Experiments in Quantum Mechanics

Experiments in Quantum Mechanics The theory of quantum mechanics developed when the classical theories of mechanics and electromagnetism were unable to provide explanation to the characteristics of atomic structure and electromagnetic radiation  (Rae, 2008). The appearance of quantum mechanics resulted in the emergence of a principle that has the ability to describe the nuclei, proton and neutron (Rae, 2008). Quantum theory has two sides, the first is the mathematical side and the second is the conceptual side. The mathematical side has been successful in estimating the atomic and subatomic phenomena, while the conceptual side â€Å"has been a subject of endless discussions without agreed conclusions† (Thankappan, 1993). 1.0 Double Slit Experiment It is known that when particles are emitted through two slits two bands are formed, while when waves are passed through two slits interference pattern is formed on the back wall. When the crest of the first wave meets the trough of the second wave, the two waves cancel each other and destructive interference occurs which result in appearance of dark lines. On the other hand, when two crests or two troughs of the wave meet each other construction interference occurs and bright lines are formed. The elegant difference is blurred by quantum mechanics. When a stream of electrons passed through one slit, a single band is formed, but when electrons emitted through two slits an interference pattern is formed, but how could a piece of matters create an interference pattern like waves? Physicists thought that particles bounced each other and created the interference pattern. This time they decided to shoot the electrons one at a time, by this method it is impossible for electrons to interfere with each other. After a time the same interference pattern is formed. The conclusion was that the single electron leaves as a particle and becomes a wave of potential then it goes through both slits and interferes with itself to hit the wall like a particle (The particle is in two places at once), but mathematically it is even stranger that the electron goes through both slits, it goes through neither, it goes through just one slit or it goes through just the other. All of these possibilities are in superposition with each other (Khutoryansky, 2013). (Perimeter Institute, 2012) Figure 1.0 Double-slit apparatus showing the pattern of electron hits on the observing screen building up over time. This made the physicist completely puzzled and they decided to install a measuring device by one slit to see which slit the electrons actually pass through, but the quantum world is far more mysterious than they could have imagined. The electron decided to act differently because it felt that the observer watched it. When they observed the electron, the electron went back to behave like a little marble, it produced a pattern of two bands and not many interference pattern as it was expected. Physicists were Perplexed, they asked what is the matter? Is it Particles or waves? (Khutoryansky, 2013) After a while they have discovered that, when the electron was observed the wave function was collapsed. 1.1 The Explanation of double slit experiment A Physicist called Max Born, one of the founders of quantum mechanics came up with a new idea for what the wave equation described. Born said that the wave is not a smeared out of electron or anything else previously encountered in science. Instead, he declared that electrons are something about a probability wave (Probability distribution), that is Born argued that the size of the wave that any location predicts the likelihood of the electron being found there. Where the wave is big that is not where most of the electrons are, that is where the electrons are most likely to be, and that is very strange, so the electron on its own sees a jumble of possibilities (Khutoryansky, 2013). â€Å"You are not allowed to ask where is the electron right now, but you are allowed to ask if I look for the electron in this little particular of space, what is the likelihood I will find it there, and that bugs anyone!†(Peter Fisher, 2012). Finally, it is shown that the implication of this experiment is that matter can have both wave and particles properties. This is known as â€Å"Wave-Particle Duality† or â€Å"Dual Nature of Particles† This is proposed by Louis de Broglie in 1923 leading to the birth of modern day quantum mechanics. Exhibiting particles or waves characteristics depends if a detector is observing the matter or not. The second implication of the double slit experiment is that the outcomes of macroscopic events can be affected by observation. This is because macroscopic objects are composed of microscopic particles acting as either waves or particles (Lejuwaan, 2010). These facts lead to the emergence of De Broglie equation as shown in (1.1) and (1.2) (1.1) (1.2) Where is the wavelength, is Plancks constant, is the frequency, and E is the total energy of the particle (Phillips, 2003). The equations (1.1) and (1.2) are equivalently equal to (1.3) (1.4) Where is the modified Planck’s constant (), k is the angular wave number (and is the angular frequency ( (Phillips, 2003). The comparison between planets in a solar system and electrons in an atom was no longer reasonable. De Broglie’s hypothesis led to the development of quantum mechanics and subsequently the Schrà ¶dinger equation. It is important to know the equations (1.1) and (1.2) to understand the concept of the Schrà ¶dinger equation that will be discussed in the next section. 