Effect of the Volume-to-Surface Ratio of Cultures on Escherichia coli Growth: An Experimental and Theoretical Analysis Haydee Martı ´nez • Thomas Buhse • Marco Rivera • Guadalupe Ayala • P. Parmananda • Joaquı ´n Sa ´nchez Received: 18 January 2012 / Accepted: 10 April 2012 / Published online: 25 April 2012 Ó Springer Science+Business Media, LLC 2012 Abstract The growth dynamics of bacterial populations are usually represented by the classical S-shaped proﬁles composed of lag, exponential and stationary growth phases. Although exceptions to this classical behavior occur, they are normally produced under non-standard conditions such as supply of two carbohydrates as sole carbon source. However, we here report variations in the classic S-shaped growth proﬁles of Escherichia coli under standard cultur- ing conditions; explicitly, we found growth during transi- tion to the stationary phase wherein the bacterial growth rate inversely depended on the volume-to-surface ratio of cultures (V/S); the reasons for this behavior were experi- mentally explored. To complement our experimental analysis, a theoretical model that rationalizes the bacterial response was developed; simulations based on the devel- oped model essentially reproduced experimental growth curves. We consequently conclude that the effect of V/S on E. coli growth reﬂects an interplay between auto-catalytic bacterial growth, bacterial growth auto-inhibition, and, the relief of that inhibition. Introduction The growth dynamics of bacterial populations are typically portrayed by the classic logistic pattern of S-shaped growth proﬁles composed of three phases: the starting phase where growth is delayed, or lag phase; the exponential phase, which is characterized by fast multiplication and lastly the stationary phase where bacterial growth ceases. Neverthe- less, a variety of exceptions to this classical growth behavior have been reported. For instance, when Esche- richia coli is grown in minimal medium with only two sugars as the sole carbon source, so-called diauxic growth curves were observed that are characterized by two expo- nential growth phases separated by a lag phase [7, 9]. Unusual growth kinetics may also occur under steady-state conditions where the culture is continuously fed with fresh medium under ﬂow conditions [8, 10]. The bacterial growth also responds to surface properties when bacteria are attached to glass beads, sand particles or stones, i.e., subjected to conditions that promote the access of bacteria to nutrients, particularly in diluted culture medium [3]. Likewise, in in vitro cultures of eukaryotic cells, a positive correlation between the culture volume and cell growth has been observed where the inoculum, i.e., the initial number Electronic supplementary material The online version of this article (doi:10.1007/s00284-012-0128-1) contains supplementary material, which is available to authorized users. H. Martı ´nez  M. Rivera Facultad de Ciencias, Universidad Auto ´noma del Estado de Morelos, Av. Universidad 1001, 62209 Cuernavaca, Morelos, Mexico T. Buhse (&) Centro de Investigaciones Quı ´micas, Universidad Auto ´noma del Estado de Morelos, Av. Universidad 1001, 62209 Cuernavaca, Morelos, Mexico e-mail: buhse@uaem.mx G. Ayala Centro de Investigacio ´n sobre Enfermedades Infecciosas, INSP, Cuernavaca, Morelos, Mexico P. Parmananda Department of Physics, IIT, Bombay, Powai, Mumbai 400076, India J. Sa ´nchez (&) Facultad de Medicina, Universidad Auto ´noma del Estado de Morelos, Av. Universidad 1001, 62209 Cuernavaca, Morelos, Mexico e-mail: joaquin.sanchez@microbio.gu.se 123 Curr Microbiol (2012) 65:60–65 DOI 10.1007/s00284-012-0128-1