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Mendel’s Genetics [6]: Examples of epistasis

In Mendel’s dihybrid cross, each gene locus(the position of a gene along a chromosome, often used to refer to the gene itself.) had an independent effect on a single phenotype. Thus, the R and r alleles affected only the shape of the seed and had no influence on seed color, while the Y and y alleles affected only seed color and had no influence on seed shape. In this case, there were two separate genes that coded for two separate characteristics.

But what happens when two different loci affect the same characteristic? For instance, what if both of the loci in Mendel’s experiment affected seed color?

Let’s begin with a relatively simple example.

example (1) 9:3:3:1→9:7

enzyme A serves to convert white substrate in an unnamed plant to white product; enzyme B synthesizes purple pigment and converts the white product to purple product.

In this case, If BOTH A & B exist, purple product is yielded;

If ONLY A OR B exists, synthesis of purple pigment cannot be completed, and purple product won’t be produced;

If NEITHER ENZYME exist, purple pigment, surely, cannot be synthesized, and purple product won’t be produced.

Based on the info above, the dihybrid F2 generation looks like this:

When the situation gets a little bit more complicated:

example (2) 9:3:3:1→9:3:4

enzyme A serves in the synthesis of red pigment and converts white substrate in an unnamed plant to red product; enzyme B synthesizes purple pigment and converts the red product to purple product.

In this case, If BOTH A & B exist, purple product is yielded;

If ONLY A exists, synthesis of red pigment can be completed but synthesis of purple pigment cannot, and red product will be produced;

If NEITHER ENZYME exist or ONLY B exists, surely, neither red or purple pigment, can be synthesized, and the the yield will be white.

Based on the info above, the dihybrid F2 generation looks like this:

A more complex situation:

example (3): 9:3:3:1→12:3:1

Here two enzymes compete for the same substrate. Enzyme A converts the substrate to a purple product, and enzyme B to a red product. BUT enzyme A has much higher affinity for the substrate than enzyme B. The difference in affinity is so marked that enzyme B can only work effectively without the presence of enzyme A

SO as long as enzyme A is present, the yield is be purple; only when enzyme B exists without enzyme A would the yield be red; and only when neither B or A exists would the yield be white.

Based on the info above, the dihybrid F2 generation looks like this:

[F2] purple: red: white=12: 3: 1

The three examples above lead us to a new concept: Epistasis.

Sometimes genes can mask each other’s presence or combine to produce an entirely new trait. Epistasis describes how gene interactions can affect phenotypes.

In a strict sense, 12: 3: 1 is the only ratio which was originally referred to as epistasis, because the presence of enzyme A can completely make the genotype of the B gene. But the term is now used wherever genes interact to alter the expected ratios.

There are several other variations of the 9:3:3:1 ratio caused by interaction between the gene products, including 9:6:1, 15:1, and 13:3.

In every case the ratios are derived by summing together the four phenotype classes 9, 3, 3, or 1 of the basic ratio.

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For more examples and explanations of the Epistasis, see Epistasis and Its Effects on Phenotype | Learn Science at Scitable

The blueprint of life [5]: spectroscopic and thermal properties of DNA

UV absorption

DNA absorbs UV light due to the conjugated aromatic nature of the bases; the sugar-phosphate backbone does not contribute appreciably(perceptibly/measurably) to absorption.

The wavelength of maximum absorption of light by both DNA and RNA is 260 nm, which is conveniently distinct from the λmax of protein(280 nm).

The absorption properties of DNA can be used for detection, quantitation and assessment of property.

Hypochromicity

UV absorption at 260nm is greatest for isolated nucleotides, intermediate for single-stranded DNA(ssDNA) or RNA, and least for double-stranded DNA(dsDNA)

The classical term for the change in absorbance is hypochromicity. For example, dsDNA is hypochromic (from the Greek for ‘less colored‘) relative to ss DNA, which is hypochromic relative to isolated nucleotides.

