Welcome to the Gerland group -

Physics of Complex Biosystems


In physics, interactions between particles follow laws. In biology, interactions between biomolecules serve a function. These very different points of view are beginning to merge as research over the past years has demonstrated how, in some exemplary cases, the laws of physics constrain the implementation of biological function.

We investigate several such cases. For instance, we study how the spatial arrangement and coordination of enzymes determines the efficiency of a multi-step reaction. These spatial arrangements can be natural (as in biomolecular complexes) or engineered with the modern methods of bio-nanotechnology. In both cases, fundamental functional tradeoffs emerge, which must be characterized to understand the optimization of such systems.

Methods from theoretical physics help to describe the functioning of these complex biomolecular systems on a quantitative level, while the biological function leads to new questions, with many parallels in the engineering disciplines. Seen from this perspective, a bacterium is a microscopic bioreactor programmed by evolution to rebuild itself from a variable set of resources and in fluctuating environments. How is this bioreactor programmed? Which strategies enable the control of a diverse set of physico-chemical processes in a way as to robustly produce a highly complex product? Quantitative analysis and modeling facilitates insight into the underlying design principles.


Recent Research Highlights

Cross-diffusion induced patterns for a single-step enzymatic reaction

Several different enzymes display an apparent diffusion coefficient that increases with the concentration of their substrate. Moreover, their motion becomes directed in substrate gradients. Currently, there are several competing models for these transport dynamics. Here, we use mathematical modeling and numerical simulations to analyze whether the enzymatic reactions can generate a significant feedback from enzyme transport onto the substrate profile. We find that this feedback can generate spontaneous spatial patterns in the enzyme distribution, with just a single-step catalytic reaction. However, patterns are formed only for a subclass of transport models. For such models, nonspecific repulsive interactions between the enzyme and the substrate, or attractive interactions between the enzyme and the product, cause the enzyme to accumulate in regions of low substrate concentration. Reactions then amplify local substrate and product fluctuations, causing enzymes to further accumulate where substrate is low. Experimental analysis of this pattern formation process could discriminate between different transport models.

Slower growth of Escherichia coli leads to longer survival in carbon starvation due to a decrease in the maintenance rate

Fitness of bacteria is determined both by how fast cells grow when nutrients are abundant and by how well they survive when conditions worsen. Here, we study how prior growth conditions affect the death rate of Escherichia coli during carbon starvation. We control the growth rate prior to starvation either via the carbon source or via a carbon‐limited chemostat. We find a consistent dependence where death rate depends on the prior growth conditions only via the growth rate, with slower growth leading to exponentially slower death. Breaking down the observed death rate into two factors, maintenance rate and recycling yield, reveals that slower growing cells display a decreased maintenance rate per cell volume during starvation, thereby decreasing their death rate. In contrast, the ability to scavenge nutrients from carcasses of dead cells (recycling yield) remains constant. Our results suggest a physiological trade‐off between rapid proliferation and long survival. We explore the implications of this trade‐off within a mathematical model, which can rationalize the observation that bacteria outside of lab environments are not optimized for fast growth.

Heterogeneous Timing of Gene Induction as a Regulation Strategy

In response to environmental changes, cells often adapt by up-regulating genes to synthesize proteins that generate a benefit in the new environment. Several such cases of gene induction have been reported where the timing was heterogeneous, with some cells responding early and others responding late, although the microbial population was genetically homogeneous and the environment was well mixed. Here, we explore under which conditions heterogeneous timing of gene induction could be advantageous for the population as a whole. We base our study on a mathematical model that accounts for the cost of protein synthesis in terms of resources, which cells must provide immediately, whereas the associated benefit accumulates only slowly over the protein lifetime. Due to this delayed benefit, gene induction can be a risky investment, if resources are scarce and the environment fluctuates rapidly and unpredictably. Unprofitable gene induction then depletes the remaining limiting resource needed for maintenance of cell viability. We show that whenever gene induction is associated with a transient risk but beneficial in the long run, the stochastic timing of gene induction maximizes the reproductive success of a population. In particular, in an environment of stochastic periods of famine and feast, an optimum emerges from a trade-off between short-term growth, favoring rapid and homogeneous responses, and long-term survival, favoring a broadly heterogeneous response. Our analysis suggests that the optimal variability of induction times is just as large as the time required for the amortization of the initial investment into protein synthesis.