CHAPTER 1: ANSWERS

 

Answer 1.1.   

               a)      First letÕs go through the matings, assuming pr and vg are on different chromosomes.  In the following notation, alleles above the horizontal line are from one homologous chromosome, and alleles below the line are from the other homologous chromosome.

 

               Parents:                    pr        vg                    x          pr+      vg+

                                                pr        vg                                pr+      vg+

 

               F1:                            pr        vg       

                                                pr+      vg+

 

               F1 backcross:           pr        vg        male     x          pr        vg        female

                                                pr+      vg+                              pr        vg

 

Expect in F2:               male gametes:

                                                            pr vg                pr  vg+                        pr+ vg          pr+ vg+

                                                            _________________________________________

female gametes   pr vg   |         pr pr vgvg       pr pr vg+vg     pr+pr vgvg      pr+pr vg+vg

 

               This predicts four different phenotypes, purple  vestigial, purple long-winged, red-eyed vestigial, and red-eyed long-winged, in equal numbers (each comprising 0.25 of the progeny).

 

               b) The actual results were markedly different.  In fact none of the recombinant phenotypes, purple long-winged and red-eyed vestigial, were observed.  This indicates that the purple and vestigial  genes are linked.  Subsequent mapping showed that they are both in the second linkage group (Drosophila has four linkage groups, corresponding to three autosomes and one pair of sex chromosomes).  Note that no measurable recombination occurred between the purple and vestigial  genes in this backcross; this is a peculiarity of male Drosophila  and the heterogametic sex in some other species.  Other experiments with heterozygous F1 females do show recombination (see part 1c).

                        Let's re-examine the predictions of the matings, now that it is clear that the genes are linked.  In the notation below, a horizontal line with more than one gene above and below it means that the genes are linked.  Again, alleles for one homologous chromosome are above the line, and those for the other chromosome are below it.

 

               Parents:        pr   vg              x          pr+  vg+

                                    pr  vg                           pr+  vg+

               F1:                pr   vg 

                                    pr+ vg+

 

               F1 backcross:           pr   vg    male   x          pr  vg     female

                                                pr+ vg+                      pr  vg

 

 

               Expect in F2:                                    male gametes:

                                                                        pr vg                pr+ vg+

                                                            _____________________

               female gametes         pr vg   |           pr  vg               pr+ vg+

                                                                        pr  vg               pr  vg

 

               Thus in the absence of recombination, one obtains equal numbers of purple vestigial and red-eyed long-winged flies in the progeny.

 

               c) In this case, the mating is

 

               F1 backcross:           pr   vg    female            x          pr  vg     male

                                                pr+ vg+                                  pr  vg

 

               and recombination does occur (as mentioned in 1.1b, the absence of recombination is peculiar to male Drosophila).  Note that the frequency of recombinant types is much less than the 50% predicted for no linkage (see 1.1a).  The purple long-winged flies have the genotype

                        pr   vg+

                        pr   vg

               and red-eyed vestigial  flies have the genotype

                        pr +  vg

                        pr    vg

               in both cases resulting from recombination between the purple and vestigial genes.  The combined number of recombinants comprises 15.2% of the progeny, and one concludes that the two genes are linked, and are 15.2 map units, or 15.2 centiMorgans apart.

 

 

Answer 1.2

            a)         Mutations 1, 3 and 5 are in the same complementation group.

            b)       The minimal number of steps in the pathway is 3, the number of complementation groups.  Note that mutations 1, 3 and 5 comprise one complementation group, 2 is a second, and 4 is a third.

 

Answer 1.3. The two mutations in the different genes are further apart than the two mutations in the same gene. Recombination occurs more often between genes that are further apart on a chromosome.

 

Answer 1.4     A substance that allows a mutant to grow is a metabolic intermediate involved in reactions downstream of the step catalyzed by the enzyme altered in that mutant.  The results show that a mutant in complementation group A is incapable of growth when provided with any of the three metabolic intermediates, substances A, B, and C.  Thus the gene altered in this mutant must encode an enzyme that catalyzes a step downstream of those that generate substances A, B or C.  So one can place enzyme A at the end of the pathway, presumably catalyzing the final formation of serine, and substance A that accumulates in this mutant is the immediate precursor to serine.  (Saying enzyme A is at the end of the pathway assumes that a saturation mutagenesis was carried out and that no other genes are in the pathway.  More accurately, enzyme A is the most terminal enzyme in the group analyzed in this experiment).  Since substance A accumulated in mutants in complementation group A, it is the substrate for this final reaction.  Thus we can conclude from the results with mutant A that the order of intermediates and product is (B or C) ¨ A ¨ Ser.