Thermodynamics of DNA

Denaturation: the transition of macromolecule from the native state to the denatured state. For DNA, under denaturing conditions (heating or high pH), double helix is separated to generate single-stranded form.

Melting Temperature(Tm): the temperature at which the rise in A260(absorbance at 260nm) is half complete during denaturation.

Factors that affect the Tm

1. G+C content: the higher G+C content, the higher Tm.

2. Ionic strength: The Tm increases as the cation (+) concentration increases. like Na+, K+ or Mg2+.

3. High pH or Agents that disrupt H-bonds or interfere with base stacking: formamide (甲酰胺)or urea (尿素)will decrease the Tm.

4. The imperfect hybridization between related but not completely complementary strands will reduce the Tm, about 1 °C for each percent mismatch.

The process of denaturation can be observed conveniently by the increase in absorbance as double-stranded nucleic acids are converted to single strands

Renaturation: Process of a macromolecule returning to its native 3-D structure. For DNA this involves the two strands of denatured DNA basepairing to restore the nature form of dsDNA. Also known as reannealing (重退火).

Requirements for renaturation:

1. Proper salt concentration: neutralize electrostatic repulsion

2. Proper reannealing temperature: 20-25℃ below Tm

Determinants for renaturation efficiency

(DNA renatures on cooling, but will form fully double-stranded native DNA only if the cooling is sufficiently slow to allow the complementary strands to anneal.)

1. Extent of base matching and

2. copy of matching regions

Thus, repetitive DNA renatures faster than single copy DNA

RENATURATION CURVES FOR E.COLI &MOUSE DNA, shown by prof. Dong

Mendel’s Genetics [5]: The dihybrid cross

Last sections we discussed inheritance where only a single gene was involved. The 3:1 ratio is the basic Mendelian ratio and everything that follows depends upon it.

The obvious next step is to look at a situation where the inheritance of two different inherited characters are studied at the same time, a dihybrid cross.

Again, we learn dihybrid cross by experiments. Let’s see what Mendel did:

He crossed two pure-bred starins of pea plants, one producing only round yellow seeds and the other only wrinkled green seeds.Round seeds are dominant over wrinkled ones; yellow seeds are dominant over green ones. Both phenotypes are determined by one single gene.

(Why did Mendel use the seed characteristics as his focus of study instead of other traits of the pea plants? )

A cross between the two parents produced a F1 generation that consisted only of round yellow seeds. Self-fertilization of F1 yielded F2 generation, the seeds of which showing considerable diversity.

Four different phenotypes could be identified. Of 556 seeds analyzed, Mendel found 315 round yellow seeds, 108 round green seeds, 101 wrinkled yellow seeds and 32 round green seeds. Close to a ratio of 9: 3: 3: 1, which is referred to as the dihybrid ratio.

dihybrid cross — THE 9:3:3:1 IN MENDEL’S EXPERIMENTS, image from Instant Notes in Genetics

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Interestingly, if we only focus on the round/wrinkled phenotype, the ratio of round seeds and wrinkled seeds is 3:1. the monohybrid ratio. Similarly, if we only focus on the yellow/green phenotype, the ratio of yellow seeds and green seeds is the monohybrid ratio as well. Just as we said “The 3:1 ratio is the basic Mendelian ratio and everything that follows depends upon it”

Now I want to introduce a little bit mathematics into this section. Let’s see what happens when we use polynomial multiplication to explain the relationship between 9: 3: 3: 1 and 3:1:

(yellow: green)× (round: wrinkled)

= (yellow·round): (yellow·wrinkled): (green·round): (green·wrinkled)

known: yellow: green=3:1; round: wrinkled=3:1

SO: (yellow: green)×(round: wrinkled)=(3:1)×(3:1)

=(3×3):(3×1):(1×3):(1×1)=9:3:3:1

Therefore, (yellow·round): (yellow·wrinkled): (green·round): (green·wrinkled)=9:3:3:1
Does this reasoning inspire you? What happens when it comes to a tri-hybrid ratio?

