To locate food sources or escape harmful elements, cells determine concentration gradients in the chemicals within their environment. Given their small size, cells must be able to detect a difference of a few tens of molecules across their length, making the detection process intrinsically stochastic. Within this constraint, Bo Hu and colleagues at the University of California, San Diego, develop a theoretical model to understand the role a cell’s shape plays in determining concentration gradients. Their work is presented in Physical Review E.
Hu et al. formulate the detection problem in terms of receptors on the surface of the cell that can be either bound (“on”) or unbound (“off”) to an external molecule. The probability of a receptor being on depends on the local concentration of chemicals. The team uses a statisticial approach to calculate the uncertainty in determining the two parameters that define a concentration gradient—magnitude and direction—by maximizing the likelihood of any one particular pattern of on and off receptors.
The authors find that cells can change the relative precision with which these two parameters can be estimated by adopting elliptical shapes, but they cannot improve the detection of a gradient’s direction and magnitude simultaneously. Similarly, cells can improve gradient detection in certain directions at the expense of others by, for example, increasing the density of chemical receptors at certain points on the cell surface. – Ralf Bundschuh