an introduction to malignant neoplasia from a theoretician ...kuang/class/mmm/lecture1.pdf · an...

An Introduction to Malignant Neoplasia from a An Introduction to Malignant Neoplasia from a TheoreticianTheoretician’’s Perspectives Perspective

John D. NagyJohn D. NagyDepartment of Life Sciences, Scottsdale Community CollegeDepartment of Life Sciences, Scottsdale Community College

Department of Mathematics and Statistics, Arizona State UniversiDepartment of Mathematics and Statistics, Arizona State Universityty

Mathematical Medicine SeminarMathematical Medicine Seminar

January 16, 2007January 16, 2007

The case history of The case history of ““MaryMary””

1) 42 year1) 42 year--old mother of 3old mother of 3

2) Cigarette smoker since she was 192) Cigarette smoker since she was 19

3) Mary developed a persistent cough some 3) Mary developed a persistent cough some time before presentationtime before presentation

4) In last few days before presentation she had 4) In last few days before presentation she had developed tremors in her hand and other developed tremors in her hand and other neurological symptomsneurological symptoms

Chest XChest X--ray 2 years before ray 2 years before presentationpresentation——film is clear.film is clear.

Not clear at presentation.Not clear at presentation.

Biopsy reveals squamous cell carcinoma of Biopsy reveals squamous cell carcinoma of the lung (a form of lung cancer).the lung (a form of lung cancer).

Squamous cell lung cancer Squamous cell lung cancer –– Gross Gross pathology, unfixedpathology, unfixed

Necrosis in Necrosis in SqCLCSqCLC

Squamous cell lung Squamous cell lung cancer cancer –– Gross Gross

pathology, formalin pathology, formalin fixedfixed

The cause The cause of Maryof Mary’’s s tremorstremors

Invasion and metastasisInvasion and metastasis

From Lynch and From Lynch and MatrisianMatrisian (2002) Differ. 70:561(2002) Differ. 70:561--573.573.

A cancer cell on the moveA cancer cell on the move

““The Hallmarks The Hallmarks of Cancerof Cancer””

From From HanahanHanahan and Weinberg. and Weinberg. (2000) Cell 100:57(2000) Cell 100:57--7070

Red indicates known cancerRed indicates known cancer--associated proteinsassociated proteins

translation="translation="MPPKTPRKTAATAAAAAAEPPAPPPPPPPEEDPEQDSGPEDLPLVRLEFEMPPKTPRKTAATAAAAAAEPPAPPPPPPPEEDPEQDSGPEDLPLVRLEFEETEEPDFTALCQKLKIPDHVRERAWLTWEKVSSVDGVLGGYIQKKKELWGICIFIARVETEEPDFTALCQKLKIPDHVRERAWLTWEKVSSVDGVLGGYIQKKKELWGICIFIARVDLDEMSFTLLSYRKTYEISVHKFFNLLKEIDTSTKVDNAMSRLLKKYDVLFALFSKLEDLDEMSFTLLSYRKTYEISVHKFFNLLKEIDTSTKVDNAMSRLLKKYDVLFALFSKLERTCELIYLTQPSSSISTEINSALVLKVSWITFLLAKGEVLQMEDDLVISFQLMLCVLDRTCELIYLTQPSSSISTEINSALVLKVSWITFLLAKGEVLQMEDDLVISFQLMLCVLDYFIKLSPPMLLKEPYKTAVIPINGSPRTPRRGQNRSARIAKQLENDTRIIEVLCKEHEYFIKLSPPMLLKEPYKTAVIPINGSPRTPRRGQNRSARIAKQLENDTRIIEVLCKEHECNIDEVKNVYFKNFIPFMNSLGLVTSNGLPEVENLSKRYEEIYLKNKDLDRRLFLDHDCNIDEVKNVYFKNFIPFMNSLGLVTSNGLPEVENLSKRYEEIYLKNKDLDRRLFLDHDKTLQTDSIDSFETQRTPRKSNLDEEVNIIPPHTPVRTVMNTIQQLMMILNSASDQPSEKTLQTDSIDSFETQRTPRKSNLDEEVNIIPPHTPVRTVMNTIQQLMMILNSASDQPSENLISYFNNCTVNPKESILKRVKDIGYIFKEKFAKAVGQGCVEIGSQRYKLGVRLYYRVNLISYFNNCTVNPKESILKRVKDIGYIFKEKFAKAVGQGCVEIGSQRYKLGVRLYYRVMESMLKSEEERLSIQNFSKLLNDNIFHMSLLACALEVVMATYSRSTSQNLDSGTDLSFMESMLKSEEERLSIQNFSKLLNDNIFHMSLLACALEVVMATYSRSTSQNLDSGTDLSFPWILNVLNLKAFDFYKVIESFIKAEGNLTREMIKHLERCEHRIMESLAWLSDSPLFDLPWILNVLNLKAFDFYKVIESFIKAEGNLTREMIKHLERCEHRIMESLAWLSDSPLFDLIKQSKDREGPTDHLESACPLNLPLQNNHTAADMYLSPVRSPKKKGSTTRVNSTANAETIKQSKDREGPTDHLESACPLNLPLQNNHTAADMYLSPVRSPKKKGSTTRVNSTANAETQATSAFQTQKPLKSTSLSLFYKKVYRLAYLRLNTLCERLLSEHPELEHIIWTLFQHTLQATSAFQTQKPLKSTSLSLFYKKVYRLAYLRLNTLCERLLSEHPELEHIIWTLFQHTLQNEYELMRDRHLDQIMMCSMYGICKVKNIDLKFKIIVTAYKDLPHAVQETFKRVLIKEQNEYELMRDRHLDQIMMCSMYGICKVKNIDLKFKIIVTAYKDLPHAVQETFKRVLIKEEEYDSIIVFYNSVFMQRLKTNILQYASTRPPTLSPIPHIPRSPYKFPSSPLRIPGGNIEEYDSIIVFYNSVFMQRLKTNILQYASTRPPTLSPIPHIPRSPYKFPSSPLRIPGGNIYISPLKSPYKISEGLPTPTKMTPRSRILVSIGESFGTSEKFQKINQMVCNSDRVLKRSYISPLKSPYKISEGLPTPTKMTPRSRILVSIGESFGTSEKFQKINQMVCNSDRVLKRSAEGSNPPKPLKKLRFDIEGSDEADGSKHLPGESKFQQKLAEMTSTRTRMQKQKMNDSMAEGSNPPKPLKKLRFDIEGSDEADGSKHLPGESKFQQKLAEMTSTRTRMQKQKMNDSMDTSNKEEKDTSNKEEK""

