Calculations for Molecular Biology and Biotechnology

A Guide to Mathematics in the Laboratory


  • Frank Stephenson, Applied Biosystems, Foster City, California

Calculations in Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory is the first comprehensive guide devoted exclusively to calculations encountered in the genetic engineering laboratory. Mathematics, as a vital component of the successful design and interpretation of basic research, is used daily in laboratory work. This guide, written for students, technicians, and scientists, provides example calculations for the most frequently confronted problems encountered in gene discovery and analysis. The text and sample calculations are written in an easy-to-follow format. It is the perfect laboratory companion for anyone working in DNA manipulation and analysis.
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Upper division students, technicians, professional lab workers, and professors teaching and working in molecular biology labs.


Book information

  • Published: June 2003
  • ISBN: 978-0-12-665751-7

Table of Contents

Introduction, Significant Digits, Rounding Off Significant Digits in Calculations, Exponents and Scientific Notation, Expressing Numbers in Scientific Notation, Converting Numbers from Scientific Notation to Decimal Notation, Adding and Subtracting Numbers Written in Scientific Notation, Multiplying and Dividing Numbers Written in Scientific Notation, Metric Prefixes, Conversion Factors and Canceling Terms, Section 2: Solutions, Mixtures, and Media Introduction, Calculating Dilutions: A General Approach, Concentrations by a Factor of X, Preparing Percent Solutions, Diluting Percent Solutions, Moles and Molecular Weight: Definitions, Molarity, Diluting Molar Solutions, Converting Molarity to Percent, Converting Percent to Molarity, Normality, PH, pKa and the Henderson-Hasselbalch Equation, Section 3: Cell Growth The Bacterial Growth Curve, Manipulating Cell Concentration, Plotting OD550 versus Time on a Linear Graph, Plotting the Logarithm of OD550 vs Time on a Linear Graph, Logarithms, Sample OD550 Data Converted to Log Values, Plotting Log OD550 versus Time, Plotting the Log of Cell Concentration versus Time, Determining Log Values, Calculating Generation Time, Slope and Growth Constant, Generation Time, Plotting Cell Growth Data on a Semilog Graph, Plotting OD550 vs Time on a Semilog Graph, Estimating Generation Time from a Semilog Plot of OD550 vs Time, Plotting Cell Concentration versus Time on a Semilog Graph, Determining Generation Time Directly from a Semilog Plot of Cell Concentration vs Time, Plotting Cell Density versus OD550 on a Semilog Graph, The Fluctuation Test, Fluctuation Test Example, Variance, Measuring Mutation Rate, The Poisson Distribution, Calculating Mutation Rate by Using Poisson Distribution, Using a Graphical Approach to Calculate Mutation Rate from Fluctuation Test Data, Mutation Rate Determined by Plate Spreading, Measuring Cell Concentration in a Hemocytometer, Section 4: Working with Bacteriophage Introduction, Multiplicity of Infection, Probabilities and moi, Measuring Phage Titer, Diluting Bacteriophage, Measuring Burst Size, Section 5: Quantitation of Nucleic Acids, Quantitation of Nucleic Acids by UV Spectroscopy, Determining the Concentration of Double-Stranded DNA, Using Absorbance and an Extinction Coefficient to Calculate Double-Stranded DNA Concentration, Calculating DNA Concentration as a Millimolar (mM) Amount, Determining the Concentration of Single-Stranded DNA Molecules, Single-Stranded DNA Concentration Expressed in µg/mL, Determining the Concentration of Large Molecular Weight Single-Stranded DNA, (ssDNA) in pmol/µL, Expressing ssDNA Concentration as a mM Amount, Oligonucleotide Quantitation, OD Units, Expressing an Oligonucleotide's Concentration in µg/mL, Oligonucleotide Concentration Expressed in pmol/µL, Measuring