BIOECONOMICS OF REGULATING NITRATES IN GROUNDWATER: TAXES, QUANTITY RESTRICTIONS, AND POLLUTION PERMITS

Soil specific, chance constrained, dynamic models of agricultural production and nitrate leaching are developed to assess the impacts of nitrogen fertilizer taxes, quantity restrictions on fertilizer or leachate, and leachate permits. A programming model uses the solutions of these bioeconomic models to determine regional impacts of the regulations.Land Economics/Use, Research Methods/ Statistical Methods,

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small sub-cellular compartment. This is achieved by applying a mesoscopic version of the quasi-steady state assumption to the exact Fokker-Planck equation associated with the Poisson Representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing sub-cellular volume, decreasing Michaelis-Menten constants and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic

How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order $\Omega^{-3/2}$ for reaction systems which do not obey detailed balance and at least accurate to order $\Omega^{-2}$ for systems obeying detailed balance, where $\Omega$ is the characteristic size of the system. Hence the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order $\Omega^{-1/2}$ and variance estimates accurate to order $\Omega^{-3/2}$. This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy

A Case Report of Thalamic Infarction after Lumbar Drain: A Unique Cause of Perioperative Stroke?

In the case presented, a patient has an unexplained episode of hypertension during aneurysm clipping. Following the procedure, the patient was discovered to have bilateral thalamic infarctions unrelated to the vascular location of the aneurysm. After a review of the case, it becomes apparent that intracranial hypotension caused by lumbar over drainage of cerebrospinal fluid (CSF) is the likely cause of both the episode of intraoperative hypertension and the thalamic infarcts. It is often presumed that having an open dura protects against intracranial hypotension and subsequent herniation. We present this case to suggest that opening the dura might not be protective in all cases and anesthesiologists must pay particular attention to the rate of CSF drainage. Lumbar CSF drainage is a technique frequently employed during neurological surgery and it is important for anesthesiologists to understand the signs, symptoms, and potential consequences of intracranial hypotension from rapid drainage

Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators

The linear noise approximation (LNA) offers a simple means by which one can study intrinsic noise in monostable biochemical networks. Using simple physical arguments, we have recently introduced the slow-scale LNA (ssLNA) which is a reduced version of the LNA under conditions of timescale separation. In this paper, we present the first rigorous derivation of the ssLNA using the projection operator technique and show that the ssLNA follows uniquely from the standard LNA under the same conditions of timescale separation as those required for the deterministic quasi-steady state approximation. We also show that the large molecule number limit of several common stochastic model reduction techniques under timescale separation conditions constitutes a special case of the ssLNA.Comment: 10 pages, 1 figure, submitted to Physical Review E; see also BMC Systems Biology 6, 39 (2012

Localization of Minoxidil Sulfotransferase in Rat Liver and the Outer Root Sheath of Anagen Pelage and Vibrissa Follicles

The precise biochemical mechanism and site(s) of action by which minoxidil stimulates hair growth are not yet clear. Minoxidil sulfate is the active metabolite of minoxidil, with regard to smooth muscle vasodilation and hair growth. Formation of minoxidil sulfate is catalyzed by specific PAPS-dependent sulfotransferase(s) and minoxidil-sulfating activities have been previously reported to be present in liver and hair follicles. One of these minoxidil-sulfating enzymes has been purified from rat liver (rat minoxidil sulfotransferase, MST) and a rabbit anti-MST antibody has been prepared. Using this anti-MST antibody, we have immunohistochernically localized minoxidil sulfotransferase in the liver and anagen hair follicles from rat. In rat pelage and vibrissa follicles, this enzyme is localized within the cytoplasm of epithelial cells in the lower outer root sheath. Although the immunolocalization of MST might not necessarily correlate with the MST activity known to be present in anagen follicles, the results of this study strongly suggest that the lower outer root sheath of the hair follicle may serve as a site for the sulfation of topically applied minoxidil

