Somatic evolution and cancer Natalia Komarova University of
- Slides: 146
Somatic evolution and cancer Natalia Komarova (University of California - Irvine)
Plan • • Introduction: The concept of somatic evolution Methodology: Stochastic processes on selection-mutation networks Two particular problems: 1. Stem cells, initiation of cancer and optimal tissue architecture (with L. Wang and P. Cheng) 2. Drug therapy and generation of resistance: neutral evolution inside a tumor (with D. Wodarz)
Darwinian evolution (of species) • Time-scale: hundreds of millions of years • Organisms reproduce and die in an environment with shared resources
Darwinian evolution (of species) • Time-scale: hundreds of millions of years • Organisms reproduce and die in an environment with shared resources • Inheritable germline mutations (variability) • Selection (survival of the fittest)
Somatic evolution • Cells reproduce and die inside an organ of one organism • Time-scale: tens of years
Somatic evolution • Cells reproduce and die inside an organ of one organism • Time-scale: tens of years • Inheritable mutations in cells’ genomes (variability) • Selection (survival of the fittest)
Cancer as somatic evolution • Cells in a multicellular organism have evolved to cooperate and perform their respective functions for the good of the whole organism
Cancer as somatic evolution • Cells in a multicellular organism have evolved to cooperate and perform their respective functions for the good of the whole organism • A mutant cell that “refuses” to co-operate may have a selective advantage
Cancer as somatic evolution • Cells in a multicellular organism have evolved to cooperate and perform their respective functions for the good of the whole organism • A mutant cell that “refuses” to co-operate may have a selective advantage • The offspring of such a cell may spread
Cancer as somatic evolution • Cells in a multicellular organism have evolved to cooperate and perform their respective functions for the good of the whole organism • A mutant cell that “refuses” to co-operate may have a selective advantage • The offspring of such a cell may spread • This is a beginning of cancer
Progression to cancer
Progression to cancer Constant population
Progression to cancer Advantageous mutant
Progression to cancer Clonal expansion
Progression to cancer Saturation
Progression to cancer Advantageous mutant
Progression to cancer Wave of clonal expansion
Genetic pathways to colon cancer (Bert Vogelstein) “Multi-stage carcinogenesis”
Methodology: modeling a colony of cells • Cells can divide, mutate and die
Methodology: modeling a colony of cells • Cells can divide, mutate and die • Mutations happen according to a “mutation -selection diagram”, e. g. u 1 (1) u 2 (r 1) u 4 u 3 (r 2) (r 3) (r 4)
Mutation-selection network (r 2) u 8 (r 3) u 8 (1) u 2 (r 1) u 5 u 2 u 5 (r 4) (r 5) (r 6) u 8 (r 7)
Stochastic dynamics on a selectionmutation network
A birth-death process with mutations Selection-mutation diagram: u (1) Fitness = 1 Fitness = r >1 (r ) Number of is i Number of is j=N-i
Evolutionary selection dynamics Fitness = 1 Fitness = r >1
Evolutionary selection dynamics Fitness = 1 Fitness = r >1
Evolutionary selection dynamics Fitness = 1 Fitness = r >1
Evolutionary selection dynamics Fitness = 1 Fitness = r >1
Evolutionary selection dynamics Fitness = 1 Fitness = r >1
Evolutionary selection dynamics Start from only one cell of the second type. Suppress further mutations. What is the chance that it will take over? Fitness = 1 Fitness = r >1
Evolutionary selection dynamics Start from only one cell of the second type. What is the chance that it will take over? Fitness = 1 Fitness = r >1 If If r=1 then = 1/N r<1 then < 1/N r>1 then > 1/N r then =1
Evolutionary selection dynamics Start from zero cell of the second type. What is the expected time until the second type takes over? Fitness = 1 Fitness = r >1
Evolutionary selection dynamics Start from zero cell of the second type. What is the expected time until the second type takes over? In the case of rare mutations, we can show that Fitness = 1 Fitness = r >1
Two-hit process (Alfred Knudson 1971) (r) (a) What is the probability that by time t a mutant of has been created? Assume that and
A two-step process
A two-step process
A two step process … …
A two-step process (1) (r) (a) Number of cells Scenario 1: gets fixated first, and then a mutant of is created; time
Stochastic tunneling …
Two-hit process (1) (r) (a) Number of cells Scenario 2: A mutant of is created before reaches fixation time
The coarse-grained description Long-lived states: x 0 …“all green” x 1 …“all blue” x 2 …“at least one red”
Stochastic tunneling Neutral intermediate mutant Disadvantageous intermediate mutant Assume that and
Stem cells, initiation of cancer and optimal tissue architecture
Colon tissue architecture
Colon tissue architecture Crypts of a colon
Colon tissue architecture Crypts of a colon
Cancer of epithelial tissues Gut Cells in a crypt of a colon
Cancer of epithelial tissues Gut Cells in a crypt of a colon Stem cells replenish the tissue; asymmetric divisions
Cancer of epithelial tissues Gut Cells in a crypt of a colon Proliferating cells divide symmetrically and differentiate Stem cells replenish the tissue; asymmetric divisions
