UC San Diego Physicist Discovers an Equation for the Control of Cell Growth

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Understanding the control of cell growth has challenged biomedical researchers for decades. Efforts to meet this challenge may have received an encouraging boost, however, from University of California San Diego physics professor Terence Hwa and colleagues. Their research, published in the Oct. 25 issue of Nature, led to the surprising discovery of a mathematical equation governing the control of cell growth.

Controlling cell growth is a very delicate act, Hwa explained. Impeding the normal process of cellular replication causes developmental abnormalities and cell death, while uncontrolled cell reproduction results in tumors and bacterial infection. By studying how the model bacterium E. coli controls its growth in response to changing environmental nutrient conditions, Hwa and colleagues established a simple equation which accurately described the timeline of how bacteria changed from growing at one rate to another. The same equation was able to quantitatively describe many conditions tested, resulting in both increases and decreases in growth, by merely specifying the starting and end state—without needing knowledge of the complex molecular interactions underlying the regulatory and metabolic processes.

“It is very rare to capture a complex cellular control process mathematically by a single equation. I believe our equation will provide a simple platform to incorporate and study many other effects on cell growth of relevance to biomedicine and biotechnology,” stated Hwa, giving the examples of the effect of antibiotics and the design of synthetic gene circuits.

How this growth control equation works can be appreciated with an analogy to the description of motion in classical physics. Newton’s Second Law prescribes that a particle experiences acceleration in response to an applied force, and the rules of calculus prescribe the subsequent velocity and trajectory of the particle resulting from the acceleration. If the growth rate of cells is like the velocity of the particle, and the external nutrient condition is like the force applied on the particle, then the crux of the work by Hwa’s team is to postulate a cellular quantity analogous to “acceleration,” which responds to the environment and whose change dictates changes in the rate of cell growth. The researchers’ equation specifies how much “acceleration” in growth results from environmental change, and how the changes in cell growth unfold in time. 

This central control quantity is postulated by the researchers as the activity of the ribosome, the protein complex responsible for the synthesis of all proteins in cells. Molecularly, it is known that the control of ribosome synthesis, which specifies the rate of cell growth, is affected by many molecules—amino acids, charged tRNAs, elongation factors—substances whose abundances directly affect the activity of the ribosome (see dashed arrows in the illustration). The key insight of this study is that a tremendous simplification occurs when the effect of these ribosomal substrates are exerted through their effect on ribosomal activity (when the dashed arrows are replaced by the solid arrow as shown in the illustration).

Using an analogy to operational research on how a factory decides on how many workers it needs, Hwa explains that this is a strategy based on worker activity: Instead of checking the amount of inventory available for use, monitor how busy the workers are—the busier each worker, the more workers are hired. Applying this activity-based strategy of ribosome biogenesis control, the researchers derived their central equation for cell growth control, bypassing all the unknown details of the complex web of molecular interactions.  

While this equation may be extended to other important areas of biomedical research, Hwa cautions that this activity-based strategy of growth control has only been studied quantitatively for common growth conditions in E. coli. “On the other hand,” he notes, “the simplicity and effectiveness of activity-based control may make it useful for organisms to adopt, not only for growth control but also as a generic strategy to regulate the synthesis of other important enzymes and processors.” 

Coauthors of this study include David W. Erickson, UC San Diego Department of Physics; Severin J. Schink and Ulrich Gerland, Physics of Complex Biosystems, Physics Department, Technical University of Munich; and Vadim Patsalo and James Williamson, Department of Integrative Structural and Computational Biology, Department of Chemistry, the Skaggs Institute for Chemical Biology, The Scripps Research Institute. The work was funded by the NIH (grants 1R01GM109069 and 1R01GM118850), the Simons Foundation (grant 330378) and by the German Research Foundation via the Excellence Cluster “Nanosystems Initiative Munich” and the priority program SPP1617 (grant GE1098/6-2).

The first students to enroll at UC San Diego in 1960 were graduate students in the Department of Physics. Part of the Division of Physical Sciences, the department is ranked #16 by U.S. News and World Report.