🧬 Interactive Biochemistry Guide

How to use this roadmap

1. Map this template to your university catalog and swap semesters for transfer credits.
2. Use the General Chemistry, Organic Chemistry, and Virtual Lab pages for refresher content tied to each milestone.
3. Track saved views & experiment results locally as you complete lab assignments.

⚡ Critical Concepts to Master

Key Thermodynamics Relationships

⚡ Critical Concepts to Master

⚡ Critical Concepts to Master

⚡ Critical Concepts to Master

⚡ Critical Concepts to Master

🎯 Quick Reference: Amino Acid Classification

⚡ Critical Concepts to Master

Quick Reference — Method Validation

Practical study tips:

• Work through example calculations: calibration curves, dilution series, RSD% and recovery.
• Practice by designing a method: sample prep → instrument → calibration → QC → report.
• Use instrument manuals & vendor application notes for instrument-specific tricks (LC-MS, ICP-MS).

⚡ Critical Concepts to Master

Michaelis-Menten Equation

Glycolysis Net Equation

⚡ Critical Concepts to Master

🎯 Quick Reference: Genetic Code Key Points

⚡ Critical Concepts to Master

⚙️ Scope of Physical Chemistry

Physical chemistry applies calculus, differential equations, linear algebra, and probability theory to describe how matter behaves at the molecular and atomic scale. It provides the mathematical foundation underlying thermodynamics, kinetics, quantum chemistry, and spectroscopy.

📐 Mathematical Toolkit Used

• Multivariable calculus: total vs partial derivatives, Jacobians
• Differential equations: reaction kinetics, diffusion
• Linear algebra: eigenvalues, diagonalization, basis transformations
• Integral calculus: partition functions, expectation values
• Optimization: equilibrium from energy minimization

📘 Full Derivation: Maxwell Relation from the Gibbs Free Energy

We derive a Maxwell relation using exact differentials and the equality of mixed partial derivatives. This connects entropy and volume — two experimentally measurable quantities.

Step 1: Definition of Gibbs Free Energy

$$ G = U + PV - TS $$ Take the total differential: $$ dG = dU + P\,dV + V\,dP - T\,dS - S\,dT $$ Using the first law for a closed system: $$ dU = T\,dS - P\,dV $$ Substitute into \( dG \): $$ dG = (T\,dS - P\,dV) + P\,dV + V\,dP - T\,dS - S\,dT $$ Simplify: $$ dG = V\,dP - S\,dT $$

Step 2: Identify Natural Variables

Since \( G = G(T,P) \): $$ dG = \left(\frac{\partial G}{\partial T}\right)_P dT + \left(\frac{\partial G}{\partial P}\right)_T dP $$ Comparing coefficients: $$ \left(\frac{\partial G}{\partial T}\right)_P = -S \quad\text{and}\quad \left(\frac{\partial G}{\partial P}\right)_T = V $$

Step 3: Equality of Mixed Partial Derivatives

Because \( G \) is a state function: $$ \frac{\partial}{\partial P} \left(\frac{\partial G}{\partial T}\right)_P = \frac{\partial}{\partial T} \left(\frac{\partial G}{\partial P}\right)_T $$ Substitute the expressions for entropy and volume: $$ \left(\frac{\partial (-S)}{\partial P}\right)_T = \left(\frac{\partial V}{\partial T}\right)_P $$ Final Maxwell Relation: $$ \boxed{ \left(\frac{\partial S}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_P } $$

Physical Meaning

• Relates entropy changes to measurable thermal expansion
• Avoids direct entropy measurement
• Used in response functions and real-gas corrections

⚡ Critical Concepts to Master

⚡ Critical Concepts to Master

⚡ Critical Concepts to Master

Study tips:

• Draw replication forks, transcriptional units and the ribosomal cycle by hand to lock steps into memory.
• Practice pedigree and Hardy–Weinberg problems until you can translate a text problem into symbolic equations quickly.
• Use real data examples (PCR gels, sequencing reads) to connect conceptual knowledge with experimental outputs.

📝 Test Your Knowledge

Practice problems covering all major topics with detailed step-by-step solutions.

