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biophysics

Folding molecules

Simulations on a computer make it possible to foresee the structure of proteins and to explain the mechanism of how anesthetics act

When the hand touches a hot saucepan, cells of the skin transform the sensation of heat into a tenuous electrical signal, transmitted from one nerve cell to another until it reaches the spinal cord, from which a reflex sets off which makes the hand move away from the saucepan. Also as electrical impulses, the message follows on its way to the brain, and there it is interpreted as a sensation of pain, in a sequence of chemical signals that happens in hundredths of a second.

It is only then that there comes an awareness of what has happened.On the basis of computer simulations, physicists and biologists from the Federal University of Rio de Janeiro (UFRJ) helped to explain the formation and propagation of these electrical signals – or nerve impulses that, as it has been demonstrated, are extremely dependent on a structure shaped like a hair grip found at the base of the pores of the membrane of the neuron.

The nerve impulses, besides activating the reflex for moving the hand away from the saucepan in response to the pain, ensure survival itself, by means of involuntary acts, making the heart beat, or voluntary ones, permitting the conscious choice of a route through the traffic, for example. Following the conclusions that the team from Rio have reached, they have created an approach that assists in detailing something extremely practical: the action of anesthetics, medicines that lessen sensitiveness to pain by blocking the passage of the electrical signals through the neurons, or nerve cells.

In another area, the group led by physicist Pedro Geraldo Pascutti, from UFRJ’s Carlos Chagas Filho Biophysics Institute, has shown how a protein quickly manages, right after being produced, to fold itself up and, in a few minutes, take on the spatial form that allows it to act in the organism more efficiently. The steps of this ballet seems simple – and indeed they are -, but no one until now knew how it is that the proteins follow this routine automatically. As they are long and flexible, they can withstand bending and take on millions of different shapes. If each possibility were to be tested, any protein would take billions of years before arriving at the most suitable shape – and even then would probably form only the more simple organisms.

Nerve impulses
The thousands of pores on the surface of neurons regulate the entry of atoms with a positive electrical charge, the so-called cations, and in this way, they control the propagation of the nerve impulse. Known as sodium channels, these pores remain closed by a sort of lid while the nerve cell is inactive. Under these conditions, the concentration of sodium on the outside of the cells becomes as much as ten times greater than in the inside, and the nerve impulse does not arise.

With a level of detail never achieved before, the team from UFRJ deduced the shape of this pore’s lid: it is a structure similar to a curved hairgrip, like a hook. The group from Rio also showed how this lid moves, undergoes deformations and manages to close the passage of the channel located in the inner side of the cells. The natural consequence of this movement is that the electrical signal is blocked from being carried over the surface of the neuron, and communication with the next nerve cell is interrupted.

Every time the neuron receives a stimulus, the lid over these channels opens up and lets the sodium pass through the membrane, a double layer of fat that separates the inside of the neuron from the external medium. As more sodium enters, more pores open up, and the nerve impulse propagates in a single direction, like a wave, until, in thousandths of a second, it hits the extremity of the neuron, releasing chemical messengers, called neurotransmitters, which pass the information on to the next cell.

The sodium channel itself, in which the lid fits, is now also better known. Thanks to the work of international research groups, it has been known for some years that the structure of the channel consists of a single protein with 1,820 amino acids (protein units). The major part of this long molecule is wound into four bundles, each one with six tubes like rods of dynamite: they are the walls of the pore through which the sodium only enters, without being able to get out.

The molecules that are going to form the pores are born as long strands in the inside of the cells, and they start to roll themselves up in a succession of spirals, or like a skein of wool. “This entanglement is a consequence of the attraction or the repulsion between the electrical charges of the stretches of the protein and of the mutual action of these charges and of uncharged segments with the molecules of water to be found both inside and outside the cell”, Pascutti explains. In the stretches in the inside of the cell, the protein proves to be less rolled up. It is one of these slimmer segments of the protein that forms the lid of the channel.

This lid is a filament of a mere 53 amino acids with an important characteristic: at two spots of its slimmer portion, the protein once again turns into a spiral and forms two distinct and compact blocks, as the team from UFRJ discovered. The larger of these blocks calls attention for working like a sort of bolt for the lid of the channel and for being very resistant. Simulations done in a computer program developed by Pascutti and physicists Kleber Mundim, from the University of Brasilia (UnB), and Paulo Bisch, from UFRJ, indicated that the region in the shape of a grip remain very rigid, even when heated up to a temperature almost four times higher than the human body.

