Investigation of thermodynamic properties of lattice and off-lattice models for proteins and polymers

了解有限长度分子链的热力学行为是非常重要的，因为对于异聚物来说，确定与序列相关的构象状态是相当困难的。我们最近开发的多规范链生长方法能够在几乎所有温度下对晶格异质聚合物进行取样。通过将其应用于蛋白质的简单晶格模型，可以分析序列和构象之间的关系，以及作为单体构象重排指标的能量和结构量的波动。这将被转移到非晶格模型，其中多范式采样和适当适应的链增长算法被应用。对于这些模型，我们将注意力集中在低温下的类玻璃行为研究上。为了对其进行充分的描述，必须引入和研究合适的系统或“顺序”参数，如结构重叠参数。此外，将我们的方法应用于d größer和三维中具有（伪）一阶类跃迁的有限长度晶格均聚物是有趣的，因为该算法绕过了与不太有利的状态相关的构象障碍。

The understanding of the thermodynamic behaviour of molecular chains with finite length is of extraordinary importance, since for heteropolymers the identification of the sequence-dependent classes of conformational states is quite difficult. Our recently developed multicanonical chain-growth method is capable to sample lattice heteropolymers at almost all temperatures. By applying it to simple lattice models for proteins, the relationship between sequence and conformation shall be analysed as well as fluctuations of energetic and structural quantities being indicators of conformational rearrangements of the monomers. This is to be carried over to off-lattice models, for which multicanonical sampling and a suitably adapted chaingrowth algorithm are applied. For these models we focus our attention to the study of the glass-like behaviour at low temperatures. For its adequate description, suitable system or "order" parameters, such as the structural overlap parameter, have to be introduced and studied. Furthermore, the application of our method to finite-length lattice homopolymers with (pseudo-)first-order-like transitions in d größer als 3 dimensions is intriguing, since the algorithm circumvents conformational barriers associated with less-favoured states.