Question

The protein calcineurin binds to the protein calmodulin with an association rate of \(8.9 \times 10^{3} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) and an overall dissociation constant, \(K_{\mathrm{d}}\), of 10 \(\mathrm{n} \mathrm{M}\). Calculate the dissociation rate, \(k_{\mathrm{d}}\), including appropriate units.

Short answer

The dissociation rate, \(k_d\), is \(8.9 \times 10^{-5} \mathrm{s}^{-1}\).

Step-by-step solution

Understand the Relationship

The association rate, the dissociation constant, and the dissociation rate are part of a relationship given by the equation: \( K_d = \frac{k_d}{k_a} \), where \(K_d\) is the dissociation constant, \(k_d\) is the dissociation rate, and \(k_a\) is the association rate.

Reorganize the Equation

To find \(k_d\), reorganize the equation: \( k_d = K_d \times k_a \). This allows us to compute the unknown dissociation rate.

Convert Units

Convert the dissociation constant \(K_d\) from nanomolar (nM) to molar (M) for consistency, as 1 nM = \(1 \times 10^{-9}\) M. Thus, 10 nM = \(10 \times 10^{-9}\) M = \(1 \times 10^{-8}\) M.

Substitute Known Values

Substitute the known values into the equation: \( k_d = (1 \times 10^{-8} \, \text{M}) \times (8.9 \times 10^3 \, \text{M}^{-1} \, \text{s}^{-1}) \).

Calculate the Dissociation Rate

Perform the multiplication to find \(k_d\): \( k_d = (1 \times 10^{-8} \, \text{M}) \times (8.9 \times 10^3 \, \text{M}^{-1} \, \text{s}^{-1}) = 8.9 \times 10^{-5} \, \text{s}^{-1} \).

Evaluate Units and Result

Ensure that the units cancel out correctly. The result has units of \( s^{-1} \), indicating a dissociation rate. Therefore, \( k_d = 8.9 \times 10^{-5} \, \text{s}^{-1} \).

Key concepts

Biochemical Kinetics

Biochemical kinetics explores the rate at which biological processes occur. It focuses on how quickly reactions reach equilibrium. This is crucial in understanding how proteins interact within cells. The speed of these interactions impacts cellular functions and overall organism health. Calculating rates such as association and dissociation helps scientists understand these processes.
To measure how proteins bind and separate, scientists often use experimental data. For instance, the association rate measures how fast two molecules bind, while the dissociation rate measures how fast the complex breaks apart. Together, these rates provide a comprehensive view of the dynamic nature of biological interactions.

Protein Interaction Analysis

Protein interaction analysis is the study of how proteins communicate and bond with each other. This field is essential since proteins perform numerous cellular tasks. Understanding these interactions can reveal the molecular mechanisms of diseases.
Studying interactions involves a variety of techniques like surface plasmon resonance and mass spectrometry. These methods help quantify how tightly a protein binds to its partner, which is critical in drug design. By evaluating the strength and rate of these bindings, researchers can manipulate these interactions for therapeutic purposes. Ultimately, protein interaction analysis helps bridge the gap between molecular biology and medicine.

Association and Dissociation Constants

Association and dissociation constants are fundamental concepts in molecular biology. The association constant, often denoted as \( k_a \), reflects how likely a protein will bind to another molecule. In contrast, the dissociation constant, \( K_d \), indicates how readily a complex will disassemble.
\( K_d \) is often used to describe a protein's affinity for a ligand. Lower \( K_d \) values suggest stronger binding, meaning the molecules are more stable together. The dissociation rate, \( k_d \), can be calculated using the formula \( K_d = \frac{k_d}{k_a} \). This calculation is vital in developing inhibitors or activators in drug therapy. Scientists can adjust these constants to control biological processes effectively.

Molecular Biology

Molecular biology involves understanding the molecular mechanisms within cells. It focuses on the interaction and regulation of genetic materials. This field has led to breakthroughs such as gene editing and cloning.
At the heart of molecular biology is the study of macromolecules, including DNA, RNA, and proteins. Proteins, being the workhorses of the cell, are the primary targets in molecular biology studies. By understanding how proteins interact and their kinetics, researchers can elucidate the entire biochemistry of living organisms. Molecular biology has reshaped our comprehension of life and continues to be a cornerstone of modern biological research.