How Molecular Competition Influences Fluxes in Gene Expression Networks

Often, in living cells different molecular species compete for binding to the same molecular target. Typical examples are the competition of genes for the transcription machinery or the competition of mRNAs for the translation machinery. Here we show that such systems have specific regulatory features and how they can be analysed. We derive a theory for molecular competition in parallel reaction networks. Analytical expressions for the response of network fluxes to changes in the total competitor and common target pools indicate the precise conditions for ultrasensitivity and intuitive rules for competitor strength. The calculations are based on measurable concentrations of the competitor-target complexes. We show that kinetic parameters, which are usually tedious to determine, are not required in the calculations. Given their simplicity, the obtained equations are easily applied to networks of any dimension. The new theory is illustrated for competing sigma factors in bacterial transcription and for a genome-wide network of yeast mRNAs competing for ribosomes. We conclude that molecular competition can drastically influence the network fluxes and lead to negative response coefficients and ultrasensitivity. Competitors that bind a large fraction of the target, like bacterial σ70, tend to influence competing pathways strongly. The less a competitor is saturated by the target, the more sensitive it is to changes in the concentration of the target, as well as to other competitors. As a consequence, most of the mRNAs in yeast turn out to respond ultrasensitively to changes in ribosome concentration. Finally, applying the theory to a genome-wide dataset we observe that high and low response mRNAs exhibit distinct Gene Ontology profiles.在活体细胞中，不同分子物种常常会竞争结合同一分子靶标。典型案例包括基因竞争转录机器（transcription machinery），或是信使RNA（messenger RNA，简称mRNA）竞争翻译机器（translation machinery）。本研究表明，这类系统具备特定的调控特性，同时阐述了其分析方法。我们针对平行反应网络中的分子竞争问题推导了一套理论，通过推导网络通量（network fluxes）随总竞争物及共同靶标库总量变化的解析表达式（analytical expressions），明确了超敏感性（ultrasensitivity）产生的精确条件以及竞争物强度的直观判定规则。该计算基于可测量的竞争物-靶标复合物浓度，研究表明通常难以测定的动力学参数（kinetic parameters）在本计算中无需使用。由于所得方程形式简洁，可轻松应用于任意维度的网络。我们以细菌转录过程中竞争结合的σ因子（sigma factors），以及酵母菌全基因组范围内竞争核糖体（ribosomes）的mRNA网络为例，对这套新理论进行了演示。研究结论显示，分子竞争可显著影响网络通量，并引发负响应系数与超敏感性现象；如细菌σ70这类可结合大量靶标的竞争物，往往会对竞争通路产生极强的影响。竞争物被靶标饱和的程度越低，其对靶标浓度变化以及其他竞争物的变化就越敏感，由此可见酵母菌中的绝大多数mRNA都会对核糖体浓度的变化呈现超敏感性响应。最后，将该理论应用于全基因组数据集时，我们发现高响应性与低响应性的mRNA分别呈现出截然不同的基因本体（Gene Ontology）特征。