Calculations for Molecular Biology and Biotechnology

1 Scientific Notation and Metric PrefixesIntroduction1.1 Significant Digits1.1.1 Rounding Off Significant Digits in Calculations1.2 Exponents and Scientific Notation1.2.1 Expressing Numbers in Scientific Notation1.2.2 Converting Numbers from Scientific Notation to Decimal Notation1.2.3 Adding and Subtracting Numbers Written in Scientific Notation1.2.4 Multiplying and Dividing Numbers Written in Scientific Notation1.3 Metric Prefixes1.3.1 Conversion Factors and Canceling TermsChapter Summary2 Solutions, Mixtures, and MediaIntroduction2.1 Calculating Dilutions – A General Approach2.2 Concentrations by a Factor of X2.3 Preparing Percent Solutions2.4 Diluting Percent Solutions2.5 Moles and Molecular Weight – Definitions2.5.1 Molarity2.5.2 Preparing Molar Solutions in Water with Hydrated Compounds2.5.3 Diluting Molar Solutions2.5.4 Converting Molarity to Percent2.5.5 Converting Percent to Molarity2.6 Normality2.7 pH2.8 pKa and the Henderson – Hasselbalch EquationChapter Summary3 Cell Growth3.1 The Bacterial Growth Curve3.1.1 Sample Data3.2 Manipulating Cell Concentration3.3 Plotting OD550 vs. Time on a Linear Graph3.4 Plotting the Logarithm of OD550 vs. Time on a Linear Graph3.4.1 Logarithms3.4.2 Sample OD550 Data Converted to Logarithm Values3.4.3 Plotting Logarithm OD550 vs. Time3.5 Plotting the Logarithm of Cell Concentration vs. Time3.5.1 Determining Logarithm Values3.6 Calculating Generation Time3.6.1 Slope and the Growth Constant3.6.2 Generation Time3.7 Plotting Cell Growth Data on a Semilog Graph3.7.1 Plotting OD550 vs. Time on a Semilog Graph3.7.2 Estimating Generation Time from a Semilog Plot of OD550 vs. Time3.8 Plotting Cell Concentration vs. Time on a Semilog Graph3.9 Determining Generation Time Directly from a Semilog Plot of Cell Concentration vs. Time3.10 Plotting Cell Density vs. OD550 on a Semilog Graph3.11 The Fluctuation Test3.11.1 Fluctuation Test Example3.11.2 Variance3.12 Measuring Mutation Rate3.12.1 The Poisson Distribution3.12.2 Calculating Mutation Rate Using the Poisson Distribution3.12.3 Using a Graphical Approach to Calculate Mutation Rate from Fluctuation Test Data3.12.4 Mutation Rate Determined by Plate Spreading3.13 Measuring Cell Concentration on a HemocytometerChapter SummaryReferences4 Working with BacteriophagesIntroduction4.1 Multiplicity of Infection (moi)4.2 Probabilities and Multiplicity of Infection (moi)4.3 Measuring Phage Titer4.4 Diluting Bacteriophage4.5 Measuring Burst SizeChapter Summary5 Nucleic Acid Quantification5.1 Quantification of Nucleic Acids by Ultraviolet (UV) Spectroscopy5.2 Determining the Concentration of Double-Stranded DNA (dsDNA)5.2.1 Using Absorbance and an Extinction Coefficient to Calculate Double-Stranded DNA (dsDNA) Concentration5.2.2 Calculating DNA Concentration as a Millimolar (mM) Amount5.2.3 Using PicoGreen® to Determine DNA Concentration5.3 Determining the Concentration of Single-Stranded DNA (ssDNA) Molecules5.3.1 Single-Stranded DNA (ssDNA) Concentration Expressed in μg/mL5.3.2 Determining the Concentration of High-Molecular-Weight Single-Stranded DNA (ssDNA) in pmol/μL5.3.3 Expressing Single-Stranded DNA (ssDNA) Concentration as a Millimolar (mM) Amount5.4 Oligonucleotide Quantification5.4.1 Optical Density (OD) Unit5.4.2 Expressing an Oligonucleotide’s Concentration in μg/mL5.4.3 Oligonucleotide Concentration Expressed in pmol/μL5.5 Measuring RNA Concentration 5.6 Molecular Weight, Molarity, and Nucleic Acid Length5.7 Estimating DNA Concentration on an Ethidium Bromide-Stained GelChapter Summary6 Labeling Nucleic Acids with RadioisotopesIntroduction6.1 Units of Radioactivity – The Curie (Ci)6.2 Estimating Plasmid Copy Number6.3 Labeling DNA by Nick Translation6.3.1 Determining Percent Incorporation of Radioactive Label from Nick Translation6.3.2 Calculating Specific Radioactivity of a Nick Translation Product6.4 Random Primer Labeling of DNA6.4.1 Random Primer Labeling – Percent Incorporation6.4.2 Random Primer Labeling – Calculating Theoretical Yield6.4.3 Random Primer Labeling – Calculating Actual Yield6.4.4 Random Primer Labeling – Calculating Specific Activity of the Product6.5 Labeling 3’ Termini with Terminal Transferase6.5.1 3’-end Labeling with Terminal Transferase – Percent Incorporation6.5.2 3’-end Labeling with Terminal Transferase – Specific Activity of the Product6.6 Complementary DNA (cDNA) Synthesis6.6.1 First Strand cDNA Synthesis6.6.2 Second Strand cDNA Synthesis6.7 Homopolymeric Tailing6.8 In Vitro TranscriptionChapter Summary7 Oligonucleotide SynthesisIntroduction7.1 Synthesis Yield7.2 Measuring Stepwise and Overall Yield by the Dimethoxytrityl (DMT) Cation Assay7.2.1 Overall Yield7.2.2 Stepwise