Structure of normal pRBStructure of normal pRB

translation="translation="MPPKTPRKTAATAAAAAAEPPAPPPPPPPEEDPEQDSGPEDLPLVRLEFEMPPKTPRKTAATAAAAAAEPPAPPPPPPPEEDPEQDSGPEDLPLVRLEFEETEEPDFTALCQKLKIPDHVRERAWLTWEKVSSVDGVLGGYIQKKKELWGICIFIARVETEEPDFTALCQKLKIPDHVRERAWLTWEKVSSVDGVLGGYIQKKKELWGICIFIARVDLDEMSFTLLSYRKTYEISVHKFFNLLKEIDTSTKVDNAMSRLLKKYDVLFALFSKLEDLDEMSFTLLSYRKTYEISVHKFFNLLKEIDTSTKVDNAMSRLLKKYDVLFALFSKLERTCELIYLTQPSSSISTEINSALVLKVSWITFLLAKGEVLQMEDDLVISFQLMLCVLDRTCELIYLTQPSSSISTEINSALVLKVSWITFLLAKGEVLQMEDDLVISFQLMLCVLDYFIKLSPPMLLKEPYKTAVIPINGSPRTPRRGQNRSARIAKQLENDTRIIEVLCKEHEYFIKLSPPMLLKEPYKTAVIPINGSPRTPRRGQNRSARIAKQLENDTRIIEVLCKEHECNIDEVKNVYFKNFIPFMNSLGLVTSNGLPEVENLSKRYEEIYLKNKDLDRRLFLDHDCNIDEVKNVYFKNFIPFMNSLGLVTSNGLPEVENLSKRYEEIYLKNKDLDRRLFLDHDKTLQTDSIDSFETQRTPRKSNLDEEVNIIPPHTPVRTVMNTIQQLMMILNSASDQPSEKTLQTDSIDSFETQRTPRKSNLDEEVNIIPPHTPVRTVMNTIQQLMMILNSASDQPSENLISYFNNCTVNPKESILKRVKDIGYIFKEKFAKAVGQGCVEIGSQRYKLGVRLYYRVNLISYFNNCTVNPKESILKRVKDIGYIFKEKFAKAVGQGCVEIGSQRYKLGVRLYYRVMESMLKSEEERLSIQNFSKLLNDNIFHMSLLACALEVVMATYSRSTSQNLDSGTDLSFMESMLKSEEERLSIQNFSKLLNDNIFHMSLLACALEVVMATYSRSTSQNLDSGTDLSFPWILNVLNLKAFDFYKVIESFIKAEGNLTREMIKHLERCEHRIMESLAWLSDSPLFDLPWILNVLNLKAFDFYKVIESFIKAEGNLTREMIKHLERCEHRIMESLAWLSDSPLFDLIKQSKDREGPTDHLESACPLNLPLQNNHTAADMYLSPVRSPKKKGSTTRVNSTANAETIKQSKDREGPTDHLESACPLNLPLQNNHTAADMYLSPVRSPKKKGSTTRVNSTANAETQATSAFQTQKPLKSTSLSLFYKKVYRLAYLRLNTLCERLLSEHPELEHIIWTLFQHTLQATSAFQTQKPLKSTSLSLFYKKVYRLAYLRLNTLCERLLSEHPELEHIIWTLFQHTLQNEYELMRDRHLDQIMMCSMYGICKVKNIDLKFKIIVTAYKDLPHAVQETFKRVLIKEQNEYELMRDRHLDQIMMCSMYGICKVKNIDLKFKIIVTAYKDLPHAVQETFKRVLIKEEEYDSIIVFYNSVFMQRLKTNILQYASTRPPTLSPIPHIPRSPYKFPSSPLRIPGGNIEEYDSIIVFYNSVFMQRLKTNILQYASTRPPTLSPIPHIPRSPYKFPSSPLRIPGGNIYISPLKSPYKISEGLPTPTKMTPRSRILVSIGESYISPLKSPYKISEGLPTPTKMTPRSRILVSIGESFGTSEKFQKINQMVCNSDRVLKRSFGTSEKFQKINQMVCNSDRVLKRSAEGSNPPKPLKKLRFDIEGSDEADGSKHLPGESKFQQKLAEMTSTRTRMQKQKMNDSMAEGSNPPKPLKKLRFDIEGSDEADGSKHLPGESKFQQKLAEMTSTRTRMQKQKMNDSMDTSNKEEKDTSNKEEK""

