The project was divided into three Work Packages.
Work Package 1: The aim of this WP was to develop a new energy potential, i.e. an extended version of the Helfrich Hamiltonian (HH), that could also work for mesoscopic simulations when the system is highly curved, creating a bridge between molecular and mesoscale models. This is an important step for modeling membranes with high curvature, as such shapes often appear in cellular contexts.
To make this extension, I first created a neck structure with periodic boundary conditions using the coarse-grained Martini model. I then performed mesoscale simulations with a membrane energy function that includes higher-order terms in curvature beyond the HH model. Next, I compared these two shapes and found that the HH model still describes the membrane shape (on average) very well, with the higher-order terms making only small changes to the description. I concluded that the higher-order terms contribute approximately 5% to the overall effect (Fig 2).
In addition, next-generation mesoscopic membrane simulation software capable of capturing large membrane bending was delivered. This is the second version of the FreeDTS software, which is publicly available at DOI 10.5281/zenodo.14278900.
Work Package 2 : The aim of this Work Package was to obtain distinct conformations of membranes of different topological genera and provide quantification of their shape.
I have successfully achieved this objective by systematically characterizing and mapping the behavior of membrane shapes across a range of topological genera (g = 1-20). The results show that most configurations observed at low topological genera closely resemble those of spherical topology, with only minor differences. However, as the genus increases beyond 10, new behaviors suddenly emerge (Fig 3). For example, stomatocyte formation occurs at high temperatures without requiring osmotic shock (Fig 4). Additionally, at lower temperatures, I observed a distinct shape not present in spherical topology. The membranes also exhibited very complex mechanical responses. Finally, upon including spontaneous curvature, many additional morphologies emerged, including all those previously observed in spherical topologies (Fig 5). I classified the shapes into multiple phase diagrams (Fig 3-6).
Work Package 3: The aim of this Work Package was to predict lateral and spatial organizations of proteins on membranes with different topological genera.
I tested two versions of the system: (i) fully decorated membranes with proteins (done by the fellow), and (ii) partially decorated membranes. In the first case, I completed the study comprehensively and identified all the relevant shapes (Fig7). In the partially decorated case, I was able to explore many configurations, though not exhaustively due to the sheer number of possible systems. Despite this limitation, I observed several interesting phenomena, including shapes resembling nuclear pore membranes. Additionally, we investigated how these membranes respond to osmotic pressure (which was beyond the original project scope). The results show that fully decorated membranes with proteins, initially arranged in a flat network configuration, tend to reorganize into space-filling, three-dimensional networks as the topological genus increases. I also identified a specific, topology-driven ordering of proteins; however, this protein ordering became progressively less distinct with increasing topology (Fig 8). In the partially decorated case, I explored many configurations, though not exhaustively due to the vast number of possible systems. Despite this limitation, we observed several interesting phenomena, including shapes resembling nuclear pore membranes. Additionally, I investigated the membranes’ response to osmotic pressure, an aspect beyond the original project scope, and discovered intriguing bimodal behavior: below a certain pressure threshold, the membranes shrink, while above it, they expand. Notably, the presence of proteins appears to stabilize the membranes under osmotic stress. Overall, these observations provide valuable design principles for biomembrane engineering.
