Glioblastoma Recurrence and the Role of MGMT Promoter ......3 Type-3 = GBM cells with unmethylated...

Glioblastoma Recurrence and the Role of MGMTPromoter Methylation

Katie Storey

University of Minnesota

IMA Workshop for Women in Mathematical BiologyMay 30, 2018

GBM recurrence and the role of MGMT promoter methylation Katie Storey 1

Glioblastoma Background

Glioblastoma multiforme (GBM) is the most aggressive form of braintumor

GBM patients have a median survival of 15 months, and a two-yearsurvival rate of 30%

GBM is typically treated with surgery, radiation, and a chemotherapydrug known as temozolomide (TMZ)

TMZ is a cytotoxic alkylating agent, so it attaches an methyl groupto the DNA, which triggers cell death

Resistance to TMZ

The MGMT gene codes for a protein (often called MGMT or AGT)that can repair the lesion created by TMZ

The region of DNA that initiates transcription of a gene is known asthe gene promoter

A gene can be silenced via methylation of a gene promoter

Methylation is a form of alkylation, in which a methyl group replacesa hydrogen atom in the DNA

Resistance to TMZ

Methylation of the MGMT repair gene prevents the cell fromrepairing the lesion created by TMZ

Cells with methylated MGMT promoter region =⇒ sensitive to TMZ

Cells with unmethylated MGMT promoter region =⇒ resistant toTMZ

Resistance to TMZ

Methylation of the MGMT repair gene prevents the cell fromrepairing the lesion created by TMZ

Cells with methylated MGMT promoter region =⇒ sensitive to TMZ

Cells with unmethylated MGMT promoter region =⇒ resistant toTMZ

MGMT methylation between diagnosis and recurrence

Several clinical studies compared the MGMT methylation status inmatched GBM samples at diagnosis and at recurrence, followingstandard treatment [2, 7, 3].

They observed a frequent reduction in MGMT methylation betweenprimary GBM and recurrent GBM (i.e. most primary tumors that areclassified as methylated transition to unmethylated recurrent tumorsafter TMZ treatment).

Question: is this shift simply a result of evolutionary selection ordoes TMZ actively influence the methylation status of MGMT?

1 Develop a stochastic model of GBM response to standard treatment

2 Calibrate parameters using clinical and experimental data

3 Integrate mechanisms of MGMT methylation and demethylationwithin the model

4 Use the model to investigate the question stated previously:

Can selection alone explain the reduction in MGMT methylationbetween tumor diagnosis and recurrence or does TMZ play an activerole?

5 Determine the optimal adjuvant TMZ dosing schedule, contingentupon the level of MGMT methylation at tumor diagnosis

Model overview

Multi-type, continuous-time branching process model

Three cellular subtypes:

1 Type-1 = GBM cells with fully methylated MGMT promoters

2 Type-2 = GBM cells with hemi-methylated MGMT promoters (oneDNA strand methylated, one unmethylated)

3 Type-3 = GBM cells with unmethylated MGMT promoters

Type-1 cells are considered drug-sensitive

Type-2 and type-3 cells are considered drug-resistant (have the abilityto repair the lesion created by TMZ)

Model overview

Three model phases:

1 Phase I: Tumor growth before detection, surgery, and three-weekrecovery

2 Phase II: Concurrent radiotherapy and chemotherapy (referred to asCRT), and three-week recovery

3 Phase III: Adjuvant chemotherapy with TMZ (repeated 28-day cycles)until tumor recurrence

Model overview

Three model phases:

Model overview

Three model phases:

Model overview

Three model phases:

Model overview

Time between surgery and recurrence Δt1

(1-ps)D1: population change due to surgery

D1: initial detection size D2: recurrent detection size

Phase 2 (P2) CRT: TMZ+ Radiation

Phase 3 (P3) Adjuvant TMZ

Surgery

Phase 1 (P1)

Treatment schedule

Standard treatment schedule for primary GBM, first introduced by RogerStupp et. al. in 2005 [6] :

