📖 ContentsChapter 13
Genetics · Chapter 13

Developmental and Cancer Genetics

A single fertilized egg builds a body with hundreds of cell types arranged in exactly the right places, and it does this with one genome that every cell carries. Cancer is what happens when the genes that run that program, the ones that tell cells when to divide, when to stop and when to die, are broken one by one in a single lineage of cells. This chapter traces the developmental tool kit found in flies, worms and plants, and how the same genes, damaged in somatic cells, drive the stepwise evolution of a tumor.

By the end of this chapter you can

  • Explain why model organisms such as Drosophila, C. elegans, zebrafish, the mouse and Arabidopsis are used, and contrast forward and reverse genetics.
  • Distinguish totipotency, pluripotency, determination and differentiation, and explain the evidence for genomic equivalence.
  • Predict offspring phenotypes for maternal effect genes such as bicoid.
  • Trace the Drosophila segmentation cascade from morphogen gradients through gap, pair rule and segment polarity genes to the Hox genes, and apply the ABC model of flower development.
  • Describe how cyclins, cyclin dependent kinases, the Rb and E2F switch and p53 enforce the cell cycle checkpoints.
  • Compare proto-oncogenes, oncogenes and tumor suppressor genes, and list the ways a proto-oncogene becomes activated.
  • Apply Knudson's two hit hypothesis and loss of heterozygosity to hereditary and sporadic cancers.
  • Explain the multistep, clonal nature of cancer using the colorectal adenoma to carcinoma sequence, age incidence data and the hallmarks of cancer.

Section 1Model organisms and developmental genetics

The central puzzle of development

A human begins as one cell and ends as roughly thirty trillion cells of more than two hundred types, yet with rare exceptions (B and T lymphocytes that rearrange their antigen receptor genes, and red cells that discard their nucleus) all of these cells carry the same DNA. Development is therefore a problem of differential gene expression: different subsets of a shared genome are switched on in different cells, at different times, in response to signals and to the cell's own history.

Genomic equivalence and cloning

Early embryologists debated whether cells lose genes as they specialize. Nuclear transfer experiments settled the question. A nucleus taken from a differentiated cell and placed into an enucleated egg can, at least sometimes, direct development of an entire organism. Frog tadpole intestinal nuclei produced swimming tadpoles and some adult frogs, and later a sheep was cloned from the nucleus of an adult mammary gland cell by somatic cell nuclear transfer. The success rate is low, because the egg must erase the donor nucleus's epigenetic marks, but the principle is clear: differentiated cells keep a complete genome. This is genomic equivalence.

A more practical demonstration came when adult skin fibroblasts were reprogrammed into induced pluripotent stem cells (iPSCs) by forcing expression of four transcription factors: Oct4, Sox2, Klf4 and c-Myc. Expression of a few master regulators was enough to reset the cell's identity, which tells us that cell type is maintained by networks of transcription factors and chromatin states, not by permanent changes to the DNA sequence.

Potency, determination and differentiation

Potency describes the range of cell types a cell can still produce. The zygote and, in mammals, the blastomeres up to about the eight cell stage are totipotent: they can form every cell of the embryo and the extraembryonic tissues such as the placenta. Cells of the inner cell mass of the blastocyst are pluripotent: they can form any cell of the body (all three germ layers and the germ line) but not the trophoblast. Embryonic stem cells are cultured pluripotent cells. Adult stem cells, such as hematopoietic stem cells, are multipotent, producing several cell types within one lineage, and some progenitors are unipotent.

Two terms are often confused. Determination is the commitment of a cell to a particular fate. A determined cell may look exactly like its neighbors, but if you transplant it to a new location it still develops according to its original fate. Differentiation is the later, visible acquisition of the specialized structure and proteins of that fate. Determination is therefore tested by transplantation, while differentiation is seen by looking at the cell. Cells become determined either by inheriting cytoplasmic determinants unevenly at division (autonomous specification) or by receiving signals from neighboring cells (induction, or conditional specification).

Developmental potential decreases from left to right Determined Differentiated Zygote totipotent Inner cell mass pluripotent Ectodermmultipotent Mesodermmultipotent Endodermmultipotent Neuron Skeletal muscle Gut epithelium Reprogramming to iPSCs with Oct4, Sox2, Klf4 and c-Myc
Figure 13.1 Developmental potency narrows as cells commit. Determination (commitment) precedes visible differentiation. The dashed arrow shows that a differentiated cell can be reset to pluripotency, evidence that it kept a complete genome.

Why model organisms

We cannot do controlled crosses or mutant screens in humans, so developmental genetics relies on model organisms: species chosen because they are easy to raise, breed quickly, produce many offspring and can be manipulated genetically. Because the core developmental genes are deeply conserved across animals, and many across all eukaryotes, discoveries in a fly or a worm routinely explain human biology.

OrganismGeneration timeStrengths for developmental geneticsLandmark contribution
Saccharomyces cerevisiae (budding yeast)About 90 minutes per divisionHaploid and diploid life cycle, easy gene replacement, temperature sensitive mutantscdc mutants that defined the cell cycle control genes
Drosophila melanogaster (fruit fly)About 10 daysFour chromosome pairs, balancer chromosomes, large mutant screens, polytene chromosomesSegmentation genes and Hox genes; maternal effect genes
Caenorhabditis elegans (nematode)About 3 daysTransparent, invariant cell lineage, self fertilizing hermaphrodites, RNA interference by feedingComplete cell lineage, genes for programmed cell death, microRNAs
Danio rerio (zebrafish)About 3 monthsTransparent embryos that develop outside the mother, large clutches, vertebrate body planVertebrate organ formation screens, heart and blood vessel development
Mus musculus (mouse)About 9 to 10 weeksMammal, knockout and conditional knockout technology, inbred strainsMammalian Hox function, models of human genetic disease and cancer
Arabidopsis thaliana (thale cress)About 6 weeksSmall genome, self pollinating, easy transformation with AgrobacteriumABC model of flower development, plant hormone signaling

Forward and reverse genetics

There are two directions of attack. In forward genetics you start with a phenotype and find the gene. Animals are treated with a mutagen such as ethyl methanesulfonate (EMS), their descendants are bred to make mutations homozygous, and offspring are screened for a developmental defect. The mutant gene is then mapped and cloned. Forward screens are unbiased; the Drosophila segmentation screens behind Section 2 were forward screens.

