Lecture 4: DNA Quantification, Protein Quantification, and Enzyme Assays

Laws of Absorption and Spectral Properties of Light

• Energy Levels and Quantization:

  • Molecules possess individual sets of energy levels derived from their chemical bonds and atomic masses.

  • These energy levels result in unique spectral properties, which are utilized to identify specific compounds.

  • Light interacts with the electronic and vibrational modes of molecules, leading to quantization.

  • Absorption occurs only when light energy exactly corresponds to the energy required for a transition from one state to another.

• Laws of Transmittance ($T$):

  • Transmittance is the measure of light that passes through a sample.

  • When light of a specific wavelength ($\lambda$) passes through a path length ($b$) of a solution at a set concentration, a defined proportion of light is absorbed.

  • Incident light energy is denoted as $I_0$.

  • Transmitted light energy (after passing through the solution) is denoted as $I$.

  • The fraction of light transmitted is expressed as: $T = \frac{I}{I_0}$.

• Laws of Absorbance ($A$):

  • Absorbance is the amount of light absorbed by the sample.

  • For homogeneous samples, each successive layer absorbs the same fraction of incident light as the preceding layer.

  • Transmittance decreases exponentially as the concentration of the colored compound or the light path length increases.

• Beer’s Law (The Beer-Lambert Law):

  • Light absorption is directly proportional to the number of molecules present in the light path.

  • The mathematical description of the fractional loss of light involves exponential decay of transmitted light relative to path length and concentration.

  • Primary Equation: $A = \epsilon bc$ (also expressed as $A = \epsilon cl$).

  • Relationship to Transmittance: $A = -\log(T)$.

  • Relationship of Transmittance to Absorbance: $T = 10^{-A}$.

  • Variables Defined:

    • $A$: Absorbance or Optical Density (e.g., $OD_{600}$).

    • $\epsilon$: Molar extinction coefficient (measured in $M^{-1}\,cm^{-1}$ or $L\,mol^{-1}$). This represents the absorbance of a $1\,M$ solution with a path length of $1\,cm$.

    • $b$: Path length (usually $1\,cm$ due to cuvette size).

    • $c$: Concentration (measured in $mol/L$).

    • $I_0$: Initial light intensity.

    • $I$: Final light intensity.

• Calculation Examples:

  • If Transmittance is $30\%$, $A = -\log(0.3) = 0.52$.

  • If Absorbance is $0.52$, $T = 10^{-0.52} = 0.30$ (or $30\%$).

  • If $\epsilon = 40,000$, $b = 1\,cm$, and $A = 0.3$: $0.3 = 40,000 \times 1 \times c \rightarrow c = 0.0000075$ or $7.5 \times 10^{-6}\,M$.

Relevant Absorbance Wavelengths and Standards

• Critical Wavelengths ($\lambda$):

  • $230\,nm$: Detection of organic contaminants.

  • $260\,nm$: Determination of DNA and RNA concentration.

  • $280\,nm$: Determination of protein concentration.

  • $340\,nm$: CDNB Assay; monitoring NADH in Pyruvate Kinase or Lactate Dehydrogenase assays.

  • $465\,nm$ and $665\,nm$: Chlorophyll absorption (high molar absorptivity: $\epsilon = 10^5\,M^{-1}\,cm^{-1}$).

  • $595\,nm$: Bradford Assay for protein concentration (color change to blue).

  • $600\,nm$: Bacterial growth monitoring in LB media.

  • $750\,nm$: Lowry Assay for protein concentration.

DNA and RNA Quantification

• DNA Quantification Principles:

  • DNA absorbance maximum occurs at $260\,nm$.

  • Standard Values:

    • $A_{260} = 1.0$ corresponds to $50\,\mu g/ml$ dsDNA.

    • $A_{260} = 1.0$ corresponds to $35\,mg/ml$ ssDNA (ssDNA absorbs more light than dsDNA). 2 strands = 2 × 35 mg/mL = 70 mg/mL for entire structure effect

  • Measurement Methods:

    • Spectrophotometer: Requires $10X$ or $100X$ dilution.

    • Nanodrop: Requires only $1\,\mu l$ sample.

    • The process is non-destructive to the sample.

• DNA Purity Assessment:

  • Purity is determined by the ratio of absorbance at $260\,nm$ to $280\,nm$ ($A_{260}:A_{280}$).

  • Adequately pure samples have a ratio > 1.5.

  • Equation for calculation provided in slide: $140.4 = 50\,ng/\mu l \times 1.5$.