Surgery

3 weeks recovery

CRT (6 weeks): •  Daily fractions of 2 Gy given 5 days per week •  Daily TMZ dose of 75 mg/m2

of body-surface area 7 days per week

3 weeks recovery

Adjuvant TMZ (28-day cycle repeated until recurrence): • Daily TMZ dose 150-200 mg/m2 of body-surface area for 5 days per cycle

Standard Treatment Schedule

In total, 60 Gy of radiotherapy is administered during CRT

Adjuvant chemotherapy continues until tumor recurrence

Intrinsic growth rates

X1(t) = type-1 cell population at time t

b1 = birth rate for each type-1 cell (day−1)

c1 = death rate for each type-1 cell in the absence of TMZ (day−1)

X2(t),X3(t) = type-2 cell population and type-3 cell population,respectively, at time t

b2 = birth rate for each type-2 and type-3 cell (day−1)

c2 = death rate for each type-2 and type-3 cell in the absence ofTMZ (day−1)

Modeling radiation effects

Cytotoxic effect of radiotherapy modeled using the standardlinear-quadratic (L-Q) model:

After each dose of d = 2 Gy, the probability of cell survival is

s(d) = e−αd−βd2,

where α = 0.1 and β = 0.01.

We remove (1− s(d))X1(t) type-1 cells, (1− s(d))X2(t) type-2 cells,and (1− s(d))X3(t) type-3 cells at the time t of each radiation dose

where α = 0.1 and β = 0.01.

Modeling chemotherapy effects

TMZ is a cytotoxic drug, so it has an additive effect on the deathrates

g1(C (t)), g2(C (t)) are the death rate components due to TMZ

C (t) is the plasma concentration of TMZ at time t, modeled as anexponential decay function C (t) = C0e

C0 and k determined using pharmacokinetic data

0 200 400 600

Dose level Z (mg/m2)

PK data

C0 = 0.28*Z

C0 (maximum plasmaconcentration)approximately a linearfunction of theadministered dose

0 200 400 600

PK data

C0 = 0.28*Z

0 200 400 600

PK data

C0 = 0.28*Z

0 200 400 600

PK data

C0 = 0.28*Z

Cell viability function vi (C ) gives the the proportion of live type-icells when exposed to concentration C of TMZ over the number oflive cells when exposed to no TMZ

Determined using data from experiments: the number of MGMT−

and MGMT+ cells were counted after 8 days of exposure to variousconcentrations of TMZ

0 50 100 150TMZ concentration ( M)

ll via

Sensitive cell data

Sens. Hill equation fit

Resistant cell data

Res. Hill equation fit

We fit vi (C ) to Hillequations:

vi (C ) =1

TMZ death rate component: gi (C (t)) = 18 ln(vi (C ))

ll via

Sensitive cell data

Resistant cell data

vi (C ) =1

ll via

Sensitive cell data

Resistant cell data

vi (C ) =1

ll via

Sensitive cell data

Resistant cell data

vi (C ) =1

DNA methylation dynamics

Conversions between cell-types are driven by methylation anddemethylation events at a representative CpG site immediately aftercell division

DNA methylation is carried out by three major DNAmethyltransferases (enzymes): DNMT1, DNMT3a, DNMT3b

DNMT1 is responsible for maintenance methylation

DNMT3a, DNMT3b are responsible for de novo methylation

—CG—CGCG— —GC—GCGC— DNA replication

—CG—CGCG— —GC—GCGC—

Dnmt3a/b

Dnmt1 Dnmt3a/b

Dnmt1 Dnmt1

Dnmt3a/b

Dnmt1 Dnmt3a/b

Dnmt1 Dnmt1

Dnmt3a/b

Dnmt1 Dnmt3a/b

Dnmt1 Dnmt1

Dnmt3a/b

Dnmt1 Dnmt3a/b

Dnmt1 Dnmt1

Dnmt3a/b

Dnmt1 Dnmt3a/b

Dnmt1 Dnmt1

Inspired by the model in [5], by L.B. Sontag et. al. (2006)

