I studied Technical Mathematics at the Vienna University of Technology. I also earned a Master's degree in Law and I finished the first ("non-clinical") part of Medical Studies at the University of Vienna. I earned my PhD in Applied Mathematics at the University of Vienna in 2007. My PhD advisor was Christian Schmeiser, my co-advisor was Peter Markowich. I spent several months at the University of Buenos Aires working with C. Lederman and at the ENS-Paris rue d'Ulm in the group of B. Perthame.
Before coming to UQ, I held post-doc positions at the Wolfgang Pauli Insitute (Vienna), University of Vienna and the Austrian Academy of Sciences (RICAM). In 2013 I won an Erwin Schrödinger Fellowship of the Austrian Science Fund (FWF). I was a post-doc researcher in the group of Alex Mogilner first at UC Davis, then at the Courant Institute of Math. Sciences (New York University).
Biological systems integrate a multitude of processes on various spatial and temporal scales. The output of biological processes is typically robust to a range of random perturbations. Mathematics is an outstanding tool to investigate such cooperative mechanisms on the molecular level which can hardly be assessed experimentally.
Building on a sound applied mathematics and partial differential equations (PDE) background, the area of my research is to identify and describe biological processes by formulating mathematical models, to evaluate them using numerical simulation and mathematical analysis and to validate such models against experimental data.
A ubiquitous example for a highly complex biological system are cells. They use cytoskeletons composed of long fibers on the micron length scale to sustain their shape mechanically. Molecular processes on the nanoscale which change the structure of these fibers as well as force generation by motor proteins promote remodeling of cell shape, cell migration and intracellular transport. This is the basis for vital processes such as muscle contraction, cell division, immune system response, wound healing and embryogenesis, and it plays a crucial role in pathological processes such as tumor metastasis and neurodegenerative deseases.
The central question of my research is: how do proteins on the nanoscale and larger protein complexes on the micronscale cooperate in living cells to promote cell movement, shape changes, force generation and intra- cellular transport? This type of research contributes to the development of new techniques in bioengineering and of new therapeutic approaches in clinical fields such as oncology and immunology.
One important aspect of biological mechanisms is insensitivity to random perturbations. Hence mathe- matical models on the microscopic level are necessarily stochastic and I employ mathematical analysis and numerical simulation such as Brownian Dynamics to analyze the sensitivity of models and to identify robust characteristics of a systems output. Especially the smallness of the molecular length scales interferes with experimental imaging techniques to assess these biological processes in vivo. For this reason an essential aspect of my research is to use asymptotic analysis to derive and justify macroscopic coarse-grained models based on thoroughly formulated microscopic models. In general this process yields partial differential equations such as reaction-drift-diffusion models and fluid dynamics models. I analyze these models, which often exhibit amazingly rich mathematical properties, analytically and by numerical simulation in order to relate the experimentally measurable macroscopic features to the microscopic dynamics of interest.
Conference Publication: Uncovering Microtubule-driven Mechanisms of Melanoma Invasion
Ju, R. J., Falconer, A. D., Dean, K. M., Fiolka, R. P., Sester, D. P., Nobis, M., Timpson, P., Lomakin, A. J., Danuser, G., White, M. D., Oelz, D. B., Haass, N. K. and Stehbens, S. J. (2024). Uncovering Microtubule-driven Mechanisms of Melanoma Invasion. 50th Annual Meeting of the Dermatological Research Working Group (ADF), Dusseldorf, Germany, 6-9 March 2024. Chichester, West Sussex United Kingdom: Wiley-Blackwell.