• RNA Quantification Principles:

  • RNA quantification is nearly identical to DNA quantification using spectrophotometry or Nanodrop.

  • Standard Value: $A_{260} = 1.0$ corresponds to $40\,\mu g/ml$.

  • RNA Purity Assessment:

    • $A_{260}:A_{280}$ ratio is used.

    • Typically must be greater than $1.8$.

  • Alternative Techniques for Cellular RNA:

    • Gel electrophoresis.

    • Northern blotting.

    • RT-qPCR.

Protein Quantification Techniques

• Overview of Methods:

  • Absorbance at $280\,nm$.

  • Amino acid analysis.

  • Chromogenic/colorimetric assays (Bradford, Biuret, Lowry, BCA).

• Absorbance at 280 nm:

  • Max absorbance occurs due to ringed amino acids (Tryptophan and Tyrosine).

  • Extinction Coefficient Calculation ($\epsilon_{280}$):

    • Depends on amino acid sequence.

    • Formula: $\epsilon=(\#protein1)\times5500+(\#protein2)\times1490$

    • $\epsilon=(\#Trp)\times5500+(\#Tyr)\times1490$

  • Limitations:

    • High variability based on absence/presence of Trp or Tyr.

    • Sample must be pure (nucleic acids absorb strongly at $280\,nm$).

    • Cannot be used for lysates or complex mixtures.

    • Requires quartz or UV-compatible plastic cuvettes.

    • Low detection range (< 0.1\,mg/ml).

  • DNA Contamination in protein Correction Formula:

    • $\text{Protein (mg/ml)} = (1.55 \times A_{280}) - (0.76 \times A_{260})$.

• Amino Acid Analysis:

  • Most reliable method for pure protein concentration.

  • Process: Acid hydrolysis, separation of amino acids, and HPLC quantification.

  • Drawbacks: Purity essential, requires special facilities, $2-5$ day turnaround, and costs approximately $250\text{ USD}$ per sample.

• Colorimetric Methods:

  • Measuring color intensity: more protein equals more intense blue color.

  • Measured in the $595-750\,nm$ range.

  • These are not the wavelengths for “blue”, but the wavelength of colors that are absorbed by blue

Specific Colorimetric Assays for Protein

• Bradford Assay:

  • Uses Coomassie Brilliant Blue dye.

  • Color shift: Red ($465\,nm$ ) to Blue ($595\,nm$) upon protein binding.

  • Mechanism: Dye forms noncovalent (van der Waals) complexes with proteins relating to positive charges, hydrophobic interactions, and specific amino acids (Phe, Tyr, Trp, Lys, Arg, His, Pro) and N-/C-termini.

  • Advantages: Fast, sensitive, compatible with most buffers and chaotropic reagents (6 M guanidine-HCl, 8 M urea).

  • Disadvantages: Nonlinear response (requires standard curve), sequence-dependent variability, incompatible with detergents, stains cuvettes.

  • Detection Range: $0.2$ to $2\,mg/ml$.

• CB-X Assay (Bradford)

  • Acetone precipitation, resolubilization

  • Compatible with all reagents

  • Eliminates inhibitory effect of detergents

Copper Based Assays

• Biuret Assay:

  • Alkaline conditions: $Cu^{2+}$ binds peptide nitrogen.

  • Absorbance wavelength: $550\,nm$.

  • Pros/Cons: Low amino acid sequence interference; not very sensitive; sensitive to Tris and ammonia buffers.

• Lowry Assay:

  • Two-step Process:

    1. Copper binds peptide bonds in basic conditions ($Cu^{2+} \rightarrow Cu^+$).

    2. $Cu^+$ reacts with Folin reagent (phosphomolybdic-phosphotungstic reagent), which reduces to blue.

  • Absorbance wavelength: $750\,nm$.

  • Advantages: Inexpensive, highly sensitive ($10-20X$ more than $A_{280}$, $100X$ more than Biuret).

  • Disadvantages: Time-consuming, unstable reagents, nonlinear response, sensitive to detergents, lipids, and pH.

  • Detection Range: $0.1$ to $1\,mg/ml$.

• DC Protein Assay:

  • A modified "Detergent Compatible" Lowry assay.

  • Upper detection limit: $~1.5\,mg/ml$.

• BCA Assay:

  • Similar to Lowry ($Cu^{2+}\rightarrow Cu^+$) but uses Bicinchoninic acid (BCA) instead of Folin reagent.

