of two chains of amino acids that are shown in orange and light blue. Individual atoms are indicated by sticks that connect bonded atoms (carbon in same orange and light blue, oxygen in red, nitrogen in blue, and sulphur in yellow). A bound Zn2+ ion is shown as a grey sphere representing the size of the ion (van der Waals radius). The atomic model parameterizes the properties of the molecular structure and electron density map and can be the starting point of molecular dynamics simulations.

Crystallographers like to consider molecular function as movements through rational, one-way transitions from structure 1 to structure 2, which then explain for example enzymatic function or receptor signalling. This is often a very fulfilling model with strong predictive power, but those who study the function of single molecules or try to model their dynamics through computer simulations will see it quite differently. Single molecules show rather stochastic dynamics with molecules jumping between different states, and often even quite different structures.

So, the molecules we describe are very different whether they represent single molecules with stochastic behaviour or rather ensemble representations with predictable, thermodynamical behaviour. This challenges the way we visualize molecular function and movements - wild and stochastic for a single molecule, and smoothly operating, almost as if engineered, for the ensemble representation. However it is important to note that if we then average many single molecule observations we should see correspondence to the behaviour and structure of ensembles.

Is this relevant to consider? Indeed yes. When a cell for example responds to a stimulus, only very few receptors may in fact be involved - not billions or millions, but only hundreds or even less than 10, so a physiological response initially may have been laid in the hands of single molecule behaviour. This imposes a very strong dependence on quality control in the hands of such "rare molecules with delicate functions" - another interesting example of how evolutionary mechanisms tune biological macromolecules.

However, an atomic model of a molecule as derived by X-ray crystallography represents at the same time a very decisive change - from an unbiased, physical represenation in the form of an electron density map to a discrete model with symbolic representations for atoms and bonds that makes an optimal fit to that map. We tend to prefer the latter where we represent a large and rather incomprehensible shape, which even possesses strange quantum mechanical behaviour, by a rational, atomic structure of familiar and colorful building blocks that we can convey and print in a book.

We can also make physical models like that to help us understand the molecule by holding and turning the model in our hands. Interestingly, however, in ordinary microscopy and electron microscopy of cells and cellular structures the actual "maps" are accepted as the representation used, thus marking a transition from microscopic objects like atoms and molecules that we cannot see to the actual macroscopic object that we can see at least with magnification and therefore accept in the form they take.

Are there then no way we can actually perceive a molecule directly. In fact there would be - the way we smell and taste molecules is all about their atomic structures, and sound marks vibration and motions, so if we were to associate molecular descriptions with smell, taste and sound rather than visual cues alone we could imagine a completely different interface technology and vocabulary on how we describe, explain and comprehend molecules and their properties and function.

Getting that into the toolbox of molecular representations and information technology is of course far from trivial, but it would attempt to communicate to us in the way we actually operate in nature - the hunter in the forest combines inputs of all senses to analyze the situation. The challenge therefore would be to transform complex information on molecules into a combination of sensory inputs and provide this to the investigator through direct (images and sound) or electrical stimuli (smell and taste).