# Structural Biochemistry/Physics

<< Fundamentals of Structural Biochemistry | Physical Basis | Chemical Basis >>

## Introduction

Physics is the scientific study of physical phenomena and the interaction between matter and energy. Generally speaking, it is the examination and inquiry of the behavior of nature. As one of the oldest branches of academia, physics is intertwined with and helps explain the fundamental nature of the living and nonliving universe.

## Thermodynamics

### First law

The "first law" of thermodynamics is simply that energy is a conserved quantity (i.e. energy is neither created nor destroyed but changes from one form to another). Although there are many different, but equivalent statements of the first law, the most basic is:

$dU=dQ+dW$ dU = infinitesimal change in internal energy,

dQ = infinitesimal heat flow and

dW = infinitesimal work.

In words, the first law states that

The heat supplied is equal to the increase in internal energy of the system plus the work done by the system. Energy is conserved if heat is taken into account.

### Entropy

Thermodynamics allows us to predict the initial and final states of a system. In other words, it’s an extremely useful tool in predicting the equilibrium position in chemical systems. The first law of thermodynamics states that energy is always conserved between the initial and final states. However, the first law does not provide information about the extent of a chemical reaction, or the equilibrium concentrations. The second law of thermodynamics introduces the concept of entropy S, a value that is a function of a system’s state. Entropy helps predict the equilibrium because the equilibrium concentrations of a system correspond to the maximum entropy of a system; entropy can act as a driving force of a reaction. Therefore, the second law of thermodynamics states that:

"Thermodynamic equilibrium in an isolated system is reached when the system's entropy is maximized"

Mathematically, entropy is expressed as

$dS\equiv {\frac {dq}{T}}$ for a reversible process in a closed system, where dq is heat energy and T is temperature. A reversible process is where the system is always very close to the equilibrium. Perturbations to the system must be small enough that the system and the surroundings can return to the initial state. The change in entropy, a more useful value, is defined as:

$\Delta S=S_{2}-S_{1}=\int _{1}^{2}{\frac {\mathrm {d} q_{rev}}{T}}$ An example of increasing entropy can be seen by watching ice melt in a closed container held at 25oC. Since the temperature is constant, it can be seen that the total thermal energy of molecules in liquid water is greater than the thermal energy of molecules in ice. Therefore, ΔS is positive, which implies that entropy has increased in order to obtain equilibrium.

Entropy is conceptually more difficult to understand than other state functions such as temperature or energy. Furthermore, entropy is a macroscopic property; one molecule does not exhibit entropy. Consider a closed container with a partition down the center of the container where one side of the partition is composed of gas A and the other side of the partition is empty. If the partition is removed, there is a very small probability that gas A will stay on one side of the container. The most probable distribution of the A molecules is that gas A will be evenly distributed throughout the container. This distribution can be viewed as the equilibrium thermodynamic state, which happens to be the most probable state and the state with the most disorder.

### Enthalpy

Enthalpy is a measurement of heat transfer done at a constant pressure and is often denoted as $H$ . Mathematically, enthalpy is expressed as

$H=E+PV$ where E is the internal energy of the system, P is internal pressure, and V is the volume. PV accounts for the energy used in expansion work.

The change in enthalpy is then expressed as

$\Delta H=\Delta E+P\Delta V$ where pressure remains constant. $\Delta H$ is then, essentially, the internal energy corrected for work.

Reaction enthalpies are assigned to chemical reactions to denote the amount of energy that is transferred into or out of the system in exchange with the surroundings. A reaction that releases heat is defined as exothermic, where $\Delta H$ is negative. A reaction that requires an input of heat is defined as endothermic, where $\Delta H$ is positive.

### Gibbs Free Energy

Free energy is a measurement of the tendency of processes to occur spontaneously. It depends upon 3 different quantities: change in entropy, change in enthalpy, and temperature. The Gibbs Free Energy is the enthalpy of the system subtracted by the temperature and the entropy of the system, G = H - TS. A positive change in free energy (such as an endergonic reaction) is thermodynamically unfavorable, whereas a negative change in free energy (such as an exergonic reaction) is thermodynamically favorable. In biological systems, many reactions that have positive free energy are coupled simultaneously to reactions that reactions that have negative free energy. Example is the synthesis of glutamine from the expense of hydrolysis of ATP.

### Endergonic Reactions

Endergonic reactions are reactions that have a positive free Gibbs energy. These reactions are not thermodynamically favored and the substrates are not readily going to form products. Energy must be out into the system to drive these reactions.

### Exergonic Reactions

Exergonic reactions are thermodynamically favored. These types of reactions have a negative free Gibbs energy an are readily able to form products. However, although these reactions are energetically favorable, it does not mean the reaction will occur at a reasonable rate. This is due to high activation energy barriers. To reduce these barriers, the introduction of a catalysis is needed.

## Charges: The Stern-Gerlach Experiment

This iconic experiment in the realm of quantum mechanics describes the nature of the charge an atom can have. This idea is pertinent to biochemistry because of the nature of how monomers, dimers, etc. bind to metal centers (for examples, iron is the metal center that hemoglobin uses as its coordination center). These protein structures bind to metal centers by coordination complexes that are in correspondence with the oxidation state of the metal ion. The oxidation state of the metal ion is influenced by the spin charge of the metal ion and it because of the Stern-Gerlach experiment that explains the nature of charge in an atom. The Stern-Gerlach experiment is an iconic quantum mechanical experiment that physically showed the spin charges of a silver atom. The electrons of the silver atoms was emitted between two vertically oriented magnets. These magnets provided the magnetic field to separate the electrons based on their apparent spin. The result of this experiment were two spins, one going up and one going down, dictated as + 1/2 and -1/2. The two beams of directionally spun electrons were then put through a second set of horizontally oriented magnets. The result of this addition were again two beams of directionaly different spun electrons except in the horizontal orientation. The last part of this experiment was sending one of the beams from the horizontally oriented spun electrons through another set of magnetic oriented in the same way as the first set. The resulting beams from this last set of magnetics is the most important realization. The main idea of the implementation with the third magnet is that two beams emerge, just as experienced with the first set of magnetics. Because of the beams of electrons shown are of the same spin nature, this in turns shows that the two beams of electrons from both magnetics after being oriented differently, are eigenvalues of each other, meaning they are of the same operator. This whole experiment displays the importance of charge and how it can be used to describe the nature of quantum behavior and the nature of coordination ligand binding.

## Foundation of Biochemistry

Physics is one of the foundations of biochemistry; it deals with different types of energy and forces. Types of forces:

1. Ionic force — charge-charge interaction
2. Dipole interactions — deals with electronegativity (trend from increasing order: P, H, S, C, Br, Cl, N, O, F) and consists of hydrophobic interactions.
3. Van der Waals — molecular repulsion
4. Hydrogen bonds