Protein Biochemsitry

Introduction

Prerequisites

• This chapter will some pre-calculus math. You should be familiar with logarithm properties if you wish to follow along with one of the derivations
• Some basic thermodynamics knowledge will be assumed. You should understand the basics of:
  • What entropy and enthalpy are, at least at a conceptual level
  • The various types of intermolecular and intramolecular forces
• Basic organic chemistry knowledge will be assumed. You should be familiar with the following:
  • Common functional group names and structures
  • Conjugation/Resonance
  • Nucleophile, electrophile

Acid-Base Chemistry

Definitions of Acid and Base

There are 3 main basic definitions of acid-base chemistry:

• Arrhenius: increases concentration of H+ (acid) or OH- (base)
• Bronsted-Lowry: proton donor (acid) and proton acceptor (base)
• Lewis: electron pair acceptor (acid) and electron pair donor (base)

The Arrhenius definition has been supplanted by the Bronsted-Lowry one, as it's more general. The Lewis definition is also very important and its acids and bases are also referred to as electrophiles and nucleophiles respectively. For clarity, future uses of the words "acid" and "base" will refer to the Bronsted-Lowry definition; Lewis acids and bases will be referred to by their aforementioned organic chemistry terms.

Henderson-Hasselbach Equation and pKa

Let us start with a generic acid dissociation equation from before with an acid dissociation constant \(K_A\): $$HA+H_2O\rightleftharpoons A^-+H_3O^+$$ The associated equilibrium equation is $$K_A=\frac{[A^-][H_3O^+]}{HA}$$ There are various ways you can algebraically manipulate the equation and take logs in order to get to the final equation, but I will get things on the right side prior to taking the log $$\frac{1}{[H_3O^+]}=\frac{1}{K_A}\times\frac{[A^-]}{[HA]}$$ Taking the log of both sides. $$\log(\frac{1}{[H^+]})=\log(\frac{1}{K_A}\times\frac{[A^-]}{[HA]})$$ Using the multiplication and division rule for the argument: $$\log(\frac{1}{[H^+]})=\log(\frac{1}{K_A})+\log(\frac{[A^-]}{[HA]})$$ Using a specific case of the log power rule, there is the relationship \(\log(1/a)=-\log(a)\), we get $$-\log([H^+])=-\log(K_A)+\log(\frac{[A^-]}{[HA]})$$ By definition, \(pKa\equiv -\log(K_A)\) and \(pH\equiv -\log([H^+])\). Thus, we arrive at the Henderson-Hasselbach equation: $$pH=pKa+\log(\frac{[A^-]}{[HA]})$$ This equation allows us to relate the pH of an environment, the pKa of an acid, and the ratio of deprotonated to protonated occurences of that acid

Amino Acids and Acid-Base Chemistry

As amino acids have both amine and carboxylic acid groups, they can all act as both acids and bases to some extent. In fact, at a neutral pH, amino acids will be predominantly Zwitterions (molecules that have both positive and negative charges); the amine group next to the alpha carbon will be protonated and the carboxylic acid group next to the alpha carbon will be deprotonated.
However, a number of the proteogenic amino acids can also participate in acid-base chemistry through their sidechains.

By Thomas.ryckmans68 Own work, CC BY-SA 4.0,    Link

One might ask - why do the amide groups in Asparagine and Glutamine not participate in acid-base chemistry? The answer has to do with conjugated pi systems. The lone pair on the nitrogen is not "available" to grab a proton because it prefers to be in a conjugated system with the carbonyl. For the same reason, in proteins, you will not see the amide backbone being charged, only the N and C termini.

For a simpler non-biological example, you can look at aniline which is benzene with an amine group. The pKa of its conjugate acid is much lower than that of a normal amine due to the above mentioned principles. However, there are cases like Histidine, which has a conjugated system, but is able to have the double-bonded nitrogen protonated as well. For histidine, the lone pair is not part of the conjugated system since you have a p orbital already with the double bond. This allows it to act as a base. Tryptophan also has a nitrogen containing heterocyclic R group, but it's not ever positively charged. You can explain this with the logic previously mentioned in this post. Simple non-biological analogous examples are pyrrole versus pyridine and why they have different basicity.

Basic pKa Example in Proteins

Let use consider Histidine (assume pKa=6.0) in an environment at pH=7.0. Let \(His^0\) denote the uncharged version and \(His\cdot H^+\) denote the protonated version. $$pH=pKa+\log(\frac{[His^0]}{[His\cdot H^+]})$$ $$pH-pKa=\log(\frac{[His^0]}{[His\cdot H^+]})$$ $$\frac{[His^0]}{[His\cdot H^+]}=10^{pH-pKa}$$ $$\frac{[His^0]}{[His\cdot H^+]}=10^{7-6}$$ $$=10$$ At pH=7.0, there are 10 uncharged histidine residues for every positively charged histidine.

