Understanding NK cell development using mathematical modeling Supervisors: Prof. Ramit Mehr Simon Michal Students: Nissim Pinhas Hila Rothschild Final project 2012

Background Natural killer (NK) cells are lymphocytes of the innate immune system, whose cellular actors also include granulocytes, macrophages, dendritic cells and mast cells. Some principle functions of NK cells include: – participate in the early control of viral infection. – participate in regulation of immune responses. – participate in tumor immunosurveillance. The developing NK cell population can be subdivided into 4 stages according to the expression of specific markers (CD11b and CD27).

NK education stages According to Vivier’s work, describing 4 stages of NK cells development, it was found that we can distinct between cells in different stages based on molecular expression. These cells also differ by their gene expression at the different stages. CD11b low CD27 low CD11b low CD27 high CD11b high CD27 high CD11b high CD27 low Nb Mb PbCb

Model Scheme

Goals Validate the 4-stage model suggested by Vivier and elucidate the rates of proliferation, death and transition between the stages in the bone-marrow. Investigate the option in which NK cells may skip maturation steps, and transfer directly from DN (CD11b low CD27 low ) to CD11b high CD27 low. CD11b low CD27 low CD11b low CD27 high CD11b high CD27 high CD11b high CD27 low Nb Mb PbCb

Methodology DT - Diphtheria toxin – was injected to the mice in order to eliminate the NK population cell in order to monitor development. BrdU staining data – BrdU is a thymidine analog that incorporates into the cell's DNA when the cell is dividing, providing visual evidence of cell division.

Experiment timeline DT BrdU 6 hours Total NK cell numbers were measured at days: 3, 6, 7, 8, 10, 13, 17, 24, 31.

Model’s mathematical equations Bone marrow population – total cell numbers: dN b /dt = S 1 + (γ Nb *(1-(N b /K Nb ))– δ NMb – δ NCb – δ Nbp – µ Nb )*N b dM b /dt = S 2 +δ NMb N b + (γ Mb *(1-(M b /K Mb ))– δ MPb – δ Mbp – µ Mb )*M b dP b /dt = δ MPb M b + (γ Pb *(1-(P b /K Pb ))– δ PCb – δ Pbp – µ Pb )*P b dC b /dt = δ PCb P b + δ NCb N b + (γ Cb *(1-(C b /K Cb )- δ Cbp – µ Cb )*C b

Modeling labeled cells Nb Mb PbCb Nb Mb PbCb Unlabeled Labeled S

Modeling labeled cells Nb Mb PbCb Nb Mb PbCb Unlabeled Labeled γ

Modeling labeled cells Nb Mb PbCb Nb Mb PbCb Unlabeled Labeled γ

Modeling labeled cells Nb Mb PbCb Nb Mb PbCb Unlabeled Labeled δ δ μ

Simulation Out simulation was constructed in Matlab Initialization – set parameter ranges Create all combinations of parameter values Are there any combinations left? Solve differential equations. calculate AIC score (Based on MLE). Yes Select best parameters according to the AIC score (based on the labeling data) Test that total number of cells in each combination is reasonable. Remove invalid combinations Plot the best result End No

Fitting the model Fitting methods – RMS (root mean square). – MLE (maximum likelihood estimation). – AIC (Akaike information criterion). Enables to receive a confident interval in order to distinguish a more suitable model.

1 st and 2 nd population 1 st - Total cell numbers1 st – Labeled cells fraction 2 nd - Total cell numbers 2 nd – Labeled cells fraction

3 rd population 3 rd - Total cell numbers3 rd – Labeled cells fraction

Findings S Mb

Hypotheses 1. Cells may express CD27 prior to expressing molecules that identify the cells as NK cells (e.g. NK1.1) Stem cell DN Mb CD27 + (NK1.1 + ) CD27↑ NK 1.1 ↑ CD27 + (NK1.1 - ) CD27↑ NK 1.1 ↑

Hypotheses 2. Perhaps the DN population (1 st population) does not evolve and could be served as a different position rather then be involved in the NK maturation process. Stem cell DN Mb Pb Cb

Hypotheses 3. Perhaps the DN population skips the second stage and differentiate directly into the 4 th population (Cb). Stem cell DN Mb Pb Cb

Further work Finish the search for the 3 rd and 4 th populations. Conclude the results and compare them to Vivier’s model. Continue with investigating NK cell dynamics in additional organs. Check correctness of our results in compare with Vivier’s development model through research. Project Research

Acknowledgements We would like to thank: – Prof. Mehr Ramit – Simon Michal and the lab. For the caring and the guidance along the way.