ρ = probability of maintaining methylation at a previously methylatedCpG site, following cell division (baseline ρ = 0.95 per cell division)

ν = probability of de novo methylation at an unmethylated CpG site,following cell division (baseline ν = 0.09 per cell division)

Below 1 denotes methylated, 0 denotes unmethylated

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Set of possible birth events

1 2 3 = type-1 cell = type-2 cell = type-3 cell

Birth event rates

b1(1-A)2 b1 2A(1-A) b1A2

A=(1-ρ)(1-ν)

b2ν2(1-A) b2(2ν(1-ν)(1-A) + ν2A)

b2(1-ν)2(1-A) b2 2ν(1-ν)A b2 A(1-ν)2

b2ν4 b2 4(ν3-ν4) b2 2ν2(1-ν)2 b2 4ν2(1-ν)2 b2 4ν(1-ν)3 b2 (1-ν)4

Methylation percentage at detection

The distribution of methylation percentages at the time of tumordetection (obtained from 100 Monte Carlo simulations):

Methylation percentage at detection

The distribution of methylation percentages at the time of tumordetection (obtained from 100 Monte Carlo simulations):

Methylation percentage at recurrence

First, we assume TMZ does not actively impact the methylationprocesses (i.e. ρ and ν are the same in the absence and presence ofTMZ)

In this case, the distribution of methylation percentages at the timeof tumor recurrence are shown below:

Methylation percentage at recurrence

First, we assume TMZ does not actively impact the methylationprocesses (i.e. ρ and ν are the same in the absence and presence ofTMZ)

In this case, the distribution of methylation percentages at the timeof tumor recurrence are shown below:

Methylation change between detection and recurrence

The distribution of the change in methylation percentage betweendetection and recurrence (ρ and ν are the same in the absence andpresence of TMZ):

Above results are not consistent with the clinically observed reductionin methylation between detection and recurrence

Suggests selection alone cannot explain these clinical observations

Does TMZ impact de novo methylation?

Let νz denote the probability of de novo methylation (i.e. theprobability that DNMT3a/b methylates an unmethylated site,immediately following cell replication) in the presence of TMZ.

When νz = 0, the distribution of methylation percentages at the timeof tumor recurrence are shown below:

Let νz denote the probability of de novo methylation (i.e. theprobability that DNMT3a/b methylates an unmethylated site,immediately following cell replication) in the presence of TMZ.

When νz = 0, the distribution of methylation percentages at the timeof tumor recurrence are shown below:

The change in methylation percentage between detection and recurrence,with νz = 0:

Modest decrease in methylation, not sizable enough to account forclinically observed MGMT methylation reduction

The change in methylation percentage between detection and recurrence,with νz = 0:

Modest decrease in methylation, not sizable enough to account forclinically observed MGMT methylation reduction

Does TMZ impact maintenance methylation?

Let ρz denote the probability of maintenance methylation (i.e. theprobability that DNMT1 methylates a site that was methylated in theparental DNA) in the presence of TMZ.

The expected methylation percentage at recurrence, as a function ofρz , is shown below:

0.2 0.4 0.6 0.8

z (per cell division)

Let ρz denote the probability of maintenance methylation (i.e. theprobability that DNMT1 methylates a site that was methylated in theparental DNA) in the presence of TMZ.

The expected methylation percentage at recurrence, as a function ofρz , is shown below:

0.2 0.4 0.6 0.8

z (per cell division)

When ρz = 0.5, the distribution of methylation percentages at thetime of tumor recurrence are shown below:

The change in methylation percentage between detection and recurrence,with ρz = 0.5:

Substantial decrease in MGMT methylation percentage betweendetection and recurrence, consistent with clinical results

Suggests that TMZ inhibition of maintenance methylation can explainthe clinically observed downward shift in methylation

Optimization of adjuvant TMZ dosing

28-day chemotherapy cycles in Phase 3 (adjuvant chemotherapyphase)

