Calculations for Molecular Biology and Biotechnology (eBook)

A Guide to Mathematics in the Laboratory

Frank H. Stephenson (Autor)

eBook Download: EPUB

2010 | 2. Auflage
460 Seiten
Elsevier Science (Verlag)
978-0-12-375691-6 (ISBN)

Infos

A must have for all Biotechnology Students and technicians. It walks readers through the minefield of laboratory calculations, helping to prevent the types of errors which could mean the loss of weeks of work.

Key Features:
* Topics range from basic scientific notations to complex subjects like nucleic acid chemistry and recombinant DNA technology
* Each chapter includes a brief explanation of the concept and covers necessary definitions, theory and rationale for each type of calculation
* Recent applications of the procedures and computations in clinical, academic, industrial and basic research laboratories are cited throughout the text

New to this Edition:
* Updated and increased coverage of real time PCR and the mathematics used to measure gene expression
* More sample problems in every chapter for readers to practice concepts

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Calculations for Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory, Second Edition, provides an introduction to the myriad of laboratory calculations used in molecular biology and biotechnology. The book begins by discussing the use of scientific notation and metric prefixes, which require the use of exponents and an understanding of significant digits. It explains the mathematics involved in making solutions; the characteristics of cell growth; the multiplicity of infection; and the quantification of nucleic acids. It includes chapters that deal with the mathematics involved in the use of radioisotopes in nucleic acid research; the synthesis of oligonucleotides; the polymerase chain reaction (PCR) method; and the development of recombinant DNA technology. Protein quantification and the assessment of protein activity are also discussed, along with the centrifugation method and applications of PCR in forensics and paternity testing. - Topics range from basic scientific notations to complex subjects like nucleic acid chemistry and recombinant DNA technology- Each chapter includes a brief explanation of the concept and covers necessary definitions, theory and rationale for each type of calculation- Recent applications of the procedures and computations in clinical, academic, industrial and basic research laboratories are cited throughout the text New to this Edition:- Updated and increased coverage of real time PCR and the mathematics used to measure gene expression- More sample problems in every chapter for readers to practice concepts