  • Mechanism: Two molecules of BCA chelate to one copper ion.

  • Absorbance: Purple color at $560\,nm$.

  • Advantages: Stable reagents, detergent compatible, lowest protein-to-protein variation ($15\%$), highly sensitive ($3.4\,ng/ml$ detection).

  • Disadvantages: Expensive, sensitive to carbohydrates, lipids, and glycerol.

The Standard Curve and Protein Unknowns

• Necessity of Standard Curves:

  • Protein absorbance does not correlate linearly with concentration across all ranges.

  • Relationship is established using Bovine Serum Albumin (BSA) or Bovine Gamma Globulin (BGG) as a standard.

  • Plotting data yields a curve equation

  • The curve follows the equation: $y = mx + b$.

  • Example regression: $y = 0.006x + 0.0043$ with $R^2 = 0.9991$.

  • Important: Users must not extrapolate beyond the measured range of the curve.

Enzyme Fundamentals and Classification

• Key Characteristics of Enzymes:

  • Lower the activation energy of a reaction.

  • Increase rate of reaction without shifting equilibrium position.

  • Highly specific for substrates and products.

  • Activity can be regulated by substrates or other molecules.

  • Most are proteins, though some RNA enzymes (ribozymes) exist.

• Enzyme Classification System:

  • 1. Oxidoreductases: Catalyze oxidation-reduction reactions (e.g., Dehydrogenases, Oxidases, Reductases).

  • 2. Transferases: Transfer functional groups (e.g., Kinases, Aminotransferases, Methyltransferases).

  • 3. Hydrolases: Cleave bonds using water (e.g., Esterases, Peptidases, Lipases).

  • 4. Lyases ("Synthases"): Cleave/add groups to double bonds (e.g., C-C Lyases).

  • 5. Isomerases: Rearrangement of molecules (e.g., Epimerases, cis-trans Isomerases).

  • 6. Ligases ("Synthetases"): Join two molecules using ATP (e.g., C-N Ligases).

Enzyme Mechanism

• Chemical Equilibrium:

  • The point where net change between forward and reverse reactions is zero.

  • Enzymes accelerate reaching equilibrium but do not change the ratio of products to reactants.

  • In the absence of enzyme, a reaction may take hours or days to reach the equilibrium position, whereas on addition of the enzyme the equilibrium position may be reached in less than 1 second

• Activation Energy and Transition State (TS):

  • Transition State: Unstable chemical form with the highest free energy, halfway between substrate and product.

  • Activation Energy: The barrier that must be overcome for a reaction to proceed.

  • Enzymes stabilize the TS, thereby lowering activation energy.

• Free Energy ($\Delta G$) and Coupling:

  • Measure of energy difference between substrates and products.

  • $\Delta G$ Negative: Energetically favorable, spontaneous.

  • $\Delta G$ Positive: Unfavorable, requires energy input (usually ATP).

  • ATP Hydrolysis: $ATP + H_2O \rightarrow ADP + P_i$ ($\Delta G = -7.3\,kcal/mol$). Favorable due to resonance, relieved repulsion, and increased entropy. Used to drive less energetically favorable reactions

• Enzyme Active Site:

  • Cleft or crevice on the surface, formed by amino acids that may be distant in the linear sequence.

  • Binding involves weak interactions: van der Waals, H-bonds, ionic bonds.

  • Usually a relatively small part of the whole enzyme molecule and is a three-dimensional entity formed by amino acids that can lie far apart in the linear polypeptide chain

• Enzyme-Substrate Models:

  • Lock and Key (Emil Fischer, 1894): Substrate and active site are perfectly complementary.

  • Induced Fit (Daniel E. Koshland, 1958): Binding induces a conformational change in the enzyme to simulate the transition state.

Lock and Key

Induced Fit

Case Studies in Enzyme Structure and Function

• Carbonic Anhydrase:

  • Reaction: $CO_2 + H_2O \rightarrow HCO_3^- + H^+$.

  • Rate: $1\,million$ reactions/second (diffusion-limited).

  • Mechanism: Includes a Zinc cofactor stabilized by His94, His96, and His119.

  • Inhibitors: NSAIDs (Aspirin, Ibuprofen) and COX-2 inhibitors may block CA, serving as potential treatments for glaucoma or cancer.

• Coenzyme A Biosynthesis Enzymes:

  • PANK (2.7.1.33): Pantothenate Kinase, used in the conversion of Pantothenate to Phosphopantothenate.