Cancer of epithelial tissues Gut Cells in a crypt of a colon Differentiated cells get shed off into the lumen Proliferating cells divide symmetrically and differentiate Stem cells replenish the tissue; asymmetric divisions
Finite branching process
What is known: • Normal cells undergo apoptosis at the top of the crypt, the tissue is renewed and cell number is constant
What is known: • Normal cells undergo apoptosis at the top of the crypt, the tissue is renewed and cell number is constant • One of the earliest events in colon cancer is inactivation of the APC gene
What is known: • Normal cells undergo apoptosis at the top of the crypt, the tissue is renewed and cell number is constant • One of the earliest events in colon cancer is inactivation of the APC gene • APC-/- cells do not undergo apoptosis at the top of the crypt
What is NOT known: ? • What is the cellular origin of cancer? • Which cells harbor the first dangerous mutaton? Are the stem cells the ones in danger? ? ? • Which compartment must be targeted by drugs?
Colon cancer initiation • Both copies of the APC gene must be mutated before a phenotypic change is observed (tumor suppressor gene) X APC+/+ APC+/- XX APC-/-
Cellular origins of cancer Gut If a stem cell acquires a mutation, the whole crypt is transformed
Cellular origins of cancer Gut If a daughter cell acquires a mutation, it will probably get washed out before a second mutation can hit
What is the cellular origin of cancer?
Colon cancer initiation
Colon cancer initiation
Colon cancer initiation
Colon cancer initiation
Colon cancer initiation
Colon cancer initiation
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
Cellular origins of cancer • The prevailing theory is that the mutations leading to cancer initiation occur is stem cells
Cellular origins of cancer • The prevailing theory is that the mutations leading to cancer initiation occur is stem cells • Therefore, all prevention and treatment strategies must target the stem cells
Cellular origins of cancer • The prevailing theory is that the mutations leading to cancer initiation occur is stem cells • Therefore, all prevention and treatment strategies must target the stem cells • Differentiated cells (most cells!) do not count
Mathematical approach: • Formulate a model which distinguishes between stem and differentiated cells • Calculate the relative probability of various mutation patterns
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
First mutation in a daughter cell
Stochastic tunneling in a heterogeneous population 1) At least one mutation happens in a stem cell (cf. the two-step process) 2) 2) Both mutations happen in a daughter cell: no fixation of an intermediate mutant (cf tunneling)
Stochastic tunneling in a heterogeneous population Lower rate 1) At least one mutation happens in a stem cell (cf. the two-step process) 2) 2) Both mutations happen in a daughter cell: no fixation of an intermediate mutant (cf tunneling)
Cellular origins of cancer • If the tissue is organized into compartments with stem cells and daughter cells, the risk of mutations is lower than in homogeneous populations
Cellular origins of cancer • If the tissue is organized into compartments with stem cells and daughter cells, the risk of mutations is lower than in a homogeneous population • Cellular origin of cancer is not necessarily the stem cell. Under some circumstances, daughter cells are the ones at risk.
Cellular origins of cancer • If the tissue is organized into compartments with stem cells and daughter cells, the risk of mutations is lower than in a homogeneous populations • Cellular origin of cancer is not necessarily the stem cell. Under some circumstances, daughter cells are the ones at risk. • Stem cells are not the entire story!!!
Optimal tissue architecture • How does tissue architecture help protect against cancer? • What are parameters of the architecture that minimize the risk of cancer? • How does protection against cancer change with the individual’s age?
Optimal number of stem cells m=1 m=2 Crypt size is n=16 m=4 m=8
Probability to develop dysplasia One stem cell Many stem cells Time (individual’s age)
Probability to develop dysplasia The optimal solution is timedependent! Optimum: many stem cells One stem cell Many stem Optimum: cells one stem cell Time (individual’s age)
Optimization problem • The optimum number of stem cells is high in young age, and low in old age • Assume that tissue architecture cannot change with time: must choose a timeindependent solution • Selection mostly acts upon reproductive ages, so the preferred evolutionary strategy is to keep the risk of cancer low while the organism is young
Probability to develop dysplasia Evolutionary compromise Many stem cells One stem cell Time (individual’s age)
Probability to develop dysplasia Evolutionary compromise Many stem cells While keeping the risk of cancer low at the young age, the preferred evolutionary strategy works against the older age, actually increasing the likelihood of cancer! One stem cell Time (individual’s age)
Cancer vs aging • Cancer and aging are two sides of the same coin…. .