 

               This conclusion is confirmed by the observation that substance A will allow mutants in complementation groups B and C to grow, so production of substance A is downstream of the steps catalyzed by enzymes B and C.  In fact, one of those enzymes should catalyze formation of substance A. 

 

               Substance A will allow a mutant in complementation group C to grow, but not mutants in the other complementation groups.  Thus production of substance A is downstream of the step catalyzed by enzyme C, production of substances B and C are upstream of this step.  This result is consistent with enzyme C catalyzing the formation of substance A.  The order of intermediates and products appears to be B¨ C ¨ A ¨ Ser.

 

               This conclusion is confirmed by the fact that mutants in complementation group B will grown when provided either substances C or A, again showing that production of these substances is downstream of the step catalyzed by enzyme B.  Note that none of the auxotrophs will grow when provided with substance B, showing that its production is upstream of all three steps.  If all steps are present, it is the first compound in the pathway.

 

               [Note that you can analyze these results column by column or row by row.  Whichever way you start the analysis (e.g. column by column), you can use the results with the other approach (e.g. row by row) to confirm your conclusions.]

 

 

Answer 1.5

               a)      The initial cross between the parental strains

                         CC shsh  (colored shrunken) x ccShSh  (white nonshrunken)

               yield F1 progeny with the genotypes Cc Shsh, which has the new phenotype colored nonshrunken.  A cross between the F1 and a homozygous recessive strain

                        Cc Shsh           x          cc shsh

               would be expected to give equal frequencies of the four possible phenotypes if the genes are not linked.

 

 

                                                C Sh                C sh                 c Sh                 c sh

                                                ______________________________________________

                        c sh      |           Cc Shsh           Cc shsh           cc Shsh            cc shsh

 

               The phenotypes would be colored nonshrunken, colored shrunken, white nonshrunken and white shrunken.

 

 

               b) The observed frequencies differ dramatically from the prediction of independent assortment, and in fact the parental phenotypes (colored shrunken and white nonshrunken) predominate in the progeny.  This indicates that the genes are linked.  The linkage relationships are indicated in the following diagrams of the crosses.

 

 

               Parents         C  sh    x          c  Sh

                                    C  sh                c  Sh

 

               F1                 C  sh    backcrossed to             c  sh

                                    c  Sh                                        c sh

 

                                                                                                Number of plants

Progeny will have parental chromosomes:       C  sh                21,379 colored shrunken

                                                                        c sh

                                                and

                                                                        c  Sh                21,096 white nonshrunken

                                                                        c  sh

 

as well as recombinant chromosomes:             C  Sh               638 colored nonshrunken

                                                                        c  sh

                                                and

                                                                        c  sh                 672 white shrunken

                                                                        c  sh

 

               The total number of plants counted is 43,785.  Recombinant phenotypes (colored nonshrunken and white shrunken), which result from the recombinant chromosomes, were seen 1310 times (638+672 = 1310).  Thus the recombination frequency between the two genes is (1310/43,785) x 100 = 3%.  The two genes are 3 map units or 3 centiMorgans apart.

 

 

Answer 1.6

               a)      Recombination between the two parental chromosomes in the F1 hybrid accounts for the new phenotypes (reflecting the new genotypes) in the F2 progeny.  Let's look at AB/AB x ab/ab in more detail, using the notation of a horizontal line to represent the chromosome on which the genes are linked (alleles from one homolog are above the line, alleles from the other are below the line).

 

               The F1          AB                   is crossed with             ab

                                    ab                                                        ab

 

               In the absence of recombination, one expects

                                                            AB       and      ab  to occur all the time.

                                                            ab                    ab

               Note that each of these diploid genotypes will produce the parental phenotypes.  What the problem tells you is that recombination occurred between the A and B genes, i.e.

                        A  B                             A  b

                          x                    -->

                        a  b                              a  B

              

               to produce gametes carrying Ab and aB . (In this notation just used, the horizontal lines represent each homologous chromosome, and the x depicts the position of a crossover event, or recombination between the two chromosomes.)  The products of the recombination are seen in the F2 generation as

                        Ab        and                  aB

                        ab                                ab

These recombinants occur in 30% of the progeny from the    AB    x ab        cross.