In reverse genetics you start with a known gene sequence and ask what it does by disrupting it: a knockout by homologous recombination or CRISPR Cas9, a knockdown by RNA interference or morpholino oligonucleotides, or targeted overexpression. A conditional knockout (for example Cre lox in mice) deletes a gene only in a chosen tissue or time, so genes needed for early survival can be studied later.

Maternal effect and zygotic genes

The earliest steps of animal development are directed by mRNAs and proteins that the mother loads into the egg before fertilization. Genes whose products work this way are maternal effect genes. Their defining genetic property is that the offspring's phenotype is determined by the mother's genotype, not by its own. A bicoid mutant female (genotype bcd/bcd) produces embryos that lack head and thorax and die, even if those embryos received a normal bcd+ allele from their father, because the father's allele is not expressed until too late. In contrast, zygotic genes are transcribed from the embryo's own genome, and their mutant phenotypes follow the embryo's genotype in the usual Mendelian way.

Study tip. Worked problem: Females heterozygous for a recessive maternal effect allele (bcd+/bcd) are crossed to bcd+/bcd males. (a) What fraction of the F1 embryos develop normally? (b) The F1 flies are allowed to mate at random. What fraction of the F2 embryos are defective? Step 1: The F1 embryos develop from eggs made by a bcd+/bcd mother. She has one working allele, so every egg is loaded with Bicoid mRNA. All F1 embryos (100 percent) are normal, even the one quarter that are bcd/bcd. Step 2: Write the F1 genotypes: 1/4 bcd+/bcd+, 1/2 bcd+/bcd, 1/4 bcd/bcd. Step 3: An F2 embryo is defective only if its mother is bcd/bcd; the father's genotype is irrelevant. With random mating, each F1 female is equally likely to be a mother, so the fraction of defective F2 embryos equals the fraction of F1 females that are bcd/bcd, which is 1/4. Answer: (a) all F1 embryos are normal; (b) 1/4 of F2 embryos are defective, and they come entirely from one quarter of the mothers, each of whom produces only defective embryos.

Lessons from the worm: lineage and programmed cell death

C. elegans is so small and transparent that every cell division can be watched under the microscope. The adult hermaphrodite has exactly 959 somatic nuclei, and its cell lineage, the complete family tree from zygote to adult, is the same in every individual. Of the 1,090 somatic cells generated, 131 die by programmed cell death (apoptosis) at predictable times and places. Screens for worms in which those 131 cells survive identified the core apoptosis genes, and every one has a human counterpart.

C. elegans geneRole in the wormHuman counterpartEffect in human cells
egl-1Triggers death in cells fated to dieBH3 only proteins (for example PUMA, NOXA, BIM)Pro-apoptotic; neutralize Bcl-2
ced-9Protects cells from deathBcl-2Anti-apoptotic; overexpressed in follicular lymphoma
ced-4Activates the death proteaseApaf-1Forms the apoptosome with cytochrome c
ced-3Executes cell deathCaspases (caspase 9, caspase 3)Cleave cellular proteins to dismantle the cell

The worm also revealed the first microRNAs, lin-4 and let-7, which time the transitions between larval stages by blocking translation of target mRNAs.

Connection. The same apoptosis machinery discovered in worms is a direct cancer drug target. A drug that mimics BH3 only proteins blocks Bcl-2 and lets cancer cells that depend on Bcl-2 for survival, such as chronic lymphocytic leukemia cells, finally undergo the death they had been avoiding.
Key point

Every cell in an organism carries essentially the same genome; development is the controlled, differential expression of that genome. Cells narrow their potency as they become determined and then differentiate. Model organisms, studied by forward screens (phenotype to gene) and reverse genetics (gene to phenotype), revealed conserved tool kits such as maternal effect genes, whose phenotypes follow the mother's genotype, and the apoptosis pathway.

Section 2Pattern formation and homeotic genes

Positional information and morphogens

Pattern formation is the process that organizes differentiated cells into a body plan with axes: anterior to posterior (head to tail), dorsal to ventral (back to belly) and, in limbs, proximal to distal. A cell needs to know where it is. One elegant solution is a morphogen: a substance produced at a localized source that spreads to form a concentration gradient. Cells read the local concentration and switch on different genes above different thresholds. A single gradient can thus specify several distinct zones.

The Drosophila segmentation cascade

The fruit fly embryo is the best understood example of pattern formation. For the first thirteen nuclear divisions, the nuclei share a common cytoplasm (a syncytium), so transcription factors can diffuse between nuclei without crossing membranes. The body is laid out by a hierarchy of gene classes, each class activated or repressed by the one above it, so that the pattern becomes progressively finer.

  1. Maternal effect (egg polarity) genes. bicoid mRNA is anchored at the anterior pole of the egg. After fertilization it is translated, and Bicoid protein diffuses to form an anterior to posterior gradient, high at the head end. Bicoid is a transcription factor that activates hunchback in the anterior half and represses translation of caudal mRNA. At the posterior pole, nanos mRNA is localized; Nanos protein blocks translation of maternal hunchback mRNA, so Hunchback protein ends up high in front and low behind. Without bicoid embryos lack head and thorax; without nanos, abdomen.
  2. Gap genes (hunchback, Krüppel, knirps, giant) are the first zygotic genes. Each is expressed in one or two broad bands. Their name comes from the mutant phenotype: loss of a gap gene removes a block of several adjacent segments, leaving a gap.
  3. Pair rule genes (even-skipped, fushi tarazu, hairy) are expressed in seven stripes, each stripe two segments wide. Each stripe has its own enhancer that reads a unique combination of gap proteins (the even-skipped stripe 2 enhancer is activated by Bicoid and Hunchback and bounded by the repressors Giant and Krüppel). Mutants lose every other segment, so the larva has half the normal number.
  4. Segment polarity genes (engrailed, wingless, hedgehog) are expressed in fourteen stripes, one per segment, and define the anterior and posterior compartment of each segment. Engrailed cells secrete Hedgehog, and neighboring cells answer with Wingless, which in turn maintains engrailed: a signaling loop that stabilizes each boundary. Mutants have segments in which one half is replaced by a mirror image of the other half.
  5. Homeotic (Hox) genes, discussed below, then give each segment its distinct identity: antennae on the head, legs on the thorax, wings on the second thoracic segment and so on.
Anterior (head) Posterior Maternal effectGap genesPair ruleSegment polarity Bicoid gradientbroad bandseven-skipped, 7engrailed, 14 hunchbackKrknigt Each class reads the class above it, so the pattern becomes finer
Figure 13.2 The segmentation cascade in the Drosophila embryo (anterior at left). A smooth maternal gradient is converted into broad gap domains (hunchback, Krüppel, knirps, giant), then seven pair rule stripes and finally fourteen segment polarity stripes.