pRB in MarypRB in Mary’’s lung cancer cellss lung cancer cells

pRB in MarypRB in Mary’’s cancer cells is always inactivateds cancer cells is always inactivated

Where does pRB come from?Where does pRB come from?

1 1 ttccggttttttccggtttt tctcaggggatctcagggga cgttgaaattcgttgaaatt atttttgtaaatttttgtaa cgggagtcggcgggagtcgg gagaggacgggagaggacgg

61 61 ggcgtgccccggcgtgcccc gcgtgcgcgcgcgtgcgcgc gcgtcgtcctgcgtcgtcct ccccggcgctccccggcgct cctccacagccctccacagc tcgctggctctcgctggctc

121 121 ccgccgcggaccgccgcgga aaggcgtcataaggcgtcat gccgcccaaagccgcccaaa accccccgaaaccccccgaa aaacggccgcaaacggccgc caccgccgcccaccgccgcc

181 181 gctgccgccggctgccgccg cggaaccccccggaaccccc ggcaccgccgggcaccgccg ccgccgccccccgccgcccc ctcctgaggactcctgagga ggacccagagggacccagag

241 241 caggacagcgcaggacagcg gcccggaggagcccggagga cctgcctctccctgcctctc gtcaggcttggtcaggcttg agtttgaagaagtttgaaga aacagaagaaaacagaagaa

301 301 cctgattttacctgatttta ctgcattatgctgcattatg tcagaaattatcagaaatta aagataccagaagataccag atcatgtcagatcatgtcag agagagagctagagagagct

361 361 tggttaactttggttaactt gggagaaagtgggagaaagt ttcatctgtgttcatctgtg gatggagtatgatggagtat tgggaggttatgggaggtta tattcaaaagtattcaaaag

421 421 aaaaaggaacaaaaaggaac tgtggggaattgtggggaat ctgtatctttctgtatcttt attgcacgagattgcacgag ttgacctagattgacctaga tgagatgtcgtgagatgtcg

481 481 ttcactttacttcactttac tgagctacagtgagctacag aaaaacatacaaaaacatac gaaatcagtggaaatcagtg tccataaatttccataaatt ctttaacttactttaactta

541 541 ctaaaagaaactaaaagaaa ttgataccagttgataccag taccaaagtttaccaaagtt gataatgctagataatgcta tgtcaagacttgtcaagact gttgaagaaggttgaagaag

601 601 tatgatgtattatgatgtat tgtttgcacttgtttgcact cttcagcaaacttcagcaaa ttggaaaggattggaaagga catgtgaactcatgtgaact tatatatttgtatatatttg

