Prequel
For our first session on Tuesday, August 31 please read Chapter 2 "Mendelian Analysis " from "An Introduction to Genetic Analysis" by A. J. F. Gnffiths et aL, 1996. You should have received a copy of this chapter as one of the handouts.

Knowledge of the principles of Mendelian genetics is essential for understanding the nature of health and disease. Individual organisms are composed of diverse tissues in each of which a network of integrated cellular processes is controlled and regulated by unique patterns of expressed genes. "Health" indicates a homeostatic (well-balanced) functioning of this network. "Disease" reflects dysregulated functioning of some component(s) of this network. Thus, a disease state indicates that the expression of one or more genes has been altered qualitatively or quantitatively. This can be due either to gene mutations or to environmental factors which affect gene transcription. In either case, such changes in gene expression will alter one or more physiological parameters; these then are detected as disease symptoms. In many, if not most, cases, the altered gene expression results in altered response to environmental stimuli. Thus, the interaction of genetic and environmental factors is an important consideration in the study and treatment of any disease.
During the next few sessions we will review the basic concepts of Mendelian genetics which are the basis for the spread of mutations and behavior of genes in populations of organisms.
To illustrate these concepts we will discuss some specific mutations in the house mouse in addition to the mutations used in the textbook. The physiologic (phenotypic) manifestations of these mutations will be used to illustrate their induction through the effects and interactions of the gene products at the cellular and tissue levels. This is an example of physiological genomics, which links the molecular biology of gene function to the physiology and metabolism of the organism. Physiological genomics seeks to understand/explain how regulation of gene expression (transcription) affects the regulation of cellular processes and their interactions in the various body tissues to maintain the homeostatic (equilibrium) functioning of the whole organism.
George L. Wolff, Ph.D.
8/31/99

Chapter 2 "Mendelian Analysis "
from "An Introduction to Genetic Analysis" by A. J. F. Gnffiths et aL, 1996

Introduction

• The concept of the gene was introduced in 1865 by Gregor Mendel
• Up to that time, "blending inheritance" was the theory in force
• Mendel proposed, "particulate inheritance".

Mendel's Experiments

• He failed his exams, and was awarded his titles posthumously.
• Mendel studied the garden pea, Pisum sativum.
• Two advantages:
  1) available in a wide array of distinct shapes and colors
  2) could self-pollinate or cross-pollinate.
• This was an expedient choice of organism.

My choice of material is freshly excised tumors. I want to dissect the tissues into two types, tumor and non-tumor selecting only the cells from which the tumor cells are differentiated.

• Mendel chose several characters to study.
• These characteristics were:
  1) round or wrinkled ripe seeds
  2) yellow or green seed interiors
  3) yellow or green unripe pods
  4) purple or white petals
  5) inflated or pinched ripe pods
  6) axial or terminal flowers
  7) long or short stems

Plants Differing in One Character

• Mendel grew for two years to create a pure line.
• He obtained seven pairs of pure lines for seven characters,
  each line differed in only one character.
• The different character expressions (version instances) are called phenotypes.

• The pure line generation is the parental or P generation.
• The first progeny generation is called first filial or F1.
• Subsequent generations produced by selfing are called F2, F3, etc.
• Mendel made reciprocal crosses.

cross(phenotypeA-male, phenotypeB-female)
cross(phenotypeB-male, phenotypeA-female)

• Mendel COUNTED the number of each phenotype that manifested at F2
• The phenotypes expressed at a ratio of 3:1
• The dominant phenotype is that which manifests in the heterozygotic condition.
• Underlying the 3:1 ratio was a 1:2:1 ratio
• Note the following quadratic forms that arise:
  Let Y = yellow seeds - dominant trait
  Let y = green seeds - recessive trait
  
  Now cross(Yy,Yy) --> {YY, Yy, Yy, yy}
  
  note that this looks like the product of (Yy) (Yy) and produces the correct ratios,
  1 YY, 2 Yy, 1 yy
  
  
• Meddle's First Law of Equal Segregation
  The two members of a gene pair segregate from each other into the gametes, so that half the gametes carry one member of the pair and the other half of the gametes carry the other member of the pair.
• Heterozygotes = Hybrids Yy
• Homozygotes = Dominant YY or Recessive yy
• Genotype YY != Genotype Yy (the potential for green exists)
• Phenotype Yy == Phenotype Yy (both are yellow)
• Y and y are alleles or variants of the gene. (Versions)
• Alleles may differ by only one nucleotide at the DNA level!

Plants Differing in Two Characters

• Monohybrid Heterozygotes are Heterozygous for one gene only.
• Cross(Yy, Yy) is a monohybrid cross.
• Dihibrid cross is Cross(AaBb, AaBb) watch:
  3:1 x 3:1 = 3x3 + 3 + 3 + 1 = 9:3:3:1

• works on tetrahyrid cross:
• 9:3:3:1 x 9:3:3:1 = 9x9+27+27+9 +27+9+9+3+27+9+9+3+3+1
• = 81:27:27:27:27:9:9:9:9:9:3:3:3:1

Meddle's Second Law of Independent Assortment
During gamete formation the segregation of alleles of one gene is independent of the segregation of the alleles of another gene (PROVIDED THE GENES ARE ON SEPARATE CHROMOSOMES OR ARE FAR APART ON THE SAME CHROMOSOME!)

• different gene pairs assort independently during gamete formation
• The product rule states that the probability of independent events occurring together is the product of the probabilities of the individual events.
• The sum rule states the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities.

Simple Mendelian Genetics in Humans

• record of matings is a pedigree analysis
• individual under scrutiny is the propositus, the dwarf, or exceptional case.