The human body comprises an incredibly large number of cells. Estimates place the number somewhere in the region of 70 trillion, and that’s even before taking into account the microbes and bacteria that live in and around the body. Yet inside each cell, a myriad of complex processes occur to conceive and sustain these micro-organisms. One such process is the shaping of molecular membranes, known as lipid bilayers, to form protective barriers around important cellular parts and also to create spherical vessels and tubular networks to transport waste and nutrients at the microscopic level.
The mechanism believed to be responsible for the shaping of membranes involves the attachment of “curvature-inducing” proteins, whose role is to directly interact with the surface and bend it. By the cooperation of hundreds to tens of thousands of proteins, the membrane is shaped into the variety of micro-structures seen in the cell.
Previous efforts to gain a physical understanding of the dynamic shaping process required the use of supercomputers simulating thousands of molecules; a lengthy and costly process. However, recent research by Oxford Mathematicians James Kwiecinski, Jon Chapman and Alain Goriely shows that the problem can be formulated as an elegant mathematical model combining results from statistical and continuum mechanics – the first model of its kind. Yet despite the model’s simplicity, the phenomena exhibited are quite complex. James explains: “one of the surprising results from the model is that the types of tubes that can form and how stable they are in the face of thermodynamic fluctuations is completely determined by the mechanical stiffness of the proteins themselves. We were also expecting that the proteins would uniformly distribute themselves around the membrane, forming a scaffold structure, almost like a mould. However, this isn’t always true; there are some instances where the proteins can aggregate, forming these complex patterns which then merge and interact.”
Asked about the future of the work, James further commented: “the research is a significant first step into a fundamental problem of cellular mechanics, and one where we’re only getting started. There are still many more interesting geometries and unanswered questions to study.”