Show Answer

Answer: pH = 4.54

Solution:

Use the Henderson-Hasselbalch equation:

pH = pKa + log([A⁻]/[HA])

pH = 4.76 + log(0.30/0.50)

pH = 4.76 + log(0.6)

pH = 4.76 + (-0.22)

pH = 4.54

Show Answer

Answer: 1.2044 × 10²⁴ molecules

Solution:

From the equation: 2H₂ + O₂ → 2H₂O

2 moles of H₂ produce 2 moles of H₂O

1 mole = 6.022 × 10²³ molecules

Therefore, 2 moles of H₂O = 2 × 6.022 × 10²³ = 1.2044 × 10²⁴ molecules

Show Answer

Answer: ~30-32 ATP per glucose

Detailed Calculation:

Glycolysis:

• 2 ATP (substrate-level)

• 2 NADH → 5 ATP (2.5 ATP per NADH with malate-aspartate shuttle)

Pyruvate → Acetyl-CoA (×2):

• 2 NADH → 5 ATP

Citric Acid Cycle (×2):

• 6 NADH → 15 ATP (2.5 ATP each)

• 2 FADH₂ → 3 ATP (1.5 ATP each)

• 2 GTP → 2 ATP

Total: 2 + 5 + 5 + 15 + 3 + 2 = 32 ATP

Note: Actual yield may vary (30-32 ATP) due to shuttle efficiency and proton leak.

Show Answer

Answer: ΔG° = -25.2 kJ/mol

Solution:

Use: ΔG° = -RT ln(Keq)

ΔG° = -(8.314 J/mol·K)(298 K) × ln(2.5 × 10⁴)

ΔG° = -2477.6 × ln(25000)

ΔG° = -2477.6 × 10.127

ΔG° = -25,088 J/mol

ΔG° = -25.2 kJ/mol

Note: Negative ΔG° indicates the reaction is thermodynamically favorable.

Show Answer

Answer: 8 stereoisomers

Solution:

Use the formula: Maximum stereoisomers = 2ⁿ

where n = number of chiral centers

2³ = 8 stereoisomers

This includes 4 pairs of enantiomers. The actual number may be less if the molecule has meso compounds.

Show Answer

Answer: Zwitterion form (⁺H₃N-CH₂-COO⁻)

Solution:

At pH 7.4:

• pH > pKa₁ (2.34) → carboxyl group is deprotonated (COO⁻)

• pH < pKa₂ (9.60) → amino group is protonated (NH₃⁺)

Result: ⁺H₃N-CH₂-COO⁻ (zwitterion)

The zwitterion is the predominant form of amino acids at physiological pH.

Show Answer

Answer: v = 75 μmol/min

Solution:

Use Michaelis-Menten equation: v = (Vmax × [S]) / (Km + [S])

v = (100 μmol/min × 6.0 mM) / (2.0 mM + 6.0 mM)

v = (600) / (8.0)

v = 75 μmol/min

Note: At [S] = 3×Km, velocity is 75% of Vmax.

Show Answer

Answer: 106 ATP

Detailed Calculation:

β-Oxidation (7 cycles for 16C):

• 7 FADH₂ → 10.5 ATP (1.5 ATP each)

• 7 NADH → 17.5 ATP (2.5 ATP each)

• Produces 8 Acetyl-CoA

Citric Acid Cycle (8 Acetyl-CoA):

• 24 NADH → 60 ATP

• 8 FADH₂ → 12 ATP

• 8 GTP → 8 ATP

Activation cost: -2 ATP

Total: 10.5 + 17.5 + 60 + 12 + 8 - 2 = 106 ATP

Show Answer

Answer: 3'-TACGATCG-5'

Solution:

Remember base pairing rules: A pairs with T, G pairs with C

Original: 5'-ATGCTAGC-3'

Step 1: Find complementary bases

A→T, T→A, G→C, C→G, T→A, A→T, G→C, C→G

Step 2: Write in antiparallel direction (3' to 5')

Complementary: 3'-TACGATCG-5'

Show Answer

Answer: Met-Ala-Lys

Solution:

Read the mRNA in triplets (codons) from 5' to 3':

AUG → Methionine (Met) - START codon

GCU → Alanine (Ala)

AAA → Lysine (Lys)

UAA → STOP codon (translation terminates)

Peptide: Met-Ala-Lys

Show Answer

Answer: GPCR → Gs protein → Adenylyl cyclase → cAMP → PKA

Signaling Cascade:

1. Hormone binds to GPCR

2. GPCR activates Gs protein (G-protein)

3. Gs protein activates adenylyl cyclase

4. Adenylyl cyclase converts ATP → cAMP (second messenger)

5. cAMP activates Protein Kinase A (PKA)

6. PKA phosphorylates target proteins

This cascade amplifies the signal - one hormone molecule can generate many cAMP molecules!

