Scaffold proteins organize cellular processes by bringing signaling molecules into interaction, sometimes by forming large signalosomes. Several of these scaffolds are known to polymerize. Their assemblies should therefore not be understood as stoichiometric aggregates, but as combinatorial ensembles. We analyze the combinatorial interaction of ligands loaded on polymeric scaffolds, in both a continuum and discrete setting, and compare it with multivalent scaffolds with fixed number of binding sites. The quantity of interest is the abundance of ligand interaction possibilities-the catalytic potential Q-in a configurational mixture. Upon increasing scaffold abundance, scaffolding systems are known to first increase opportunities for ligand interaction and then to shut them down as ligands become isolated on distinct scaffolds. The polymerizing system stands out in that the dependency of Q on protomer concentration switches from being dominated by a first order to a second order term within a range determined by the polymerization affinity. This behavior boosts Q beyond that of any multivalent scaffold system. In addition, the subsequent drop-off is considerably mitigated in that Q decreases with half the power in protomer concentration than for any multivalent scaffold. We explain this behavior in terms of how the concentration profile of the polymer-length distribution adjusts to changes in protomer concentration and affinity. The discrete case turns out to be similar, but the behavior can be exaggerated at small protomer numbers because of a maximal polymer size, analogous to finite-size effects in bond percolation on a lattice.

中文翻译：

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聚合支架上的组合蛋白-蛋白相互作用。

支架蛋白通过使信号分子相互作用（有时通过形成大的信号体）来组织细胞过程。这些支架中的几种已知会聚合。因此，它们的组装不应理解为化学计量的聚集体，而应理解为组合的聚集体。我们分析了聚合物支架上的配体在连续和离散环境下的组合相互作用，并将其与具有固定数目结合位点的多价支架进行了比较。感兴趣的量是在构型混合物中的大量配体相互作用可能性-催化势Q-。随着支架丰度的增加，已知支架系统首先增加配体相互作用的机会，然后随着配体在不同支架上分离而关闭它们。聚合体系的突出之处在于，Q对原质浓度的依赖性在由聚合亲和力确定的范围内从第一级变为第二级。这种行为使Q值超出了任何多价支架系统。另外，由于任何前者浓度的Q值是任何多价支架的一半，Q值的降低就大大减轻了后续的下降。我们用聚合物长度分布的浓度分布图如何调整以改变原浓度和亲和力来解释这种行为。离散情况证明是相似的，但是由于聚合物的最大尺寸，在较小的protomer数下，行为可能会被夸大，类似于晶格上键渗渗的有限尺寸效应。