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.
Journal Article: Space dependent adhesion forces mediated by transient elastic linkages: new convergence and global existence results
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
Journal Article: 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
Book Chapter: 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). In Frederik Graw, Franziska Matthäus and Jürgen Pahle (Ed.), Modeling cellular systems (pp. 141-159) Cham, Switzerland: Springer. doi:10.1007/978-3-319-45833-5_7
How motor proteins contract the cell cortex and form a cell division ring
(2018–2021) ARC Discovery Projects
Modelling and simulation of contraction and pattern formation in the epithelial cell cortex.
Doctor Philosophy
Ergodic theory and coherent structures for non-autonomous dynamical systems
Doctor Philosophy
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). In Frederik Graw, Franziska Matthäus and Jürgen Pahle (Ed.), Modeling cellular systems (pp. 141-159) 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. In Arnaud Chauviere, Luigi Preziosi and Claude Verdier (Ed.), Cell mechanics: from single scale-based models to multiscale modelling (pp. 133-157) Boca Raton, FL, United States: Chapman and Hall / CRC Press. doi:10.1201/9781420094558-c5
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
How motor proteins contract the cell cortex and form a cell division ring
(2018–2021) ARC Discovery Projects
Modelling and simulation of contraction and pattern formation in the epithelial cell cortex.
Doctor Philosophy — Principal Advisor
Other advisors:
Ergodic theory and coherent structures for non-autonomous dynamical systems
Doctor Philosophy — Associate Advisor
Other advisors: