INSTRUMENTOS FINANCIEROS

The description, successful computation and eventually prediction of the transport properties of ion channels is the ultimate goal of our research. In this Chapter, we have discussed transport properties (conduction, selectivity, AMFE etc), and described the structure of one of the most frequently-studied channels, KcsA. We have also outlined some applications of the theory to medicine and technol- ogy. In the next Chapter, we provide quantitative methods estimating the above- mentioned properties, discuss their strengths and weaknesses and formulate the aim of the work done in the following chapters.

2. Research methods to study ion

channels

Theories of liquids do not have a small parameter.

L. D. Landau

Recent research has provided a rich arsenal of methods to investigate the trans- port properties of ion channels [17, 20, 91]. These methods can be divided into experimental and theoretical approaches. It is the interplay between the two that is believed to drive the discoveries in the field.

In this Chapter we discuss most the most influential experimental and theoret- ical methods. In particular we shall analyse the strengths and weaknesses of each theoretical method. This will serve as justification for the goals of the thesis.

2.1

Experimental techniques

There are two main experimental approaches to understanding ion channels. The first is probing the structure through crystallography from which transport prop- erties can be inferred or learned through simulation/theory. The second is direct measurements of ionic current or water flow which are traditionally effected by the patch clamp technique.

2.1.1

Structure studies: X-ray crystallography and cryo-

EM

In order to gain information about the spatial and chemical composition of the biological structure, X-ray crystallography was historically the first method [92]. It involves preparing a sample with the protein dissolved in a suitable solvent, rapidly freezing it to 4–100◦K and thus getting a solid crystal structure. Next, X-rays in the frequency band 1016_{− 10}18_{Hz are scattered from the electron clouds}

of the comprising molecules, giving rise to an exposure image. This procedure is repeated multiple times to generate enough data. These images are further analysed and the electron density maps of the compound are reconstructed. Using sophisticated techniques [92], researchers are able to further identify and label the chemical groups of the given structure. This scrupulous process results in a 3D structure of the molecule where all constituents and distances are known and can be measured up to some level of precision. Roderick MacKinnon and Peter Agre were awarded the Nobel prize in 2003 for the development of this technique.

Recently another closely related technique has been developed. Cryo-electron microscopy (cryo-EM) [93] suggests freezing the sample and exposing it to a beam of electrons, resulting in scattering patterns. Analogously, the scattering patterns are analysed, and from reverse engineering a 3D structure of the protein can be produced. The reconstructed structures are routinely published at the website RCSB Protein Data Bank [94].

One of the disadvantages of these techniques is that the structure is measured at non-physiological low temperatures [95]. As a result the structure is of a rigid pore that does not include the room temperature fluctuations [34]. Moreover, ions transiting the pore can result in structural changes [34] making flexibility and fluctuations essential for rapid conduction. Therefore, the structural information should be treated with care [15].

Figure 2.1: Stages of the patch clamp experimenting. From the cell-attached configuration, one can switch either to the whole-cell configuration, or initiate the single-channel recordings (inside-out or outside-out). Taken from [100, 101].

2.1.2

Patch clamp

In the patch-clamp technique [96–98], the researcher establishes an electric contact with the contents of a biological cell, which in turn allows measurement of the current or voltage across the cellular membrane. Due to its ability to study the involvement of ion channels in fundamental cellular processes, this method became the gold standard in biophysics decades ago [2, 99].

The overall workflow is shown in Fig. 2.1. Typically, one first prepares the bathing and intrapipette solutions checking the equality of their pH levels. Then the pipette is placed in contact with the surface of the cell. By applying nega- tive pressure one establishes the high-resistance (10–100 Giga-Ohm) contact with the surface, which literally means no current flow through the gap between the glass pipette and the membrane surface. At this stage, several configurations are possible:

flowing through one or several channels. The advantage here, is that there is minimal disturbance to the cell. The apparent disadvantage is the inability to alter the contents of the cell during the experiment, which may be of interest if one is investigating solely the membrane properties.

2. Whole-cell. With further short negative pressure pulse (suction) the mem- brane is ruptured such that the pipette becomes attached to the cell. During several minutes after that the cytosol is substituted by the intrapipette so- lution [96, 102]. The latter point thus allows to study the conductive proper- ties of the cellular membrane as the chemical composition across it is known explicitly and the transmembrane potential is set. However, in this configu- ration cellular organelles may be washed out through the pipette tip [96,102] what makes this configuration unsuitable for studies where the natural cel- lular processes are of interest.

3. Perforated patch clamp. If the pipette contains the appropriate antibi- otic, the latter will make small holes in the membrane (Perforated patch). Thus, the penetration of the pipette solution into the cell is impeded. The washout of intracellular organelles becomes prevented as well. Thus, one can measure electric properties of a cell with little intervention in its function- ing. However, there is little control over the chemical composition of the cell, therefore this configuration is rarely used in ion channel experiments.

4. Inside-out and outside-out patch clamp. If one tears off a patch of the membrane into the pipette, this will be an inside-out configuration (what was inside is now outside). If, additionally, the ends of the patch anneal, this is an outside-out configuration (what was outside stays outside). This allows one to extract a wealth of information about a single ion channel.

Once a particular configuration is established, one begins experiments accord- ing to a specified protocol. For instance, applying a voltage-stepping protocol one measures a set of currents through the channel at different voltages. These

recordings provide information about the selective and conductive properties of the membrane, consisting of the channels of interest.

2.2

Theoretical techniques to study nanochan-