Cancer: Brief Introduction First stage: Mutations in genes progressively accumulate so that there is unrestrained cell proliferation
There has to be mutational amplification Over lifetime about 10 16 divisions per human About 4 or 5 independent events needed for cancer 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 10 16 cell divisions Prob(cancer) ~ 10-12 What s wrong with this?
Mutations 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 2 categories of genes that are commonly found: proto-oncogenes: activate cell proliferation human 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
Cellular decision-making 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. Clock Per2 Bmal1 cmyc p21 Wee1 G1/S G2/M Cell Cycle Progression sequestration by p300/cbp 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. ARF HDM2 Bax DNA Repair Induction of proapoptocic genes Bax, PUMA, DR5 p53 p53 Repression of antiapoptotic genes: BCL-xL, XIAP, A20 P P50 Nf-kB RelA P RelA Induction of proapoptotic genes: Fas, FasL, DR5 includes p53 E2F1 Induction of antiapoptotic genes: BCL-xL, XIAP, IAP1, IAP2, A20
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 E2F1 prb Cyclin D/Cdk4-6 P prb prb Cyclin E/Cdk2 Cdh1, Skp2 p21 Cyclin A/Cdk2 Cdh1 P P G1 G1/S S + S/G2 Biological links between the cell cycle and the circadian clock 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 BMAL1 CLOCK Cyclin B/Cdk1 Wee1 Cdc20 after Gerrard & Goldbeter (2011) G2 + G2/M Chromotherapy 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
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
Suggested reading 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)