Show Answer

Answer: The chiral center is R

Steps to determine R/S configuration:

1. Assign priorities to the four substituents around the chiral center (highest priority to lowest)

2. Orient the molecule so that the lowest priority group is pointing away from you (into the page)

3. Trace a path from highest priority to second highest to third highest

4. If the path is clockwise, it's R; if counterclockwise, it's S

In this case, the path from NH2 → COOH → CH2SH is clockwise, so the configuration is R.

Show Answer

Answer: O2

Explanation:

Oxygen (O2) is the final electron acceptor in the electron transport chain. It accepts electrons from the electron transport chain and combines with protons to form water (H2O).

Show Answer

Answer: Pentose Phosphate Pathway

Explanation:

The Pentose Phosphate Pathway is responsible for generating NADPH (used in reductive biosynthesis) and ribose-5-phosphate (used in nucleotide synthesis).

Show Answer

Answer: Phosphofructokinase (PFK)

Explanation:

Phosphofructokinase (PFK) is the key regulatory enzyme in glycolysis. It catalyzes the phosphorylation of fructose-6-phosphate to fructose-1,6-bisphosphate, which is the committed step in glycolysis and is highly regulated by cellular energy status.

Show Answer

Answer: DNA polymerase

Explanation:

DNA polymerase is the enzyme responsible for synthesizing the new DNA strand by adding nucleotides to the 3' end during DNA replication. It ensures accurate copying of the genetic material.

Show Answer

Answer: Uracil

Explanation:

Uracil is the nucleotide found in RNA but not in DNA. In DNA, thymine is present instead of uracil.

Show Answer

Answer: Lipid synthesis and detoxification

Explanation:

The Smooth Endoplasmic Reticulum (SER) is involved in the synthesis of lipids, metabolism of carbohydrates, and detoxification of drugs and poisons in the cell.

Show Answer

Answer: Protein modification and sorting

Explanation:

The Golgi apparatus modifies, sorts, and packages proteins and lipids for secretion or delivery to other organelles.

Show Answer

Answer: Competitive inhibition

Explanation:

Competitive inhibition can be overcome by increasing substrate concentration because the inhibitor competes with the substrate for the active site of the enzyme.

Show Answer

Answer: Non-competitive inhibition

Explanation:

Non-competitive inhibition decreases the Vmax because the inhibitor binds to an allosteric site, not the active site, and this binding reduces the overall number of active enzyme molecules. However, it does not affect the Km because the affinity of the enzyme for the substrate remains unchanged.

Show Answer

Answer Summary:

Explanation:

(a) Starting from the differential rate law:

−d[A]/[A] = k dt

Integrating both sides:

∫_[A]0^[A] −d[A]/[A] = ∫₀^t k dt

ln([A]₀/[A]) = kt

(b) When [A] = 0.25[A]₀:

ln([A]₀ / 0.25[A]₀) = kt

ln(4) = kt

t = ln(4) / 0.693 ≈ 2.00 minutes

(c) The half-life is obtained by setting [A] = 0.5[A]₀:

ln(2) = kt_1/2

t_1/2 = ln(2) / k

Since [A]₀ cancels during integration, the half-life is independent of the initial concentration — a defining feature of first-order kinetics.

Show Answer

Answer Summary:

Explanation:

(a) Pressure is obtained from the Helmholtz free energy via:

P = −(∂A/∂V)_T

Taking the derivative:

∂A/∂V = −nRT /(V − nb) + a n² / V²

P = nRT /(V − nb) − a n² / V²

(b) Rearranging:

(P + a n² / V²)(V − nb) = nRT

which is the van der Waals equation of state.

(c) Mechanical stability requires:

(∂P/∂V)_T < 0

Differentiating:

(∂P/∂V)_T = −nRT /(V − nb)² + 2a n² / V³

Mechanical instability occurs when this derivative equals zero, defining the spinodal curve of the real gas.

Show Answer

Answer: 1/4

Explanation:

When two heterozygous tall plants (Tt) are crossed, the possible genotypes of offspring are TT, Tt, tT, and tt. Only the tt genotype results in short plants. Since there are 4 equally likely outcomes and only 1 is short (tt), the probability is 1/4.

⚡ Critical Concepts to Master

What this section teaches

The core calculus skills used across thermodynamics, kinetics, statistical mechanics and quantum chemistry: limits & series, single-variable derivatives & integrals, multivariable calculus (partials, total diffs), ODEs/PDEs, transforms (Laplace/Fourier), approximation methods (Taylor, saddle-point, Stirling), and numerical solvers (Runge–Kutta, Newton–Raphson).