Threshold for Onset of Injury in Chinook Salmon from Exposure to Impulsive Pile Driving Sounds

The risk of effects to fishes and other aquatic life from impulsive sound produced by activities such as pile driving and seismic exploration is increasing throughout the world, particularly with the increased exploitation of oceans for energy production. At the same time, there are few data that provide insight into the effects of these sounds on fishes. The goal of this study was to provide quantitative data to define the levels of impulsive sound that could result in the onset of barotrauma to fish. A High Intensity Controlled Impedance Fluid filled wave Tube was developed that enabled laboratory simulation of high-energy impulsive sound that were characteristic of aquatic far-field, plane-wave acoustic conditions. The sounds used were based upon the impulsive sounds generated by an impact hammer striking a steel shell pile. Neutrally buoyant juvenile Chinook salmon (Oncorhynchus tshawytscha) were exposed to impulsive sounds and subsequently evaluated for barotrauma injuries. Observed injuries ranged from mild hematomas at the lowest sound exposure levels to organ hemorrhage at the highest sound exposure levels. Frequency of observed injuries were used to compute a biological response weighted index (RWI) to evaluate the physiological impact of injuries at the different exposure levels. As single strike and cumulative sound exposure levels (SELss, SELcum respectively) increased, RWI values increased. Based on the results, tissue damage associated with adverse physiological costs occurred when the RWI was greater than 2. In terms of sound exposure levels a RWI of 2 was achieved for 1920 strikes by 177 dB re 1 µPa2⋅s SELss yielding a SELcum of 210 dB re 1 µPa2⋅s, and for 960 strikes by 180 dB re 1 µPa2⋅s SELss yielding a SELcum of 210 dB re 1 µPa2⋅s. These metrics define thresholds for onset of injury in juvenile Chinook salmon

Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

The application of the quasi-steady-state approximation to the Michaelis-Menten reaction embedded in large open chemical reaction networks is a popular model reduction technique in deterministic and stochastic simulations of biochemical reactions inside cells. It is frequently assumed that the predictions of the reduced master equations obtained using the stochastic quasi-steady-state approach are in very good agreement with the predictions of the full master equations, provided the conditions for the validity of the deterministic quasi-steady-state approximation are fulfilled. We here use the linear-noise approximation to show that this assumption is not generally justified for the Michaelis-Menten reaction with substrate input, the simplest example of an open embedded enzyme reaction. The reduced master equation approach is found to considerably overestimate the size of intrinsic noise at low copy numbers of molecules. A simple formula is obtained for the relative error between the predictions of the reduced and full master equations for the variance of the substrate concentration fluctuations. The maximum error is reached when modeling moderately or highly efficient enzymes, in which case the error is approximately 30%. The theoretical predictions are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis and fermentation.Comment: Main text (5 pages, 1 figure) and Supplementary information (2 pages), accepted by J. Chem. Phys. (Communication

Spectroscopic perspective on the interplay between electronic and magnetic properties of magnetically doped topological insulators

We combine low energy muon spin rotation (LE-$\mu$SR) and soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to study the magnetic and electronic properties of magnetically doped topological insulators, (Bi,Sb)$_2$Te$_3$. We find that one achieves a full magnetic volume fraction in samples of (V/Cr)$_x$(Bi,Sb)$_{2-x}$Te$_3$ at doping levels x $\gtrsim$ 0.16. The observed magnetic transition is not sharp in temperature indicating a gradual magnetic ordering. We find that the evolution of magnetic ordering is consistent with formation of ferromagnetic islands which increase in number and/or volume with decreasing temperature. Resonant ARPES at the V $L_3$ edge reveals a nondispersing impurity band close to the Fermi level as well as V weight integrated into the host band structure. Calculations within the coherent potential approximation of the V contribution to the spectral function confirm that this impurity band is caused by V in substitutional sites. The implications of our results on the observation of the quantum anomalous Hall effect at mK temperatures are discussed