Computer Simulation and Data Analysis in Molecular Biology and Biophysics

Transcription

1 Victor Bloomfield Computer Simulation and Data Analysis in Molecular Biology and Biophysics An Introduction Using R Springer

2 Contents Part I The Basics of R 1 Calculating with R Installing R Demos Finding help with R Some interface aids Arithmetic Complex numbers Assigning variables Example: Conversions between units Standard mathematical functions Rounding Vectors Operations on vectors Functions that operate on vectors Character vectors Generating sequences Generating regular sequences Generating sequences of random numbers Logical vectors Matrices Arithmetic operations on matrices Matrix multiplication Determinant of a matrix Transpose of a matrix Diagonal matrix Matrix inverse Eigenvalues and eigenvectors Other matrix functions Other data structures 19 ix

3 x Contents Data frames Factors Lists Problems 20 2 Plotting with R Some common plots Data plot Bar plot Function plot Histogram Three-dimensional plot Customizing plots Different plot characters Plotting data with a line Adding title and axis labels Adding colors Adding straight lines to a plot Adjusting the axes Customizing ticks and axes Setting default graph parameters Adding text to a plot Adding math expressions and arrows Constructing a diagram Superimposing data series in a plot Placing two or more plots in a figure Error bars Locating and identifying points on a plot Problems 46 3 Functions and Programming Built-in functions in R Sorting Splines Sampling User-defined functions Gaussian function ph titration curves Programming Conditional execution with i f () Looping with for () Looping with while () Looping with repeat Choosing with which () Numerical analysis with R 58

4 3.4.1 Finding a zero of a function Finding the roots of a polynomial Solving a system of simultaneous linear equations Solving a system of nonlinear equations Numerical integration of functions Numerical integration of data using splinefun Numerical differentiation Problems 65 4 Data and Packages Writing and reading data to files Changing directories Writing data to a file Reading data from a file using scan() Writing and reading tables Reading and writing spreadsheet files Saving the R environment between sessions Packages Data frames Factors The contributed package seqinr Problems 81 Part II Simulation of Biological Processes 5 Equilibrium and Steady State Calculations Equilibrium in reacting mixture Binding of a ligand L to a protein or polymer P Fitting binding data with a Scatchard plot using linear model (lm) Strong and weak binding Cooperative binding Oxygen binding by hemoglobin Hill plot Experimental determination of equilibrium constants Temperature dependence of equilibrium constants: the van't Hoff equation Single strand-double helix equilibrium in oligonucleotides Steady-state enzyme kinetics Michaelis-Menten kinetics Lineweaver-Burk fitting Eadie-Hofstee fitting Competitive inhibition Non-linear least-squares fitting Problems 110 xi

5 Contents Differential Equations and Reaction Kinetics Analytically solvable models Exponential growth Exponential decay Chemical Conversion Exponential decay to a constant value Model of limited growth Kinetics of bimolecular reactions Numerical integration of ODEs Integrating a single ODE by the Euler method Integrating a system of ODEs by the Euler method Integrating a system of ODEs by the improved Euler method Integrating a system of equations using 4th-order Runge-Kutta lsoda, a sophisticated differential equation solver Stability of systems of ODEs Numerical solution of second-order ODEs Stochastic differential equations Problems 135 Population Dynamics Models of homogeneous populations of organisms Verhulst-Pearl (logistic) equation Variable carrying capacity and the logistic Lotka-Volterra model of predation Modifications of the Lotka-Volterra model Volterra's model for two-species competition Models of microbial growth Monod model of microbial growth Microbial growth in batch culture and chemostat Multiple limiting nutrients Competition for limiting nutrients Toxic inhibition of microbial growth Models of Epidemics The simple SIR model The SIR model with births and deaths SI model of fatal infections SIS model of infection without immunity A model for an epidemic of gonorrhea Problems 155 Diffusion and Transport Transport by simple diffusion Fick's laws of diffusion Analytical solutions of Fick's second law in one dimension. 160

6 8.1.3 Numerical solutions of Fick's second law in one dimension Diffusion in spherical and cylindrical geometries Diffusion in a driving field: electrophoresis Countercurrent diffusion Diffusion as a random process: Brownian motion Compartmental models in physiology and pharmacokinetics Periodic dose administration to a single compartment Liver function A two-compartment model Multi-compartment model of liver function Oscillations in calcium metabolism Problems Regulation and Control of Metabolism Successive enzyme reactions One-substrate, one-product reaction Successive one-substrate, one-product reactions Steady-state flux calculation Metabolic control analysis Flux control coefficients Elasticities Biochemical systems theory Linear pathway with feedback inhibition Transitions in reaction network behavior Problems Models of Regulation Regulation of transcription: Feed-forward loops Regulation of signaling: Bacterial Chemotaxis Modeling of Chemotaxis as a biased random walk Robust model of Chemotaxis Regulation of development: Morphogenesis Exponential morphogen gradients are not robust Self-enhanced morphogen degradation to form robust gradients Patterning in the dorsal region of Drosophila Problems 202 Part III Analyzing DNA and Protein Sequences 11 Probability and Population Genetics Some fundamentals of probability Review of basic probability ideas Conditional probability The law of total probability Bayes' theorem Stochastic population models 210 xiii

7 xiv Contents Stochastic modeling of population growth Stochastic simulation of radioactive decay Markov chains Markov chain model of diffusion out of and into a cell Probability distribution functions R's four basic functions for a statistical distribution Uniform distribution Normal distribution Binomial distribution Poisson distribution Geometric distribution Exponential distribution Other distributions Population Genetics Hardy-Weinberg Principle Effect of selection Selection for heterozygotes Mutation Selection involving sex-linked recessive genes Problems DNA Sequence Analysis Getting a sequence from the Web Using Entrez Making the sequence usable by R Converting letters to numbers Single base sequences and frequencies Counting the number of each type of base Simulating a random sequence of bases Simulating the distribution of the number of A residues in a sequence Dinucleotide sequences and frequencies Probability of observing dinucleotides Markov chain simulation of dinucleotide frequencies Simulation of restriction sites Detecting periodicity in a sequence Problems 248 Part IV Statistical Analysis in Molecular and Cellular Biology 13 Statistical Analysis of Data Summary statistics for a single group of data Summary statistics Histograms Cumulative distribution 253

8 XV Test of normal distribution using qqnorm Boxplots Summary statistics for grouped data using tapply {) Statistical comparison of two samples One-sample t test Two-sample t test Two-sample Wilcoxon test Paired t test Statistical power calculations Analysis of spectral data Fitting to a sum of decaying exponentials Fitting a superposition of Gaussian spectra Processing mass spectrometry data Problems 276 Microarrays Introduction Preprocessing overview The af f у package Importing data not in standard form The need for preprocessing Preprocessing steps The Dilution dataset Preliminary inspection MAplot Background correction Normalization PM correction Summarization Combining preprocessing steps with expresso Using the results of preprocessing ExpressionSet Identifying highly expressed genes Statistical analysis of differential gene expression Paired samples Unpaired samples Bootstrapping Analysis of variance (anova) for more than two groups Detecting groups of genes Correlation Distance measures Clustering Principal component analysis Power analysis lproblems 307

9 xvi Contents A Basic String Manipulations in R 309 References 313 Index 317