Journal Article: A mathematical model for axonal transport of large cargo vesicles
Rahman, Nizhum and Oelz, Dietmar B. (2023). A mathematical model for axonal transport of large cargo vesicles. Journal of Mathematical Biology, 88 (1) 1, 1-22. doi: 10.1007/s00285-023-02022-3
Journal Article: Super-resolved trajectory-derived nanoclustering analysis using spatiotemporal indexing
Wallis, Tristan P., Jiang, Anmin, Young, Kyle, Hou, Huiyi, Kudo, Kye, McCann, Alex J., Durisic, Nela, Joensuu, Merja, Oelz, Dietmar, Nguyen, Hien, Gormal, Rachel S. and Meunier, Frédéric A. (2023). Super-resolved trajectory-derived nanoclustering analysis using spatiotemporal indexing. Nature Communications, 14 (1) 3353, 1-16. doi: 10.1038/s41467-023-38866-y
How motor proteins contract the cell cortex and form a cell division ring
(2018–2023) ARC Discovery Projects
Computational Biomechanical Modelling and simulation of cellular migration in heterogeneous 3D environment
Doctor Philosophy
Fractional Differential Equations in Mathematical Biology - modelling and simulation.
Doctor Philosophy
A study of mathematical models for collective cell migration and axonal transport
(2023) Doctor Philosophy
Collective Cell Migration in Development
This project deals with simulation of collective cell migration in tissues. It will include collaboration with experimentists at IMB and with Prof. Zhiyong Li .
Stress fibers: structure, dynamics and mechanotransduction
This project deals with emergent structures in the cortex of living cells. We will perform agent based simulations (Brownian Dynamics) and investigate the nucleation and growth of contractile stress fibres in the cortex.
Mechano-biological regulation of immune cell cytotoxicity (applied/computational mathematics, data science)
Investigate mechano-biological regulation of cytotoxicity of immune cells through material properties of target cells and their cell nuclei. Use modelling and simulation of fluctuating membranes in order to characterise how area and persistence of interaction zones is controlled by cytoskeletal stress and nuclear elasticity.
This PhD project will involve both computational simulation of stochastic partial differential equations and formal mathematical (asymptotic) analysis as well as collaboration with experimentalists Alexis Lomakin and it might also involve data analysis and statistical inference of parameter values.
Numerical treatment of the Filament-Based Lamellipodium Model (FBLM)
Manhart, Angelika , Oelz, Dietmar , Schmeiser, Christian and Sfakianakis, Nikolaos (2017). Numerical treatment of the Filament-Based Lamellipodium Model (FBLM). Modeling cellular systems. (pp. 141-159) edited by Frederik Graw, Franziska Matthäus and Jürgen Pahle. Cham, Switzerland: Springer. doi: 10.1007/978-3-319-45833-5_7
How do cells move? Mathematical modeling of cytoskeleton dynamics and cell migration
Ölz, Dietmar and Schmeiser, Christian (2010). How do cells move? Mathematical modeling of cytoskeleton dynamics and cell migration. Cell mechanics: from single scale-based models to multiscale modelling. (pp. 133-157) edited by Arnaud Chauviere, Luigi Preziosi and Claude Verdier. Boca Raton, FL, United States: Chapman and Hall / CRC Press. doi: 10.1201/9781420094558-c5
A mathematical model for axonal transport of large cargo vesicles
Rahman, Nizhum and Oelz, Dietmar B. (2023). A mathematical model for axonal transport of large cargo vesicles. Journal of Mathematical Biology, 88 (1) 1, 1-22. doi: 10.1007/s00285-023-02022-3
Super-resolved trajectory-derived nanoclustering analysis using spatiotemporal indexing
Wallis, Tristan P., Jiang, Anmin, Young, Kyle, Hou, Huiyi, Kudo, Kye, McCann, Alex J., Durisic, Nela, Joensuu, Merja, Oelz, Dietmar, Nguyen, Hien, Gormal, Rachel S. and Meunier, Frédéric A. (2023). Super-resolved trajectory-derived nanoclustering analysis using spatiotemporal indexing. Nature Communications, 14 (1) 3353, 1-16. doi: 10.1038/s41467-023-38866-y
