Biochemistry has many examples of linear chain polymers, i.e., molecules formed from a sequence of units from a finite set of possibilities; examples include proteins, RNA, single-stranded DNA, and paired DNA. In the field of mass spectrometry, it is useful to consider the idea of weighted alphabets, with a word inheriting weight from its letters. We describe the distribution of the mass of these words in terms of a simple recurrence relation, the general solution to that relation, and a canonical form that explicitly describes both the exponential form of this distribution and its periodic features, thus explaining a wave pattern that has been observed in protein mass databases. Further, we show that a pure exponential term dominates the distribution and that there is exactly one such purely exponential term. Finally, we illustrate the use of this theorem by describing a formula for the integer mass distribution of peptides and we compare our theoretical results with mass distributions of human and yeast peptides.

中文翻译：

---

线性链聚合物的质量分布

生物化学有许多线性链聚合物的例子，即由一组有限可能性的单元序列形成的分子；例子包括蛋白质、RNA、单链 DNA 和配对 DNA。在质谱领域，考虑加权字母的概念很有用，单词从其字母继承权重。我们根据简单的递推关系、该关系的一般解以及明确描述该分布的指数形式及其周期特征的规范形式来描述这些词的质量分布，从而解释了一种波型已在蛋白质质量数据库中观察到。此外，我们表明纯指数项支配分布，并且确实存在一个这样的纯指数项。最后，