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

作为纳米级机器的大分子复合物提供了生物系统的功能。理解复杂事物的几何结构和功能，例如，不同部分是如何相互相对运动的，是生物学的中心目标。低温电子显微镜提供了许多（例如，100,000）复合体实例中的每个实例的一张噪声图像。本研究的目的是从图像中计算出机器的统计描述，然后根据统计描述计算出机器的力学模型。了解现有复合体的功能是工程改变其功能的核心。实现这些变化将产生广泛的影响，例如，在癌症治疗（通过将化疗药物从肿瘤细胞中抽出来抑制保护肿瘤细胞的复合物）和提高生物燃料生产中涉及的复合物的效率方面。进一步的影响包括培养两名博士生，他们将来自不同的学生群体。所讨论的复合体将被描述为具有随机高斯权重的基函数的加权和。使用极大似然估计器来估计权重的均值和协方差。估计量是通过期望最大化算法计算的，由于图像的投影方向未知，需要大量的计算。热力学平衡中的“弹簧和质量”力学模型预测了平均值和协方差。通过将力学模型的预测值与Kullback-Leibler散度估计的均值和协方差进行比较，估计了力学模型的参数。

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.