This is just one illustration of a universal feature of cells: their behaviors are often stochastic, meaning that they display variability in their protein content and therefore exhibit variations in phenotypes. In addition to the asymmetric partitioning of molecules following cell division, variability can originate from many chemical reactions. Imagine, for example, that our mother cell contains a simple gene regulatory circuit with a positive feedback loop like that shown in Figure 8–80B. Even if both daughter cells receive a copy of this circuit, including one copy of the initial transcription activator protein, there will be variability in the time required for promoter binding—and it will be statistically nearly impossible for the genes in the two daughter cells to become activated at precisely the same time. If the system is bistable and poised near a switching point, then variability in the response might flip the switch in only one daughter cell. Two daughter cells that were born identical can thereby acquire, by chance, a dramatic difference in phenotype.
More generally, isogenic populations of cells grown in the same environment display diversity in size, shape, cell-cycle position, and gene expression. These differences arise because biochemical reactions require probabilistic collisions
Figure 8–86 How a coherent feed-forward motif responds to various inputs. (A) Diagram of a coherent feed-forward motif in which the transcription activators A1 and A2 together activate expression of gene X using the AND logic of Figure 8–83B. (B) The response to a brief input can be either weak (as shown) or nonexistent. This allows the motif to ignore random fluctuations in the concentration of signaling molecules. (C) A prolonged input produces a strong response that can turn off rapidly.
between randomly moving molecules, with each event resulting in changes in the number of molecular species by integer amounts. The amplified effect of fluctuations in a molecular reactant, or the compounded effects of fluctuations across many molecular reactants, often accumulates as an observable phenotype. This can endow a cell with individuality and generate non-genetic cell-to-cell variability in a population.
Non-genetic variability can be studied in the laboratory by single-cell measurements of fluorescent proteins expressed from genes under the control of a specific promoter. Live cells can be mounted on a slide and viewed through a fluorescence microscope, revealing the striking variability in protein expression levels (Figure 8–87). Another approach is to use flow cytometry, which works by streaming a dilute suspension of cells past an illuminator and measuring the fluorescence of individual cells as they flow past the detector (see Figure 8–2). Fluorescence values can be used to build histograms that reveal the variability in a process across a population of cells, with a broad histogram indicating higher variability.
Several Computational Approaches Can Be Used to Model the Reactions in Cells
We have focused primarily on the use of ordinary differential equations to model the dynamics of simple regulatory circuits. These models are called deterministic, because they do not incorporate stochastic variability and will always produce the same result from a specific set of parameters. As we have seen, such models can provide useful insights, particularly in the detailed mechanistic analysis of small regulatory circuits. However, other types of computational approaches are also needed to comprehend the great complexity of cell behavior. Stochastic models, for example, attempt to account for the very important problem of random variability in molecular networks. These models do not provide deterministic predictions about the behavior of molecules; instead, they incorporate random variation into molecule numbers and interactions, and the purpose of these models is to obtain a better understanding of the probability that a system will exist in a certain state over time.