Macro molecular complexes that act as nano-scale machines provide the function of biological systems. Understanding the geometry and functioning of the complex as a machine, for instance, how do the various parts move relative to each other, is a central goal of biology. Cryo electron microscopy provides one noisy image of each of many (e.g., 100,000) instances of the complex. The objective of this research is to compute a statistical description of the machine from the images and then compute a mechanical model of the machine from the statistical description. Understanding how existing complexes function is central to engineering changes in their function. Achieving changes would have broad impact, for instance, in cancer treatment (inhibiting complexes that pro- tect tumor cells by pumping chemotherapy drugs out of tumor cells) and in improving the efficiency of complexes involved in the production of biofuels. Further impacts include the training of two Ph.D. students who will come from a diverse pool of students.
The complex in question will be described as a weighted sum of basis functions with random Gaussian weights. A maximum likelihood estimator is used to estimate the mean and covariance of the weights. The estimator is computed by an expecta- tion maximization algorithm which requires substantial computation due to the unknown projection directions of the images. A "spring and mass" mechanical model in thermodynamic equilibrium predicts the mean and covariance. By comparing the predictions of the mechanical model to the estimated mean and covariance by Kullback-Leibler divergence, the parameters in the mechanical model are estimated.
