Objective

Apply nonlinear models to understand the impact of factors on a cell growth.

Background

You are attempting to grow a “wild type” bacteria and three genetically altered variants. You want to alter the percent of maltose in the growth media to see how the growth of the cell lines change. You plan to grow your cells in a 48-well plate and measure growth with absorbance at 600nm (optical density). Optical density is used to measure the amount of light scattered by microbial cells, since the more cells there are, the higher the optical density value. Your goals are to:

• Find the percent of maltose that achieves the “best growth” for each cell line (highest rate and highest final optical density).
• Find the best overall combination of maltose and cell line to achieve the highest number of cells.

The growth of bacteria generally follows a set growth profile that represents different phases of growth. Scientists are interested in capturing the occurrence of these stages to learn more about their microbe of study and to improve processes. The primary stages of growth are:

• Lag phase: The initial period where cells are inoculated and acclimate to their conditions (environmental and media). In production processes, scientists want to ensure that the lag phase is as short as possible to reduce the total production time and reduce costs.
• Exponential phase: The period of exponential growth of the cells as they consume a readily available supply of nutrients. The growth rate during this stage is important to understand, as desirable rates are a balance between quick growth (reducing production time) and avoiding overwhelming a fermenter (i.e., consuming too much oxygen and nutrients leading to faster cell death). The midpoint of this phase (the midexponential) is a key characteristic that is considered when transferring seed/starting cultures into production processes.
• Stationary phase: The period when nutrients begin to deplete or toxic by-products begin to accumulate, leading to an equal portion of cell death and cell growth. The time that this occurs and the maximum value of biomass that is achieved are important as we often need processes that create high biomass and, in some cases, desired products are only expressed during the stationary phase. In this example, the stationary phase is not completely flat; even when a primary nutrient is depleted or toxins accumulate, cells can still grow (slowly) on alternative nutrients, if available.
• Death phase: The period when cells exhaust all nutrients or toxins build up to a level above tolerance. Cell death typically marks the end of a productive process, so knowing when it occurs can help inform when a production needs to stop.

When trying to analyze a growth curve, scientists want to profile the whole curve shape and find parameters that best represent each of these stages, which can be achieved with nonlinear regression/curve fitting.

The Task

You are entrusted with the following tasks:

• Test a range of maltose concentrations on the four different cell lines and measure the growth via optical density measurements.
• Use nonlinear curve analysis to understand how the curve shape is affected by changing factors.
• Identify optimized conditions for the growth of the cells.

You decide to grow each cell line using a 48-well plate, growing them under 0.25, 0.5, 1, 1.5, and 2% maltose in individual wells and incubating for 24.2 hours on a shaking plate reader. You run each cell line/maltose combination in triplicate.