论文标题
关于$ n $二维核糖体流模型中的夹带
On the gain of entrainment in the $n$-dimensional ribosome flow model
论文作者
论文摘要
核糖体流模型（RFM）是沿1D链条$ n $站点的颗粒流的现象学模型。在翻译过程中，它已广泛用于研究沿mRNA分子的核糖体流动。当沿链的过渡速率是时间变化的，并共同$ t $ periodic的RFM入口，即，RFM的每个轨迹都会收敛到唯一取决于过渡速率的唯一$ t $周期解决方案，但不取决于初始条件。通常，在众多天然和人造系统中，捕获了24小时太阳日或电网的50Hz频率等周期性激发。一个有趣的问题，称为RFM中的夹带（GOE），是沿mRNA的周期性翻译速率的适当协调是否会导致较大的平均蛋白质产生速率。在RFM中分析GOE是非平凡的，并且仅适用于具有尺寸的RFM $ n = 1,2 $的RFM。我们使用一种新的方法来在一般$ n $维度RFM中获得多个结果。也许令人惊讶的是，我们严格地表征了没有GOE的几种情况，因此，在这些情况下，最大化平均生产率是最佳选择是沿着整个链条使用恒定的过渡速率。
The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a 1D chain of $n$ sites. It has been extensively used to study ribosome flow along the mRNA molecule during translation. When the transition rates along the chain are time-varying and jointly $T$-periodic the RFM entrains, i.e., every trajectory of the RFM converges to a unique $T$-periodic solution that depends on the transition rates, but not on the initial condition. In general, entrainment to periodic excitations like the 24h solar day or the 50Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE) in the RFM, is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analyzing the GOE in the RFM is non-trivial and partial results exist only for the RFM with dimensions $n=1,2$. We use a new approach to derive several results on the GOE in the general $n$-dimensional RFM. Perhaps surprisingly, we rigorously characterize several cases where there is no GOE, so to maximize the average production rate in these cases, the best choice is to use constant transition rates all along the chain.
