Upscaling diffusion through first-order volumetric sinks: a homogenization of bacterial nutrient uptake

In mathematical models that include nutrient delivery to bacteria, it is prohibitively expensive to include a pointwise nutrient uptake within small bacterial regions over bioreactor length-scales, and so such models often impose an effective uptake instead. In this paper, we systematically investigate how the effective uptake should scale with bacterial size and other microscale properties under first-order uptake kinetics. We homogenize the unsteady problem of nutrient diffusing through a locally periodic array of spherical bacteria, within which it is absorbed. We introduce a general model that could also be applied to other single-cell microorganisms, such as cyanobacteria, microalgae, protozoa, and yeast and we consider generalizations to arbitrary bacterial shapes, including some analytic results for ellipsoidal bacteria. We explore in detail the three distinguished limits of the system on the timescale of diffusion over the macroscale. When the bacterial size is of the same order as the distance between them, the effective uptake has two limiting behaviours, scaling with the bacterial volume for weak uptake and with the bacterial surface area for strong uptake. We derive the function that smoothly transitions between these two behaviours as the system parameters vary. Additionally, we explore the distinguished limit in which bacteria are much smaller than the distance between them and have a very strong uptake. In this limit, we find that the effective uptake is bounded above as the uptake rate grows without bound; we are able to quantify this and characterise the transition to the other limits we consider

Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway

The mevalonate pathway is normally found in eukaryotes, and allows for the production of isoprenoids, a useful class of organic compounds. This pathway has been successfully introduced to Escherichia coli, enabling a biosynthetic production route for many isoprenoids. In this paper, we develop and solve a mathematical model for the concentration of metabolites in the mevalonate pathway over time, accounting for the loss of acetyl-CoA to other metabolic pathways. Additionally, we successfully test our theoretical predictions experimentally by introducing part of the pathway into Cupriavidus necator. In our model, we exploit the natural separation of time scales as well as of metabolite concentrations to make significant asymptotic progress in understanding the system. We confirm that our asymptotic results agree well with numerical simulations, the former enabling us to predict the most important reactions to increase isopentenyl diphosphate production whilst minimizing the levels of HMG-CoA, which inhibits cell growth. Thus, our mathematical model allows us to recommend the upregulation of certain combinations of enzymes to improve production through the mevalonate pathway

Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway

The mevalonate pathway is normally found in eukaryotes, and allows for the production of isoprenoids, a useful class of organic compounds. This pathway has been successfully introduced to Escherichia coli, enabling a biosynthetic production route for many isoprenoids. In this paper, we develop and solve a mathematical model for the concentration of metabolites in the mevalonate pathway over time, accounting for the loss of acetyl-CoA to other metabolic pathways. Additionally, we successfully test our theoretical predictions experimentally by introducing part of the pathway into Cupriavidus necator. In our model, we exploit the natural separation of time scales as well as of metabolite concentrations to make significant asymptotic progress in understanding the system. We confirm that our asymptotic results agree well with numerical simulations, the former enabling us to predict the most important reactions to increase isopentenyl diphosphate production whilst minimizing the levels of HMG-CoA, which inhibits cell growth. Thus, our mathematical model allows us to recommend the upregulation of certain combinations of enzymes to improve production through the mevalonate pathway

Brief Note Elemental Analysis of Biological Material in the Fresh-Frozen State

Author Institution: Department of Zoology and Department of Surgery, The Ohio State Universit

Using singular perturbation theory to determine kinetic parameters in a non-standard coupled enzyme assay

We investigate how to characterize the kinetic parameters of an aminotransaminase using a non-standard coupled (or auxiliary) enzyme assay, where the peculiarity arises for two reasons. First, one of the products of the auxiliary enzyme is a substrate for the primary enzyme and, second, we explicitly account for the reversibility of the auxiliary enzyme reaction. Using singular perturbation theory, we characterize the two distinguished asymptotic limits in terms of the strength of the reverse reaction, which allows us to determine how to deduce the kinetic parameters of the primary enzyme for a characterized auxiliary enzyme. This establishes a parameter-estimation algorithm that is applicable more generally to similar reaction networks. We demonstrate the applicability of our theory by performing enzyme assays to characterize a novel putative aminotransaminase enzyme, CnAptA (UniProtKB Q0KEZ8) from Cupriavidus necator H16, for two different omega-amino acid substrates

