Periodic Reporting for period 1 - HighGenMem (Conformations of High Topological Genus Membranes)
Berichtszeitraum: 2023-04-01 bis 2025-05-31
Biomembranes are an integral component of cellular architecture. They provide identity to the cell itself as well as to many internal organelles. Moreover, model membranes such as vesicles have a wide range of applications in biotechnology, including drug delivery and vaccine development. A key feature of both cellular and artificial membranes is their ability to adopt a variety of configurations, as seen in the diverse morphologies of cellular organelles such as the endoplasmic reticulum and mitochondria. Membrane shape remodeling is essential for many cellular processes, including endocytosis, cell division, and mitochondrial respiration. Genetic mutations that disrupt cellular membrane architecture are implicated in diseases such as spinal muscular atrophy and liver dysfunction. While membranes are flexible and easily bent, their surface topology is much more resistant to change. Altering topology requires processes such as membrane fission and fusion, which are hindered by high energy barriers and typically rely on active mechanisms. As a result, in most membrane remodeling processes, the surface topology can be considered effectively constant. Topology is characterized by the topological genus g, which counts the number of handles attached to a sphere (Fig. 1). Over the past decades, the shapes of fluid lipid membranes with spherical topology (g=0) have been extensively studied experimentally, theoretically, and through computer simulations. However, our understanding of membranes with higher genus remains extremely limited. High-genus membrane shapes are of interest for two main reasons: (i) organelle membranes such as those in mitochondria and the Golgi apparatus exhibit high-genus topologies, and (ii) such structures allow for a much broader range of membrane shapes, which is essential for material design, for instance in the division machinery of artificial cells. Therefore, expanding our understanding of membranes with high-genus topologies is critical for both biological and biotechnological applications. The goal of this research proposal is to describe and characterize the conformations of high-genus membranes using multiscale computer simulation techniques.
Throughout the project, the aim was to advance the following objectives: not only to provide a clear understanding of the importance of high-genus membranes (Ob2,Ob3):
Ob1) To develop a new energy potential, beyond Helfrich Hamiltonian (HH) for mesoscopic simulation of biomembranes.
Ob2) To leverage the advanced mesoscopic and the new energy potential to model and describe different shape classes of high-genus membranes.
Ob3) To describe the lateral and spatial organizations of complex membranes of high-genus topology.
Throughout the project, the aim was to advance the following objectives: not only to provide a clear understanding of the importance of high-genus membranes (Ob2,Ob3):
Ob1) To develop a new energy potential, beyond Helfrich Hamiltonian (HH) for mesoscopic simulation of biomembranes.
Ob2) To leverage the advanced mesoscopic and the new energy potential to model and describe different shape classes of high-genus membranes.
Ob3) To describe the lateral and spatial organizations of complex membranes of high-genus topology.
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.
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.
This project was very fruitful and produced many contributions and results beyond the state of the art. Two primary important outcomes were the development of two software packages for use by the broader computational community:
1. TS2CG 2.0 (DOI: 10.5281/zenodo.15240476)
https://github.com/weria-pezeshkian/TS2CG-v2.0(öffnet in neuem Fenster)
2. FreeDTS version 2.0 (2024); DOI: 10.5281/zenodo.14278900
https://github.com/weria-pezeshkian/FreeDTS(öffnet in neuem Fenster)
The methodology of the first software has also been accepted in the Journal of Chemical Theory and Computation; however, at the time of this report it is not yet online, although a preprint has already been published on BioRxiv.
Beyond software development, the project also led to several major discoveries. One of these is how membrane necks, such as those forming in the nuclear pore membrane and in membrane invaginations, respond to membrane tension or osmotic pressure. We found that they exhibit a two-phase behavior: below a certain threshold, necks constrict as the pressure gradient increases, while above that threshold, they dilate. This response arise from the intrinsic mechanics of the membrane and depends on the magnitude of the pressure gradient, the initial diameter of the neck, and the membrane’s bending rigidity. We also provide a simple equation that links the threshold tension, neck diameter, and bending rigidity, offering a useful tool to quickly assess different scenarios. Our results further show that protein complexes in the neck partially counteract both constriction and dilation, stabilizing neck size while preserving the same two-phase response to membrane tension. These findings uncover a novel, previously overlooked membrane property with important implications for organelle shape and function.
Furthermore, we obtained numerous membrane shape configurations arising solely from their topological genus, some of which closely resemble those observed in organelle membranes such as the nuclear envelope and endoplasmic reticulum. This provides a promising avenue for advancing our understanding of organelle morphogenesis.
1. TS2CG 2.0 (DOI: 10.5281/zenodo.15240476)
https://github.com/weria-pezeshkian/TS2CG-v2.0(öffnet in neuem Fenster)
2. FreeDTS version 2.0 (2024); DOI: 10.5281/zenodo.14278900
https://github.com/weria-pezeshkian/FreeDTS(öffnet in neuem Fenster)
The methodology of the first software has also been accepted in the Journal of Chemical Theory and Computation; however, at the time of this report it is not yet online, although a preprint has already been published on BioRxiv.
Beyond software development, the project also led to several major discoveries. One of these is how membrane necks, such as those forming in the nuclear pore membrane and in membrane invaginations, respond to membrane tension or osmotic pressure. We found that they exhibit a two-phase behavior: below a certain threshold, necks constrict as the pressure gradient increases, while above that threshold, they dilate. This response arise from the intrinsic mechanics of the membrane and depends on the magnitude of the pressure gradient, the initial diameter of the neck, and the membrane’s bending rigidity. We also provide a simple equation that links the threshold tension, neck diameter, and bending rigidity, offering a useful tool to quickly assess different scenarios. Our results further show that protein complexes in the neck partially counteract both constriction and dilation, stabilizing neck size while preserving the same two-phase response to membrane tension. These findings uncover a novel, previously overlooked membrane property with important implications for organelle shape and function.
Furthermore, we obtained numerous membrane shape configurations arising solely from their topological genus, some of which closely resemble those observed in organelle membranes such as the nuclear envelope and endoplasmic reticulum. This provides a promising avenue for advancing our understanding of organelle morphogenesis.