Dorsal and ventral

The dorsal to ventral axis uses a different maternal system. Signaling through the Toll receptor on the ventral side of the embryo causes the transcription factor Dorsal to enter nuclei, but only ventrally, forming a nuclear gradient that is high on the belly side. High Dorsal activates twist and snail, specifying mesoderm; intermediate levels specify neurogenic ectoderm; and Dorsal represses decapentaplegic (dpp), so Dpp is made only on the back. (Loss of dorsal makes embryos that are entirely dorsal, hence the name.)

Homeotic genes and the homeobox

Homeotic mutations transform one body part into another body part that normally develops elsewhere. In the dominant gain of function Antennapedia mutation, the gene is wrongly switched on in the head, and the fly grows legs where its antennae should be. In combinations of loss of function Ultrabithorax mutations, the third thoracic segment takes on the identity of the second, so the fly develops a second pair of wings instead of its balancers (halteres). Notice the logic: losing a Hox gene usually makes a segment look like a more anterior segment, because the remaining, more anterior Hox genes take over.

The Drosophila Hox genes lie in two clusters on chromosome 3: the Antennapedia complex (labial, proboscipedia, Deformed, Sex combs reduced, Antennapedia) and the Bithorax complex (Ultrabithorax, abdominal-A, Abdominal-B). Remarkably, the order of the genes along the chromosome matches the order of the body regions in which they are expressed, from head to tail. This is colinearity.

All Hox genes share a 180 base pair sequence, the homeobox, which encodes a 60 amino acid DNA binding homeodomain folded into three alpha helices (a helix turn helix variant). Hox proteins are therefore transcription factors; each one switches on a battery of downstream "realizator" genes that build the structures of its segment.

Antennapedia complex Bithorax complex labpbDfdScrAntp Ubxabd-AAbd-B HeadT1T2T3A1 to A4A5 to A8 Body axis: anterior to posterior (T = thoracic, A = abdominal segment)
Figure 13.3 Colinearity of the Drosophila Hox genes. Gene order along the chromosome matches the head to tail order of the regions they specify. Boundaries are simplified; real expression domains overlap, with the more posterior gene dominant where they do.

Hox genes in vertebrates

Vertebrates have the same genes, multiplied. Mammals carry 39 Hox genes in four clusters (HOXA, HOXB, HOXC, HOXD) on four different chromosomes, arranged in 13 paralog groups. Colinearity holds in both space and time: genes at the 3' end of a cluster are expressed earlier and more anteriorly, and genes at the 5' end later and more posteriorly. Hox codes specify vertebral identity, hindbrain regions and limb segments. Excess retinoic acid, a teratogen, shifts Hox expression and disrupts the body plan.

Pattern in plants: the ABC model

Plants evolved their own homeotic system. An Arabidopsis flower has four concentric whorls: sepals (whorl 1, outermost), petals (whorl 2), stamens (whorl 3) and carpels (whorl 4, center). The ABC model explains floral organ identity with three classes of genes, most of which encode MADS box transcription factors rather than homeodomain proteins:

GenotypeWhorl 1Whorl 2Whorl 3Whorl 4
Wild typeA: sepalA + B: petalB + C: stamenC: carpel
A mutant (C spreads outward)C: carpelB + C: stamenB + C: stamenC: carpel
B mutantA: sepalA: sepalC: carpelC: carpel
C mutant (A spreads inward)A: sepalA + B: petalA + B: petalA: sepal (and the flower keeps growing new whorls)
Study tip. Worked problem: Predict the flower of a double mutant lacking both B and C function. Step 1: Remove B from every whorl, leaving A in whorls 1 and 2 and C in whorls 3 and 4. Step 2: Now remove C. Because A and C repress each other, losing C lets A spread into whorls 3 and 4. Step 3: Every whorl now has A alone, and A alone specifies sepal. Answer: sepal, sepal, sepal, sepal, and because C normally also stops the floral meristem from growing, the flower is indeterminate, a repeating set of leaflike sepals. Method: fill in letters, apply A and C antagonism, then translate letters into organs.
Key point

Pattern is built by a cascade of transcription factors. In Drosophila, maternal morphogen gradients (Bicoid, Nanos, Dorsal) set the axes; gap genes make broad bands, pair rule genes make seven stripes and segment polarity genes make fourteen; Hox genes, colinear on the chromosome and sharing the homeobox, then assign each segment its identity. Plants use MADS box genes in the ABC model, where losing one function lets an antagonist spread and converts organs into other organs.

Section 3Cell cycle control

The phases of the cycle

Development requires cells to divide at the right times and stop at the right times, and cancer is, at its core, a failure of that control. The eukaryotic cell cycle has four phases. In G1 (gap 1) the cell grows and decides whether to divide. In S phase (synthesis) it replicates its DNA, so a human cell goes from a 2C to a 4C DNA content (C is the amount of DNA in one haploid set). In G2 it prepares for division and checks that replication is complete. In M phase it carries out mitosis (prophase, prometaphase, metaphase, anaphase, telophase) and cytokinesis. G1, S and G2 together are called interphase. A typical cultured human cell cycles in about 24 hours: roughly 11 hours in G1, 8 hours in S, 4 hours in G2 and only about 1 hour in M. Cells that stop dividing exit into quiescent G0; neurons stay there for life, whereas liver cells can re-enter the cycle after injury.

Study tip. Worked problem: In an asynchronously growing culture with a doubling time of 20 hours, a sample of 1,000 cells is sorted by flow cytometry into 600 cells with 2C DNA, 250 with DNA between 2C and 4C, and 150 with 4C DNA. Estimate the length of G1, S and G2 plus M, and say which phase the 4C cells could be in. Step 1: Assign DNA content to phases. 2C cells are in G1 (or G0); cells between 2C and 4C are in S; 4C cells are in G2 or M (they have replicated but not yet divided). Step 2: To a first approximation, the fraction of cells in a phase equals the fraction of the cycle spent in that phase. G1: 600/1,000 = 0.60, and 0.60 × 20 h = 12 h. S: 250/1,000 = 0.25, and 0.25 × 20 h = 5 h. G2 + M: 150/1,000 = 0.15, and 0.15 × 20 h = 3 h. Step 3: Check: 12 + 5 + 3 = 20 h. Answer: G1 about 12 h, S about 5 h, G2 plus M about 3 h. To separate G2 from M, count the mitotic index, the fraction of cells with condensed chromosomes, under the microscope.