A genetic assay for gene essentiality in Clostridium

Essential genes of pathogens are potential therapeutic targets, but are difficult to verify. Here, gene essentiality was determined by targeted knockout following engineered gene duplication. Null mutants of candidate essential genes of Clostridium difficile were viable only in the presence of a stable second copy of the gene

Effects of ionic strength on the regulation of Na/H exchange and K-Cl cotransport in dog red blood cells

Dog red cell membranes contain two distinct volume-sensitive transporters: swelling-activated K-Cl cotransport and shrinkage- activated Na/H exchange. Cells were prepared with intracellular salt concentration and weight percentage of cell water (%cw) varied independently by transient permeabilization of the cell membrane to cations. The dependence of transporter-mediated Na and K influxes upon %cw and upon extracellular salt concentration (c(ext)) was measured in cells so prepared. It was found that the critical value of %cw at which transporters are activated, called the set point, is similar for the two transporters, and that the set points for the two transporters decrease similarly with increasing extracellular salt concentration. These findings suggest a common mechanism of regulation of these two transporters. Cellular Na, K, and Cl concentrations were measured as functions of %cw and c(ext). Using these data together with data from the literature for other solute concentrations, empirical expressions were developed to describe the dependence of the intracellular concentrations of all significant small molecule electrolytes, and therefore the intracellular ionic strength, upon %cw and c(ext). A mechanistic model for the dependence of the set point of an individual transporter upon intracellular ionic strength is proposed. According to this model, the set point represents a critical extent of association between the transporter and a postulated soluble regulatory protein, called regulator. Model functions are presented for the calculation of the thermodynamic activity of regulator, and hence extent of regulator- transporter association, as a function of total intracellular protein concentration (or %cw) and ionic strength. The experimentally observed dependence of set point %cw on c(ext) are simulated using these functions and the empirical expressions described above, together with reasonable but not uniquely determined values of model parameters

Astrophysical and Astrobiological Implications of Gamma-Ray Burst Properties

Combining results for the local cosmic rate and mean peak luminosity of GRBs with the cosmic history of the star formation rate, we provide estimates for the local GRB rate per unit blue luminosity in galaxies. We find a typical GRB rate per unit B luminosity of 2.4x10^-17 h_{70}^2/Lsun/yr. The corresponding mean rate in the Milky Way is 5.5x10^-7 h_{70}^2/yr. We conclude: 1) the ratio of supernova rate to isotropic equivalent GRB rate is large: more than 6000 SNIbc per GRB or 30,000 SNII per GRB. GRBs could arise in a large fraction of black hole-forming events only with collimation in the range 0.01 - 0.001 and a steep enough slope of the IMF; 2) GRBs cannot account for the majority of large HI holes observed in galaxies; 3) the probability that the solar system was exposed to a fluence large enough to melt the chondrules during the first 10^7 yr of solar system history is negligibly small; 4) Even for very opaque atmospheres, a significant fraction of the GRB energy is transmitted as UV lines due to excitation by secondary electrons. For eukaryotic-like organisms in thin atmospheres (e.g. contemporary Mars), or for UV line exposure in thick atmospheres (e.g. Earth), biologically significant events occur at a rate of about 100--500 /Gyr. The direct contribution of these "jolts" to mutational evolution may, however, be negligible because of the short duration of the GRBs. Evolutionary effects due to partial sterilizations and to longer-lived disruptions of atmospheric chemistry should be more important. (Abridged)Comment: 36 pages, no figures Accepted by Astrophysical Journal Oct. 2001. First submitted December,1999. Substantially rewritten discussion of burst source count distributions and of biological implication

The indirect action of ions upon amino acid transport system L in the S37 cell

The uptake into S37 ascites cells of an L-system specific analog, 2-amino-bicyclo-(3,2,1)-octanecarboxylic acid (ABOCA), wasinconsistently inhibited by deletion of sodium ion from the incubation medium. We note that there have been conflicting reports from various other laboratories as to the effect of sodium ion on the transport of L-system specific analogs. The uptake of labeled exo-2-aminobicyclo-(2.2,1)-heptane-2-carboxylic acid (BCH) wasalso diminished by the removal of sodium from the medium. The Km values for these substrates were increased and [nu]max values decreased as the sodium ion concentration was decreased or abolished. Transport behavior was also found to be affected by varying the medium potassium ion concentration with valinomycin present. The sodium effect was abolished by preincubation with cyanide and deoxyglucose. The results suggest an indirect effect of sodium ion upon transport system L: system L is energetically supported by a membrane potential.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24714/1/0000136.pd