  • PPCS (6.3.2.5): Phosphopantothenoylcysteine Synthetase.

  • PPCDC (4.1.1.36): Phosphopantothenoylcysteine Decarboxylase.

  • PPAT (2.7.7.3): Phosphopantetheine Adenylyltransferase (stabilizes PPi, H-bonding to ATP).

  • DPCK (2.7.1.24): Dephosphocoenzyme A Kinase. Alignment of 25 bacterial DPCKs shows 19 identically conserved residues including Walker A and Walker B motifs.

Amino acids that are conserved between homologs indicate;

• their importance in the protein’s structure or function

• Mutations can’t occur at this location in the protein’s sequencebecause such changes are likely to disrupt crucial interactions necessary for catalytic activity and structural integrity.

Enzyme Kinetics and Inhibition

Saturation: The rate asymptotically approaches a limiting value, called Vmax, becoming zero-order with respect to substrate concentration (not varying with concentration)

• Reaction Velocity:

  • First Order: Rate varies with substrate concentration.

  • Zero Order: Rate is maximal ($V_{max}$) and independent of concentration (saturation).

• Enzyme Rate

  • Rate: inherent velocity of the enzyme affected by concentrations of enzyme/substrates, temperature, pH, coenzymes

  • Decrease in reaction rate due to approach in equilibrium, substrate depletion, product inhibition, loss of function, inactivation of enzyme

• Michaelis-Menten Model:

  • Equation: Equal to the sum of the rates of breakdown of ES complex over its rate of formation

  • A measure of the stability of the ES complex (or the affinity of an enzyme for its substrate)

    • $K_m$ (Michaelis Constant): Substrate concentration at which velocity is half of $V_{max}$.

    • Low $K_m =$ strong binding/high affinity; High $K_m =$ weak binding.

  

  • Catalytic efficiency is better measure of enzyme activity and is measured as $k_{cat}/K_m$.

• Lineweaver-Burk Plot (Double Reciprocal):

  • Equation: $𝑣=\frac{(𝑉_{max}[𝑆])}{\left(𝐾_{𝑚}+[𝑆]\right)}$ .

  • Slope: $K_m/V_{max}$.

  • Y-intercept: $1/V_{max}$.

  • X-intercept: $-1/K_m$.

• Enzyme Inhibition Types:

  • Competitive: Inhibitor binds to the active site; prevents substrate binding. $V_{max}$ stays same, $K_m$ increases. On graph lines intersect at same y-intercept which = $V_{\max}$

  • Noncompetitive (Allosteric): Inhibitor binds elsewhere, altering active site structure. Substrate may still bind, but reaction is hindered. $V_{max}$ decreases, $K_m$ stays same. On graph all lines intersect at different x-intercepts which = $K_{m}$

Enzyme Assay Applications

Enzyme assays involve measuring the conversion of substrate to product to determine rates of catalyzed reactions

• High substrate concentrations are used to measure initial rate

• NADH/NADPH, which absorb light at 340 nm, are often used to monitor the progress of an enzyme reaction

• Purpose: Assess activity of mutants, determine kinetics, study drugs, diagnose deficiencies.

• CDNB Assay:

  • Measures Glutathione-S-Transferase (GST) activity.

  • GST removes toxins from cells.

  • The CDNB enzyme assay calculates GST’s reaction velocity/activity

  • Track GST during protein purification

• Coupled Continuous Assay (PK-LDH):

  • Used for reactions that hydrolyze ATP to produce ADP.

  • Pyruvate Kinase-Lactate Dehydrogenase Assay: Glycerol Kinase is assayed continuously by measuring the decrease in absorbance at 340 nm as NADH is converted to NAD+

  1. Glycerol + ATP $\xrightarrow{GK}$ Glycerophosphate + ADP

  2. ADP + Phosphoenolpyruvate $\xrightarrow{PK}$ ATP + Pyruvate

  3. Pyruvate + NADH $\xrightarrow{LDH}$ Lactate + NAD+

  • Detection: Measured by a decrease in absorbance at $340\,nm$ (NADH consumption).

• Kinase Assay:

  • Add "Hot" ATP (ATP radiolabeled with radioactive phosphate $^{32}P$).

  • Target protein is phosphorylated; sample is run on gel and analyzed via autoradiography or scintillation counter.

  • Analyze sample (western, sequencing, scintillator)

  • Can be used to study signaling pathways or test inhibitors

  • Modern assays avoid radioactive ATP and use compounds that emit light