Drug therapy and generation of resistance
Leukemia • Most common blood cancer • Four major types: Acute Myeloid Leukemia (AML), Chronic Lymphocytic Leukemia (CLL), Chronic Myeloid Leukemia (CML), Acute Lymphocytic Leukemia (ALL)
Leukemia • Most common blood cancer • Four major types: Acute Myeloid Leukemia (AML), Chronic Lymphocytic Leukemia (CLL), Chronic Myeloid Leukemia (CML), Acute Lymphocytic Leukemia (ALL)
CML • Chronic phase (2 -5 years) • Accelerated phase (6 -18 months) • Blast crisis (survival 3 -6 months)
Targeted cancer drugs • Traditional drugs: very toxic agents that kill dividing cells
Targeted cancer drugs • Traditional drugs: very toxic agents that kill dividing cells • New drugs: small molecule inhibitors • Target the pathways which make cancerous cells cancerous (Gleevec)
Gleevec: a new generation drug Bcr-Abl
Gleevec: a new generation drug Bcr-Abl
Small molecule inhibitors
Targeted cancer drugs • Very effective • Not toxic
Targeted cancer drugs • Very effective • Not toxic • Resistance poses a problem Gleevec Bcr-Abl protein
Targeted cancer drugs • Very effective • Not toxic • Resistance poses a problem Mutation Gleevec Bcr-Abl protein
Treatment without resistance treatment time
Development of resistance treatment
How can one prevent resistance? • In HIV: treat with multiple drugs • It takes one mutation to develop resistance of one drug. It takes n mutations to develop resistance to n drugs. • Goal: describe the generation of resistance before and after therapy.
Mutation network for developing resistance against n=3 drugs
During a short time-interval, Dt, a cell of type Ai can: • Reproduce faithfully with probability Li(1 -Suj) Dt
During a short time-interval, Dt, a cell of type Ai can: • Reproduce faithfully with probability Li(1 -Suj) Dt • Produce one cell identical to itself, and a mutant cell of type Aj with probability Liuj Dt
During a short time-interval, Dt, a cell of type Ai can: • Reproduce faithfully with probability Li(1 -Suj) Dt • Produce one cell identical to itself, and a mutant cell of type Aj with probability Liuj Dt • Die with probability Di Dt
The method Assume just one drug. xij(t) is the probability to have i susceptible and j resistantcells at time t. F(x, y; t)=Sxij(t)xjyi is the probability generating function.
The method xij(t) is the probability to have i susceptible and j resistant cells at time t. F(x, y; t)=Sxij(t)xjyi is the probability generating function.
For multiple drugs: xi 0, i 1, …, im(t) is the probability to have is cells of type As at time t. F(x 0, x 1, …, xm; t) = S xi 0, i 1, …, im(t) x 0 im …xmi 0 is the probability generating function. F(0, 1, …, 1; t) is the probability that at time t there are no cells of type Am F(0, 0, …, 0; t) is the probability that at time t the colony is extinct
The method The probability that at time t the colony is extinct is F(0, 0, …, 0; t) =xn. M(t), where M is the initial # of cells and xn is the solution of The probability of treatment failure is
The questions: 1. Does resistance mostly arise before or after the start of treatment? 2. How does generation of resistance depend on the properties of cancer growth (high turnover D~L vs low turnover D<<L) 3. How does the number of drugs influence the success of treatment?