                                                                                                ab        ab

Likewise, recombinants occur in 10% of the progeny from the AC   x            ac        cross,

                                                                                                ac                    ac

and recombinants occur in 25% of the progeny from the        BC    x bc        cross.

                                                                                                bc        bc

               The latter two cases indicate that recombination has occurred between genes A  and C and between B and C, respectively.

 

               b)  There are many more sites for potential recombinations (recombination can occur at each nucleotide pair) than there are actual recombination events during meiosis.  Thus the further apart two genes are, the more likely it is that recombination will occur between them.  Thus recombination frequency should be proportional to the distance between the two genes.

 

               For the three genes in this problem, genes A and B have the largest distance between them (30% recombination frequency), genes B and C are less far apart (25% recombination frequency), and genes A and C are the closest together (10% recombination frequency).

 

               c)  The linkage map shown below fits the data given:

 

               A____10%___C____________25%_____________B

               _________________30%______________________

 

               Note that the distances between the genes are roughly, but not precisely, additive.

 

 

Answer 1.7

 

               a)      The probability that both independent events will occur is the product of the individual probabilities, which are the individual frequencies of recombination.  Using the notation described in the problem, this product is

                        (ac )(cb).

 

               b) The combined probabilities will be the same as in part 1.4.a, i.e.

                        (cb)(ac).

 

               c) This relationship can be expressed as

                        ab = ac + cb - 2(ac)(cb)

 

               Using the numbers from problem 3, we obtain

                        0.30 = 0.10 + 0.25 - 2(0.10)(0.25)

                        0.30 = 0.35 - 0.05

                        0.30 = 0.30

               So the observed frequency of recombination between the outside markers A and B was decreased by multiple crossovers from 35% to 30%.

 

               d) A better estimate of distance between genes A and B is 35%, the sum of the recombination frequencies between A and C and between C and B.  The effect of multiple crossovers gets larger as genes are further apart.  The additive nature of recombination frequencies allows one to construct large linkage maps.  As you probably realize by now, a recombination frequency greater than 50% cannot be measured in a cross between two members of a diploid species (do you see why?), but genetic distances greater than 50 map units (or centiMorgans) between genes can be mapped using the combined recombination data for genes that occupy shorter intervals between them.

 

 

 

 

 

Answer 1.8

                        a)

                        1-                                                                                             3-         2-

                        |                                                                                               |           |

                                                                        0.099                                       0.001

 

                        b)

                        1) Mutations 1 and 2 are in different genes, since they complement in trans.  They encode diffusible products.

                        2)         Mutations 1 and 3 are in different genes.

                        3)         Mutations 2 and 3 are in the same genes; they do not complement in trans.

 

 

 

Answer 1.9

               a)      1 and 4 do not complement (the total number of phage is the same as the number of wild-type recombinants), 2 will complement 1, 3 and 4 (each pairwise co-infection gives 1010 total phage), and 3 will also complement all other mutants (1, 2 and 4).  Thus mutants 1 and 4 are in the same complementation group, which is distinct from the two other complementation groups represented by mutant 2 and by mutant 3.  One concludes that there are at least three genes (complementation groups) in the pathway for growth on the restrictive host.

 

               b)      Mutations 1 and 4 have the shortest distance between them, as shown by the fact that mutants 1 and 4 have a lower recombination frequency than any other pairwise co-infections.  (Note that 1 and 4 are in the same complementation group.)

 

               c)      Mutations 1 and 3, as well as 3 and 4, have a higher recombination frequency than other pairwise combinations. In both cases, the co-infections generated 107 wild-type recombinants, so both pairs are equally far apart. 

 

               d)      A correct map is shown below.  In this diagram, the vertical bars mark the ends of the genes.  The number of the mutant indicates positions of the mutations.  Note that in this map, mutations 1 and 4 are in the same gene, and the distances between the genes fit the recombination frequencies.

