The abundance of a particular protein varies both over time within a single mammalian cell and between cells of a genetically identical population. Here, we investigate the properties of such noisy protein expression in mammalian cells by combining theoretical and experimental approaches. The gamma distribution model is well-known to describe cell-to-cell variability in protein expression in a variety of common scenarios. This model predicts, and experiments show, that when protein levels are manipulated by altering transcription rates or mRNA half-life, protein expression noise, defined as the squared coefficient of variation, is constant. In contrast, we also demonstrate that when protein levels are manipulated by changing protein half-life, as mean levels increase, noise decreases. Thus, in mammalian cells, the scaling relationship between mean protein levels and expression noise depends on how mean levels are perturbed. Therefore it may be important to consider how common experimental manipulations of protein expression affect not only mean levels, but also noise levels. In the context of knockdown experiments, natural cell-to-cell variability in protein expression implies that a particular cell from the knockdown population may have higher protein levels than a cell from the control population. Simulations and experimental data suggest that approximately three-fold knockdown in mean expression levels can reduce such so-called "overlap probability" to less than ~10%. This has implications for the interpretation of knockdown experiments when the readout is a single cell measure.