Cyclins and cyclin dependent kinases

The engine of the cycle is a family of protein kinases called cyclin dependent kinases (CDKs). A CDK is inactive by itself. It becomes active only when bound to a regulatory partner, a cyclin, whose levels rise and fall during the cycle (hence the name). CDK levels stay fairly constant; it is the oscillating cyclins, made by transcription and destroyed by ubiquitin mediated proteolysis, that give the cycle its rhythm. Each cyclin and CDK pair phosphorylates a different set of target proteins, which pushes the cell through a particular transition.

Cyclin and CDK pairWhen activeMain jobKey regulators
Cyclin D with CDK4 or CDK6Mid to late G1Begins phosphorylation of Rb in response to growth factorsCyclin D is made when mitogens signal through Ras and MAP kinase; inhibited by p16 (INK4 family)
Cyclin E with CDK2Late G1 into SCompletes Rb phosphorylation, starts DNA replicationInhibited by p21 and p27 (Cip/Kip family)
Cyclin A with CDK2S phaseFires replication origins and prevents rereplicationInhibited by p21
Cyclin B with CDK1 (MPF)Late G2 through metaphaseChromosome condensation, nuclear envelope breakdown, spindle assemblyInhibited by Wee1 phosphorylation; activated by Cdc25 phosphatase; cyclin B destroyed by APC/C

Cyclin B with CDK1 was first found biochemically as maturation promoting factor (MPF), which drove frog oocytes into meiosis; yeast cdc (cell division cycle) mutant screens identified the same kinase, and sea urchin eggs revealed cyclins as proteins destroyed at every division.

CDK activity is regulated at several levels, which is why it can act as a switch:

MG1SG2 Cell cycle about 24 h G2/M checkpoint Spindle assembly checkpoint G1/S checkpoint (restriction point) G0 Cyclin and CDK pairs Cyclin D + CDK4/6: G1 Cyclin E + CDK2: G1 to S Cyclin A + CDK2: S phase Cyclin B + CDK1 (MPF): G2 to M
Figure 13.4 The cell cycle and its checkpoints. Phases are drawn roughly to scale for a 24 hour human cycle, with M the shortest. Red bars mark the three major checkpoints; cells leaving G1 without committing enter quiescent G0.

The restriction point: Rb and E2F

In mammalian cells the most important decision is made in late G1, at the restriction point. Before it, a cell needs continuous growth factor signaling to proceed; after it, the cell is committed to complete the cycle even if growth factors are removed. The molecular switch is the retinoblastoma protein (Rb). Unphosphorylated (hypophosphorylated) Rb binds the transcription factor E2F and blocks its activation domain, and it recruits histone deacetylases that keep E2F target genes silent. Growth factor signals raise cyclin D; cyclin D with CDK4/6 begins phosphorylating Rb, which releases some E2F. E2F then turns on the gene for cyclin E, and cyclin E with CDK2 phosphorylates Rb further, releasing more E2F. This positive feedback loop converts a gradual rise in growth signals into a sharp, irreversible commitment. Free E2F activates S phase genes such as cyclin A and DNA polymerase subunits.

Early G1: genes off Late G1: genes on E2F Rb S phase genes OFF Cyclin D with CDK4/6, then cyclin E with CDK2, phosphorylate Rb blocked by p16 and p21 E2F Rb PPP S phase genes ON (cyclin E, DNA polymerase)
Figure 13.5 The restriction point switch. Hypophosphorylated Rb holds E2F inactive. Sequential phosphorylation by G1 cyclin and CDK complexes releases E2F, which activates S phase genes, including cyclin E itself, closing a positive feedback loop.

Checkpoints

A checkpoint is a surveillance pathway that halts the cycle until a condition is met. Checkpoints were defined genetically: yeast rad9 mutants with damaged DNA fail to pause and die. Because the pause is imposed by a separate control system, it can be lost by mutation, as happens in cancer.

CheckpointWhat it monitorsSensors and signalsHow it stops the cycle
G1/S (restriction point and DNA damage)Growth signals, cell size, DNA damageATM (double strand breaks) and ATR (single stranded DNA), checkpoint kinases Chk2 and Chk1, p53p53 induces p21, which blocks cyclin E with CDK2; Rb stays bound to E2F
Intra SStalled replication forks, damage during replicationATR and Chk1Blocks firing of late origins until repair
G2/MComplete, undamaged DNA replicationATM, ATR, Chk1 and Chk2Chk1 inhibits Cdc25, so CDK1 stays phosphorylated by Wee1 and inactive
Spindle assembly (metaphase to anaphase)Attachment of every kinetochore to the spindle under tensionMad2, BubR1 and other proteins at unattached kinetochoresMad2 sequesters Cdc20, so APC/C cannot destroy securin; separase stays inactive and cohesin is not cut

Sister chromatids are held by cohesin. At anaphase, APC/C with Cdc20 destroys securin, freeing separase to cut cohesin. A single unattached kinetochore can hold this off; a weakened spindle checkpoint produces aneuploid daughter cells, common in tumors.

p53, guardian of the genome

The protein p53, encoded by TP53, is a transcription factor that integrates stress signals. In unstressed cells it is kept at very low levels by MDM2, an E3 ubiquitin ligase that tags p53 for proteasomal destruction (and whose gene is itself switched on by p53, a negative feedback loop). DNA damage activates ATM and ATR, which phosphorylate p53 and MDM2 and block their interaction; p53 accumulates, forms tetramers and binds DNA. Its targets fall into three groups:

Oncogene activation can also activate p53, through the protein ARF (encoded by the same CDKN2A locus as p16), which inhibits MDM2. Thus p53 guards against both damaged DNA and inappropriate proliferation signals.

Study tip. Students often think a checkpoint "repairs" damage. It does not; it only stops the cycle and buys time, and in mammals p53 can also choose death. To test yourself, ask what each checkpoint protein inhibits: p21 inhibits CDKs, Chk1 inhibits Cdc25, Mad2 inhibits Cdc20. Every arrest works by turning a positive driver of the cycle off.
Key point

The cell cycle is driven by CDKs whose activity depends on oscillating cyclins, activating and inhibitory phosphorylation, CDK inhibitors and timed proteolysis. Commitment occurs at the restriction point, where G1 cyclin and CDK complexes phosphorylate Rb and release E2F. Checkpoints at G1/S, G2/M and the spindle stop the cycle when DNA is damaged or chromosomes are unattached, with p53 inducing arrest through p21 or apoptosis when damage is severe.