Yield7.3 Calculating Micromoles of Nucleoside Added at Each Base Addition StepChapter Summary8 The Polymerase Chain Reaction (PCR)Introduction8.1 Template and Amplification8.2 Exponential Amplification8.3 Polymerase Chain Reaction (PCR) Efficiency 8.4 Calculating the Tm of the Target Sequence8.5 Primers8.6 Primer Tm8.6.1 Calculating Tm Based on Salt Concentration, G/C Content, and DNA Length8.6.2 Calculating Tm Based on Nearest-Neighbor Interactions8.7 Deoxynucleoside Triphosphates (dNTPs)8.8 DNA Polymerase8.8.1 Calculating DNA Polymerase’s Error Rate8.9 Quantitative Polymerase Chain Reaction (PCR)Chapter SummaryReferencesFurther Reading9 The Real-time Polymerase Chain Reaction (RT-PCR)Introduction9.1 The Phases of Real-time PCR9.2 Controls9.3 Absolute Quantification by the TaqMan Assay9.3.1 Preparing the Standards9.3.2 Preparing a Standard Curve for Quantitative Polymerase Chain Reaction (qPCR) Based on Gene Copy Number9.3.3 The Standard Curve9.3.4 Standard Deviation9.3.5 Linear Regression and the Standard Curve9.4 Amplification Efficiency9.5 Measuring Gene Expression9.6 Relative Quantification – The ΔΔCT Method9.6.1 The 2-ΔΔCT Method – Deciding on an Endogenous Reference9.6.2 The 2-ΔΔCT Method – Amplification Efficiency9.6.3 The 2-ΔΔCT Method – is the Reference Gene Affected by the Experimental Treatment?9.7 The Relative Standard Curve Method9.7.1 Standard Curve Method for Relative Quantitation9.8 Relative Quantification by Reaction Kinetics9.9 The R0 Method of Relative Quantification9.10 The Pfaffl ModelChapter SummaryReferencesFurther Reading10 Recombinant DNAIntroduction10.1 Restriction Endonucleases10.1.1 The Frequency of Restriction Endonuclease Cut Sites10.2 Calculating the Amount of Fragment Ends10.2.1 The Amount of Ends Generated by Multiple Cuts10.3 Ligation10.3.1 Ligation Using λ-Derived Vectors10.3.2 Packaging of Recombinant λ Genomes10.3.3 Ligation Using Plasmid Vectors10.3.4 Transformation Efficiency10.4 Genomic Libraries – How Many Clones Do You Need?10.5 cDNA Libraries – How Many Clones are Enough?10.6 Expression Libraries10.7 Screening Recombinant Libraries by Hybridization to DNA Probes10.7.1 Oligonucleotide Probes10.7.2 Hybridization Conditions10.7.3 Hybridization Using Double-Stranded DNA (dsDNA) Probes10.8 Sizing DNA Fragments by Gel Electrophoresis10.9 Generating Nested Deletions Using Nuclease BAL 31Chapter SummaryReferences11 ProteinIntroduction11.1 Calculating a Protein’s Molecular Weight from Its Sequence11.2 Protein Quantification by Measuring Absorbance at 280 nm11.3 Using Absorbance Coefficients and Extinction Coefficients to Estimate Protein Concentration11.3.1 Relating Absorbance Coefficient to Molar Extinction Coefficient11.3.2 Determining a Protein’s Extinction Coefficient11.4 Relating Concentration in Milligrams Per Milliliter to Molarity11.5 Protein Quantitation Using A 280 When Contaminating Nucleic Acids are Present11.6 Protein Quantification at 205 nm11.7 Protein Quantitation at 205 nm When Contaminating Nucleic Acids are Present11.8 Measuring Protein Concentration by Colorimetric Assay – The Bradford Assay11.9 Using β-Galactosidase to Monitor Promoter Activity and Gene Expression11.9.1 Assaying β-Galactosidase in Cell Culture11.9.2 Specific Activity11.9.3 Assaying β-Galactosidase from Purified Cell Extracts11.10 Thin Layer Chromatography (TLC) and the Retention Factor (Rf)11.11 Estimating a Protein’s Molecular Weight by Gel Filtration11.12 The Chloramphenicol Acetyltransferase (CAT) Assay11.12.1 Calculating Molecules of Chloramphenicol Acetyltransferase (CAT)11.13 Use of Luciferase in a Reporter Assay11.14 In Vitro Translation – Determining Amino Acid Incorporation11.15 The Isoelectric Point (pI) of a ProteinChapter SummaryReferencesFurther Reading12 CentrifugationIntroduction12.1 Relative Centrifugal Force (RCF) (g Force)12.1.1 Converting g Force to Revolutions Per Minute (rpm)12.1.2 Determining g Force and Revolutions Per Minute (rpm) by Use of a Nomogram12.2 Calculating Sedimentation TimesChapter SummaryReferencesFurther Reading13 Forensics and PaternityIntroduction13.1 Alleles and Genotypes13.1.1 Calculating Genotype Frequencies13.1.2 Calculating Allele Frequencies13.2 The Hardy – Weinberg Equation and Calculating Expected Genotype Frequencies13.3 The Chi-Square Test – Comparing Observed to Expected Values13.3.1 Sample Variance13.3.2 Sample Standard Deviation13.4 The Power of Inclusion (Pi)13.5 The Power of Discrimination (Pd)13.6 DNA Typing and Weighted Average13.7 The Multiplication Rule13.8 The Paternity Index (PI)13.8.1 Calculating the Paternity Index (PI) When the Mother’s Genotype is not Available13.8.2 The Combined Paternity Index (CPI)Chapter SummaryReferencesFurther ReadingAppendix AIndex