 

 

                                    Gene A                 Gene B                   Gene C

                                    |__4__1__|_____|___2__|________|___3_____|

 

 

 

Answer 1.10.

a. The induced mutation hypothesis says that there is a certain probability that a cell will mutate to phage resistance in the presence of the selective agent, i.e. the infecting phage. Every cell in the culture has the same probability of undergoing this mutation, and the presence of the phage induce them to mutate. These mutations then would occur simultaneously in all the cultures, when the phage are added. Thus if the probability of mutating to phage resistance is about 1 in 107 and 108 bacteria are examined in each culture, then each culture should generate about 10 resistant colonies. The number of resistant colonies per culture should be normally distributed around 10 as the mean.

 

 

In contrast, if mutations arise spontaneously, not as a response to selection, then they should occur at any time in the growth of the culture. All the progeny of a resistant cell (a clone) will also be resistant. In some cultures, the spontaneous mutation to phage resistance occurs in a cell early in its growth, and as this resistnat clone propogates, many more resistant cells are produced. In other cultures, the mutation to resistance occurs later, or not at all. When the selective agent is added (the T1 phage), the cultures that acquired resistant clones early in their growth will make many resistant colonies on the selective plates. These will be "jackpots" with many T1r colonies. Those cultures that acquired resistant clones late in their growth will make few resistant colonies. The number of colonies of resistant bacteria will fluctuate, depending on when the spontaneous mutation occurred. The distribution of numbers of resistant bacteria in cultures should form a Poisson distribution.

 

b. Different cultures vary dramatically in the numbers of resistant cells, with some ÒjackpotsÓ with many resistant colonies seen. In fact, the actual results in the table fit a Poisson distribution, as predicted by the spontaneous mutation hypothesis. Hence one concludes that mutations arise spontaneously, not in response to selection.

 

 

ANSWERS

CHAPTER 2

STRUCTURES OF NUCLEIC ACIDS

 

 

2.1                   Almost 1/10 of the volume of the nucleus is occupied by DNA.  This is calculated in the following analysis.

 

            The volume of a cylinder, Vc, can be determined from knowing its radius, r, and its length, l:

                                    Vc = p r2 l

 

            Consider DNA to be a cylinder whose r is 0.95 nm (the diameter of B form DNA is 1.9 nm).  The length is determined by the number of base pairs; B form DNA has one bp every 0.34 nm.  We will treat the volume of the nucleus in mm3, so the dimensions should be expressed in mm (1 mm = 1000 nm).  The volume of cylindrical DNA with 6 billion base pairs is:

 

                        Vc = p (9.5«10-4 mm)2 (6«109 bp « 3.4«10-4 mm/bp)

                        Vc = 5.78 mm3

 

            Consider the nucleus to be a sphere whose radius, r, is 2.5 mm.  The volume of the sphere, Vs, is given by

 

                        Vs = 4/3 « pr3

                        Vs = 4/3 « p « (2.5 mm)3

                        Vs = 65.4 mm3

 

            The fraction of the volume of the nucleus occupied by this volume of DNA is:

 

                        = = 0.088, or almost 0.1

 

2.2         (a) The complementarity between A and T, and between G and C, in the two strands of duplex DNA explained Chargaff's rules, i.e. that the sum of pyrimidine nucleotides equals that of the purine nucleotides in DNAs from (virtually) all species.  A=T, G=C, and A+G=C+T for duplex DNA.  The fraction of M13 that is A (23%) does not equal that of T (36%), nor does that of G (21%) equal that of C (20%).  A+G = 44%, whereas C+T = 56%.  This lack of equality between purine nucleotides and pyrimidine nucleotides shows that M13 DNA is not double stranded, because it does not show the relationships expected as a result of complementarity between the two strands of duplex DNA.

 

(b) LetÕs use the percentages as an average number of a specific nucleotide per 100 nucleotides, so 23% A is the same as 23 AÕs for every 100 nucleotides. Each A on the viral strand corresponds to a T on the complementary strand, and each T on the viral strand corresponds to an A on the complementary strand (ChargaffÕs rules). So in duplex form there will be 23 AÕs on the viral strand and 36 AÕs on the complementary strand (determined by the number of TÕs on the viral strand). This gives (23+36)/200 = 0.295, or 29.5% A for the 100 nucleotides on the viral strand plus the 100 nucleotides on the complementary strand. Likewise, the T composition is (36+23)/200 = 0.295, or 29.5%. The G composition is (21+20)/200 = 0.205. or 20.5%. The C composition is (20+21)/200 = 0.205. or 20.5%. Note that the mole fractions of A=T and G=C.