Section 4Oncogenes and tumor suppressor genes

Cancer is a genetic disease of somatic cells

Cancer is a group of diseases in which cells divide without regard to the normal controls and invade surrounding tissue. It is a genetic disease in the sense that it is caused by changes in genes, but in most cases those changes are somatic mutations, acquired during life in one cell lineage and not passed to children. A minority of cancers (roughly 5 to 10 percent overall) arise in people who inherited a germline mutation that gave every cell in the body a head start. Carcinogens are usually mutagens, tumors are clonal (descended from one altered cell) and specific inherited mutations predispose families to specific cancers.

Two broad classes of genes are involved, and the clearest way to keep them apart is the car analogy. Oncogenes are like an accelerator stuck to the floor: a gain of function in a gene that normally promotes growth. Tumor suppressor genes are like brakes that fail: a loss of function in a gene that normally restrains growth, repairs DNA or triggers apoptosis.

Proto-oncogenes and their activation

The first oncogenes were found in tumor causing retroviruses. The Rous sarcoma virus of chickens carries a gene, v-src, that transforms cells. A nearly identical gene, c-src, turned up in every normal vertebrate genome: the virus had captured a cellular gene in altered form. Such normal cellular genes are called proto-oncogenes. They encode the components of the pathways that tell a cell to divide: growth factors, growth factor receptors, signal transducers such as Ras, nuclear transcription factors such as Myc, and cell cycle proteins such as cyclin D. When mutated or overexpressed, they become oncogenes.

Because one activated allele is enough, oncogenes act dominantly at the level of the cell. The main routes to activation are:

Mechanism of activationWhat changesClassic exampleAssociated cancer
Point mutationA hyperactive protein that cannot be turned offKRAS codon 12, 13 or 61 mutations block GTP hydrolysisPancreatic (about 90 percent), colorectal, lung adenocarcinoma
Gene amplificationMany copies of a normal gene, so too much normal proteinERBB2 (HER2) receptor; MYCNAbout 20 percent of breast cancers; neuroblastoma
Chromosomal translocation forming a fusion geneA new chimeric protein with unregulated activityBCR-ABL1 from t(9;22), the Philadelphia chromosomeChronic myeloid leukemia
Translocation to a strong enhancerA normal protein made at the wrong time or levelMYC moved next to the immunoglobulin heavy chain enhancer, t(8;14)Burkitt lymphoma
Insertional or viral activationA viral promoter or a viral copy of the gene drives expressionRetroviral insertion near MYC; v-srcAnimal leukemias and sarcomas

Ras is the most frequently mutated oncogene family in human cancer, altered in roughly one quarter to one third of tumors. Ras, a small GTP binding protein linking receptor tyrosine kinases to the MAP kinase cascade, is on when bound to GTP and turns itself off by hydrolysis, aided by GTPase activating proteins (GAPs). Codon 12, 13 or 61 mutations cripple hydrolysis and lock Ras on. The GAP neurofibromin, encoded by NF1, is a tumor suppressor: one pathway holds both accelerator and brake.

Tumor suppressor genes and the two hit hypothesis

The classic tumor suppressor is the RB1 gene, discovered through retinoblastoma, a cancer of the developing retina in young children (roughly 1 in 15,000 to 20,000 births). About 40 percent of cases are hereditary: these children usually develop tumors in both eyes (bilateral), often several tumors, at an earlier age, and they have an increased risk of other cancers, especially osteosarcoma. The remaining 60 percent are sporadic: a single tumor in one eye (unilateral), appearing later, with no family history.

By comparing the age of onset in the two groups, Alfred Knudson proposed the two hit hypothesis. Retinoblastoma requires two mutational events in the same cell. In hereditary cases the first hit is inherited, so one somatic hit suffices, and among millions of retinal cells that happens several times; in sporadic cases both hits must strike one cell, a much rarer event. Both copies of RB1 must be lost for the tumor to form, so tumor suppressor genes are recessive at the level of the cell. Yet the predisposition is inherited as an autosomal dominant trait with about 90 percent penetrance, because nearly every carrier will experience a second hit somewhere in the retina. This recessive mechanism with dominant inheritance is a heavily tested idea.

normal RB1 allele mutant RB1 allele Hereditary Sporadic 1 hitgrows hit 1hit 2 inherited inevery cell two normalalleles Often multipleand bilateral,early onset Single tumor,unilateral,later onset
Figure 13.6 Knudson's two hit model. In hereditary retinoblastoma one mutant RB1 allele is present in every cell, so a single somatic event in any retinal cell produces a tumor. In sporadic cases, two independent somatic events must strike the same cell.

Loss of heterozygosity

The second hit is often not a new point mutation. More commonly, the cell loses the remaining normal allele by deleting part of the chromosome, losing the whole chromosome (often followed by duplication of the mutant one), or by mitotic recombination or gene conversion that copies the mutant allele onto the homolog. Each of these converts a heterozygous cell into one that carries only the mutant allele, an event called loss of heterozygosity (LOH). LOH is detectable with nearby DNA markers: a person heterozygous for markers around RB1 in blood cells shows only one marker allele in tumor cells. The second hit can also be epigenetic: hypermethylation of CpG islands in a promoter can silence the remaining allele (common for MLH1, BRCA1 and CDKN2A).

Study tip. Worked problem: Suppose a developing retina contains about 2 × 106 retinoblasts that are at risk, and the chance that any given RB1 allele is inactivated in a given cell during development is 1 × 10-6 (counting all mechanisms). Estimate the expected number of tumors in one eye for (a) a child who inherited a mutant allele and (b) a child who did not. Step 1 (hereditary): each cell already has one bad allele and needs one hit on its single good allele. Expected number of cells hit = 2 × 106 × 1 × 10-6 = 2 tumors per eye. Step 2: Since 2 tumors per eye are expected, both eyes are very likely affected, matching bilateral, multifocal disease. (Using the Poisson distribution, the probability of zero tumors in one eye is e-2 = 0.135, so the chance an eye is spared is about 13.5 percent.) Step 3 (sporadic): a cell must lose both alleles. Probability per cell = (2 × 10-6 for a first hit on either allele) × (1 × 10-6 for the second) = 2 × 10-12. Expected tumors per eye = 2 × 106 × 2 × 10-12 = 4 × 10-6. Answer: about 2 tumors per eye versus about 4 in a million, a difference of roughly 500,000 fold. The numbers are illustrative, but they show why one inherited hit turns a vanishingly rare event into a near certainty.