1. How important is pre-existence of mutants?
Single drug therapy
Single drug therapy Pre-existance = Generation during treatment
Single drug therapy Unrealistic! Pre-existance = Generation during treatment
Single drug therapy Pre-existance >> Generation during treatment
Multiple drug therapies Fully susceptible Partially susceptible Fully resistant
Development of resistance Fully susceptible Partially susceptible Fully resistant
1. How important is pre-existence of resistant mutants? For both single- and multiple-drug therapies, resistant mutants are likely to be produced before start of treatment, and not in the course of treatment
2. How does generation of resistance depend on the turnover rate of cancer? • Low turnover (growth rate>>death rate) Fewer cell divisions needed to reach a certain size • High turnover (growth rate~death rate) Many cell divisions needed to reach a certain size
Single drug therapy Low turnover cancer, D<<L
Single drug therapy High turnover cancer, D~L More mutant colonies are produced, but the probability of colony survival is proportionally smaller…
2. How does generation of resistance depend on the turnover rate of cancer? • Single drug therapies: the production of mutants is independent of the turnover
2. How does generation of resistance depend on the turnover rate of cancer? • Single drug therapies: the production of mutants is independent of the turnover • Multiple drug therapies: the production of mutants is much larger for cancers with a high turnover
3. The size of failure • Suppose we start treatment at size N • Calculate the probability of treatment failure • Find the size at which the probability of failure is d=0. 01
3. The size of failure • Suppose we start treatment at size N • Calculate the probability of treatment failure • Find the size at which the probability of failure is d=0. 01 • The size of failure increases with # of drugs and decreases with mutation rate
Minimum # of drugs for different parameter values 1013 cells u=10 -8 -10 -9 is the basic point mutation rate, u=10 -4 is associated with genetic instabilities
Minimum # of drugs for different parameter values 1013 cells u=10 -8 -10 -9 is the basic point mutation rate, u=10 -4 is associated with genetic instabilities
Minimum # of drugs for different parameter values 1013 cells u=10 -8 -10 -9 is the basic point mutation rate, u=10 -4 is associated with genetic instabilities
Minimum # of drugs for different parameter values 1013 cells u=10 -8 -10 -9 is the basic point mutation rate, u=10 -4 is associated with genetic instabilities
Minimum # of drugs for different parameter values 1013 cells u=10 -8 -10 -9 is the basic point mutation rate, u=10 -4 is associated with genetic instabilities
CML leukemia • • Gleevec u=10 -8 -10 -9 D/L between 0. 1 and 0. 5 (low turnover) Size of advanced cancers is 1013 cells
Log size of treatment failure u=10 -8 u=10 -6
Application for CML • The model suggests that 3 drugs are needed to push the size of failure (1% failure) up to 1013 cells
Conclusions • Main concept: cancer is a highly structured evolutionary process • Main tool: stochastic processes on selection-mutation networks • We addressed questions of cellular origins of cancer and generation of drug resistance • There are many more questions in cancer research…
Multiple drug treatments • For fast turnover cancers, adding more drugs will not prevent generation of resistance
Size of failure for different turnover rates
- Howard university cancer center
- Thermoreceptors
- Chapter 29 somatic symptom and dissociative disorders
- What is the difference between somatic and gamete cells
- Somatic symptom and related disorders
- Distinguish between general senses and special senses.
- 副交感神経
- Autonomic receptors
- Somatic death vs cellular death
- Somatic and special senses
- Spinal nerves
- Somatic reflex vs visceral reflex
- Hoarding disorder بالعربي
- Sns somatic nervous system
- Somatic motor pathways
- Types of sensory receptors
- How are somatic cells different from gametes
- Delusional disorder treatment
- Caliper motion of ribs
- Site of somatic motor neuron cell bodies
- Sam byron
- Visceral afferent vs efferent
- Erbs palsy
- Process of somatic embryogenesis
- Somatic reflex
- Rib somatic dysfunction
- Why dna is more stable than rna
- Somatic motor neuron
- Inborn error of metabolism
- Affinity maturation somatic hypermutation
- Soap note
- Motor (efferent) division
- Malingering
- Rigor mortis vs livor mortis
- Pre ganglionic
- Sensory modality examples
- Law of segregation vs law of independent assortment
- Germ cell vs somatic cells
- Somatic motor function
- Ans
- Medulla structure
- What is the medulla of the hair
- Somatic motor function
- J segment
- Somatic origin of hair
- Somatic nervous system
- Parasympathetic nervous system def
- Protoplast fusion
- Corticospinal tract
- Pomato somatic hybrid
- Urt
- Somatic symptoms
- Autonomic nervous system skeletal muscle
- Somatic tremor artifact
- Somatic pathway
- Somatic ganglion
- Cell cycle
- Application of somatic hybridization
- Dreyer and bennett hypothesis
- Dura mater meaning
- Somatoform disorders
- Vindicate mnemonic
- Somatic symptoms
- Somatic
- Somatic hybridization diagram
- Tabes dorsalis syphilis
- Nerves
- Somatic sx disorder
- Pns
- Pns
- Pain receptors in brain
- Save a life
- Gamete mutation definition
- An ipsilateral intersegmental spinal somatic reflex
- Semaphore semmelweis
- Body cells are also called
- Chapter 17 somatic symptom disorders
- Cell division vocabulary
- Chapter 24 the immune and lymphatic systems and cancer
- The lymphatic capillaries are
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