(3:1)×(3:1)×(3:1)=

(3×3×3):(3×3×1):(3×1×3):(3×1×1):(1×3×3):(1×3×1):(1×1×3):(1×1×1)

=27 : 9 : 9 : 9 : 3 : 3 : 3 : 1

See? Quite easy. The ratios for the three groups of phenotypes are simply multiplied across, and the 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1 ratio is obtained.

SO what happens when it comes to tetra-hybrid, penta-, hex-? What happens when it comes to n-hybrid?

I’m sure the answer is easy for you now, make the n phenotypes multiplied across, and the expected ratio is obtained. In plain mathematics, (3:1)^n

——————————————————————————-As noted before the 3:1 ratio can be distorted by factors such as incomplete dominance or lethal alleles. These also affect the 9:3:3:1 ratio, but other factors can also modify this ratio.

The two different genes must not act on the same character. For instance, if the proteins encoded by the two genes are involved in the same biochemical pathway then the ratios of phenotypes resulting from the genotypes will be altered.
If the two genes lie close together on the same chromosome, linkage happens and the ratio won’t be 9:3:3:1 either, as we mentioned in Review of Mendel’s Genetics, the very beginning of our Genetics study.

Testcross

As with the monohybrid cross, it is also possible to conduct a testcross with F1 generation of the dihybrid cross.

The blueprint of life [4]: Tertiary Structure of DNA

Finally, we come to the last part of the molecular structure of DNA.

4. Tertiary Structure of DNA – superhelix structure

Advanced folding and intertwining of DNA molecules over the secondary structure .

DNA topology

1. Linear DNA:

Commonly seen in eukaryotes,
with extreme length,
complementary sequence
included in the chromatin (the combination or complex of DNA and proteins that make up the contents of the nucleus of a cell)
interacting with other cellular components.

2. Circular DNA:

(DNA frequently occurs in nature as closed-circular molecules, where the two single strands are each circular and linked together. The number of links is known as the linking number(Lk).)

Usually seen in prokaryotes, e.g. plasmid (质粒), circular bacterial chromosomes and many viral DNA molecules
cccDNA (covalently closed circular DNA) → supercoiled or Relaxed; ncDNA (nicked circular DNA): a nick (缺刻)formed by breaking one phosphodiester bond
two complementary single strands are each joined into circles, 5′ to 3′, and are twisted around one another by the helical path of DNA.
The molecule has no free ends and the two single strands are linked together a number of times corresponding to the number of double-helical turns in the molecule.

cccDNA Topology

Supercoiled DNA

Negative superhelix: natural status of cccDNA with less intra- molecular tension (underwound effect)

Positive superhelix: unnatural status with higher tension (overwound effect)

Relaxed circular DNA: intermediate between negative superhelix and positive superhelix

Topological Equation of cccDNA

L = T + W

L=Linking number=total number of times one strand of the double helix links the other

T=Twisting number= the number of times one strand completely wraps around the other strand

W=Writhing number= the number of times that the long axis of the double helical DNA crosses over itself in 3-D space

Features

1. The linking number of a closed-circular DNA is a topological property, that is one which cannot be changed without breaking one or both of the DNA backbones. (A molecule of a given linking number is known as a topoisomer. Topoisomers differ only in their linking number)

2. Twisting number

For B DNA, T>0(10 bp per turn)

For A DNA, T>0(10.5 bp per turn)

For Z DNA, T<0 (12 bp per turn)

3. Writhing number

Relaxed: W=0

Negative supercoils: W<0

Positive supercoils: W >0

TWIST &WRITHE, from Instant Notes in Molecular Biology(3rd edition)

Topoisomerases (enzymes used to regulate the level of supercoiling of DNA molecules)

To alter the linking number of DNA, the enzymes must transiently break one or both stands. There are two classes of topoisomerases:

Type I Topoisomerase nick one strand of the DNA, changing 1 Linking-number at a time(+/-1 Lk)

Type II Topoisomerase, which requires the hydroloysis of ATP, break two strands of DNA, changing 2 Linking-number at a time(+/-2Lk); also able to unlink DNA molecules.

