Cancer: Brief Introduction

First stage: Mutations in genes progressively accumulate so that there is unrestrained cell proliferation

Over lifetime about 1016 divisions per human

• spontaneous mutation of the gene ~10-6 per cell per generation

• must have mutated both copies ~ 10-8

• frequency of mutation that activate genes ~ 10-8 - 10-9

• frequency of other necessary changes ~ 10-7

• need four such events ~ (10-7)4 = 10-28

• since only 1016 cell divisions Prob(cancer) ~ 10-12

There has to be mutational amplification

About 4 or 5 “independent” events needed for cancer

What’s wrong with this?

2 categories of genes that are commonly found:

proto-oncogenes: activate cell proliferationhuman suppressor genes: inhibit cell proliferation

One of the most common mutations is to a gene called p53 which is critically involved in:• activation of DNA repair mechanisms• inducing growth arrest by stopping cell division• initiating apoptosis, programmed cell death if DNA damage is sensed

The rate of mitosis sets one of the major risk factors

Some genetic changes increase cell proliferation:• prevent senescence• inhibit programmed cell death (apoptosis)• avoid destruction by the immune system• produce factors to induce new blood vessels that feed tumours• need to migrate and produce secondary tumours

Mutations

Cellular decision-making

Clock

includes p53

p53

sequestration by p300/CBP

E2F1

Wee1

HDM2

p21

Induction of pro-apoptocic genesBax, PUMA, DR5

Repression of anti-apoptotic genes:

BCL-xL, XIAP, A20

Induction of pro-apoptotic genes: Fas, FasL, DR5

Induction of anti-apoptotic genes:

BCL-xL, XIAP, IAP1, IAP2, A20

Nf-kBPP

ARF

p53RelA

P50 RelA

Cell Cycle ProgressionG2/M

G1/ScMyc

Bax

Per2

Bmal1

DNA Repair

Complex networks of interactions test the internal state of the cell and the external environment and induce activation and inactivation of genes and turn on and off various signalling pathways. This leads to a cellular decision e.g. to divide, to grow, to resist death signals, or to commit to programmed cell death.

It turns out that associated with each of the classes of cellular decisions there are key genes that control the pathways associated with this decisions. For example the GNP 53 is a key gene in the process which senses DNA damage and then decide what to do about it and the GNFB is central to the cells decision about what to do to control inflammation.

Cell cycle

Cell cycle

Another view

From The Cell Cycle: Principles of Control by David O Morgan

Cell cycle

time

Circadian clock

Circadian clock

Circadian clock

Linking the clock to the cell cycle and measuring them

CLOCK

Cyclin D/Cdk4-6

Cyclin E/Cdk2

pRB

Wee1 Cdc20

Cdh1

Cyclin B/Cdk1

p21

Cyclin A/Cdk2

G1

G1/S

S

+

S/G2

G2

+

G2/M

E2F1

Cdh1, Skp2

pRB

BMAL1

P

pRBP

P

pRB

after Gerrard & Goldbeter (2011)

Chromotherapy

Biological links between the cell cycle and the circadian clock

Poor safety is the main cause of attrition of new anticancer drugs.

Chronotherapy data support • up to five-fold improvement of tolerability• near doubling of efficacy.

However, much more effective for men than women.

Hypothesis is that this is due to variability of their clocks

Clock gates the cell cycle so that it is stopped at some times of the circadian day.

Disruption of the clock frees the cell cycle to replicate cells faster.

The clock is disrupted in most cancer cells.

It is also disrupted in people who suffer a lot of jet-lag and who work shifts, and these people have higher rates of some cancers

• gain knowledge of the way in which mathematics can aid the understanding of complex biological systems and diseases

• understand and appreciate how one can model molecular and cellular systems

• by understanding how to do this for some simple but significant models, gain insight into the way in which more complex and realistic models can be constructed and analysed

• understand how differential equations can be used in such models

• gain some skills in analysis of differential equations

• get an introduction to some interesting mathematical ideas about dynamical systems such as stability and instability, bimodality, bifurcations, nonlinearity, and oscillations

Molecular biology of the cell (Alberts et al 1994). Chapter 17 is an excellent short introduction to the physiology, genetics and biochemistry of the cell cycle.

The cell cycle. An introduction (Murray and hung Hunt 1993) contains more details about the physiology, genetics and biochemistry of the cell cycle.

The Cell Cycle. Principles of Control. (Morgan 2007, New Science Press) More up to date treatment with lots of details about mechanisms involved in the cell cycle.

Chemical kinetic theory: understanding cell cycle regulation by Tyson et al is a kinder general introduction to modelling of the cell cycle (Tyson et al 1996)

Suggested reading