In this new series of posts, I will report the slides of some of the seminars/lessons that I have delivered in the past years. Some of the information is updated but still, there is a wealth of useful information. In some cases, I have also added descriptions of the contents of the slides for others you can refer to other posts or the original paper that I describe my research results.
I hope you enjoy them and remember to add your feedback and to subscribe to have email notifications about my new blog posts.
In the year 1648, Isaac Newton published his first edition of the Principia Mathematica, one of the greatest scientific masterpieces of all time. On page 12 of this magnum opus, the famous three laws that bear his name and from which classical mathematical physics evolved are enunciated. More than 350 years after that publication, the same laws, formulated to explain the motion of stars and planets, still remain valuable for us, when trying to simplify the description of the atomic world. In the first decades of the last century, the birth of quantum mechanics marked the beginning of the exact description of atomic physics. The equation of Schrödinger, to the same extent as Newton’s equations, allowed for the mathematically elegant formulation of the shining theoretical intuitions and the experimental data accumulated in the previous decades. Although in principle, this equation could be used in order to describe the physicochemical behaviour of any molecular system, it turns out to be impossible to resolve analytically, when the number of electrons in-game is larger than two. The invention of electronic computers, after World War II, facilitated the numerical solution of this equation for polyatomic systems. However, despite the continuous and rapid development of computer performance, the ab-initio quantum-mechanical approach to describe static and dynamic properties of molecules containing hundreds or even thousands of atoms, as for biological macromolecules, is still far from becoming a routine computational tool. In fact, this approach requires a number of calculations that can be proportional to , where N is the total number of electrons in the system. To overcome this problem, it was clear since the beginning that a reduction, by means of ad hoc approximations, of the description of the dynamic behavior of atoms, using a classic physics model would be necessary. In the classical representation, the electrons on the atoms are not explicitly considered but their mean-field effect is taken into account. The first simulation of an atomic fluid using this approximation was performed approximately 63 years ago by Alder and Wainwright (1957). They developed and used the method in order to study simple fluids by means of a model that represented atoms as discs and rigid spheres. These first pioneer studies mark the birth of the classical molecular dynamics (MD) simulation technique. The successive use of more realistic interaction potentials has allowed obtaining simulations comparable to experimental data, showing that MD can be used as a valid tool for surveying the microscopical properties of real systems. The first simulations of this type were carried out by Rahman and Verlet (1964): in these simulations, a Lennard-Jones type potential was used in order to describe the atomic interactions of argon in the liquid state. Another very important hallmark in this field was the simulation of the first protein (the bovine pancreatic trypsin inhibitor) by McCammon and Karplus in 1977. In the following years, the success obtained in reproducing structural properties of proteins and other macromolecules led to a great spread of the MD within the studies of structural biology. The continuous increase of computer power and improvement of programming languages has concurred to a further refinement of the technique. Its application was progressively expanded to more complex biological systems, comprising large protein complexes in a membrane environment. In this way, MD is becoming a powerful and flexible tool with application in disparate fields reaching from structural biology to material science.Continue reading