Most topoisomerases reduce the level of positive or negative supercoiling, that is, they operate in the energetically favorable direction. (However, DNA gyrase, a bacterial type II enzyme, uses the energy of ATP hydrolysis to introduce negative supercoiling into hence removing positive supercoiling generated during replication.)

Topoisomerases are essential enzymes in all organisms; they are involved in replication, recombination and transcription.

Both type I and II enzymes are the target of anti-tumor agents in humans.

DNA superhelix

Biological significance of Superhelix:

DNA packing:

Eg.

This is a famous electron micrograph of an E. coli cell that has been carefully lysed, then all the proteins were removed, and it was spread on an EM grid to reveal all of its DNA.

DNA functioning:

Negative supercoils serve as a store of free energy that aids in processes requiring strand separation, such as DNA replication and transcription; Strand separation can be accomplished more easily in negatively supercoiled DNA than in relaxed DNA.

1. DNA in cells is negatively supercoiled;

2.(-)supercoiling introduced by a topoisomerase II (gyrase 促旋酶) in prokaryotes and by nucleosome (核小体)in eukaryotes

3.Cruciform or bubble structures introduced by (-) supercoiling are potential protein-binding sites

The blueprint of life [3] secondary and some special structures of DNA

Let’s pick up where we dropped, the secondary structure of DNA.

IN FACT, a number of different forms of nucleic acid double-helix have been observed and studied, all having the basic pettern of two helically-wound antiparallel strands.

Polymorphism （多样性）of DNA Secondary Structure

―due to conformational changes of sugar-ring on the nucleotide chain.

1. B-form:

right-handed
the structure identified by Watson and Crick,
the most common form,
believed to be the idealized form of the structure adopted by virtually all DNAin vivo (in the living body of a plant or animal), or, at physiological (characteristic of or appropriate to an organism’s healthy or normal functioning) pH and salt concentration.

characterized by:

a helical repeat of 10bp/turn (although now it is known that ‘real’ B-DNA has a repeat closer to 10.5bp/turn);
the presence of base pairs lying on the helix axis and almost perpendicular to it;
having well-defined, deep major and minor grooves.

2. A-form:

right handed
adopted by DNA in vivo under unusual circumstances, (conversed from B-form in low moisture (<75%))
presents in certain DNA-protein complexes

characterized by:

a helical repeat of 11 bp/turn.
the presence of base pairs tilted with respect to the helix axis, and actually lying off the axis.
being the helix formed by RNA and DNA-RNA hybrids. (Similar to some RNA-DNA duplex or RNA-RNA duplex.)

3. Z-form:

left-handed
formed by stretches of alternating pyrimidine-purine sequence, e.g. GCGCGC, especially in negatively supercoiled DNA in high saline (盐) solution.
not easily form even in DNA regions of repeating GCGCGC, since the boundaries between the left-handed Z-form and the surrounding B-form would be very unstale

characterized by:

a zigzag (锯齿型) pattern where its name comes from
12 bp/turn

(1)

A. B, Z-DNA — slide shown by prof.Dong,COMPARISON AMONG A-,B-,Z-DNA

(2)

picture from Instant Notes in Molecular Biology (3rd Edtion)

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Some special structures of DNA

1. Inverted repeats and direct repeats

Inverted Repeat is functionally important as recognition sites on the DNA for the binding of a variety of proteins (e.g. restriction and modification enzymes)

Inverted Repeat is either discontinuous or continuous,

Continuous → palindromic structure (回文结构:inverted repetitions of base sequence over the two strands form a symmetric structure )

Discontinuous→ hairpin & cruciform (发卡、十字结构:self complementary within each of the strands )

hairpin structure & cruciform structure — hairpin structure & cruciform structur

2. DNA triplex (The intramolecular triplex (H-DNA) as an example)

• AG-rich strand vs. CT-rich strand with Hoogsten hydrogen bond

(a quick glance at Hoodsten hydrogen bond:

• Mirror inverted repeat

• a barrier for different DNA and RNA polymerases, and so it is a negative regulator for gene expression.