2. The Schrà ¶dinger wave equation Quantum mechanics is all about solving the Schrà ¶dinger equation. There are many Schrà ¶dinger equations, each physical scenario for which you want to apply. Quantum mechanics has its own Schrà ¶dinger equation, they are all slightly different and all require slightly different solution techniques. The reason why there are many different Schrà ¶dinger equations is that the situation over under which you want to solve the Schrà ¶dinger equation enters the Schrà ¶dinger equation as a potential function and we know that potential function influence the physics of quantum mechanics. The Schrà ¶dinger equation is a wave equation that describes the behavior of particles by taking account the fact that matter also has these wave-like properties. â€Å"The role of the Schrà ¶dinger equation in quantum mechanics is analogous to that of Newton’s Laws in classical mechanics. Both describe motion. Newton’s Second Law is a differential equation which describes how a classical particle moves, whereas the Schrà ¶dinger equation is a partial differential equation which describes how the wave function representing a quantum particle ebbs and flows. In addition, both were postulated and then tested by experiment† (Phillips, 2003). The Schrà ¶dinger wave equation helped in the emergence of quantum mechanics and Erwin Schrà ¶dinger was the reason of establishing an equation that considered as one of the fundamentals of quantum mechanics (Freiberger, 2012). There are two forms of the Schrodinger equation, the first form is time dependent Schrà ¶dinger equation and the second form is time independent Schrà ¶dinger equation (The Schrodinger Wave Equation, n.d.). 2.1 Time dependent Schrà ¶dinger wave equation: (1.5) Where is the imaginary unit, is the modified Planck’s constant (), indicates a partial derivative with respect to time t, is the wave function of the quantum system, and is the Hamiltonian operator (Wikipedia, 2014). (1.6) Where m is the mass of particle, V is the potential energy and is the Laplacian. The equation (1.5) is the general equation, while the equation (1.6) is the â€Å"single non-relativistic particle† of the time dependent Schrà ¶dinger equation. By solving time dependent Schrà ¶dinger equation, we can determine the probability of detection of particle in some region as a function of time (Phillips, 2003). 2.2 Time independent Schrà ¶dinger wave equation: Time independent Schrodinger equation is used more than time dependent Schrodinger equation, because the time is measured on a small scale. â€Å"The time-independent Schrà ¶dinger equation predicts that wave functions can form standing waves, called stationary states† (Wikipedia, 2014). The time independent Schrà ¶dinger equation has another important use that is making the time dependent Schrà ¶dinger equation to be solved easily once the stationary states are predicated by the time independent Schrà ¶dinger equation (Phillips, 2003). Eψ (1.7) (1.8) The equation (1.7) is the general equation, while the equation (1.8) is the â€Å"single non-relativistic particle† of time independent Schrà ¶dinger equation. 3. The Role of Quantum Mechanics in Structure-Based Drug Design Most drugs are very small molecules compered to their targets that are enzymes. In order for drugs to take its effect it has to bind to the active site of the enzyme. We can think about this as an engine that has moving parts that moving, and a little drug get stuck in the gears of the engine and hence the entire engine stopped working. This is how drugs are working. In order to design drug pharmaceuticals must know much information about the active site of the enzyme; it will help them a lot if they have a very high-resolution structure so they can know the active site of the enzyme. There are important enzymes whose structure is strange such as catalase which shown in figure (1.9) and it will be easier to design drugs if the structure of the active site is known (Kalyaanamoorthy and Chen, 2011). Over many decades, specialists used the high technological abilities to displace the hard obstructions that they faced along the path of drug discovery. This allowed them to improve the methods