Tam, Alexander K. Y., Mogilner, Alex and Oelz, Dietmar B. (2022). F-actin bending facilitates net actomyosin contraction By inhibiting expansion with plus-end-located myosin motors. Journal of Mathematical Biology, 85 (1) 4, 1-35. doi: 10.1007/s00285-022-01737-z
Rahman, Nizhum, Marangell, Robert and Oelz, Dietmar (2022). Classification and stability analysis of polarising and depolarising travelling wave solutions for a model of collective cell migration. Applied Mathematics and Computation, 421 126954, 126954. doi: 10.1016/j.amc.2022.126954
Schenk, Elaine B., Meunier, Frederic A. and Oelz, Dietmar B. (2022). Spatial redistribution of neurosecretory vesicles upon stimulation accelerates their directed transport to the plasma membrane. PLoS One, 17 (3) e0264521, e0264521. doi: 10.1371/journal.pone.0264521
Protein friction and filament bending facilitate contraction of disordered actomyosin networks
Tam, Alexander K.Y., Mogilner, Alex and Oelz, Dietmar B. (2021). Protein friction and filament bending facilitate contraction of disordered actomyosin networks. Biophysical Journal, 120 (18), 4029-4040. doi: 10.1016/j.bpj.2021.08.012
Oelz, Dietmar B. (2021). Quasi-steady-state reduction of a model for cytoplasmic transport of secretory vesicles in stimulated chromaffin cells. Journal of Mathematical Biology, 82 (4) 29, 29. doi: 10.1007/s00285-021-01583-5
Polarization wave at the onset of collective cell migration
Oelz, Dietmar, Khataee, Hamid, Czirok, Andras and Neufeld, Zoltan (2019). Polarization wave at the onset of collective cell migration. Physical Review E, 100 (3) 032403, 032403. doi: 10.1103/PhysRevE.100.032403
Bidirectional sliding of two parallel microtubules generated by multiple identical motors
Allard, Jun, Doumic, Marie, Mogilner, Alex and Oelz, Dietmar (2019). Bidirectional sliding of two parallel microtubules generated by multiple identical motors. Journal of Mathematical Biology, 79 (2), 571-594. doi: 10.1007/s00285-019-01369-w
Milišić, Vuk and Oelz, Dietmar (2018). Space dependent adhesion forces mediated by transient elastic linkages: new convergence and global existence results. Journal of Differential Equations, 265 (12), 6049-6082. doi: 10.1016/j.jde.2018.07.007
Microtubule dynamics, kinesin-1 sliding, and dynein action drive growth of cell processes
Oelz, Dietmar B., del Castillo, Urko, Gelfand, Vladimir I. and Mogilner, Alex (2018). Microtubule dynamics, kinesin-1 sliding, and dynein action drive growth of cell processes. Biophysical Journal, 115 (8), 1614-1624. doi: 10.1016/j.bpj.2018.08.046
Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles
Hirsch, Stefanie, Oelz, Dietmar and Schmeiser, Christian (2016). Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles. Discrete and Continuous Dynamical Systems - Series A, 36 (9), 4945-4962. doi: 10.3934/dcds.2016014
A drift-diffusion model for molecular motor transport in anisotropic filament bundles
Oelz, Dietmar and Mogilner, Alex (2016). A drift-diffusion model for molecular motor transport in anisotropic filament bundles. Discrete and Continuous Dynamical Systems - Series A, 36 (8), 4553-4567. doi: 10.3934/dcds.2016.36.4553
Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array
Oelz, Dietmar and Mogilner, Alex (2016). Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array. Physica D: Nonlinear Phenomena, 318-319, 70-83. doi: 10.1016/j.physd.2015.10.005
Milisic, Vuk and Oelz, Dietmar (2016). Tear-off versus global existence for a structured model of adhesion mediated by transient elastic linkages. Communications in Mathematical Sciences, 14 (5), 1353-1372. doi: 10.4310/CMS.2016.v14.n5.a7
A combination of actin treadmilling and cross-linking drives contraction of random actomyosin arrays
Oelz, Dietmar B., Rubinstein, Boris Y. and Mogilner, Alex (2015). A combination of actin treadmilling and cross-linking drives contraction of random actomyosin arrays. Biophysical Journal, 109 (9), 1818-1829. doi: 10.1016/j.bpj.2015.09.013