RNA Concentration, Molecular Weight, Molarity, and Nucleic Acid Length, Estimating DNA Concentration on an Ethidium Bromide Stained Gel, Section 6: Labeling Nucleic Acids with Radioisotopes Introduction, Using Radioactivity - The Curie, Estimating Plasmid Copy Number, Labeling DNA by Nick Translation, Determination of Percent Incorporation of Radioactive Label , Calculating Specific Radioactivity of a Nick Translation Product, Random Primer Labeling of DNA, Random Primer Labeling - Percent Incorporation, Random Primer Labeling - Calculating Theoretical Yield, Random Primer Labeling - Calculating Actual Yield, Random Primer Labeling - Calculating SpecificActivity of the Product, Labeling 3' Termini with Terminal Transferase, 3'-End Labeling with Terminal Transferase -Percent Incorporation, 3'-End Labeling with Terminal Transferase - Specific Activity of the Product, cDNA Synthesis, First Strand cDNA Synthesis, Second Strand cDNA Synthesis, Homopolymeric Tailing, In vitro Transcription, Section 7: Oligonucleotide Synthesis Introduction, Synthesis Yield, Measuring Stepwise and Overall Yield by the DMT Cation Assay, Overall Yield, Stepwise Yield, Calculating Micromoles of Nucleoside Added at Each Base Addition Step, Section 8: The Polymerase Chain Reaction Introduction, Template and Amplification , Exponential Amplification, PCR Efficiency, Calculating the Tm of the Target Sequence, Primers, Primer Tm, Calculating Tm Based on Salt Concentration, G/C Content, and DNA Length, Calculating Tm Based on Nearest Neighbor Interactions, DNTPs, DNA Polymerase, Calculating DNA Polymerase's Error Rate, Quantitative PCR, Section 9: Recombinant DNA Introduction, Restriction Endonucleases, The Frequency of Restriction Endonuclease Cut Sites, Calculating the Amount of Fragment Ends, The Amount of Ends Generated by Multiple Cuts, Ligation, Ligation Using Lambda-Derived Vectors, Packaging of Recombinant Lambda Genomes, Ligation Using Plasmid Vectors, Transformation Efficiency Genomic Libraries: How Many Clones do You Need? , cDNA Libraries: How Many Clones is Enough? , Expression Libraries, Screening Recombinant Libraries by Hybridization to DNA Probes, Oligonucleotide Probes, Hybridization Conditions, Hybridization Using Double-Stranded DNA Probes, Sizing DNA Fragments by Gel Electrophoresis, Generating Nested Deletions Using Nuclease BAL 31, Section 10: Protein Introduction, Protein Quantitation by Measuring Absorbance at 280 nm, Using Absorbance Coefficients and Extinction Coefficients to Estimate Protein, Concentration, Relating Absorbance Coefficient to Molar Extinction Coefficient, Determining a Protein's Extinction Coefficient, Relating mg/mL Concentration to Molarity, Protein Quantitation Using A280 when Contaminating Nucleic Acids are Present, Protein Quantitation at 205 nm, Protein Quantitation at 205 nm when Contaminating Nucleic Acids are Present, Measuring Protein Concentration by Colorimetric Assay - The Bradford Assay, Using b-Galactosidase to Monitor Promoter Activity and Gene Expression, Assaying b-Galactosidase in Cell Culture, Specific Activity, Assaying b-Galactosidase from Purified Extracts, The CAT Assay, Calculating Molecules of CAT, Use of Luciferase in a Reporter Assay, In vitro Translation - Determining Amino Acid Incorporation, Section 11: Centrifugation Introduction, Relative Centrifugal Force (g Force, ) Converting g Force to rpm, Determining g Force and rpm by Use of a Nomogram, Calculating Sedimentation Times, Section 12: Forensic Science Introduction, Alleles and Genotypes, Calculating Genotype Frequencies, Calculating Allele Frequencies, The Hardy-Weinberg Equation and Calculating Expected Genotype Frequencies, The Chi-square Test: Comparing Observed to Expected Values, Sample Variance, Sample Standard Deviation, Pi: The Power of Inclusion, Pd: The Power of Discrimination, DNA Typing and a Weighted Average, The Multiplication Rule, Index