Inhalt

Front Cover 1
Calculations for Molecular Biology and Biotechnology 4
Copyright Page 5
Contents 6
CHAPTER 1 Scientific Notation and Metric Prefixes 16
Introduction 16
1.1 Significant Digits 16
1.1.1 Rounding Off Significant Digits in Calculations 17
1.2 Exponents and Scientific Notation 18
1.2.1 Expressing Numbers in Scientific Notation 18
1.2.2 Converting Numbers from Scientific Notation to Decimal Notation 20
1.2.3 Adding and Subtracting Numbers Written in Scientific Notation 21
1.2.4 Multiplying and Dividing Numbers Written in Scientific Notation 22
1.3 Metric Prefixes 25
1.3.1 Conversion Factors and Canceling Terms 25
Chapter Summary 29
CHAPTER 2 Solutions, Mixtures, and Media 30
Introduction 30
2.1 Calculating Dilutions – A General Approach 30
2.2 Concentrations by a Factor of X 32
2.3 Preparing Percent Solutions 34
2.4 Diluting Percent Solutions 35
2.5 Moles and Molecular Weight – Definitions 39
2.5.1 Molarity 40
2.5.2 Preparing Molar Solutions in Water with Hydrated Compounds 43
2.5.3 Diluting Molar Solutions 45
2.5.4 Converting Molarity to Percent 47
2.5.5 Converting Percent to Molarity 48
2.6 Normality 49
2.7 pH 50
2.8 pK[sub(a)] and the Henderson–Hasselbalch Equation 55
Chapter Summary 58
CHAPTER 3 Cell Growth 60
3.1 The Bacterial Growth Curve 60
3.1.1 Sample Data 64
3.2 Manipulating Cell Concentration 65
3.3 Plotting OD[sub(550)] vs. Time on a Linear Graph 68
3.4 Plotting the Logarithm of OD[sub(550)] vs. Time on a Linear Graph 69
3.4.1 Logarithms 69
3.4.2 Sample OD[sub(550)] Data Converted to Logarithm Values 69
3.4.3 Plotting Logarithm OD[sub(550)] vs. Time 69
3.5 Plotting the Logarithm of Cell Concentration vs. Time 71
3.5.1 Determining Logarithm Values 71
3.6 Calculating Generation Time 72
3.6.1 Slope and the Growth Constant 72
3.6.2 Generation Time 73
3.7 Plotting Cell Growth Data on a Semilog Graph 75
3.7.1 Plotting OD[sub(550)] vs. Time on a Semilog Graph 75
3.7.2 Estimating Generation Time from a Semilog Plot of OD[sub(550)] vs. Time 76
3.8 Plotting Cell Concentration vs. Time on a Semilog Graph 77
3.9 Determining Generation Time Directly from a Semilog Plot of Cell Concentration vs. Time 78
3.10 Plotting Cell Density vs. OD[sub(550)] on a Semilog Graph 79
3.11 The Fluctuation Test 81
3.11.1 Fluctuation Test Example 82
3.11.2 Variance 84
3.12 Measuring Mutation Rate 86
3.12.1 The Poisson Distribution 86
3.12.2 Calculating Mutation Rate Using the Poisson Distribution 87
3.12.3 Using a Graphical Approach to Calculate Mutation Rate from Fluctuation Test Data 88
3.12.4 Mutation Rate Determined by Plate Spreading 93
3.13 Measuring Cell Concentration on a Hemocytometer 94
Chapter Summary 95
References 96
CHAPTER 4 Working with Bacteriophages 98
Introduction 98
4.1 Multiplicity of Infection (moi) 98
4.2 Probabilities and Multiplicity of Infection (moi) 100
4.3 Measuring Phage Titer 106
4.4 Diluting Bacteriophage 108
4.5 Measuring Burst Size 110
Chapter Summary 113
CHAPTER 5 Nucleic Acid Quantification 114
5.1 Quantification of Nucleic Acids by Ultraviolet (UV) Spectroscopy 114
5.2 Determining the Concentration of Double-Stranded DNA (dsDNA) 115
5.2.1 Using Absorbance and an Extinction Coefficient to Calculate Double-Stranded DNA (dsDNA) Concentration 117
5.2.2 Calculating DNA Concentration as a Millimolar (mM) Amount 119
5.2.3 Using PicoGreen® to Determine DNA Concentration 120
5.3 Determining the Concentration of Single-Stranded DNA (ssDNA) Molecules 123
5.3.1 Single-Stranded DNA (ssDNA) Concentration Expressed in & #956
5.3.2 Determining the Concentration of High-Molecular-Weight Single-Stranded DNA (ssDNA) in pmol/& #956
5.3.3 Expressing Single-Stranded DNA (ssDNA) Concentration as a Millimolar (mM) Amount 125
5.4 Oligonucleotide Quantification 126
5.4.1 Optical Density (OD) Units 126
5.4.2 Expressing an Oligonucleotide's Concentration in & #956
5.4.3 Oligonucleotide Concentration Expressed in pmol/& #956
5.5 Measuring RNA Concentration 130
5.6 Molecular Weight, Molarity, and Nucleic Acid Length 130
5.7 Estimating DNA Concentration on an Ethidium Bromide-Stained Gel 135
Chapter Summary 136
CHAPTER 6 Labeling Nucleic Acids with Radioisotopes 138
Introduction 138
6.1 Units of Radioactivity – The Curie (Ci) 138
6.2 Estimating Plasmid Copy Number 139
6.3 Labeling DNA by Nick Translation 141
6.3.1 Determining Percent Incorporation of Radioactive Label from Nick Translation 142
6.3.2 Calculating Specific Radioactivity of a Nick Translation Product 143
6.4 Random Primer Labeling of DNA 143
6.4.1 Random Primer Labeling – Percent Incorporation 144
6.4.2 Random Primer Labeling – Calculating Theoretical Yield 145
6.4.3 Random Primer Labeling – Calculating Actual Yield 146
6.4.4 Random Primer Labeling – Calculating Specific Activity of the Product 147
6.5 Labeling 3& #8242
6.5.1 3& #8242
6.5.2 3& #8242
6.6 Complementary DNA (cDNA) Synthesis 150
6.6.1 First Strand cDNA Synthesis 150
6.6.2 Second Strand cDNA Synthesis 154
6.7 Homopolymeric Tailing 156
6.8 In Vitro Transcription 162
Chapter Summary 164
CHAPTER 7 Oligonucleotide Synthesis 170
Introduction 170
7.1 Synthesis Yield 171
7.2 Measuring Stepwise and Overall Yield by the Dimethoxytrityl (DMT) Cation Assay 173
7.2.1 Overall Yield 174
7.2.2 Stepwise Yield 175
7.3 Calculating Micromoles of Nucleoside Added at Each Base Addition Step 176
Chapter Summary 177