of drug design (Kalyaanamoorthy and Chen, 2011). There were many computational approaches that used at different stages of drug design process. These computational approaches were successful in decreasing the number of ligands (â€Å"a molecule such as drug that binds to receptor† (Dictionary.com, 2014).) In addition, in form the computational approaches helped in reducing the period and costs of drug discovery. The computational approach that we will discuss about is the structure-based drug design (SBDD). It is a method that depends on 3-D structures of biological targets. SBDD has two phases; hit identification and lead identification. The first phase is about exhibiting powerfulness against the target by the recognition of chemical compounds called â€Å"hits†. â€Å"Whereas, the latter engages evaluation of the screened hits to identify the promising lead molecules before proceeding toward a large-scale lead optimization†(Kalyaanamoorthy and Chen, 2011). On of the most successful examples of the history of SBDD is the development of human immunodeficiency virus (HIV) proteinase inhibitor (Meyer and Swanson et al., n.p.). 3.1 Target Identification Identifying the right target is only the first stage of a long process. Scientists need to find a protein or gene that is associated with the disease (Kalyaanamoorthy and Chen, 2011). Proteins come from genes, and it is easier to study genes than to study proteins. One approach to find a new drug target, involves comparing the genes of healthy individuals with those of people with the disease. The differences between two genetics maps can help to generate hypotheses in which proteins or lack of thereof cause the disease. It is also possible to do the opposite, by changing one gene at a time in cells or simple organisms, and then observing the resulting effects that will happen, so it called the phenotype of the mutation. If the phenotype has some similarity with the disease’s states, it can give ideas about the possible relation between the mutated gene and the disease. The third approach of target identification is to start already with a bioactive substance such as a natural medicine used in traditional medicine, a compound from basic research or known drugs with unexpected effects (Kalyaanamoorthy and Chen, 2011). When targets are identified they, another process occurs which called drug validation. Drug validation is on of the most important steps in SBDD; many drugs that failed were because it was not checked by â€Å"drug validation process† (Hughes and Rees et al., 2011). When the target and the active site have been identified then the hit discovery process starts. One of the successful validation tools is the transgenic animal (animals that carry foreign genes) as they allow observing the phenotypic endpoints (Hughes and Rees et al., 2011). 3.2 Hit Identification When the targets are discovered and being checked for target validation, the next step is hit identification. Hit identification is about getting a small molecule that has some of the initial properties that pharmaceuticals want in their final drugs. It is very early in the process of a drug discovery. The â€Å"hit† is defined as a molecule that binds to the target. There are some ways that used to determine identify the hit. One way is to start with a natural substrate and to make it drug-like. The second way is to design a De novo hit by SBDD. This way works if pharmaceuticals are familiar with the binding site as well as the protein structure. High throughput screening (HTS) is a process that aims to find inhibitors for the targets by using rapid assays. With HTS there is no need to be familiar with the nature of chemotype likely to have activity at the target protein (Hughes and Rees et al., 2011). HTS is considered as one of the main processes for hit identification (Hug hes and Rees et al., 2011). The disadvantage of HTS is that it requires a lot of materials and time to do a huge combinatorial space (high cost) (Hughes and Rees et al., 2011). When starting with HTS pharmaceuticals need to screen a lot of molecules to find a drug. HTS screens more than hundred thousand to million compounds or even more than a million compounds (Hughes and Rees et al., 2011). Most of the molecules will not be active against the â€Å"biology†, while a large number of molecules will be active against the â€Å"biology† and the process keeps going until there is only one molecule that is active against the â€Å"biology† 3.3 Hit to Lead Phase â€Å"Hit to lead† phase is an elevated level of SBDD phases. It helps pharmaceuticals to get closer to a drug that is safe and efficacious in people because it helps to identify compounds with improved potency (Hughes and Rees et al., 2011). â€Å"A lead compound is a compound that demonstrate a desired a biological activity on a validated molecular target† (Pharmacelsus GmbH, 2013). The key