Now what about if pH were lower by 2; i.e., pH=5.0: $$\frac{[His^0]}{[His\cdot H^+]}=10^{5-6}$$ $$=0.1$$ Now, there are 10 charged histidines for every uncharged one by lowering the pH by 2.

Effect of Local Environment on pKa

The pKa values quoted in the previous figure were for the lone amino acid. The pKa values in proteins can drastically differ based on the environment. Imagine a histidine that is in proximity to an aspartic acid residue. Thie histidine can take a proton off of the aspartic acid, resulting in a positive charged histidine next to a negatively charged aspartate. This creates a favorable electrostatic interaction. Because of this, we would expect that the histidine would have a higher affinity for protons. This would lead to the histidine residue having a higher pKa (more likely to be protonated).

This is a classic example of a common occurrence in biology used to enhance reactivity of side chains in proteins. These two residues can be joined by a Serine residue to form something known as a catalytic triad. This more basic histidine can help deprotonate the serine residue, causing it to be a stronger nucleophile (think H2O versus OH- in terms of nucleophilic strength).

The opposite can occur as well. Imagine a histidine next to an arginine. Arginine has a very high pKa and is almost always positively charged. If the histidine were to also become protonated, then you would have two like charged together, which is not energetically favorable. Because of this, we would expect this particular histidine to be have less affinity for protons. The pKa for this histidine would thus be lower.

Enzymes

Enzymes are primarily composed of proteins, with a few exceptions (e.g., ribozymes, which are catalytic RNA molecules). The three-dimensional structure of enzymes is essential for their function. The relationship between an enzyme's structure and its catalytic activity is encapsulated in the "lock-and-key" model and the "induced-fit" model.

Mechanisms

1. Enzymes stabilize high-energy transition states, making it easier for reactions to occur.
Enzymes bring substrates into close proximity and orient them favorably for reaction.
2. Enzymes can donate or accept protons to facilitate reactions.

In the Michaelis-Menten chapter, we study the kinetics behind enzyme reactions.

Post-Translational Modifications

Introduction

To expand their functional diversity and regulatory capabilities, proteins undergo various modifications after their synthesis.

Phosphorylation

Phosphorylation is one of the most prevalent and versatile PTMs. It involves the addition of a phosphate group (PO4) to specific amino acid residues, typically serine, threonine, or tyrosine. Protein kinases catalyze phosphorylation, while protein phosphatases reverse the process. Phosphorylation regulates protein activity, localization, and interactions, making it crucial in signal transduction and cell cycle control.

Glycosylation

Glycosylation involves the attachment of carbohydrate chains (glycans) to proteins. It occurs predominantly on asparagine (N-linked) or serine/threonine (O-linked) residues. Glycosylation impacts protein stability, cell adhesion, and immunity. Aberrant glycosylation is associated with diseases such as cancer.

Methylation

Methylation adds a methyl group (CH3) to amino acid residues, primarily lysine and arginine. Histone methylation can activate or repress gene expression, depending on the context and specific amino acid modifications. Methylation promotes positive electric charges on lysines since they can be methylated up to 3 times, leaving the nitrogen with a positive formal charge.

Acetylation

Acetylation adds an acetyl group (CH3CO-) to lysine residues, often influencing chromatin structure and gene expression. Histone acetylation, for example, plays a pivotal role in epigenetics by altering DNA accessibility to transcription factors.

Ubiquitination

Ubiquitination involves the attachment of ubiquitin molecules to target proteins, typically lysine residues. The pattern and location of the ubiquitination determines what type of signal it sends, but is most often known for its role in degredation of proteins.

Protein Biochemistry Exercises

1. What are acids and bases according to the Arrhenius definition?
2. How do the Bronsted-Lowry and Lewis definitions of acids and bases differ from Arrhenius' definition?
3. What is the Henderson-Hasselbalch equation and what does it describe?
4. What is a conjugate acid-base pair?
5. Explain the role of water in acid-base reactions.
6. How do amino acids exhibit acid-base properties?
7. What are the ionizable groups present in amino acids?
8. Describe the relationship between pH and the protonation state of amino acids.
9. What are zwitterions and how do they relate to amino acids?
10. Explain the effect of the surrounding environment on the protonation state of amino acids.