A noisy linear map underlies oscillations in cell size and gene expression in bacteria.

During bacterial growth, a cell approximately doubles in size before division, after which it splits into two daughter cells. This process is subjected to the inherent perturbations of cellular noise and thus requires regulation for cell-size homeostasis. The mechanisms underlying the control and dynamics of cell size remain poorly understood owing to the difficulty in sizing individual bacteria over long periods of time in a high-throughput manner. Here we measure and analyse long-term, single-cell growth and division across different Escherichia coli strains and growth conditions. We show that a subset of cells in a population exhibit transient oscillations in cell size with periods that stretch across several (more than ten) generations. Our analysis reveals that a simple law governing cell-size control-a noisy linear map-explains the origins of these cell-size oscillations across all strains. This noisy linear map implements a negative feedback on cell-size control: a cell with a larger initial size tends to divide earlier, whereas one with a smaller initial size tends to divide later. Combining simulations of cell growth and division with experimental data, we demonstrate that this noisy linear map generates transient oscillations, not just in cell size, but also in constitutive gene expression. Our work provides new insights into the dynamics of bacterial cell-size regulation with implications for the physiological processes involved.

Particle size distributions from Fraunhofer diffraction

info:eu-repo/semantics/published

Physiological levels of PTEN control the size of the cellular Ins(1,3,4,5,6)P5 pool

To understand how a signaling molecule's activities are regulated, we need insight into the processes controlling the dynamic balance between its synthesis and degradation. For the Ins(1,3,4,5,6)P5 signal, this information is woefully inadequate. For example, the only known cytosolic enzyme with the capacity to degrade Ins(1,3,4,5,6)P5 is the tumour-suppressor PTEN [J.J. Caffrey, T. Darden, M.R. Wenk, S.B. Shears, FEBS Lett. 499 (2001) 6 ], but the biological relevance has been questioned by others [E.A. Orchiston, D. Bennett, N.R. Leslie, R.G. Clarke, L. Winward, C.P. Downes, S.T. Safrany, J. Biol. Chem. 279 (2004) 1116 ]. The current study emphasizes the role of physiological levels of PTEN in Ins(1,3,4,5,6)P5 homeostasis. We employed two cell models. First, we used a human U87MG glioblastoma PTEN-null cell line that hosts an ecdysone-inducible PTEN expression system. Second, the human H1299 bronchial cell line, in which PTEN is hypomorphic due to promoter methylation, has been stably transfected with physiologically relevant levels of PTEN. In both models, a novel consequence of PTEN expression was to increase Ins(1,3,4,5,6)P5 pool size by 30-40% (p<0.01); this response was wortmannin-insensitive and, therefore, independent of the PtdIns 3-kinase pathway. In U87MG cells, induction of the G129R catalytically inactive PTEN mutant did not affect Ins(1,3,4,5,6)P(5) levels. PTEN induction did not alter the expression of enzymes participating in Ins(1,3,4,5,6)P5 synthesis. Another effect of PTEN expression in U87MG cells was to decrease InsP6 levels by 13% (p<0.02). The InsP6-phosphatase, MIPP, may be responsible for the latter effect; we show that recombinant human MIPP dephosphorylates InsP6 to D/L-Ins(1,2,4,5,6)P5, levels of which increased 60% (p<0.05) following PTEN expression in U87MG cells. Overall, our data add higher inositol phosphates to the list of important cellular regulators [Y. Huang, R.P. Wernyj, D.D. Norton, P. Precht, M.C. Seminario, R.L. Wange, Oncogene, 24 (2005) 3819 ] the levels of which are modulated by expression of the highly pleiotropic PTEN protein.

Hydrocarbon field size distributions: a case study in mixed integer nonlinear programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.

Performance analysis of a register insertion ring with a variable size buffer

There has been a recent revival of interest in the register insertion (RI) protocol because of its high throughput and low delay characteristics. Several variants of the protocol have been investigated with a view to integrating voice and data applications on a single local area network (LAN). In this paper the performance of an RI ring with a variable size buffer is studied by modelling and simulation. The chief advantage of the proposed scheme is that an efficient but simple bandwidth allocation scheme is easily incorporated. Approximate formulas are derived for queue lengths, queueing times, and total end-to-end transfer delays. The results are compared with previous analyses and with simulation estimates. The effectiveness of the proposed protocol in ensuring fairness of access under conditions of heavy and unequal loading is investigated.