Monitoring the regulation of gene expression in a growing organ using a fluid mechanics formalism

Abstract

Background: Technological advances have enabled the accurate quantification of gene expression, even within single cell types. While transcriptome analyses are routinely performed, most experimental designs only provide snapshots of gene expression. Molecular mechanisms underlying cell fate or positional signalling have been revealed through these discontinuous datasets. However, in developing multicellular structures, temporal and spatial cues, known to directly influence transcriptional networks, get entangled as the cells are displaced and expand. Access to an unbiased view of the spatiotemporal regulation of gene expression occurring during development requires a specific framework that properly quantifies the rate of change of a property in a moving and expanding element, such as a cell or an organ segment.

Results: We show how the rate of change in gene expression can be quantified by combining kinematics and real-time polymerase chain reaction data in a mechanistic model which considers any organ as a continuum. This framework was applied in order to assess the developmental regulation of the two reference genes Actin11 and Elongation Factor 1-beta in the apex of poplar root. The growth field was determined by time-lapse photography and transcript density was obtained at high spatial resolution. The net accumulation rates of the transcripts of the two genes were found to display highly contrasted developmental profiles. Actin11 showed pulses of up and down regulation in the accelerating and decelerating parts of the growth zone while the dynamic of EF1beta were much slower. This framework provides key information about gene regulation in a developing organ, such as the location, the duration and the intensity of gene induction/repression.

Conclusions: We demonstrated that gene expression patterns can be monitored using the continuity equation without using mutants or reporter constructions. Given the rise of imaging technologies, this framework in our view opens a new way to dissect the molecular basis of growth regulation, even in non-model species or complex structures.

Figure 1

Velocity, relative elemental growth rate and growth trajectory along the root apex. (A) Displacement velocity profile along the root apex (reference point is the root tip). Mean ± standard error of mean (SEM; n = 6). (B) Relative elemental growth rate (spatial derivative of displacement velocity) along the root apex. Mean ± SEM (n = 6). C: Growth trajectory of a meristem-derived element initially located at 1 mm from the root tip - the time at which it reached a given distance from the tip along its developmental movement away from the meristem. Growth trajectory was calculated from mean velocity data. It was drawn only from 1 mm onwards, since velocity was almost nil in the apical first mm, making the calculated displacement time uncertain.

Figure 2

Spatial and temporal specifications of Actin11 and EF1β transcript density. Actin11 (A) and EF1β (B) transcript density (a.u. mm^-1) in 1 mm-long segments of the primary root. Mean ± standard error of mean (SEM; n = 3). The black line corresponds to the cubic spline interpolation of the means. Actin11 (C) and EF1β (D) transcript density as a function of time in an element moving across the growth zone. Mean ± SEM (n = 3).

Figure 3

Material derivative of Actin11 and EF1β transcript densities. Convective (A, B) and dilutive (C, D) components of the material derivative (E, F) - the net accumulation rate of Actin11 and EF1β transcripts, respectively - as a function of the distance from the root tip (Eulerian specification). The material derivative and its components are expressed in arbitrary unit mm^-1 min^-1. The black lines were calculated from the mean values of each parameter using equation (3). Box-and-whisker plots are the distribution of 1000 replicates (obtained by random resampling). The central mark is the median, the edges are the 25th and 75th percentiles, and the whiskers extend to 10th and the 90th percentiles.

Figure 4

Total RNA density and its material derivative. (A) Total RNA density (ng mm^-1) in 1 mm-long segments of the primary root. Mean ± standard error of mean (n = 3). The black line corresponds to the cubic spline interpolation of the means. (B) Material derivative - the net accumulation rate, of total RNA (ng mm^-1 min^-1). The black line was calculated from the mean values of each parameter using equation (3). Box-and-whisker plots are the distribution of 1000 replicates (obtained by random resampling). The central mark is the median, the edges are the 25th and 75th percentiles, and the whiskers extend to 10th and the 90th percentiles.

Figure 5

Spatio-temporal mapping of gene regulation. Lagrangian representation of Actin11 (A), EF1β (B) transcript accumulation rate (a.u. mm^-1 min^-1) and total RNA accumulation rate (C) (ng mm^-1 min^-1) along the primary root apex and with time. Net accumulations rates (Z axis) are plotted along the growth trajectory of an element (curve in the XY, see Figure 1C). Computed on Matlab software.