661 661 acacaacccaacacaaccca gcagttcgatgcagttcgat atctactgaaatctactgaa ataaattctgataaattctg cattggtgctcattggtgct aaaagtttctaaaagtttct

721 721 tggatcacattggatcacat ttttattagcttttattagc taaaggggaataaaggggaa gtattacaaagtattacaaa tggaagatgatggaagatga tctggtgatttctggtgatt

781 781 tcatttcagttcatttcagt taatgctatgtaatgctatg tgtccttgactgtccttgac tattttattatattttatta aactctcaccaactctcacc tcccatgttgtcccatgttg

841 841 ctcaaagaacctcaaagaac catataaaaccatataaaac agctgttataagctgttata cccattaatgcccattaatg gttcacctcggttcacctcg aacacccaggaacacccagg

Structure of pRB geneStructure of pRB gene

901 901 cgaggtcagacgaggtcaga acaggagtgcacaggagtgc acggatagcaacggatagca aaacaactagaaacaactag aaaatgatacaaaatgatac aagaattattaagaattatt

961 961 gaagttctctgaagttctct gtaaagaacagtaaagaaca tgaatgtaattgaatgtaat atagatgaggatagatgagg tgaaaaatgttgaaaaatgt ttatttcaaattatttcaaa

1021 1021 aattttatacaattttatac cttttatgaacttttatgaa ttctcttggattctcttgga cttgtaacatcttgtaacat ctaatggactctaatggact tccagaggtttccagaggtt

1081 1081 gaaaatctttgaaaatcttt ctaaacgatactaaacgata cgaagaaattcgaagaaatt tatcttaaaatatcttaaaa ataaagatctataaagatct agatcgaagaagatcgaaga

1141 1141 ttatttttggttatttttgg atcatgataaatcatgataa aactcttcagaactcttcag actgattctaactgattcta tagacagttttagacagttt tgaaacacagtgaaacacag

1201 1201 agaacaccacagaacaccac gaaaaagtaagaaaaagtaa ccttgatgaaccttgatgaa gaggtgaatagaggtgaata taattcctcctaattcctcc acacactccaacacactcca

1261 1261 gttaggactggttaggactg ttatgaacacttatgaacac tatccaacaatatccaacaa ttaatgatgattaatgatga ttttaaattcttttaaattc tgcaagtgattgcaagtgat

1321 1321 caaccttcagcaaccttcag aaaatctgataaaatctgat ttcctattttttcctatttt aacaactgcaaacaactgca cagtgaatcccagtgaatcc aaaagaaagtaaaagaaagt

1381 1381 atactgaaaaatactgaaaa gagtgaaggagagtgaagga tataggatactataggatac atctttaaagatctttaaag agaaatttgcagaaatttgc taaagctgtgtaaagctgtg

1441 1441 ggacagggttggacagggtt gtgtcgaaatgtgtcgaaat tggatcacagtggatcacag cgatacaaaccgatacaaac ttggagttcgttggagttcg cttgtattaccttgtattac

1501 1501 cgagtaatggcgagtaatgg aatccatgctaatccatgct taaatcagaataaatcagaa gaagaacgatgaagaacgat tatccattcatatccattca aaattttagcaaattttagc

1561 1561 aaacttctgaaaacttctga atgacaacatatgacaacat ttttcatatgttttcatatg tctttattggtctttattgg cgtgcgctctcgtgcgctct tgaggttgtatgaggttgta

1621 1621 atggccacatatggccacat atagcagaagatagcagaag tacatctcagtacatctcag aatcttgattaatcttgatt ctggaacagactggaacaga tttgtctttctttgtctttc

1681 1681 ccatggattcccatggattc tgaatgtgcttgaatgtgct taatttaaaataatttaaaa gcctttgattgcctttgatt tttacaaagttttacaaagt gatcgaaagtgatcgaaagt

1741 1741 tttatcaaagtttatcaaag cagaaggcaacagaaggcaa cttgacaagacttgacaaga gaaatgataagaaatgataa aacatttagaaacatttaga acgatgtgaaacgatgtgaa


1801 1801 catcgaatcacatcgaatca tggaatcccttggaatccct tgcatggctctgcatggctc tcagattcactcagattcac ctttatttgactttatttga tcttattaaatcttattaaa

1861 1861 caatcaaaggcaatcaaagg accgagaaggaccgagaagg accaactgataccaactgat caccttgaatcaccttgaat ctgcttgtccctgcttgtcc tcttaatctttcttaatctt

