PoL – Physics of Life | Benjamin Friedrich

Benjamin Friedrich Group

Biological Algorithms: Spatio-temporal dynamics of cells and tissues

Our Research Mission

How do cells and tissues process noisy information and robustly self-organize into functional structures? How do local interactions at small scales give rise to emergent dynamics and self-organized spatio-temporal patterns at large scales in living matter – despite noise, variations, and an ever-fluctuating environment?

The Biological Algorithms Group wants to understand the nonlinear dynamics of biological systems and the underlying mechanisms of feedback control. Biological systems of interest include the dynamics of cilia, cellular navigation, and pattern formation during embryonic development and regeneration – e.g. how muscle cells form crystal-like myofibrils, diatom cells build their intricate glass shells, and axolotl regrow lost limbs of correct size. We use tools from nonlinear dynamics, stochastic processes, statistical physics and information theory in close collaboration with biologists. We aim at quantitative theoretical descriptions of biological dynamics in cells and tissues, calibrated by experimental data and allowing for testable predictions, to decipher algorithms of life.

News material for APS March Meeting: Sperm chemotaxis in turbulent flow

In many species, sperm cells can "smell" the egg, and navigate towards it. Marine species spawn their sperm and eggs directly into the ocean, where turbulent flows distort the "scent trails" released by the eggs. We developed theory and computer simulations of sperm navigation in small-scale turbulent flow, and show that, surprisingly, a little bit of flow is helpful. Understanding cellular navigation in physiological environments with external flow is important not only for marine invertebrates, but also to better understand the ecology of foraging marine bacteria, or to improve the design of microswimmers for envisioned biomedical applications.

Biological cells can navigate in concentration gradients of signaling molecules. They can "smell" the diretion to go, a process called chemotaxis, which has been studied by many researchers, but mostly for idealized conditions of still water only. However, natural gradients are subject to many distortions, e.g., by turbulent flows in the ocean. Understanding cellular navigation in external flows is important for the ecology of foraging marine bacteria, the design of microswimmers for envisioned biomedical applications, and to predict fertilization in marine invertebrates that spawn sperm and eggs directly into the ocean. As a case study of chemotaxis in such physiological environments, we developed a theory of sperm chemotaxis in marine invertebrates in small-scale turbulent flow. Surprisingly, a little bit of flow helps: Our theory explains the existence of an optimal turbulence strength at which fertilization is maximal. In short, externals flows shape concentration filaments into long filaments, along which sperm cells can "surf" to the egg. Stronger flows make these filaments longer, which is beneficial as the chances to hit the filament increase, but stronger flows also make these filaments thiNner, which is disadvAntageous, because sperm cells may not get captured even if they hit the filament, or it may take them to much time to reach the egg before intermittent turbulent flow erase the concentration field again. Hence, the optimal flow strength, which in fact agrees with the strength of flow in typical habitats of sea urchins and sea snails. Moreover our theory agrees with previous fertilization experiments in controlled shear flow. 

Movies:

Simulation of sperm cell navigating in concentration plume in small-scale turbulent flow

Computer simulation of the distorted "scent trail" (blue) of signaling molecules released by a floating egg cell (yellow), together with the simulated swimming path of a sperm cell (black). Sperm cells can measure the local concentration of signaling molecules, and steer their path by a simple feedback loop, which allows them to surf along the concentration filaments towards the egg. 

Simulation of sperm cell navigating in concentration plume in idealized shear flow

To understand the physics of the search of sperm cells, we consider also idealized conditions of more regular flow, for which we were able to develop a semi-analytical theory and thus predict the chances to find the egg as function of flow strength.

Link to original publication:

S. Lange, B.M. Friedrich: Sperm chemotaxis in marine species is optimal at physiological flow rates according theory of filament surfing. PLoS Comp. Biol. 17(4), 2021

Our theory explains the existence of an optimal turbulence strength at which fertilization is maximal. In short, externals flows shape concentration filaments into long filaments, along which sperm cells can "surf" to the egg. Stronger flows make these filaments longer, which is beneficial as the chances to hit the filament increase, but stronger flows also make these filaments thinner, which is disadvantageous, because sperm cells may not get captured even if they hit the filament, or it may take them to much time to reach the egg before intermittent turbulent flow erase the concentration field again. Hence, the optimal flow strength, which in fact agrees with the strength of flow in typical habitats of sea urchins and sea snails.

Copyright notice:

Images and movies can be re-used under CC-BY 3.0 if reference to original publication is given.