A Model Describing the Effect of P-gp Pumps on Drug Resistance in Solid Tumors

Transcription

1 A Describing the Effect of P-gp Pumps on Drug Resistance in Solid Tumors Matt Becker University of Maryland, College Park November 15, 216 Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 1

2 Outline Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 2

3 Background Resistance to chemotherapy remains (one of) the largest obstacle for cancer treatment. The two main mechanisms for resistance are selection and induction. The over-expression of P-glycoprotein (P-gp) pumps is widely understood to play a large role in multi-drug resistance (MDR). Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 3

4 Drug Resistance Housman et. al (214) Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 4

5 Heterogeneity Resistance is considered based on the amount of P-gp pumps on any given cell. The current model breaks this into a discrete case in which a cell is either "sensitive" or "resistant" to therapy. Sensitive cells can become temporarily resistant due to proximity to resistant cells. Intracellular membrane nanotubes act as short distance P-gp carriers. Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 5

6 Duran Duran et. al (216) created a simple ODE model to describe transfer of drug resistance with P-gp pumps. ds dt dr dt ds R dt = S τ s (1 R+S+S R K ) SR τ c = R τ r (1 R+S+S R = S R K ) K τr (1 R+S+S R ) + SR τ c + S R τ S R τ (1) Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 6

7 Schematic Greene et. al (214) Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 7

8 Integro-Differential Equation t dsq dt = α sps q(t) α asq S q(t) + 2 f p(t t ; µ, σ)(1 ξ)α ( t sps q(t ) 1 α asp (s)ds ) dt t t +2 f p(t t ; µ, σ)ξα ( t sps q(t ) 1 α asp (s)ds ) dt, t t drq dt = α rpr q(t) α arq R q(t) + 2 f p(t t ; µ, σ)α ( t rpr q(t ) 1 α arp (s)ds ) dt, t dsp dt drp dt dtp dt t = (1 ξ)α sps q(t) α asp S p f p(t t ; µ, σ)(1 ξ)α ( t sps q(t ) 1 α asp (s)ds ) dt, t t = α rpr q(t) α arp R p f p(t t ; µ, σ)α ( t rpr q(t ) 1 α arp (s)ds ) dt, t t = ξα sps q α atp T p f p(t t ; µ, σ)ξα ( t sps q(t ) 1 α asp (s)ds ) dt, t (2 da dt = α asq S q + α arq R q + α asp S p + α arp R p + α atp T p t f a(t t )[α asq S q(t ) + α arq R q(t ) + α asp S p(t ) + α arp R p(t ) + α atp T p(t )]dt, Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 8

9 Comparison 1.9 of Sensitive Cells Sensitive Data Sensitive of Resistant Cells Resistant Data Resistant Duran et. al. (216) Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 9

10 Comparison 1.9 of Sensitive Cells Sensitive Data Sensitive of Resistant Cells Resistant Data Resistant Duran et. al. (216) Becker AMSC Seminar 216 University of Maryland, College Park November 15, 216 1

11 Comparison 1.9 of Sensitive Cells Sensitive Data Sensitive of Resistant Cells Resistant Data Resistant Duran et. al. (216) Becker AMSC Seminar 216 University of Maryland, College Park November 15,

12 of Sensitive/Resistant Cells; 5% initially sensitive.6 of Sensitive/Resistant Cells; 87.5% initially sensitive Sensitive Resistant Data Sensitive Data Resistant Sensitive Resistant Data Sensitive Data Resistant of Sensitive/Resistant Cells; 75% initially sensitive.75 Sensitive.7 Resistant Data Sensitive.65 Data Resistant The initial jump in resistant population is the result of the transition from Sq to Tp Becker AMSC Seminar 216 University of Maryland, College Park November 15,

13 1 5 Overall Population Population Becker AMSC Seminar 216 University of Maryland, College Park November 15,

14 Going Forward Immediate Steps We ll amend the model to allow for temporary resistance to last more than one generation. Once we re satisfied with this work we ll add a cytotoxic drug term. Future Step Eventually we ll change resistance from discrete to continuous to turn this into a PDE model. Becker AMSC Seminar 216 University of Maryland, College Park November 15,