1921 1921 cctctccagacctctccaga ataatcacacataatcacac tgcagcagattgcagcagat atgtatctttatgtatcttt ctcctgtaagctcctgtaag atctccaaagatctccaaag

1981 1981 aaaaaaggttaaaaaaggtt caactacgcgcaactacgcg tgtaaattcttgtaaattct actgcaaatgactgcaaatg cagagacacacagagacaca agcaacctcaagcaacctca

2041 2041 gccttccagagccttccaga cccagaagcccccagaagcc attgaaatctattgaaatct acctctctttacctctcttt cactgttttacactgtttta taaaaaagtgtaaaaaagtg

2101 2101 tatcggctagtatcggctag cctatctccgcctatctccg gctaaatacagctaaataca ctttgtgaacctttgtgaac gccttctgtcgccttctgtc tgagcacccatgagcaccca

2161 2161 gaattagaacgaattagaac atatcatctgatatcatctg gacccttttcgacccttttc cagcacaccccagcacaccc tgcagaatgatgcagaatga gtatgaactcgtatgaactc

2221 2221 atgagagacaatgagagaca ggcatttggaggcatttgga ccaaattatgccaaattatg atgtgttccaatgtgttcca tgtatggcattgtatggcat atgcaaagtgatgcaaagtg

2281 2281 aagaatatagaagaatatag accttaaattaccttaaatt caaaatcattcaaaatcatt gtaacagcatgtaacagcat acaaggatctacaaggatct tcctcatgcttcctcatgct

2341 2341 gttcaggagagttcaggaga cattcaaacgcattcaaacg tgttttgatctgttttgatc aaagaagaggaaagaagagg agtatgattcagtatgattc tattatagtatattatagta

2401 2401 ttctataactttctataact cggtcttcatcggtcttcat gcagagactggcagagactg aaaacaaataaaaacaaata ttttgcagtattttgcagta tgcttccacctgcttccacc

2461 2461 aggccccctaaggcccccta ccttgtcaccccttgtcacc aatacctcacaatacctcac attcctcgaaattcctcgaa gcccttacaagcccttacaa gtttcctagtgtttcctagt

2521 2521 tcacccttactcacccttac ggattcctggggattcctgg agggaacatcagggaacatc tatatttcactatatttcac ccctgaagagccctgaagag tccatataaatccatataaa

2581 2581 atttcagaagatttcagaag gtctgccaacgtctgccaac accaacaaaaaccaacaaaa atgactccaaatgactccaa gatcaagaatgatcaagaat cttagtatcacttagtatca

2641 2641 attggtgaatattggtgaat cattcgggaccattcgggac ttctgagaagttctgagaag ttccagaaaattccagaaaa taaatcagattaaatcagat ggtatgtaacggtatgtaac


2701 2701 agcgaccgtgagcgaccgtg tgctcaaaagtgctcaaaag aagtgctgaaaagtgctgaa ggaagcaaccggaagcaacc ctcctaaaccctcctaaacc actgaaaaaaactgaaaaaa

2761 2761 ctacgctttgctacgctttg atattgaaggatattgaagg atcagatgaaatcagatgaa gcagatggaagcagatggaa gtaaacatctgtaaacatct cccaggagagcccaggagag

2821 2821 tccaaatttctccaaatttc agcagaaactagcagaaact ggcagaaatgggcagaaatg acttctactcacttctactc gaacacgaatgaacacgaat gcaaaagcaggcaaaagcag

2881 2881 aaaatgaatgaaaatgaatg atagcatggaatagcatgga tacctcaaactacctcaaac aaggaagagaaaggaagaga aatgaggatcaatgaggatc tcaggacctttcaggacctt

2941 2941 ggtggacactggtggacact gtgtacacctgtgtacacct ctggattcatctggattcat tgtctctcactgtctctcac agatgtgactagatgtgact gtataactttgtataacttt

3001 3001 cccaggttctcccaggttct gtttatggccgtttatggcc acatttaataacatttaata tcttcagctctcttcagctc tttttgtggatttttgtgga tataaaatgttataaaatgt

3061 3061 gcagatgcaagcagatgcaa ttgtttgggtttgtttgggt gagtcctaaggagtcctaag ccacttgaaaccacttgaaa tgttagtcattgttagtcat tgttatttattgttatttat

3121 3121 acaagattgaacaagattga aaatcttgtgaaatcttgtg taaatcctgctaaatcctgc catttaaaaacatttaaaaa gttgtagcaggttgtagcag attgtttcctattgtttcct