Manhart, Angelika, Oelz, Dietmar, Schmeiser, Christian and Sfakianakis, Nikolaos (2015). An extended filament based lamellipodium model produces various moving cell shapes in the presence of chemotactic signals. Journal of Theoretical Biology, 382, 244-258. doi: 10.1016/j.jtbi.2015.06.044
A free boundary problem for aggregation by short range sensing and differentiated diffusion
Haskovec, Jan and Oelz, Dietmar (2015). A free boundary problem for aggregation by short range sensing and differentiated diffusion. Discrete and Continuous Dynamical Systems - Series B, 20 (5), 1461-1480. doi: 10.3934/dcdsb.2015.20.1461
Milisic, Vuc and Oelz, Dietmar (2015). On a structured model for the load dependent reaction kinetics of transient elastic linkages mediating nonlinear friction. SIAM Journal on Mathematical Analysis, 47 (3), 2104-2121. doi: 10.1137/130947052
A viscous two-phase model for contractile actomyosin bundles
Oelz, Dietmar (2014). A viscous two-phase model for contractile actomyosin bundles. Journal of Mathematical Biology, 68 (7), 1653-1676. doi: 10.1007/s00285-013-0682-6
Analysis of a relaxation scheme for a nonlinear Schrodinger equation occurring in plasma physics
Oelz, Dietmar and Trabelsi, Saber (2014). Analysis of a relaxation scheme for a nonlinear Schrodinger equation occurring in plasma physics. Mathematical Modelling and Analysis, 19 (2), 257-274. doi: 10.3846/13926292.2014.910279
Convergence of the penalty method applied to a constrained curve straightening flow
Oelz, Dietmar (2014). Convergence of the penalty method applied to a constrained curve straightening flow. Communications in Mathematical Sciences, 12 (4), 601-621. doi: 10.4310/CMS.2014.v12.n4.a1
Simulation of lamellipodial fragments
Oelz, Dietmar and Schmeiser, Christian (2012). Simulation of lamellipodial fragments. Journal of Mathematical Biology, 64 (3), 513-528. doi: 10.1007/s00285-011-0421-9
On the asymptotic regime of a model for friction mediated by transient elastic linkages
Milisic, Vuk and Oelz, Dietmar (2011). On the asymptotic regime of a model for friction mediated by transient elastic linkages. Journal de Mathematiques Pures et Appliquees, 96 (5), 484-501. doi: 10.1016/j.matpur.2011.03.005
On the curve straightening flow of inextensible, open, planar curves
Oelz, D. (2011). On the curve straightening flow of inextensible, open, planar curves. SeMA Journal, 54 (1), 5-24. doi: 10.1007/BF03322585
Derivation of a model for symmetric lamellipodia with instantaneous cross-link turnover
Oelz, Dietmar and Schmeiser, Christian (2010). Derivation of a model for symmetric lamellipodia with instantaneous cross-link turnover. Archive for Rational Mechanics and Analysis, 198 (3), 963-980. doi: 10.1007/s00205-010-0304-z
Size distribution dependence of prion aggregates infectivity
Calvez, Vincent, Lenuzza, Natacha, Oelz, Dietmar, Deslys, Jean-Philippe, Laurent, Pascal, Mouthon, Franck and Perthame, Benoît (2009). Size distribution dependence of prion aggregates infectivity. Mathematical Biosciences, 217 (1), 88-99. doi: 10.1016/j.mbs.2008.10.007
A quasilinear parabolic singular perturbation problem
Lederman, Claudia and Oelz, Dietmar (2008). A quasilinear parabolic singular perturbation problem. Interfaces and Free Boundaries, 10 (4), 447-482. doi: 10.4171/IFB/197
Modeling of the actin-cytoskeleton in symmetric lamellipodial fragments
Oelz, Dietmar, Schmeiser, Christian and Small, J Victor (2008). Modeling of the actin-cytoskeleton in symmetric lamellipodial fragments. Cell adhesion & migration, 2 (2), 117-126. doi: 10.4161/cam.2.2.6373
Non linear diffusions as limit of kinetic equations with relaxation collision kernels
Dolbeault, Jean, Markowich, Peter, Oelz, Dietmar and Schmeiser, Christian (2007). Non linear diffusions as limit of kinetic equations with relaxation collision kernels. Archive for Rational Mechanics and Analysis, 186 (1), 133-158. doi: 10.1007/s00205-007-0049-5
Model hierarchies for cell aggregation by chemotaxis