3. G-quadruplex structure

G-rich sequence(s) to form 4-stranded structure by unusual G-G

H-bonds

Mendel’s Genetics[3]: Variations of the 3:1ratio

Variations of the 3:1 ratio

The simple 3-to-1 monohybrid ratio is not always observed in instances where only one gene is responsible for a particular phenotype.

A number of factors:

Partial or incomplete dominance

Complete dominance means the phenotype of first filial generation(heterozygous) is exactly identical to that of one of the parents(both homozygous). Partial or incomplete dominance means the first filial has phenotype somewhere between that of both parents.

For example, When two pure-bred snapdragons, with white and red petals respectively, cross, their first filial generation has pink petal rather than red or white.

In this case, the homozygous phenotypes are red, or white petals while heterozygous one is between white and red: pink petal.

Thus, it is conceivable that when it comes to the second filial generation, which was produced by the self fertilization of the heterozygous F1, F2 should have three different phenotypes, white, pink, and red. And we can also deduce the ratio of them is 1:2:1.

Codominance

Codominance is similar to incomplete dominance, but here the heterozygote displays both alleles(两种等位基因均被表达).

For example, in humans the MN blood group is controlled by a single gene.

In humans the main blood group systems are the ABO system, the Rh system and theMN system.

Only two alleles exist, M and N. Children whose father is an NN homozygote with N blood and whose mother is a MM homozygote with group M blood are MN heterozygotes and have group MN blood.Both phenotypes are identifiable in the hybrid. And the ratio also switches from 3:1 to 1:2:1.

Lethal alleles

Some alleles affect the viability of individuals that carry them.

In most cases the homozygous recessive does not survive but the heterozygotes may have a normal lifespan.

The best-known example of lethal alleles is the inheritance of yellow coat color in mice.

Yellow fur can arise in strain of mice with different colors, or instance, black. Yellow coat color is dominant to black coat. Mice with BB alleles are back, with BB^yare yellow, with B^yB^y alleles are supposed to be yellow as well, but B^yB^y alleles are lethal and any mice with this genotype die in utero(in the uterus : before birth).

SO it is conceivable that when two yellow mices are mated ratio of the different phenotypes of their first generation is 2 : 1, rather than 3 : 1 or 1 : 2 :1.

NOTE: The allele B^yis recessive in its relation to its effect on viability (only homozygous B^yB^ys die, while the heterozygotes survive ), but dominant in relation to coat color(heterozygotes present in yellow fur in stead of black fur.).

Other examples where alleles are lethal when homozygous but have a dominant effect when heterozygous, include :

tailless Manx cats

genetics — a manx cat, image from the Internet

a breed of domestic cat(Felis catus) originating on the Isle of Man, with a naturally occurring mutation that shortens the tail.

The Manx taillessness gene is dominant and highly penetrant; kittens from two Manx parents are generally born without any tail. Being homozygous for the taillessnees gene is lethal in utero.Thus, tailless cats can only be heterzygous. Because of the danger of having homozygous taillessness gene, breeders avoid breeding two entirely tailless Manx cats together.(wikipedia: Manx (cat))

short-legged Creeper chickens.

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(Annie: If none of the homozygous yellow mice can survive before birth, then where did all the heterozygous yellow mice come from in the first place???????)

Answer: Through mutation. The presence of one mutant allele alters development so as to produce characteristic changes to the animal, but when two of the mutant alleles are present, development is so aberrant as to cause death.

This may occur in utero as described above or resulted in shortened life expectancy as found in several examples in humans, such as Tay-Sachs disease, Huntington’s syndrome（亨丁顿舞蹈症） or sickle-cell anemia（镰刀形红血球病）. (from Instant Notes)

the blueprint of life [2]: primary and secondary structure of DNA

Molecular structure of DNA:

professor Dong first showed us where DNA is:

Then he introduced the molecular structure of DNA with 4 parts:

1. Primary structure of DNA:

Arrangement of nucleotides along a DNA chain.