thing about the hit to lead phase is to identify compounds that is not only binds to the protein, but they in fact work inside a cell, and they show the selectivity in a cell (Hughes and Rees et al., 2011). The key aspect of hit to lead stage is a repeated process in which it not only shows that the compound works in a biochemical assay, but it also demonstrate that it works effectively and selectively in a cell-based assay (Hughes and Rees et al., 2011). Therefore, it can go through the cell membrane, reach the target inside the cell, and engage that protein in a cell-based assay. In starting the hit to lead phase, the compounds start off with potencies that are weaker than pharmaceuticals would like. What pharmaceuticals looking for is compounds that will make the medicinal chemistry that will improve the potency of the hit compound at least a factor of ten, and ideally a factor of twenty in the biochemical assay (Kalyaanamoorthy and Chen, 2011). Also, pharmaceuticals look for things to start off with from the hit stage that have weak cellular potency, but with medicinal chemistry that correlates with the biochemical potency mentioned above (Kalyaanamoorthy and Chen, 2011). Furthermore, it drives the cellular potency to be more potent in the cell. This is all toward the goal that pharmaceuticals want to get potent compounds that are cell active. Also, there are several other important properties such that, if Pharmaceuticals do not want the compound to bond to other off-target that may cause toxicity then they prefer compound to have potency that at least ten-fold weaker to the closest related target. We will not discuss in detail. Knowing the active site is a very important thing in drug designing, there are several ways that used to determine the active site for unknown drugs active sites. 4. Quantitative Structure-Activity Relationship (QSAR) The quantitative structure-activity relationship (QSAR) is considered as one of the earliest approaches to drug design. This approach is all about finding a relationship between how active the compound is as a drug and the physical activities of the compound. The fundamental principle of QSAR is that the change in structural properties of the compound can lead to a change in the biological activities of the compound. QSAR allowed us to determine where approximately the drug settles in the human body. This is determined by a physical property that used which called the distribution coefficients between octanol and water (is the ratio between the concentration of a compound in the mixture). â€Å"QSAR depends on bulk properties of the potential drug molecules† (Moore, 2002). A new method is emerged, it is called 3D-QSAR, 3D-QSAR is considered to be an effective tool in the design of pharmaceuticals drugs that helps to connect the activity of a molecule with the properties that d epends on a special part of the molecular structure. We superimpose by a computer a set of molecules that we know their activities. By this method, the set of molecules with similar groups will be in the same place. Furthermore, a small box is drowned that divided into lattice of n points along each side and 200pm apart from each other (Moore, 2002). The box contains all the molecules. A box containing one molecule is shown in figure 2.0 5.1 QM/MM studies of pharmaceutically relevant targets In this section we will discuss about an experiment that Alessio and Marco (2012) did to show that QM/MM could predict the binding orientation of a reference inhibitor. The experiment is all about the interaction of fatty acid amide hydrolase (FAAH) and carbamic acid aryl ester inhibitors (URB524) (Lodola and De Vivo, 2012, pp. 337-362). â€Å"In general, SBDD depends on the accuracy of ligand docking, and the ability to identify binding modes† (Lodola and De Vivo, 2012, pp. 337-362). When FAHH is docked with URB524 inhibitors, there are two possible of this docking. Tools that applied in drug discovery were not able to distinguish between the two binding orientations. On the other hand, when QM/MM was used to model the inhibitor binding process, it made such a good success in revealing that (Lodola and De Vivo, 2012, pp. 337-362). QM/MM calculations showed that, the second orientation was energetically preferred. This QM/MM calculation’s suggested that the notably higher barrier in the first orientation led to an unstable product. (Lodola and De Vivo, 2012, pp. 337-362). By QM/MM we can gain a detailed understanding of the binding site interactions, and hence QM/MM can contribute practically to drugs design. On the other hand, although QM/MM gives a detailed understanding of the binding site interactions, QM/MM has not yet played an important role in drug designing. Due to the high computational abilities that QM/MM has, it looks like that QM/MM will be a main and an indispensable tool in drug design in the recent years.