Chalub, Fabio, Dolak-Struss, Yasmin, Markowich, Peter, Oelz, Dietmar, Schmeiser, Christian and Soreff, Alexander (2006). Model hierarchies for cell aggregation by chemotaxis. Mathematical Models and Methods in Applied Sciences, 16 (SUPPL. 1), 1173-1197. doi: 10.1142/S0218202506001509
Multistep navigation of leukocytes: A stochastic model with memory effects
Oelz, Dietmar, Schmeiser, Christian and Soreff, Alexander (2005). Multistep navigation of leukocytes: A stochastic model with memory effects. Mathematical Medicine and Biology, 22 (4), 291-303. doi: 10.1093/imammb/dqi009
Uncovering Microtubule-driven Mechanisms of Melanoma Invasion
Ju, R. J., Falconer, A. D., Dean, K. M., Fiolka, R. P., Sester, D. P., Nobis, M., Timpson, P., Lomakin, A. J., Danuser, G., White, M. D., Oelz, D. B., Haass, N. K. and Stehbens, S. J. (2024). Uncovering Microtubule-driven Mechanisms of Melanoma Invasion. 50th Annual Meeting of the Dermatological Research Working Group (ADF), Dusseldorf, Germany, 6-9 March 2024. Chichester, West Sussex United Kingdom: Wiley-Blackwell.
Fractional order modified Treves model: simulation and learning
Vats, Yash, Mehra, Mani, Oelz, Dietmar and Gandhi, Saurabh R. (2023). Fractional order modified Treves model: simulation and learning. 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), Ajman, United Arab Emirates, 14-16 March 2023. Piscataway, NJ, United States: IEEE. doi: 10.1109/icfda58234.2023.10153321
Wallis, Tristan P., Jiang, Anmin, Young, Kyle, Hou, Huioyi, Kudo, Kye, McCann, Alex, Durisic, Nela, Joensuu, Merja, Oelz, Dietmar, Nguyen, Hien, Gormal, Rachel S. and Meunier, Frederic A. (2023). Data for NASTIC. The University of Queensland. (Dataset) doi: 10.48610/0901bca
How motor proteins contract the cell cortex and form a cell division ring
(2018–2023) ARC Discovery Projects
Computational Biomechanical Modelling and simulation of cellular migration in heterogeneous 3D environment
Doctor Philosophy — Principal Advisor
Fractional Differential Equations in Mathematical Biology - modelling and simulation.
Doctor Philosophy — Principal Advisor
Modelling and simulation of cellular contractility and mechano-transduction in epithelial tissue.
Doctor Philosophy — Principal Advisor
Other advisors:
A study of mathematical models for collective cell migration and axonal transport
(2023) Doctor Philosophy — Principal Advisor
Other advisors:
(2021) Doctor Philosophy — Associate Advisor
Other advisors:
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
Collective Cell Migration in Development
This project deals with simulation of collective cell migration in tissues. It will include collaboration with experimentists at IMB and with Prof. Zhiyong Li .
Stress fibers: structure, dynamics and mechanotransduction
This project deals with emergent structures in the cortex of living cells. We will perform agent based simulations (Brownian Dynamics) and investigate the nucleation and growth of contractile stress fibres in the cortex.
Mechano-biological regulation of immune cell cytotoxicity (applied/computational mathematics, data science)
Investigate mechano-biological regulation of cytotoxicity of immune cells through material properties of target cells and their cell nuclei. Use modelling and simulation of fluctuating membranes in order to characterise how area and persistence of interaction zones is controlled by cytoskeletal stress and nuclear elasticity.
This PhD project will involve both computational simulation of stochastic partial differential equations and formal mathematical (asymptotic) analysis as well as collaboration with experimentalists Alexis Lomakin and it might also involve data analysis and statistical inference of parameter values.
Emergence of assymetry in hydra spheroids
In this project, we are investigating how hydra spheroids which emerge from surface patches cut out of living hydra determine a polar axis. The project involves the mechanical description of the spheroids (solid mechanics of shells) and the description of their microstructure (actin filament network).