Graf Group

Theory of biological homeostasis and plasticity

The Graf group uses tools from theoretical biophysics to investigate how living systems can robustly function despite being highly complex, intrinsically noisy, and subject to changing environmental conditions.


One astonishing property of living systems is their capability to function robustly in a broad range of dynamically changing environmental conditions. This property requires two seemingly conflicting skills: to adapt to new situations (to be plastic) and at the same time to maintain internal functionality (to be homeostatic/robust). How can living systems achieve these two goals simultaneously? The Graf group will address this question using tools from statistical physics, nonlinear dynamics, and information theory, while working closely with experimental collaborators.

Previous and current research

Many living organisms exhibit incredible sensitivity to weak signals – so weak that information from many  noisy measurements must be aggregated to get a statistically significant, amplified readout. A particularly striking example is the infrared sensing capability of pit vipers. Individual nerve fibers in the sensory organ of this snake reliably respond to milli-Kelvin level changes in temperature, far more sensitive than the underlying microscopic sensors, which only respond to Kelvin level changes. How did the snake learn to amplify this molecular response by a factor of a thousand?

A plausible mechanism for the integration of the molecular channel information into a collective, neural response is that amplification is achieved via proximity to a special point in the parameter space, a so-called critical or bifurcation point (Graf, Machta, 2024). In this scenario, the snake’s brain can get almost as much information about temperature as it would if it could read out all the measurements from the individual ion channels. Interestingly, a simple feedback mechanism can robustly maintain the snake’s astonishing sensitivity even when the ambient temperature changes by several degrees between day and night.

This robustness suggests that similar feedback and design principles might be found in other sensory systems which also need to detect tiny signals against varying backgrounds, and we are currently investigating whether related self-tuned critical mechanisms allow for high sensitivity and robustness in E. coli chemosensing and sound amplification in the mammalian inner ear.

Interestingly, recent experimental evidence suggests that even far more complex biological systems might tune themselves close to critical points. For instance, cells seem to actively adapt their incredibly complex plasma membrane composition to reside close to a critical miscibility transition point, but there is little understanding of how this active adaptation works and what the broad principles underlying membrane homeostasis are. How can cells robustly navigate and regulate their high-dimensional space, given that they only have limited information about their microscopic state? We have recently developed a theoretical framework indicating that the phase and critical behaviour of multicomponent mixtures like membranes are determined by only a few coarse-grained control parameters based on the physical interaction structure between the components (Graf, Machta, 2022). Can we use these insights to understand how, mechanistically, lipid homeostasis maintains cell membranes close to a miscibility critical point?

Future projects and goals

We will build conceptual and mechanistic physics-based models to gain insights into collective, emergent properties of biological systems and to understand questions like:

  1. How can sensory systems efficiently amplify and integrate information from their dynamic environment and at the same time adapt to changing conditions?
  2. How can homeostasis work in highly complex living systems that only have access to limited information?
  3. What are the functional benefits of (dynamical) critical points for sensing and decision making?

Figure 1: Comparison to experimental data suggests that the snake’s pit organ (blue square) is close to the bifurcation point (located at 0 on the x-axis on the left), where the action potential frequency is a highly non-linear function of temperature and small changes in temperature (e.g., 2 mK on the right) are strongly amplified into a large change in the action potential readout before the system adapts back to pre-stimulus level. (Modified from Graf, Machta, 2024)

Figure 2: The phase and critical behaviour of multicomponent mixtures can be understood from the distribution of components in the typically low-dimensional space of interaction features rather than the very high-dimensional space of the mixture composition. (Modified from Graf, Machta, 2022)