CHAPTER 8 The Polymerase Chain Reaction (PCR) 180
Introduction 180
8.1 Template and Amplification 180
8.2 Exponential Amplification 182
8.3 Polymerase Chain Reaction (PCR) Efficiency 185
8.4 Calculating the T[sub(m)] of the Target Sequence 188
8.5 Primers 191
8.6 Primer T[sub(m)] 196
8.6.1 Calculating T[sub(m)] Based on Salt Concentration, G/C Content, and DNA Length 197
8.6.2 Calculating T[sub(m)] Based on Nearest-Neighbor Interactions 198
8.7 Deoxynucleoside Triphosphates (dNTPs) 204
8.8 DNA Polymerase 206
8.8.1 Calculating DNA Polymerase's Error Rate 207
8.9 Quantitative Polymerase Chain Reaction (PCR) 210
Chapter Summary 222
References 224
Further Reading 224
CHAPTER 9 The Real-time Polymerase Chain Reaction (RT-PCR) 226
Introduction 226
9.1 The Phases of Real-time PCR 227
9.2 Controls 230
9.3 Absolute Quantification by the TaqMan Assay 231
9.3.1 Preparing the Standards 231
9.3.2 Preparing a Standard Curve for Quantitative Polymerase Chain Reaction (qPCR) Based on Gene Copy Number 235
9.3.3 The Standard Curve 239
9.3.4 Standard Deviation 242
9.3.5 Linear Regression and the Standard Curve 245
9.4 Amplification Efficiency 247
9.5 Measuring Gene Expression 251
9.6 Relative Quantification – The & #916
9.6.1 The 2[equation omitted] Method – Deciding on an Endogenous Reference 254
9.6.2 The 2[equation omitted] Method – Amplification Efficiency 265
9.6.3 The 2[equation omitted] Method – is the Reference Gene Affected by the Experimental Treatment? 274
9.7 The Relative Standard Curve Method 291
9.7.1 Standard Curve Method for Relative Quantitation 291
9.8 Relative Quantification by Reaction Kinetics 309
9.9 The R[sub(0)] Method of Relative Quantification 314
9.10 The Pfaffl Model 318
Chapter Summary 321
References 325
Further Reading 325
CHAPTER 10 Recombinant DNA 328
Introduction 328
10.1 Restriction Endonucleases 328
10.1.1 The Frequency of Restriction Endonuclease Cut Sites 330
10.2 Calculating the Amount of Fragment Ends 331
10.2.3 The Amount of Ends Generated by Multiple Cuts 332
10.3 Ligation 334
10.3.1 Ligation Using & #955
10.3.2 Packaging of Recombinant & #955
10.3.3 Ligation Using Plasmid Vectors 345
10.3.4 Transformation Efficiency 350
10.4 Genomic Libraries – How Many Clones Do You Need? 351
10.5 cDNA Libraries – How Many Clones are Enough? 352
10.6 Expression Libraries 354
10.7 Screening Recombinant Libraries by Hybridization to DNA Probes 355
10.7.1 Oligonucleotide Probes 357
10.7.2 Hybridization Conditions 359
10.7.3 Hybridization Using Double-Stranded DNA (dsDNA) Probes 365
10.8 Sizing DNA Fragments by Gel Electrophoresis 366
10.9 Generating Nested Deletions Using Nuclease BAL 31 374
Chapter Summary 378
References 382
CHAPTER 11 Protein 384
Introduction 384
11.1 Calculating a Protein's Molecular Weight from Its Sequence 384
11.2 Protein Quantication by Measuring Absorbance at 280 nm 388
11.3 Using Absorbance Coefficients and Extinction Coefficients to Estimate Protein Concentration 389
11.3.1 Relating Absorbance Coefficient to Molar Extinction Coefficient 392
11.3.2 Determining a Protein's Extinction Coefficient 393
11.4 Relating Concentration in Milligrams Per Milliliter to Molarity 395
11.5 Protein Quantitation Using A[sub(280)] When Contaminating Nucleic Acids are Present 397
11.6 Protein Quantification at 205 nm 398
11.7 Protein Quantitation at 205 nm When Contaminating Nucleic Acids are Present 398
11.8 Measuring Protein Concentration by Colorimetric Assay – The Bradford Assay 400
11.9 Using & #946
11.9.1 Assaying & #946
11.9.2 Specific Activity 405
11.9.3 Assaying & #946
11.10 Thin Layer Chromatography (TLC) and the Retention Factor (R[sub(f)]) 407
11.11 Estimating a Protein's Molecular Weight by Gel Filtration 409
11.12 The Chloramphenicol Acetyltransferase (CAT) Assay 414
11.12.1 Calculating Molecules of Chloramphenicol Acetyltransferase (CAT) 416
11.13 Use of Luciferase in a Reporter Assay 418
11.14 In Vitro Translation – Determining Amino Acid Incorporation 419
11.15 The Isoelectric Point (pI) of a Protein 420
Chapter Summary 423
References 426
Further Reading 427
CHAPTER 12 Centrifugation 428
Introduction 428
12.1 Relative Centrifugal Force (RCF) (g Force) 428
12.1.1 Converting g Force to Revolutions Per Minute (rpm) 430
12.1.2 Determining g Force and Revolutions Per Minute (rpm) by Use of a Nomogram 431
12.2 Calculating Sedimentation Times 433
Chapter Summary 435
References 436
Further Reading 436
CHAPTER 13 Forensics and Paternity 438
Introduction 438
13.1 Alleles and Genotypes 439
13.1.1 Calculating Genotype Frequencies 440
13.1.2 Calculating Allele Frequencies 441
13.2 The Hardy–Weinberg Equation and Calculating Expected Genotype Frequencies 442
13.3 The Chi-Square Test – Comparing Observed to Expected Values 445
13.3.1 Sample Variance 449
13.3.2 Sample Standard Deviation 450
13.4 The Power of Inclusion (P[sub(i)]) 450
13.5 The Power of Discrimination (P[sub(d)]) 451
13.6 DNA Typing and Weighted Average 452
13.7 The Multiplication Rule 453
13.8 The Paternity Index (PI) 454
13.8.1 Calculating the Paternity Index (PI) When the Mother's Genotype is not Available 456
13.8.2 The Combined Paternity Index (CPI) 458
Chapter Summary 459
References 460
Further Reading 460
Appendix A 462
Index 470
A 470
B 470
C 470
D 470
E 470
F 471
G 471
H 471
I 471
L 471
M 471
N 471
O 472
P 472
Q 472
R 472
S 473
T 473
V 473
Z 473