3181 3181 cttccaaagtcttccaaagt aaaattgctgaaaattgctg tgctttatggtgctttatgg atagtaagaaatagtaagaa tggccctagatggccctaga gtgggagtccgtgggagtcc

3241 3241 tgataacccatgataaccca ggcctgtctgggcctgtctg actactttgcactactttgc cttcttttgtcttcttttgt agcatataggagcatatagg tgatgtttgctgatgtttgc

3301 3301 tcttgttttttcttgttttt attaatttatattaatttat atgtatatttatgtatattt ttttaatttattttaattta acatgaacacacatgaacac ccttagaaaaccttagaaaa

3361 3361 tgtgtcctattgtgtcctat ctatcttccactatcttcca aatgcaatttaatgcaattt gattgactgcgattgactgc ccattcaccaccattcacca aaattatcctaaattatcct

3421 3421 gaactcttctgaactcttct gcaaaaatgggcaaaaatgg atattattagatattattag aaattagaaaaaattagaaa aaaattactaaaaattacta attttacacaattttacaca

3481 3481 ttagattttattagatttta ttttactattttttactatt ggaatctgatggaatctgat atactgtgtgatactgtgtg cttgttttatcttgttttat aaaattttgcaaaattttgc

3541 3541 ttttaattaattttaattaa ataaaagctgataaaagctg gaagcaaagtgaagcaaagt ataaccatatataaccatat gatactatcagatactatca tactactgaatactactgaa


3601 3601 acagatttcaacagatttca tacctcagaatacctcagaa tgtaaaagaatgtaaaagaa cttactgattcttactgatt attttcttcaattttcttca tccaacttattccaacttat

3661 3661 gtttttaaatgtttttaaat gaggattattgaggattatt gatagtactcgatagtactc ttggtttttattggttttta taccattcagtaccattcag atcactgaatatcactgaat

3721 3721 ttataaagtattataaagta cccatctagtcccatctagt acttgaaaaaacttgaaaaa gtaaagtgttgtaaagtgtt ctgccagatcctgccagatc ttaggtatagttaggtatag

3781 3781 aggaccctaaaggaccctaa cacagtatatcacagtatat cccaagtgcacccaagtgca ctttctaatgctttctaatg tttctgggtctttctgggtc ctgaagaattctgaagaatt

3841 3841 aagatacaaaaagatacaaa ttaattttacttaattttac tccataaacatccataaaca gactgttaatgactgttaat tataggagcctataggagcc ttaattttttttaatttttt

3901 3901 tttcatagagtttcatagag atttgtctaaatttgtctaa ttgcatctcattgcatctca aaattattctaaattattct gccctccttagccctcctta atttgggaagatttgggaag

3961 3961 gtttgtgtttgtttgtgttt tctctggaattctctggaat ggtacatgtcggtacatgtc ttccatgtatttccatgtat cttttgaactcttttgaact ggcaattgtcggcaattgtc

4021 4021 tatttatctttatttatctt ttatttttttttattttttt aagtcagtataagtcagtat ggtctaacacggtctaacac tggcatgttctggcatgttc aaagccacataaagccacat

4081 4081 tatttctagttatttctagt ccaaaattacccaaaattac aagtaatcaaaagtaatcaa gggtcattatgggtcattat gggttaggcagggttaggca ttaatgtttcttaatgtttc

4141 4141 tatctgattttatctgattt tgtgcaaaagtgtgcaaaag cttcaaattacttcaaatta aaacagctgcaaacagctgc attagaaaaaattagaaaaa gaggcgcttcgaggcgcttc

4201 4201 tcccctcccctcccctcccc tacacctaaatacacctaaa ggtgtatttaggtgtattta aactatcttgaactatcttg tgtgattaactgtgattaac ttatttagagttatttagag

4261 4261 atgctgtaacatgctgtaac ttaaaataggttaaaatagg ggatatttaaggatatttaa ggtagcttcaggtagcttca gctagcttttgctagctttt aggaaaatcaaggaaaatca

4321 4321 ctttgtctaactttgtctaa ctcagaattactcagaatta tttttaaaaatttttaaaaa gaaatctggtgaaatctggt cttgttagaacttgttagaa aacaaaatttaacaaaattt

4381 4381 tattttgtgctattttgtgc tcatttaagttcatttaagt ttcaaacttattcaaactta ctattttgacctattttgac agttattttgagttattttg ataacaatgaataacaatga

4441 4441 cactagaaaacactagaaaa cttgactccacttgactcca tttcatcatttttcatcatt gtttctgcatgtttctgcat gaatatcatagaatatcata caaatcagttcaaatcagtt