Availing himself of this same program (which was given the name of  Thor, the Germanic god of thunder, for its robustness), Pascutti, his former student for a master’s degree, Fernanda Leite Sirota and Argentinean physicist Celia Anteneodo, from the Brazilian Center for Research in Physics (CBPF in the Brazilian acronym), saw that these two more compact stretches of the lid move in conjunction and, in this way, provide the necessary firmness for opening and closing the channel. Connected by flexible rods to the longest part of the protein, this bolt is subject to changes in the distribution of electrical charges in the region close to the internal opening of the channel. “It is these alterations that make the pore open or remain closed”, the physicist says.

It is possible to imagine this lid like a pyramid-shaped trap to catch birds, made of bits of wood. The structure of the trap corresponds to the lid, and the wooden lever that keeps it set, to a sort of barrier of energy created by the difference in electrical charges between the channel and the lid. Any alteration caused by the change of charges lowers this energy barrier and, like the level that is pulled away, makes the pore close. .

The team from Rio found that the position of the larger rod was fundamental for the workings of the channel. “When the cylinder shows an inclination in relation to the inner face of the membrane, a barrier of energy prevents the closing of the channel”, Pascutti explains. Alterations in the distribution of the electrical charges in the region, though, lead to the inclination of the rod and to the closing of the pore. “We believe that anesthetics bring about a lowering of this energy barrier, the closing of the channels, and as a result prevents the nerve impulse from passing”, comments the physicist, who consolidated these findings in March 2002, in the Biophysical Journal.

Rachel Klevit, from the University of Washington, in the United States, had already detected only the form of the larger rod, by means of nuclear magnetic resonance, a technique used to produce images of the human body. It was left to the team from Rio to reveal the details, in an independent study. The originality of this work was dealing with the membrane and the aqueous medium inside and outside the cells as two regions with a different capacity to conducting an electric current.  The idea was born in the mid-90s, when Pascutti began to work at the CBPF with Paulo Bisch and Kleber Mundim.

Adopting this focus, they described the interaction between the proteins and the membranes of the cells, adapting Coulomb’s Law, a mathematical expression formulated in 1785 by the French physicist Charles-Augustin de Coulomb. Applying this method makes it possible to simulate, without the need for supercomputers, the movement of these and of other molecules in membranes for up to 10 nanoseconds (one nanosecond is the billionth fraction of a second), a time that is one hundred times greater than other methods.

In a study published in 1999 in the European Biophysics Journal , using the same method, Pascutti’s team showed that the cell membrane itself assists the molecules that do not have a stable shape when they circulate in the medium between the cells, by quickly taking on their most efficient spatial structure. The researchers worked with a peptide (a piece of protein) called a melanocyte-stimulating hormone, which induces the production of melanin, a substance that gives color to the skin. Once again using computer simulations, they discovered that this peptide, when it meets the membrane, takes on its most stable form and slides over the membrane until slotting into the receptors and transmitting to the inside of the cell the order to release more melanin.

The ballet of the proteins
With small adjustments, the same mathematical model helps to explain the means by which long molecules like proteins manage to roll themselves up quickly and reach their functional form in a few minutes. If it were to seek its functional conformation by trial and error, a small protein made up of only 100 amino acids would take 1019 (the number 1 followed by 19 zeros) billion years, according to Pascutti. “Should it follow this logic, this small protein would neverarrive at its biologically most effective form, since it would take a time far superior to the age of the universe”, the researcher comments.

In an article published in 2001 in Physical Review E , Pascutti, Marcelo Moret, from the State University of Feira de Santana (UEFS), and Edvaldo Nogueira Júnior, from the Federal University of Bahia (UFBA), put forward an explanation for this contradiction, showing that the energy that keeps the atoms of a protein united follows a pattern that repeats itself on different scales, the so-called fractal systems. One example of a fractal system is a bracken leaf, in which each follicle is an exact reproduction, but in miniature, of the whole leaf.

To make the quest for more stable positions, in which the amount of energy of the atoms is smaller, the researchers selected structures of polyalanine, a protein formed by the repetition of the amino acid alanine, with a greater probability of existing – not all of them are viable, because of the repulsion caused by the proximity of the atoms – using a mathematical model proposed by physicist Constantino Tsallis, from the CBPF, a Greek who moved to Brazil 28 years ago.

Formulated in 1988, this method, known as the Tsallis statistics, had already proved useful in other areas of knowledge, such as in economics, by indicating how to get greater productivity from any good, at the lowest cost. Pascutti imagined that he could use this approach to study the rolling up of proteins, because it would make it possible to cast lots for the more stable forms to be tested in a more focused manner. The Tsallis method was much quicker, indicating that a polyalanine of 16 amino acids can arrive at its most stable form in 15,000 movements, as they showed in 2002 in the Biophysical Journal . According to the traditional method, the Boltzmann-Gibbs equilibrium, a polyalanine with 16 amino acids would not come to the end of its dance in less than 150 million steps.

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