Textauszug

Chapter 1

Scientific notation and metric prefixes

Publisher Summary

Certain techniques in molecular biology, as in other disciplines of science, rely on types of instrumentation capable of providing precise measurements. An indication of the level of precision is given by the number of digits expressed in the instrument’s readout. The numerals of a measurement representing actual limits of precision are referred to as significant digits. This chapter discusses scientific notation and metric prefixes methods in expressing numbers. When expressing numbers in scientific notation, move the decimal point to the right of the leftmost nonzero digit, drop all zeros lying outside the string of significant figures, and express the new number as being multiplied by 10 having an exponent equal to the number of places the decimal point was moved from its original position (using a negative exponent if the decimal point was moved to the right). When adding or subtracting numbers expressed in scientific notation, rewrite the numbers such that they all have the same exponent value as that having the highest exponent, then perform the calculation. When multiplying numbers expressed in scientific notation, add the exponents. When dividing numbers expressed in scientific notation, subtract the exponent of the denominator from the exponent of the numerator to obtain the new exponent value. Numbers written in scientific notation can also be written using metric prefixes that will bring the value down to its lowest number of significant digits.

Introduction

There are some 3 000 000 000 base pairs (bp) making up human genomic DNA within a haploid cell. If that DNA is isolated from such a cell, it will weigh approximately 0.000 000 000 003 5 grams (g). To amplify a specific segment of that purified DNA using the polymerase chain reaction (PCR), 0.000 000 000 01 moles (M) of each of two primers can be added to a reaction that can produce, following some 30 cycles of the PCR, over 1 000 000 000 copies of the target gene.

On a day-to-day basis, molecular biologists work with extremes of numbers far outside the experience of conventional life. To allow them to more easily cope with calculations involving extraordinary values, two shorthand methods have been adopted that bring both enormous and infinitesimal quantities back into the realm of manageability. These methods use scientific notation and metric prefixes. They require the use of exponents and an understanding of significant digits.

1.1 Significant Digits

Certain techniques in molecular biology, as in other disciplines of science, rely on types of instrumentation capable of providing precise measurements. An indication of the level of precision is given by the number of digits expressed in the instrument’s readout. The numerals of a measurement representing actual limits of precision are referred to as significant digits.

Although a zero can be as legitimate a value as the integers one through nine, significant digits are usually nonzero numerals. Without information on how a measurement was made or on the precision of the instrument used to make it, zeros to the left of the decimal point trailing one or more nonzero numerals are assumed not to be significant. For example, in stating that the human genome is 3 000 000 000 bp in length, the only significant digit in the number is the 3. The nine zeros are not significant. Likewise, zeros to the right of the decimal point preceding a set of nonzero numerals are assumed not to be significant. If we determine that the DNA within a sperm cell weighs 0.000 000 000 003 5 g, only the 3 and the 5 are significant digits. The 11 zeros preceding these numerals are not significant.

