ENERGY DISTRIBUTION OF THE COMPACT STATES OF A PEPTIDE

如何确定三维的问题 一级肽编码的蛋白质结构 序列被认为是最重要的问题之一 在生物物理学的许多领域， 生物学寻找算法来完成这项任务 一般包括三个步骤： 1)肽折叠模型的确定 链在三维空间中。 2)确定正确的哈密顿量来描述 肽上残基之间的相互作用能 链，因为它是在三维空间折叠。 3)构建一个算法，将折叠肽 链到最小的能量配置， 计算成本 也许最简单的哈密顿量就是所谓的随机 能量模型（REM），假设 残基是随机的，接触能是分布的 以高斯的方式。 我们考虑一个更复杂的模型 其中，哈密顿量是具有特定 指定的残基之间的相互作用，我们允许 接触具有自然产生的依赖性， 因为有些会有相同的残留物我们一直 能够证明能量谱仍然是高斯分布， 接触的实际数量的限制， proteins.其他属性也已建立， 工作已经出版。 在一个相关的发展中， 给出了一种计算概率的统计方法 一个独特的自然状态， 紧凑构象的能量应该是 采样是已知的。此方法可在以下情况下应用： 分布不是高斯分布， 接触是一个变量。一篇论文正在印刷中.进一步工作 计划使用相同的方法，这将使我们能够 回答一些问题的影响不准确的 哈密顿矩阵元一个问题出现在 这个功是能量尾部的形式 分子的分布，当个体 相互作用能由能量矩阵决定。作为 我们已经注意到，这应该是大约 高斯。关于极端的尾部可以说些什么，其中 预计会发生折叠？我们已经开发出一种方法 基于带障碍的随机游动， 一幅关于能量极端尾部的精确图像 模型分子的密度，其能量由 能量矩阵能量密度被发现是 近似高斯分布到自然能量， 但当你移动时， 降低能量。我们用这种方法研究了 不同结构特征的信息量 蛋白质如二级结构，三级接触， 和溶剂可及性。已经编写了一份文件， 描述这些结果。 我们运用随机游走法也是为了 我们称之为能量分布模型， 一个模型肽链的紧凑状态的立方 应该对晶格进行采样。然后，我们应用统计 预测方法来估计的概率， 随机游走产生的特定能量 对应于一个本机（主导玻尔兹曼概率） 状态序列和结构对对应于 然后使用本机状态来测试 从联系人数据中提取能量矩阵。

The problem of how to determine the three dimensional structure of the protein coded by a primary peptide sequence is considered one of the most important problems in biophysics with implications in many areas of molecular biology. The search for algorithms to accomplish this task has generally involved three steps: 1) Determination of a model for the folding of a peptide chain in three dimensional space. 2) Determination of a correct Hamiltonian to describe the energy of interactions between the residues on the peptide chain as it is folded in three dimensional space. 3) Construction of an algorithm which will fold the peptide chain into the minimal energy configuration with reasonable computational cost. Perhaps the simplest Hamiltonian is the so-called random energy model(REM) that assumes the contacts between residues are random and the contact energy is distributed in a Gaussian manner. We consider a more complicated model in which the Hamiltonian is an energy matrix with specific interactions between residues specified and we allow contacts to have the dependencies that naturally arise because some will involve the same residue. We have been able to show that the energy spectrum is still Gaussian in the limit of realistic numbers of contacts as seen in proteins. Other properties are established as well and this work has been published. In a related development we have given a statistical method of computing the probability of a unique native state when the energy distribution from which the energies of the compact conformations are to be sampled is known. This method may be applied when the distribution is not Gaussian and when the number of contacts is a variable. A paper is in press. Further work is planned using the same methods, which should allow us to answer some questions on the effect of inaccuracies in the Hamiltonian matrix elements. One question that comes up in this work is the form of the tails of the energy distribution for a molecule, when the individual interaction energies are dictated by an energy matrix. As already noted we see that this should be approximately Gaussian. What can be said about the extreme tails, where folding is expected to occur? We have developed a method based on random walks with barriers which allows us to give an accurate picture of the extreme tails of the energy density for model molecules with energies determined by an energy matrix. The energy density is found to be approximately Gaussian out to roughly the native energy, but then deviates markedly from the Gaussian as one moves to lower energies. We have used the method to study the amount of information in different structural features of proteins such as secondary structure, tertiary contacts, and solvent accessibility. A paper has been prepared describing these results. We are applying the random walk method also to develop what we call a model energy distribution from which the energies of the compact states of a model peptide chain on a cubic lattice should be sampled. We then apply our statistical prediction methods to estimate the probability that a particular energy generated by the random walk will correspond to a native (dominant Boltzman probability) state. The sequence and structure pairs that correspond to native states are then used to test the recovery of the energy matrix from the contact data.