Worked Example — Partition function → mean energy

Partition function \( Z(\beta)=\sum_i e^{-\beta E_i} \) (or integral for continuous spectrum). The mean energy: \[ \langle E\rangle = -\frac{\partial}{\partial \beta}\ln Z(\beta). \] Technique used: differentiate log of integral/sum; sometimes evaluate using approximation (saddle point or integral approximation).

Worked Example — First-order kinetics

Rate law: \( \frac{d[A]}{dt} = -k [A] \). Separate variables: \[ \frac{d[A]}{[A]} = -k\, dt \quad\Rightarrow\quad \ln [A] - \ln [A]_0 = -kt, \] so \( [A](t) = [A]_0 e^{-kt} \). Use linearization (\(\ln [A]\) vs \(t\)) to find \(k\).

Thermodynamics — Partial derivatives & Maxwell relations

Use total differentials and equality of mixed partial derivatives to derive Maxwell relations. Example (Gibbs): \( dG = V\,dP - S\,dT \) so \( \left(\frac{\partial S}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_P \). See the physical chemistry section for the derivations and applications of this derivation.

Numerical Methods (practical)

• Root finding: Newton–Raphson for nonlinear equations (watch initial guess and convergence)
• ODE integrators: Euler (simple), but use 4th-order Runge–Kutta (RK4) for accuracy; stiff solvers (BDF) for stiff kinetics
• Numerical integration: Simpson’s rule, Gaussian quadrature for high-accuracy integrals
• Eigenvalue problems: use library solvers (numpy.linalg.eig) for matrices in quantum problems

Practice problems (try these)

1. Show the integrated form for a 2nd-order reaction: \( \frac{d[A]}{dt} = -k[A]^2 \).
2. Use Stirling's approximation to show \( \ln \binom{N}{m} \) ≈ expression for large N (stat mech combinatorics).
3. Solve the 1D diffusion equation \( \partial_t c = D \partial_{x}^2 c \) with initial δ-function (use Fourier transform).
4. Derive expression for average energy of a harmonic oscillator using partition function.

Show quick answers / hints

• 2nd-order: separate to get \( \frac{1}{[A]} - \frac{1}{[A]_0} = kt \).
• Stirling hint: start with \( \ln N! \) and approximate integral of \( \ln x \).
• Diffusion: solution is Gaussian \( c(x,t) = \frac{1}{\sqrt{4\pi D t}} e^{-x^2/(4Dt)} \).
• Harmonic oscillator: discrete energies \( E_n = \hbar\omega(n+\tfrac12) \) → geometric series for Z → differentiate ln Z.

Study tips:

• Work derivations by hand — that builds intuition for which approximation to use.
• Link math to measured quantities (e.g., how a partial derivative becomes a measurable coefficient).
• Practice numerical solutions in Python (RK4, SciPy solvers) for kinetics problems you can't solve analytically.

This project is an interactive, web-based biochemistry platform designed to visualize molecular structures and reinforce core chemistry and biochemistry concepts through hands-on exploration.

The goal of this project was to build a technically non-trivial frontend application that demonstrates strong JavaScript fundamentals, interactive graphics, and thoughtful UI state management while leveraging my academic background in biochemistry.

My Role & Contributions

• Designed and implemented the entire frontend architecture as a solo developer
• Built an interactive 3D molecular viewer using Three.js
• Implemented dynamic UI components, tab-based navigation, and expandable content cards
• Added persistent client-side state using LocalStorage for saved molecular views
• Integrated MathJax to render chemical equations and mathematical expressions
• Ensured responsive layout and accessible UI patterns across screen sizes
• Virtual Lab that uses a custom made engine to simulate enzyme kinetics and molecular interactions

Technical Focus

• Vanilla JavaScript (ES6+), HTML5, CSS3
• 3D scene setup, camera controls, and animation loops
• DOM-driven state management without external frameworks
• Separation of concerns between rendering logic, UI, and data

Why This Project

This project highlights my ability to translate complex scientific concepts into usable software products. It demonstrates problem-solving, self-directed learning, and end-to-end ownership of a client-side application, from design and architecture to implementation and polish.

Created by Grant Culbertson — Biochemistry graduate, frontend-focused software developer.

Central repositories, tools, and learning platforms

Authoritative references, databases, visualization tools, protocols, and practice resources aligned with the subjects on this site.