Annie: So…the primary structure of DNA is a line.

Conventionally, the repeating monomers of DNA are represented by their single letters A, T, G, C.

Professor: There’s a convention to write the DNA sequence with 5′ at the left, that is, in a 5′ to 3′ orientation from left to right.

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2. Secondary structure of DNA—stabilized partial structure formed by polymers of nucleotide

Professor Dong: First, please familiarize yourselves with Chargaff’s Rule:

A+G=T+C & G+T=A+C

↓↓

A=T & G=C

(Chargaff’s Rule)

(Based on analysis of the chemical composition of duplex DNA in the early 1950s, E. Chargaff deduced these rules about the amounts of different nucleotides in DNA.)

Professor: The secondary structure of DNA is a partial structure formed by polymers of nucleotide. The structure is referred to as the double-helix structure.

Two separate chains of DNA are wound around each other, each following a helical (coiling) path, resulting in a right-handed double helix structure.

In 1953, Watson and Click proposed the DNA double-helix structure based on Chargaff’s Rule and DNA Crystallography and X-ray diffraction images of DNA structure by Wilkins and Franklin. (Rosalind Franklin, who was not that well-known as Watson, Click and Wilkins but apparently played a equally significant role in the discovery of the structure.The whole was later nominated Nobel Prize but her, is that even fair?)

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The backbone of duplex DNA is a serious of phosphodiester group (the covalent linkage of a phosphate group between the 5′-hydroxyl of one sugar and the 3′-hydroxyl of the next, that is , repeats of P-sugar unit) linked by phosphodiester bond.

—————————————————————————

The strands are joined noncovalently by hydrogen bonding between the bases on opposite strands, to form base pairs.

There are around 10 base pairs per turn in the DNA double-helix. The two strands are oriented in opposite directions in terms of their 5’to3′ direction(the nucleotides in one strand is opposite to their direction in the other strand).

More crucially, the two strands are complementary in terms of sequence. The bases hydrogen-bond to each other as purine-pyrimidine pairs which have very similar geometry and dimensions.

A–T: 2 H-bonds ; C–G: 3 H-bonds

5’- A T G T C -3’

¦¦ ¦¦ ¦¦¦ ¦¦ ¦¦¦

3’- T A C A G -5’

Thus, the sequence of one strand uniquely specifies the sequence of the other, with all that which implies for the mechanism of replication of DNA and its transcription to RNA.

——————————————————————————-

Professor Dong added:

Between the backbone stands run the major and minor grooves.

In a detailed analysis of DNA structure, there are two types of grooves that can be seen; the major groove has the nitrogen and oxygen atoms of the base pairs pointing inward toward the helical axis, while in the minor groove,the nitrogen and oxygen atoms point outwards;

Shown by prof.Dong, MAJOR GROOVE A-T

Shown by prof.Dong, MAJOR GROOVE G-C

Major Groove Minor Groove

Depth: 8.5 Å Depth: 7.5 Å

Width: 11.7 Å Width: 5.7 Å

Å

Definition: Symbol for Ångström, a unit equal to 0.1 nanometer, mainly used in expressing sizes of atoms, lengths of chemical bonds, and wavelengths of electromagnetic radiation.

Supplement: The unit is named after the Swedish physicist, Ångström, Anders Jonas.

picture from Instant Notes in Molecular Biology

Professor: The major groove is more dependent on base composition. and major grooves and minor grooves are also recognition and binding sites for certain protein factors, and are involved in the regulation of gene expression.

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Professor: Summary of “Double Helix” Model (B-DNA):

Right Handed Double Helix

Outside: P-Sugar backbone

Inside: Base pairing linked by H-bonds

Minor and Major grooves

（note: bp=base pair(s)）

Let’s begin with a relatively simple example.

When the situation gets a little bit more complicated:

A more complex situation:

The three examples above lead us to a new concept: Epistasis.

UV absorption

Thermodynamics of DNA

DNA topology

DNA superhelix

Thermodynamics of DNA