Major tumor suppressors and their pathways

Tumor suppressors are often divided into gatekeepers, which directly control cell proliferation or death (such as RB1, APC and TP53), and caretakers, which maintain genome integrity (such as the mismatch repair genes and BRCA1 and BRCA2). Caretaker loss raises the mutation rate rather than driving growth directly.

GeneNormal functionInherited syndromeMain tumors
RB1Binds E2F; restriction point brakeHereditary retinoblastomaRetinoblastoma, osteosarcoma
TP53Transcription factor for arrest, repair and apoptosisLi-Fraumeni syndromeSarcomas, breast, brain, adrenocortical, leukemia
APCTargets beta catenin for destruction (Wnt pathway)Familial adenomatous polyposisHundreds to thousands of colon polyps, colorectal cancer
BRCA1, BRCA2Homologous recombination repair of double strand breaksHereditary breast and ovarian cancerBreast, ovarian, prostate, pancreatic
MLH1, MSH2, MSH6, PMS2DNA mismatch repairLynch syndromeColorectal (with microsatellite instability), endometrial
NF1GAP that turns off RasNeurofibromatosis type 1Neurofibromas, malignant nerve sheath tumors

Not every tumor suppressor obeys the strict two hit rule. Some are haploinsufficient: losing one copy already reduces protein enough to give cells an advantage (PTEN is an example). And because p53 works as a tetramer, a missense mutant subunit can poison normal ones, a dominant negative effect. TP53 is mutated in about half of all human cancers, more than any other gene.

FeatureOncogenesTumor suppressor genes
Normal rolePromote growth and division (proto-oncogenes)Restrain division, repair DNA, promote apoptosis
Type of mutationGain of functionLoss of function
Alleles needed in the cellOne (dominant in the cell)Usually two (recessive in the cell)
Inherited germline formRare (exceptions: RET in multiple endocrine neoplasia type 2, MET)Common; predisposition shows autosomal dominant inheritance
Typical lesionsPoint mutation, amplification, translocationDeletion, nonsense or frameshift mutation, LOH, promoter methylation
Connection. Knowing which gene is broken guides treatment. Imatinib blocks the ATP pocket of the BCR-ABL kinase and turned chronic myeloid leukemia from a fatal disease into a manageable one for most patients. Antibodies against the HER2 receptor help women whose breast cancers carry ERBB2 amplification, which is why every breast cancer is tested for HER2.
Key point

Proto-oncogenes become oncogenes through gain of function (point mutation, amplification or translocation), and one activated allele is enough. Tumor suppressor genes cause cancer through loss of function of both alleles, the second often by loss of heterozygosity or promoter methylation; an inherited first hit makes cancer predisposition behave as an autosomal dominant trait, as Knudson's analysis of retinoblastoma showed. Gatekeepers control growth directly, while caretakers protect the genome.

Section 5The multistep nature of cancer

One mutation is not enough

If a single mutation could cause cancer, cancers would be far more common than they are, and their incidence would not rise so steeply with age. Several independent observations show that cancer requires the accumulation of multiple mutations in one cell lineage:

Age incidence and the number of steps

Suppose a cancer requires k rare, independent, rate limiting mutations in one cell. The probability that all have occurred by age t rises roughly as tk, and the incidence (new cases per year) rises roughly as tk-1. On a plot of log incidence against log age, the data fall on a straight line with slope k - 1. For many common carcinomas the slope is about 5 to 6, suggesting about six or seven rate limiting steps. The model is an approximation. A person who inherits one step needs one fewer somatic event, so hereditary cancers show a shallower slope and arise earlier.

0.11101001000 203040506080 Age in years (log scale) Incidence per 100,000 per year (log) 10 at age 40 640 Sporadic, slope 6 Hereditary, slope 5 Slope 6 suggests about 7 steps
Figure 13.7 Log incidence against log age for a hypothetical carcinoma. A slope of 6 is consistent with about seven rate limiting events. Inheriting one step gives a shallower line that is shifted upward, so hereditary cases appear earlier.
Study tip. Worked problem: The incidence of a cancer is 10 per 100,000 per year at age 40 and 640 per 100,000 per year at age 80. Assuming incidence is proportional to agek-1, estimate k. Step 1: Write the ratio: 640/10 = (80/40)k-1, so 64 = 2k-1. Step 2: Since 26 = 64, k - 1 = 6. (With logarithms: k - 1 = log 64 / log 2 = 1.806/0.301 = 6.0.) Step 3: k = 7. Answer: about seven rate limiting steps. Check: a slope of 6 means doubling age multiplies incidence by 26 = 64, which matches 10 to 640. A useful shortcut: every doubling of age multiplies incidence by 2 raised to the slope.

The colorectal paradigm

Colorectal cancer is the best mapped example of multistep progression because the intermediate stages, polyps of increasing size and dysplasia, can be removed at colonoscopy and analyzed. The classic sequence, worked out by comparing mutations in polyps and cancers, is:

  1. Loss of APC (both alleles) in a colonic crypt cell. APC normally helps destroy beta catenin; without it, beta catenin accumulates, enters the nucleus and, with TCF transcription factors, keeps Wnt target genes such as MYC on. The crypt cell keeps dividing instead of differentiating, forming a small adenoma. This is the gatekeeper step and it occurs in about 80 percent of sporadic colorectal tumors.
  2. Activating mutation of KRAS, which accelerates growth of the adenoma.
  3. Loss of chromosome 18q, including SMAD4, which removes growth inhibition by TGF beta signaling, in late adenomas.
  4. Loss of TP53, typically at the transition from adenoma to invasive carcinoma, allowing cells with damaged genomes to survive.
  5. Further changes that permit invasion and metastasis.

The order is a tendency; the accumulation matters more than the exact sequence. A second route, seen in Lynch syndrome and in about 15 percent of sporadic tumors, starts with loss of mismatch repair. These tumors show microsatellite instability and carry many more mutations, including frameshifts in genes with short repeats such as the TGF beta receptor type II gene.