4501 4501 agtttttaggagtttttagg tcaagggctttcaagggctt actatttctgactatttctg ggtcttttgcggtcttttgc tactaagttctactaagttc acattagaatacattagaat

4561 4561 tagtgccagatagtgccaga attttaggaaattttaggaa cttcagagatcttcagagat cgtgtattgacgtgtattga gatttcttaagatttcttaa ataatgcttcataatgcttc

4621 4621 agatattattagatattatt gctttattgcgctttattgc ttttttgtatttttttgtat tggttaaaactggttaaaac tgtacatttatgtacattta aaattgctataaattgctat

4681 4681 gttactatttgttactattt tctacaattatctacaatta atagtttgtcatagtttgtc tattttaaaatattttaaaa taaattagtttaaattagtt gttaagagtcgttaagagtc


1801 1801 catcgaatcacatcgaatca tggaatcccttggaatccct tgcatggctctgcatggctc tcagattcactcagattcac ctttatttgactttatttga tcttattaaatcttattaaa

1861 1861 caatcaaaggcaatcaaagg accgagaaggaccgagaagg accaactgataccaactgat caccttgaatcaccttgaat ctgcttgtccctgcttgtcc tcttaatctttcttaatctt

1921 1921 cctctccagacctctccaga ataatcacacataatcacac tgcagcagattgcagcagat atgtatctttatgtatcttt ctcctgtaagctcctgtaag atctccaaagatctccaaag

1981 1981 aaaaaaggttaaaaaaggtt caactacgcgcaactacgcg tgtaaattcttgtaaattct actgcaaatgactgcaaatg cagagacacacagagacaca agcaacctcaagcaacctca

2041 2041 gccttccagagccttccaga cccagaagcccccagaagcc attgaaatctattgaaatct acctctctttacctctcttt cactgttttacactgtttta taaaaaagtgtaaaaaagtg

2101 2101 tatcggctagtatcggctag cctatctccgcctatctccg gctaaatacagctaaataca ctttgtgaacctttgtgaac gccttctgtcgccttctgtc tgagcacccatgagcaccca

2161 2161 gaattagaacgaattagaac atatcatctgatatcatctg gacccttttcgacccttttc cagcacaccccagcacaccc tgcagaatgatgcagaatga gtatgaactcgtatgaactc

2221 2221 atgagagacaatgagagaca ggcatttggaggcatttgga ccaaattatgccaaattatg atgtgttccaatgtgttcca tgtatggcattgtatggcat atgcaaagtgatgcaaagtg

2281 2281 aagaatatagaagaatatag accttaaattaccttaaatt caaaatcattcaaaatcatt gtaacagcatgtaacagcat acaaggatctacaaggatct tcctcatgcttcctcatgct

2341 2341 gttcaggagagttcaggaga cattcaaacgcattcaaacg tgttttgatctgttttgatc aaagaagaggaaagaagagg agtatgattcagtatgattc tattatagtatattatagta

2401 2401 ttctataactttctataact cggtcttcatcggtcttcat gcagagactggcagagactg aaaacaaataaaaacaaata ttttgcagtattttgcagta tgcttccacctgcttccacc

2461 2461 aggccccctaaggcccccta ccttgtcaccccttgtcacc aatacctcacaatacctcac attcctcgaaattcctcgaa gcccttacaagcccttacaa gtttcctagtgtttcctagt

2521 2521 tcacccttactcacccttac ggattcctggggattcctgg agggaacatcagggaacatc tatatttcactatatttcac ccctgaagagccctgaagag tccatataaatccatataaa

2581 2581 atttcagaagatttcagaag gtctgccaacgtctgccaac accaacaaaaaccaacaaaa atgactccaaatgactccaa gatcaagaatgatcaagaat cttagtatcacttagtatca

2641 2641 attggtgaatattggtgaat cattcgcattcg gacgac ttctgagaagttctgagaag ttccagaaaattccagaaaa taaatcagattaaatcagat ggtatgtaacggtatgtaac

Structure of MaryStructure of Mary’’s cancer pRB genes cancer pRB gene

What went wrong in MaryWhat went wrong in Mary’’s cells?s cells?

Is Is pRBpRB mutation a sufficient explanation of the mutation a sufficient explanation of the etiology of squamous cell lung cancer?etiology of squamous cell lung cancer?

One can attack this question with a very simple Markov chainOne can attack this question with a very simple Markov chain

1) Assume the number of cells in an organ is fixed at 1) Assume the number of cells in an organ is fixed at NN..