 

 

2.3 

              Here is a simple example. See how the base composition differs for a short single strand:

 

                                                            A         G         C         T

                        AGGGCTAAGC        30%     40%     20%     10%

 

                             versus the double strand form:

 

                        AGGGCTAAGC        20%     30%     30%     20%

                        TCCCGATTCG

The duplex will have a different base composition than the single strand, and it shows equality between the compositions of the complementary nucleotides.

 

2.4.  a)

                       

 

 

 

              b)

                       

 

              c)       The T has to be moved considerably, relative to its position in an A-T base pair, in order to get H-bonding with G.  This is most easily seen by examining the position of the N-glycosidic bond from T to the the deoxyribose.  Note how it is displaced "upward" relative to that seen for the A-T base pair.  The DNA would have to be distorted greatly to accomodate this alteration, and indeed G does not pair with ketoT in duplex DNA.

                       

 

              d) Now with the T in the enol tautomer, 3 H-bonds can readily be formed with G, without distortion of the DNA duplex.  Thus if T shifts to the enol conformation after incorportation into DNA, it will pair with G during replication, and thus cause an alteration in the sequence, i.e. a mutation. 

 

                       

 

              This exercise should also illustrate the importance of using the correct tautomers of the bases in deducing a structure for DNA.  Watson and Crick were initially building their model in the early 1950's with the enol tautomers, and were unable to make their model fit with Chargaff's rules.  They were greatly aided by a colleague who pointed out to them that the keto tautomers were greatly favored - and have the opposite base pairing properties to the enol tautomers!

 

2.5   a)  In terms of nearest neighbor frequencies (or dinucleotide frequencies):

 

            Same orientation                      Opposite orientation

            TpA = ApT                              TpA = TpA

            ApG = TpC                             ApG = CpT

            GpA = CpT                             GpA = TpC

            ApC = TpG                             ApC = GpT

 

                        b)  The data support an antiparallel polarity to the DNA strands.  Using the predictions in part a), we see that, in terms of frequency,

            TpA = TpA,     0.012 = 0.012

            ApG = CpT,    0.045 = 0.045

            GpA = TpC,    0.065 = 0.061

            ApC = GpT,    0.064 = 0.060

                        The predictions of the parallel polarity, or same orientation, are not observed.  You should check this for yourself.

 

                        (c.1.)  The radioactive phosphate has been transferred from the 5Õ position of the labeled nucleotide to its nearest neighbor on the 5Õ side.

 

            Consider the following DNA segment made in the presence of          [a32P]dATP.

 

            5Õ pGpCpCpT*pApG 3Õ

            (The * means the adjacent p, or phosphate, is labeled).

 

                        After cleavage to generate deoxynucleoside-3Õ-monophosphates (or 3Õ mononucleotides), one has the following:

 

            5Õ pGp/Cp/Cp/T*p/Ap/G 3Õ

                        or 2 moles of Cp, 1 of Ap, and 1 of Tp, and only the Tp is labeled.  The 5Õ terminal G ends up as pGp, and the 3Õ terminal G has no phosphate.

 

                        Note that the label originally with the [a32P]dATP is now with the deoxythymidine-3Õ-monophosphate.

 

                        (c.2.)  Since the label is transferred to the nucleotide on the 5Õ side of the originally labeled nucleotide, these data provide information on

            TpA, ApA, CpA, and GpA.

 

                        (c.3.)  To obtain the frequency of occurrence of each dinucleotide, simply multiply the fraction of label that is in each mononucleotide by the mole fraction of A in the genome, i.e. multiply the number given in the problem by 0.162.  The results are

            TpA     0.012

            ApA     0.024

            CpA     0.063

            GpA    0.065

 

                        Analysis of the results using labeled dTTP, dGTP and dCTP gave the results quoted in part b.

 

2.6                   (a) False. Adjacent nucleotide pairs are off-set from each other. The rotations between nucleotide pairs is 1/10 of the rotation of a full circle, since there are 10 nucleotide pairs per turn of the double helix. Thus this rotation between  adjacent nucleotide pairs is 360o/10 = 36o.

 

            (b) True. Nucleic acids in the A form, such as RNA-RNA hybrids, have a wider diameter and more base pairs per turn.

 

            (c ) True. The guanine base is rotated