Mutations accumulate over 10 or more years APC lossKRAS activationSMAD4 loss (18q)TP53 loss Epithelium Submucosa NormalEarly adenomaIntermediateLate adenomaCarcinoma
Figure 13.8 The adenoma to carcinoma sequence in the colon. Each stage is associated with an additional driver mutation; only the carcinoma breaks through into the submucosa. The slow pace is what makes screening and polyp removal effective.

Clonal evolution

Tumor progression is Darwinian evolution inside the body. A cell acquires a mutation that lets it divide a little more than its neighbors; its descendants form a clone; within that clone one cell acquires a second advantageous mutation and its subclone expands; and so on. Each clonal expansion enlarges the target for the next hit. Tumors therefore become heterogeneous mixtures of related subclones, and treatment can select for resistant ones, which is why a cancer that responds at first may relapse.

Genomic instability speeds the process. Loss of caretaker genes raises the point mutation rate (mismatch repair defects) or produces chromosomal instability, with frequent gains and losses of whole chromosomes and arms (spindle checkpoint defects, telomere crisis, loss of p53). Most solid tumors are aneuploid.

The hallmarks of cancer

A useful way to organize the many mutations is by the capabilities they give the cell. The widely taught hallmarks of cancer are:

HallmarkTypical genetic basisExample of a targeted therapy
Sustaining proliferative signalingActivated RAS, EGFR, ERBB2, MYCEGFR and HER2 inhibitors
Evading growth suppressorsLoss of RB1, CDKN2ACDK4/6 inhibitors
Resisting cell deathLoss of TP53, Bcl-2 overexpressionBcl-2 inhibitors
Enabling replicative immortalityReactivation of telomerase (TERT promoter mutations)Under investigation
Inducing angiogenesisIncreased VEGF, loss of VHLVEGF antibodies and receptor inhibitors
Activating invasion and metastasisLoss of E-cadherin, protease secretionLimited so far
Reprogramming energy metabolismAerobic glycolysis (Warburg effect), IDH1 mutationsIDH inhibitors
Evading immune destructionPD-L1 expression, loss of antigen presentationImmune checkpoint inhibitors (anti PD-1)

Two enabling characteristics, genome instability and tumor promoting inflammation, help cells acquire the hallmarks. Normal human cells divide only about 40 to 60 times (the Hayflick limit) as telomeres shorten; about 85 to 90 percent of cancers reactivate telomerase.

Environmental causes: mutagens and viruses

Most carcinogens cause cancer by damaging DNA. Tobacco smoke contains polycyclic aromatic hydrocarbons that form bulky DNA adducts and leave a signature of G to T transversions in TP53 of lung tumors. Ultraviolet light forms pyrimidine dimers and leaves C to T changes in skin cancers. The Ames test screens chemicals for mutagenicity, using Salmonella strains with a his mutation that cannot make histidine. Bacteria are plated without histidine plus the chemical, usually with rat liver extract (S9) for metabolic activation; only revertants form colonies.

Study tip. Worked problem: In an Ames test, control plates (solvent plus S9) average 25 revertant colonies. Plates with compound X alone average 30 colonies; plates with compound X plus S9 average 275. A common rule calls a result positive when revertants are at least twice the control. Interpret. Step 1: Without S9, fold increase = 30/25 = 1.2, below 2, so X itself is not detectably mutagenic. Step 2: With S9, fold increase = 275/25 = 11, well above 2. Step 3: The difference means liver enzymes convert X into a mutagen. Answer: X is a promutagen (and a likely carcinogen) that requires metabolic activation, just as benzo[a]pyrene from tobacco smoke is activated by cytochrome P450 enzymes to its DNA binding epoxide.

Viruses cause an estimated 10 to 15 percent of cancers worldwide. High risk human papillomavirus types (16 and 18) cause nearly all cervical cancers and many oropharyngeal and anal cancers; their E6 protein targets p53 for degradation and their E7 protein binds and inactivates Rb, knocking out both key brakes at once. Hepatitis B and C, Epstein Barr virus and HTLV-1 are other cancer viruses, and the bacterium Helicobacter pylori drives gastric cancer.

Connection. The multistep model is the reason cancer screening works. Removing a colonic adenoma at colonoscopy, or treating cervical precancer found by a Pap or HPV test, interrupts the sequence years before invasion. HPV vaccination prevents the first step altogether, and countries with high vaccination coverage are already seeing large drops in cervical precancer.

Exploiting the genetics of cancer: synthetic lethality

Restoring a lost tumor suppressor is hard, but its absence creates a weakness. Two genes are synthetically lethal when losing either alone is tolerated but losing both kills the cell. Cells lacking BRCA1 or BRCA2 cannot repair double strand breaks by homologous recombination and depend heavily on other repair pathways. Drugs that inhibit PARP, an enzyme involved in single strand break repair, cause single strand breaks to become double strand breaks during replication; normal cells repair them, but BRCA deficient tumor cells die. PARP inhibitors are now used for BRCA associated cancers.

Key point

Cancer develops through the accumulation of several driver mutations in one cell lineage, each followed by clonal expansion. Steep age incidence (log slope about 5 to 6), the stepwise colorectal sequence (APC, KRAS, SMAD4, TP53) and tumor genome sequencing all support the multistep model. Genomic instability accelerates the process; mutagens and viruses supply hits; and the resulting hallmarks, from sustained signaling to immune evasion, point to targeted therapies and screening strategies.

The chapter in one breath

  • Development is differential gene expression from a shared genome; nuclear transfer and iPSC reprogramming prove genomic equivalence.
  • Cells narrow from totipotent to pluripotent to multipotent; determination (commitment) precedes visible differentiation.
  • Model organisms are studied by forward genetics (phenotype to gene) and reverse genetics (gene to phenotype, as in knockouts).
  • Maternal effect phenotypes follow the mother's genotype; whole broods are affected.
  • In Drosophila, morphogen gradients (Bicoid, Nanos, Dorsal) drive gap, pair rule (7 stripes) and segment polarity (14 stripes) genes, and colinear Hox genes with a 180 bp homeobox assign segment identity.
  • The ABC model specifies floral organs; A and C repress each other, so losing one lets the other spread.
  • Cyclins activate CDKs; Wee1, Cdc25, CKIs (p16, p21, p27) and proteolysis by SCF and APC/C make transitions sharp and irreversible.
  • At the restriction point, cyclin D and E complexes phosphorylate Rb, releasing E2F; checkpoints at G1/S, G2/M and the spindle stop the cycle, with p53 inducing p21 or apoptosis.
  • Proto-oncogenes become oncogenes by gain of function (point mutation, amplification, translocation) and act dominantly in the cell.
  • Tumor suppressors need two hits (Knudson), often via loss of heterozygosity; an inherited first hit produces autosomal dominant predisposition.
  • Cancer is multistep and clonal: age incidence slopes of about 6, the APC, KRAS, SMAD4, TP53 colorectal sequence and the hallmarks of cancer describe how tumors evolve.
  • Mutagens (detected by the Ames test) and viruses such as HPV supply hits; synthetic lethality (PARP inhibitors in BRCA deficient tumors) turns lost genes into targets.

