Mathematical Biophysics

The group pursues a mathematical physics-approach to study phenomena in biophysics. Our analytical efforts complement the research activities of the Theoretical and Computational Biophysics Department, as well as of the Computational Biomolecular Dynamics Group

Our main research focus is currently the non-equilibrium statistical mechanics of single molecules. In particular we aim at a trajectory-based description of macromolecular conformation dynamics as well as of their spatial transport, binding, and reactions. In our work we employ rigorous analysis complemented by computer simulations. 

Interested in joining us? Please see Open Positions for available positions.

Recent research activities

First passage time theory: trajectory-to-trajectory fluctuations in biochemical reactions at low-copy numbers


The first passage time, the time needed for some stochastic observable to  reach a given preset value for the first time along a given trajectory, is central to our understanding kinetics across many disciplines, such as diffusion-controlled chemical reactions, biological signaling cascades, transport in disordered media, bacteria and animals foraging for food, up to the global spreading of diseases and stock market dynamics. Modern single-molecule tracking and imaging methods nowadays allow us to probe single binding and reaction events in living cells. These experiments reveal striking sample-to-sample fluctuations in binding/encounter times. It is therefore timely and important to extend the traditional mean-rate paradigm in (bio)chemical reaction kinetics to the full distribution of first passage time. In this spirit we recently obtained rigorous results on the first passage time universality class for dynamics in finite systems, and explained a universal proximity effect in the context of so-called kinetics in the few-encounter limit, which provides a simple explanation for the observed robustness of both the speed and precision of transcription regulation in biological cells [a1]. In our work we also explained the importance of a broken translational symmetry of the medium [b1], of the presence of disorder [c1] and of the existence of multiple transport channels [d1] on the statistics of first passage time.

[a1] A. Godec and R. Metzler, Universal proximity effect in target search kinetics in the few-encounter limitPhys. Rev. X 6, 041037 (2016). [PDF]

[b1] A. Godec and R. Metzler, First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage timeSci. Rep. 6, 20349 (2016). [PDF]

       A. Godec and R. Metzler, Optimization and universality of Brownian search in a basic model of quenched heterogeneous mediaPhys. Rev. E 91, 052134 (2015). [PDF]

[c1] H. Kruesemann, A. Godec and R. Metzler, Ageing first passage time density in continuous time random walks and quenched energy landscapesJ. Phys. A: Math. Theor. 48, 285001 (2015). [PDF]

       H. Kruesemann, A. Godec and R. Metzler, First-passage statistics for aging diffusion in systems with annealed and quenched disorderPhys. Rev. E 89, 040101(R) (2014). [PDF]

[d1] A. Godec and R. Metzler, First passage-time statistics for two-channel diffusionJ. Phys. A: Math. Theor. 50, 084001 (2017). [PDF]

Physical limits to biochemical signaling coupled to active molecular motor-mediated transport


We developed a linear response theory quantifying the fundamental mean field precision limit for receptor signaling coupled to active molecular motor-mediated intracellular transport. In the model we couple the so-called intermittent search model with reversible Markovian binding to the receptor. Our results demonstrate the existence of active signal focusing enabling a faster and more precise delivery of the molecular cue to the corresponding receptor site [a2]. In addition, we explain the unconditional improvement of the signaling precision in effectively one-dimensional structures such as neuronal cells in terms of breaking of the recurrence in the motion of the signaling molecule [b2].

[a2] A. Godec and R. Metzler, Signal focusing through active transportPhys. Rev. E 92, 010701(R) (2015). [PDF]

[b2] A. Godec and R. Metzler, Active transport improves the precision of linear long distance molecular signallingJ. Phys. A: Math. Theor. 49, 364001 (2016). [PDF]

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