In the standard schedule, 5 TMZ doses of 150-200 mg/m2 areadministered daily at the beginning of each cycle

We use linear optimization of the number of doses per adjuvant TMZcycle, to minimize the mean tumor size after 4 cycles of treatment

Based on previous investigations, we let ρz = 0.5

First, we calculate the cellular population means for use in the dosingoptimization

Population means

Recall:

Birth event rates

b1(1-A)2 b1 2A(1-A) b1A2

A=(1-ρ)(1-ν)

b2ν2(1-A) b2(2ν(1-ν)(1-A) + ν2A)

b2(1-ν)2(1-A) b2 2ν(1-ν)A b2 A(1-ν)2

Let µj ,ki (t) denote the probability that a type-i cell gives rise to atype-j and type-k cell

Let uj ,ki (t) := biµj ,ki (t) (e.g. u1,12 = b2ν

2(1− A))

Population means

Recall:

Birth event rates

b1(1-A)2 b1 2A(1-A) b1A2

A=(1-ρ)(1-ν)

b2ν2(1-A) b2(2ν(1-ν)(1-A) + ν2A)

b2(1-ν)2(1-A) b2 2ν(1-ν)A b2 A(1-ν)2

2(1− A))

Population means

Recall:

Birth event rates

b1(1-A)2 b1 2A(1-A) b1A2

A=(1-ρ)(1-ν)

b2ν2(1-A) b2(2ν(1-ν)(1-A) + ν2A)

b2(1-ν)2(1-A) b2 2ν(1-ν)A b2 A(1-ν)2

2(1− A))

Population means

Let Ti denote the sum of the event rates for cell type-i :

Ti (t) := di (t) +∑

1≤j ,k≤3

uj ,ki (t), 1 ≤ i ≤ 3.

For s = (s1, s2, s3), where 0 ≤ s1, s2, s3 ≤ 1, the probability generatingfunctions of the offspring distributions are:

fi (s, t) = (Ti (t))−1

di (t) +∑

1≤j ,k≤3

uj ,ki (t)sjsk

Population means

Let Ti denote the sum of the event rates for cell type-i :

Ti (t) := di (t) +∑

1≤j ,k≤3

uj ,ki (t), 1 ≤ i ≤ 3.

For s = (s1, s2, s3), where 0 ≤ s1, s2, s3 ≤ 1, the probability generatingfunctions of the offspring distributions are:

fi (s, t) = (Ti (t))−1

di (t) +∑

1≤j ,k≤3

uj ,ki (t)sjsk

Population means

Using the backward Kolmogorov equation, we obtain the infinitesimalgenerator for the branching process:

[Ti (t)

(∂fi (s, t)

∣∣∣∣s=(1,1,1)

− δij

)]1≤i ,j≤3

where the mean matrix M(t) = {mij(t); 1 ≤ i , j ≤ 3} must satisfy:

dt= GtM(t).

Hence:

M(t) = exp

(∫ t

0Gs ds

and E([X1(t) X2(t) X3(t)

] ∣∣ [X1(0) X2(0) X3(0)]

=[1 0 0

])=[1 0 0

]M(t).

Population means

Using the backward Kolmogorov equation, we obtain the infinitesimalgenerator for the branching process:

[Ti (t)

(∂fi (s, t)

∣∣∣∣s=(1,1,1)

− δij

)]1≤i ,j≤3

where the mean matrix M(t) = {mij(t); 1 ≤ i , j ≤ 3} must satisfy:

dt= GtM(t).

Hence:

M(t) = exp

(∫ t

0Gs ds

and E([X1(t) X2(t) X3(t)

] ∣∣ [X1(0) X2(0) X3(0)]

=[1 0 0

])=[1 0 0

]M(t).

Let n = number of TMZ doses in one cycle

Administered dose of TMZ (in mg/m2): Z (n) = 1000/n

0 5 10 15 20 25Number of TMZ doses per cycle

Total population after 4 cycles

Optimal dose number (n=6)

Dosing schedule that minimizes the the mean tumor population after4 adjuvant cycles is n = 6 with Z (6) = 166.67 mg/m2.

n = 6 yields similar results to the standard treatment schedule (n = 5)

Tumor population decomposition into TMZ-sensitive (type-1) andTMZ-resistant (type-2 and type-3):

Total population

Fully methylated cells (Type-1)

Non-methylated cells (Type-2+Type-3)

Using baseline set of parameters (expected methylation percentage atdiagnosis ≈ 76%)

Optimization with low methylation at diagnosis

Inter-tumor heterogeneity leads to differing levels of methylation atdiagnosis

We identified a set of birth rates (b1, b2) that preserved the netgrowth of the tumor and led to 30% methylation at diagnosis

In this case, we observe:

Total population

n = 3 is optimal in this case

However, 3 doses does not provide a significant advantage over noTMZ treatment at all

Total population

n = 3 is optimal in this case

However, 3 doses does not provide a significant advantage over noTMZ treatment at all

Conclusions

Our stochastic model indicates that evolutionary selection is notenough to explain the clinically observed drop in MGMT methylationbetween GBM diagnosis and recurrence.

Model simulations suggest that TMZ actively inhibits maintenancemethylation, driving the downward shift in MGMT methylationbetween tumor diagnosis and recurrence.

Optimization for a tumor with a high level of methylation at diagnosisshows that 6 daily doses per adjuvant cycle is optimal, but thestandard schedule is near optimal.

For primary GBM with low methylation levels at diagnosis, a smallernumber of larger TMZ doses is optimal, but not very beneficial.

Conclusions

Discussion/Future work

A potential mechanism for TMZ-mediated inhibition of maintenancemethylation:

TMZ may activate the protein kinase C (PKC) pathway, which leads tothe phosphorylation of DNMT1, thereby inhibiting maintenancemethylation within the affected GBM cells [1, 4].

For unmethylated primary tumors, it may be more beneficial toadminister a therapy to use in combination with TMZ, that canstimulate MGMT methylation, counteracting TMZ’s inhibition ofmaintenance methylation.

Future directions:

Incorporate the oncogenic IDH1 mutation and investigate thehypothesis that it drives increased methylation in gliomas

Investigate the role of the stem cell marker CD133+ and its impact onthe evolution of TMZ resistance

Future directions:

Thank you for listening!

Thanks to my collaborators:

Kevin Leder1, Andrea Hawkins-Daarud2, Kristin Swanson3, AtiqueAhmed4, Russ Rockne5, and Jasmine Foo6

1University of Minnesota2Mayo Clinic Arizona3Mayo Clinic Arizona4Northwestern University5Beckman Research Institute6University of Minnesota

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AA Brandes, E Franceschi, A. Tosoni, et al.O6-methylguanine DNA-methyltransferase methylation status canchange between first surgery for newly diagnosed glioblastoma andsecond surgery for recurrence: clinical implications.Neuro-Oncology, 12(3):283–288, 2010.

M. Christmann, G. Nagel, S. Horn, et al.MGMT activity, promoter methylation and immunohistochemistry ofpretreatment and recurrent malignant gliomas: a comparative studyon astrocytoma and glioblastoma.Int. J. Cancer, 127:2106–2118, 2010.

G Lavoie, P-O Estve, NB Laulan, S Pradhan, and Y St-Pierre.PKC isoforms interact with and phosphorylate DNMT1.

BMC Biology, 9(31):doi:10.1186/1741–7007–9–31, 2011.

L.B. Sontag, M.C. Lorincz, and E.G.Luebeck.Dynamics, stability and inheritance of somatic DNA methylationimprints.Journal of Theoretical Biology, 242(4):890 – 899, 2006.

R. Stupp, W. P. Mason, M. J. van den Bent, et al.Radiotherapy plus concomitant and adjuvant temozolomide forglioblastoma.New England Journal of Medicine, 352(10):987–996, 2005.

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