Words worth knowing

TermWhat it means
TotipotentAble to give rise to every cell of the organism, including extraembryonic tissues such as the placenta.
Induced pluripotent stem cell (iPSC)A differentiated cell reprogrammed to pluripotency by expressing a few transcription factors such as Oct4, Sox2, Klf4 and c-Myc.
DeterminationCommitment of a cell to a particular fate, shown by transplantation, before any visible specialization.
Forward geneticsStarting from a mutant phenotype and identifying the gene responsible.
Maternal effect geneA gene whose product, deposited in the egg by the mother, determines the offspring phenotype regardless of the offspring's own genotype.
MorphogenA substance whose concentration gradient gives cells positional information and specifies different fates at different thresholds.
Gap genesZygotic segmentation genes expressed in broad bands; mutants lose blocks of adjacent segments.
Pair rule genesSegmentation genes expressed in seven stripes; mutants lose every other segment.
Segment polarity genesGenes expressed in fourteen stripes that define the anterior and posterior parts of each segment.
Homeotic (Hox) geneA gene that specifies the identity of a body region; mutations transform one structure into another.
HomeoboxA conserved 180 base pair sequence encoding the 60 amino acid DNA binding homeodomain.
Cyclin dependent kinase (CDK)A protein kinase that drives cell cycle transitions and is active only when bound to a cyclin.
Restriction pointThe point in late G1 after which a cell is committed to divide even without further growth factor signals.
CheckpointA surveillance pathway that halts the cell cycle until a condition, such as intact DNA or full spindle attachment, is met.
Proto-oncogeneA normal gene that promotes cell growth or division and can be converted into an oncogene.
OncogeneA mutated or overexpressed form of a proto-oncogene with a gain of function that promotes cancer.
Tumor suppressor geneA gene whose normal product restrains growth or protects the genome; cancer results when both copies lose function.
Two hit hypothesisKnudson's model that both alleles of a tumor suppressor must be inactivated, one of which may be inherited.
Loss of heterozygosity (LOH)Loss of the remaining normal allele in a heterozygous cell by deletion, chromosome loss or recombination.
Driver mutationA mutation that gives a cancer cell a selective growth advantage.
Ames testA bacterial reversion assay that detects chemical mutagens, often with liver extract to mimic metabolic activation.
Synthetic lethalityA relationship in which loss of either of two genes is tolerated but loss of both kills the cell.

Check yourself

A mouse is cloned by transferring the nucleus of an adult skin cell into an enucleated egg. What does this demonstrate, and why is the success rate low?
Answer. It demonstrates genomic equivalence: the differentiated nucleus still contains all the genetic information needed to build an organism. Success is low because the donor's epigenetic marks are often incompletely reset.
A cell from a frog embryo is transplanted to a new region and still forms the tissue it would have formed in its original location, although it looked identical to its new neighbors. Is it determined, differentiated or both?
Answer. Determined but not yet differentiated. Fate that survives transplantation defines determination; it is not yet visibly specialized.
A nanos/nanos female is mated with a wild type male. What phenotype do the embryos have, and what phenotype will the embryos of her nanos+/nanos daughters have?
Answer. All of her embryos lack abdominal segments, because the phenotype depends on the mother's genotype and she supplies no Nanos. Her daughters are heterozygous and supply Nanos to their eggs, so all of their embryos are normal.
A larva has only half the normal number of segments, with every other segment missing. Which class of segmentation gene is most likely mutated, and how is it expressed in the normal embryo?
Answer. A pair rule gene, such as even-skipped or fushi tarazu. In normal embryos these genes are expressed in seven stripes, each two segments apart, so losing one removes alternate segments.
An Arabidopsis mutant has flowers with carpel, stamen, stamen, carpel from outside to inside. Which ABC function is missing? Explain.
Answer. A function. Without A, C is no longer repressed and spreads into whorls 1 and 2. Whorl 1 then has C alone (carpel), whorl 2 has B plus C (stamen), while whorls 3 and 4 are unchanged (stamen, carpel).
A cell line carries a mutation that makes Cdc25 unable to be inhibited by Chk1. What happens when these cells are irradiated in G2?
Answer. The G2/M checkpoint fails. Uninhibitable Cdc25 removes the Wee1 phosphate from CDK1, so cells enter mitosis with broken chromosomes, causing chromosome loss, aneuploidy or death.
Why does phosphorylation of Rb commit a cell to S phase rather than just nudging it forward?
Answer. Released E2F activates the cyclin E gene, and cyclin E with CDK2 phosphorylates more Rb, releasing more E2F. This positive feedback loop turns a graded growth signal into an all or none switch that no longer needs growth factors.
Tumor suppressor gene mutations are recessive at the cellular level, yet hereditary retinoblastoma is inherited as an autosomal dominant trait. Resolve the paradox.
Answer. A carrier inherits one mutant RB1 allele in every cell. Among millions of retinal cells, a second somatic hit (often LOH) almost certainly occurs somewhere, so about 90 percent of carriers develop tumors. The predisposition is dominant; the tumor needs both alleles lost.
Name three mechanisms that convert a proto-oncogene into an oncogene, with one example each.
Answer. Point mutation (KRAS codon 12, which blocks GTP hydrolysis), gene amplification (ERBB2 in breast cancer or MYCN in neuroblastoma) and chromosomal translocation (BCR-ABL1 fusion in chronic myeloid leukemia, or MYC next to an immunoglobulin enhancer in Burkitt lymphoma).
The incidence of a cancer rises from 5 to 160 per 100,000 per year as age doubles from 35 to 70. Estimate the number of rate limiting steps.
Answer. About six. The ratio is 160/5 = 32 = 25, so the slope k - 1 = 5 and k = 6. Each doubling of age multiplies incidence by 2 raised to the slope.