Optical density (OD) measurements of microbial growth are one of the most common techniques used in microbiology, with applications ranging from studies of antibiotic efficacy to investigations of growth under different nutritional or stress environments, to characterization of different mutant strains, including those harbouring synthetic circuits. OD measurements are performed under the assumption that the OD value obtained is proportional to the cell number, i.e. the concentration of the sample. However, the assumption holds true in a limited range of conditions, and calibration techniques that determine that range are currently missing. Here we present a set of calibration procedures and considerations that are necessary to successfully estimate the cell concentration from OD measurements.

Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time derivatives as a function of time from time-series data. Our approach is based on Gaussian processes and applies to a wide range of data. In tests, the method is at least as accurate as others, but has several advantages: it estimates errors both in the inference and in any summary statistics, such as lag times, and allows interpolation with the corresponding error estimation. As illustrations, we infer growth rates of microbial cells, the rate of assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies. Our algorithm should thus be broadly applicable.

For most cells, a sudden decrease in external osmolarity results in fast water influx that can burst the cell. To survive, cells rely on the passive response of mechanosensitive channels, which open under increased membrane tension and allow the release of cytoplasmic solutes and water. Although the gating and the molecular structure of mechanosensitive channels found in Escherichia coli have been extensively studied, the overall dynamics of the whole cellular response remain poorly understood. Here, we characterize E. coli's passive response to a sudden hypoosmotic shock (downshock) on a single-cell level. We show that initial fast volume expansion is followed by a slow volume recovery that can end below the initial value. Similar response patterns were observed at downshocks of a wide range of magnitudes. Although wild-type cells adapted to osmotic downshocks and resumed growing, cells of a double-mutant (ΔmscL, ΔmscS) strain expanded, but failed to fully recover, often lysing or not resuming growth at high osmotic downshocks. We propose a theoretical model to explain our observations by simulating mechanosensitive channels opening, and subsequent solute efflux and water flux. The model illustrates how solute efflux, driven by mechanical pressure and solute chemical potential, competes with water influx to reduce cellular osmotic pressure and allow volume recovery. Our work highlights the vital role of mechanosensation in bacterial survival.osmotic downshock | bacterial mechanosensing | single-cell imaging B iology offers an array of intriguing mechanical solutions, both active and passive, often exceeding what is currently possible with man-made methods. Understanding how biological systems achieve different functionalities under mechanical stimuli can inform new, thus-far-unexplored design principles. One such passive control system is the bacterial response to sudden decreases in external osmolarities.A Gram-negative cell's fluid cytoplasm is separated from the external environment by the inner membrane, the periplasmic space, and the outer membrane. Ordinarily, the total solute concentration within the cytoplasm is higher than that of the environment, resulting in a positive osmotic pressure on the cell wall (termed turgor pressure) (1). Escherichia coli is able to respond to both increases and decreases in external concentrations. An increase in external osmolarity (hyperosmotic shock or upshock) results in water efflux from the cell interior, causing cellular volume to shrink and osmotic pressure to drop to zero (2). E. coli responds by actively accumulating specific solutes (osmolytes), such as potassium, proline, and glycine-betaine (2). Accumulation of osmolytes in the cell's cytoplasm causes reentry of water, cell volume increase, and recovery of osmotic pressure (3, 4). A downward shift in external osmolarity (termed hypoosmotic shock or downshock) causes fast water influx into the cell's cytoplasm. As a result, the osmotic pressure increases and the cell expands in a nonlinear fashion (5,6

Optical density (OD) measurements of microbial growth are one of the most common techniques used in microbiology, with applications ranging from studies of antibiotic efficacy to investigations of growth under different nutritional or stress environments, to characterization of different mutant strains, including those harbouring synthetic circuits. OD measurements are performed under the assumption that the OD value obtained is proportional to the cell number, i.e. the concentration of the sample. However, the assumption holds true in a limited range of conditions, and calibration techniques that determine that range are currently missing. Here we present a set of calibration procedures and considerations that are necessary to successfully estimate the cell concentration from OD measurements.Bacteria and yeast are widely studied microorganisms of great economic, medical and societal interest. Much of our understanding of bacterial and yeast life cycles stems from monitoring their proliferation in time and the most routine way of doing so is using optical density (OD) measurements. The applications of such measurements range from routine checks during different cloning techniques 1 ; through studying cellular physiology and metabolism 2,3 ; to determining the growth rate for antibiotic dosage 4,5 ; and monitoring of biomass accumulation during bio-industrial fermentation 6 . Here we introduce a set of calibration techniques that take into account the relevant parameters affecting OD measurements, including at high culture densities, in a range of conditions commonly used by researchers.OD measurements have become synonymous with measurements of bacterial number (N) or concentration (C), in accordance with the Beer-Lambert law. However, OD measurements are turbidity measurements 7,8 , thus the Beer-Lambert law can be applied, with some considerations, only for microbial cultures of low densities. OD measurements in plate readers, increasingly used for high-throughput estimates of microbial growth, operate predominantly at higher culture densities where OD is expected to have a parabolic dependency on N 8 . Additionally, the proportionality constants (either in low or high density regimes) strongly depend on several parameters, for example cell size, which need to be included in robust calibration techniques. Yet, these techniques, essential when using OD measurements for quantitative studies of microbial growth, including growth rates, lag times and cell yields, have thus far not been established.The Beer-Lambert law (Supplementary Note 1) assumes that light is only absorbed to derive OD ~ C, which is true if the light received by the detector of a typical spectrophotometer is the light that did not interact with the sample in any way 7,9 . In general, when microbial cells are well dispersed in the solution (for the cases where N is small, i.e. single scattering regime) and the geometry of the spectrophotometer is suitable, the Beer-Lambert law is a good approximation for turbidity measurements, and N (or C) is ~...

Often the time-derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time-derivatives as a function of time from time-series data. Our approach is based on established properties of Gaussian processes and therefore applies to a wide range of data. In tests, the method is at least as accurate as others, but has several advantages: it estimates errors both in the inference and in any summary statistics, such as lag times, allows interpolation with the corresponding error estimation, and can be applied to any number of experimental replicates. As illustrations, we infer growth rate from measurements of the optical density of populations of microbial cells and estimate the rate of in vitro assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies in a single yeast cell. Being accessible through both a GUI and from scripts, our algorithm should have broad application across the sciences.Estimating the time-derivatives of a signal is a common task in science. A well-known example is the growth rate of a population of cells, which is defined as the time-derivative of the logarithm of the population size [1] and is used extensively in both the life sciences and biotechnology.A common approach to estimate such derivatives is to fit a mathematical equation that, say, describes cellular growth and so determine the maximum growth rate from the best-fit value of a parameter in the equation [2]. Such parametric approaches rely, however, on the mathematical model being a suitable description of the underlying biological or physical process, and, at least for cellular growth, it is common to find examples where the standard models are not appropriate [3].The alternative is to use a non-parameteric method and so estimate time-derivatives directly from the data. Examples include taking numerical derivatives [4] or using local polynomial or spline estimators [5]. Although these approaches do not require knowledge of the underlying process, it can be difficult to determine the error in their estimation [5] and to incorporate experimental replicates, which with wide access to high throughput technologies, are now the norm.