Problem 1.1

How many significant digits are there in each of the following measurements?

a) 3 001 000 000 bp

b) 0.003 04 g

c) 0.000 210 liters (L) (volume delivered with a calibrated micropipettor).

Solution 1.1

a) Number of significant digits: 4; they are: 3001

b) Number of significant digits: 3; they are: 304

c) Number of significant digits: 3; they are: 210

1.1.1 Rounding off significant digits in calculations

When two or more measurements are used in a calculation, the result can only be as accurate as the least precise value. To accommodate this necessity, the number obtained as solution to a computation should be rounded off to reflect the weakest level of precision. The guidelines in the following box will help determine the extent to which a numerical result should be rounded off.

Guidelines for rounding off significant digits

1. When adding or subtracting numbers, the result should be rounded off so that it has the same number of significant digits to the right of the decimal as the number used in the computation with the fewest significant digits to the right of the decimal.

2. When multiplying or dividing numbers, the result should be rounded off so that it contains only as many significant digits as the number in the calculation with the fewest significant digits.

Problem 1.2

Perform the following calculations, and express the answer using the guidelines for rounding off significant digits described in the preceding box

a) 0.2884 g+28.3 g

b) 3.4 cm × 8.115 cm

c) 1.2 L × 0.155 L

Solution 1.2

a) 0.2884 g+28.3 g = 28.5884 g

The sum is rounded off to show the same number of significant digits to the right of the decimal point as the number in the equation with the fewest significant digits to the right of the decimal point. (In this case, the value 28.3 has one significant digit to the right of the decimal point.)

b) 3.4 cm × 8.115 cm = 27.591 cm2

The answer is rounded off to two significant digits since there are as few as two significant digits in one of the multiplied numbers (3.4 cm).

c) 1.2 L÷0.155 L = 7.742 L

The quotient is rounded off to two significant digits since there are as few as two significant digits in one of the values (1.2 L) used in the equation.

1.2 Exponents and Scientific Notation

An exponent is a number written above and to the right of (and smaller than) another number (called the base) to indicate the power to which the base is to be raised. Exponents of base 10 are used in scientific notation to express very large or very small numbers in a shorthand form. For example, for the value 103, 10 is the base and 3 is the exponent. This means that 10 is multiplied by itself three times (103 = 10 × 10 × 10 = 1000). For numbers less than 1.0, a negative exponent is used to express values as a reciprocal of base 10. For example,

1.2.1 Expressing numbers in scientific notation

To express a number in scientific notation:

1. Move the decimal point to the right of the leftmost nonzero digit. Count the number of places the decimal has been moved from its original position.

2. Write the new number to include all numbers between the leftmost and rightmost significant (nonzero) figures. Drop all zeros lying outside these integers.

3. Place a multiplication sign and the number 10 to the right of the significant integers. Use an exponent to indicate the number of places the decimal point has been moved.

a. For numbers greater than 10 (where the decimal was moved to the left), use a positive exponent.

b. For numbers less than one (where the decimal was moved to the right), use a negative exponent.

Problem 1.3

Write the following numbers in scientific notation

a) 3 001 000 000

b) 78

c) 60.23 × 1022

Solution 1.3

a) Move the decimal to the left nine places so that it is positioned to the right of the leftmost nonzero digit.

Write the new number to include all nonzero significant figures, and drop all zeros outside of these numerals. Multiply the new number by 10, and use a positive 9 as the exponent since the given number is greater than 10 and the decimal was moved to the left nine positions.

b) Move the decimal to the left one place so that it is positioned to the right of the leftmost nonzero digit. Multiply the new number by 10, and use a positive 1 as an exponent since the given number is greater than 10 and the decimal was moved to the left one position.

c) 60.23 × 1022

Move the decimal to the left one place so that it is positioned to the right of the leftmost nonzero digit. Since the decimal was moved one position to the left, add 1 to the exponent (22+1 = 23 = new exponent value).

Problem 1.4

Write the following numbers in scientific...

Produkt-Details

• Erscheint lt. Verlag: 30.7.2010
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber ► Beruf / Finanzen / Recht / Wirtschaft ► Bewerbung / Karriere
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Medizin / Pharmazie ► Allgemeines / Lexika
• Themenwelt: Studium ► Querschnittsbereiche ► Epidemiologie / Med. Biometrie
• Themenwelt: Naturwissenschaften ► Biologie ► Genetik / Molekularbiologie
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• ISBN-10: 0-12-375691-X / 012375691X
• ISBN-13: 978-0-12-375691-6 / 9780123756916