AF:CIF:Small:Computational structural biology: Reconstruction and understanding for heterogeneous biological macro molecular complexes based on electron microscopy images

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Macro molecular complexes that act as nano-scale machines provide thefunction of biological systems. Understanding the geometry and functioning ofthe complex as a machine, for instance, how do the various parts move relativeto each other, is a central goal of biology. Cryo electron microscopy providesone noisy image of each of many (e.g., 100,000) instances of the complex. Theobjective of this research is to compute a statistical description of the machinefrom the images and then compute a mechanical model of the machine fromthe statistical description. Understanding how existing complexes function iscentral to engineering changes in their function. Achieving changes would havebroad impact, for instance, in cancer treatment (inhibiting complexes that pro-tect tumor cells by pumping chemotherapy drugs out of tumor cells) and inimproving 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 randomGaussian weights. A maximum likelihood estimator is used to estimate themean and covariance of the weights. The estimator is computed by an expecta-tion maximization algorithm which requires substantial computation due to theunknown projection directions of the images. A "spring and mass" mechanicalmodel in thermodynamic equilibrium predicts the mean and covariance. Bycomparing the predictions of the mechanical model to the estimated mean andcovariance by Kullback-Leibler divergence, the parameters in the mechanicalmodel are estimated.