2) At every time step, exactly one cell dies and one cell reprod2) At every time step, exactly one cell dies and one cell reproduces; uces; therefore, tissue homeostasis is preserved (therefore, tissue homeostasis is preserved (notnot a feature of cancer).a feature of cancer).

Healthy LungHealthy Lung SCLC, equivalent scaleSCLC, equivalent scale

Source: Source: fybio.bio.usyd.edu.aufybio.bio.usyd.edu.au Source: Nagy, 2005. MBE 2: 381Source: Nagy, 2005. MBE 2: 381--418.418.



3) Every cell exists in one of two states3) Every cell exists in one of two states——healthy or malignant.healthy or malignant.

4) Whenever a healthy cell reproduces, it 4) Whenever a healthy cell reproduces, it breeds truebreeds true with with constantconstantprobability 1 probability 1 –– uu, , or it or it ““mutatesmutates”” into a malignant cell into a malignant cell with probability with probability uu..

5) Reproduction is biased, usually in favor of malignant cells. 5) Reproduction is biased, usually in favor of malignant cells. The The measure of this bias is measure of this bias is rr. When . When rr > 1, selection favors malignancy.> 1, selection favors malignancy.

7) Probability of mortality is uniformly distributed across all 7) Probability of mortality is uniformly distributed across all existing existing cells, and is independent of reproduction.cells, and is independent of reproduction.



Let Let aa and and b b be the number of healthy and malignant cells, respectively; be the number of healthy and malignant cells, respectively; a + b = Na + b = N. .

The reproduction probabilities are:The reproduction probabilities are:

Healthy cell reproduces, Healthy cell reproduces, breeds truebreeds true

Mortality probabilities for healthy and malignant cells are Mortality probabilities for healthy and malignant cells are a/Na/N and and b/Nb/N, , respectively.respectively.

(1 )u aa rb

−+

ba rb+

uaa rb+

Healthy cell Healthy cell reproduces, mutatesreproduces, mutates

Malignant cell Malignant cell reproducesreproduces

The transition matrix for this processThe transition matrix for this process

Let Let P(i,jP(i,j)) be the probability of transitioning from state be the probability of transitioning from state b = ib = i to to b = jb = j. . ThenThen

( ), 1,

(1 )( ), 1,( , )

1 ( , 1) ( , 1), ,0, elsewhere,

i

i

u N i ri N ij i

A N

u N i ij iP i j

A NP i i P i i j i

− + − = +

− −= −=

− − − + =

for 0 , , and .ii j N A N i ri≤ ≤ = − −

Immediate ResultImmediate Result

{ | 0} (0, )ST S TP b j b P j+ = = =

From a well known result of the theory of Markov chains, at timeFrom a well known result of the theory of Markov chains, at time steps steps TT, , S S > 0 and for > 0 and for jj > 0, > 0,

0 1 2 N......

⇒ If a cohort is large during a period of study of length If a cohort is large during a period of study of length SS, cancer , cancer risk*risk* in the cohort will be essentially constant regardless of the agin the cohort will be essentially constant regardless of the age e of the cohort.of the cohort.

{ | 0} depends on , not T S TP b j b S T+ = =

Epidemiological risk = Epidemiological risk = ““proportion of persons unaffected at the beginning of a study perproportion of persons unaffected at the beginning of a study period who iod who [get cancer] during the study period.[get cancer] during the study period.”” ((JekelJekel et al., 1996)et al., 1996)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

20 30 40 50 60 70 80

Age (Years)

Can

cer

Ris

k (%

)

Lung Cancer

Breast Cancer

Typical Risk Curves Contradict the Previous ResultTypical Risk Curves Contradict the Previous Result

1010--year ageyear age--dependent risk of lung cancerdependent risk of lung cancerSource: Center for Disease Control and Prevention Source: Center for Disease Control and Prevention www.cdc.gov/cancer/lung/statistics/risk_age.htmwww.cdc.gov/cancer/lung/statistics/risk_age.htm

Observations like this Observations like this are responsible for the are responsible for the

acceptance of the multiacceptance of the multi--hit theory of cancer hit theory of cancer

etiologyetiology

0 1 2 N......A Second Immediate ResultA Second Immediate Result

( , ) 1 is absorbing.P N N b N= ⇔ =

For ( , ) 1 All other states are transient

i NP i i

≠< ⇒

⇒ Eventually all cells will become malignant (almost always) Eventually all cells will become malignant (almost always)

3) Number of states is finite3) Number of states is finite

2)2)

1)1)

an introduction to malignant neoplasia from a theoretician ...kuang/class/mmm/lecture1.pdf · an...

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