An inverse algorithm for a mathematical model of an avian urine concentrating mechanism

A nonlinear optimization technique, in conjunction with a single-nephron, single-solute mathematical model of the quail urine concentrating mechanism, was used to estimate parameter sets that optimize a measure of concentrating mechanism efficiency, viz., the ratio of the free-water absorption rate to the total NaCl active transport rate. The optimization algorithm, which is independent of the numerical method used to solve the model equations, runs in a few minutes on a 1000 MHz desktop computer. The parameters varied were: tubular permeabilities to water and solute; maximum active solute transport rates of the ascending limb of Henle and the collecting duct (CD); length of the prebend enlargement (PBE) of the descending limb; fractional solute delivery to the CD; solute concentration of tubular fluid entering the CD at the cortico-medullary boundary; and rate of exponential CD population decrease along the medullary cone. Using a base-case parameter set and parameter bounds suggested by physiologic experiments, the optimization algorithm identified a maximum-efficiency set of parameter values that increased efficiency by 40% above base-case efficiency; a minimum-efficiency set reduced efficiency by about 41%. When maximum-efficiency parameter values were computed as medullary length varied over the physiologic range, the PBE was found to make up 88% of a short medullary cone but only 8% of a long medullary cone.     

A region-based model framework for the rat urine concentrating mechanism

The highly structured organization of tubules and blood vessels in the outer medulla of the mammalian kidney is believed to result in preferential interactions among tubules and vessels; such interactions may promote solute cycling and enhance urine concentrating capability. In this study, we formulate a new model framework for the urine concentrating mechanism in the outer medulla of the rat kidney. The model simulates preferential interactions among tubules and vessels by representing two concentric regions and by specifying the fractions of tubules and vessels assigned to each of the regions. The model equations are based on standard expressions for transmural transport and on solute and water conservation. Model equations, which are derived in dynamic form, are solved to obtain steady-state solutions by means of a stable and efficient numerical method, based on the semi-Lagrangian semi-implicit method and on Newton’s method. In this application, the computational cost scales as O(N ²), where N is the number of spatial subintervals along the medulla. We present representative solutions and show that the method generates approximations that are second-order accurate in space and that exhibit mass conservation.     

An efficient simulation method for discrete-value controlled large-scale neuromyoskeletal system models

An efficient Euler-Adams hybrid integration scheme for simulating on the computer discrete-value controlled large-scale neuromyoskeletal system models is presented. If, as discussed in the model, the differential equations describing the recruitment and excitation dynamics of the muscular subsystem are independent of the corresponding contraction-dynamical state variables, they can be integrated separately over certain time intervals by a modified Euler routine that handles discontinuous right-hand sides efficiently. The resulting myostates can then be stored and used as continuous input values for the subsequent integration by an Adams predictor-corrector algorithm of the remaining contraction-dynamical and skeletomechanical state differential equations. With such an Euler-Adams hybrid integration routine one avoids the detrimental effects and efficiency losses associated with frequent stop-restart cycles of otherwise efficient Adams-type algorithms, which cycles are forced by discontinuities on the right-hand side of the myostate equations. In the example presented, a reduction in the execution time by a factor of about 5 could be achieved by implementing the proposed technique.     

Role of structural organization in the urine concentrating mechanism of an avian kidney

The organization of tubules and blood vessels in the quail medullary cone is highly structured. This structural organization may result in preferential interactions among tubules and vessels, interactions that may enhance urine concentrating capability. In this study, we formulate a model framework for the urine concentrating mechanism of the quail kidney. The model simulates preferential interactions among renal tubules by representing two concentric cores and by specifying the fractions of tubules assigned to each of the concentric cores. The model equations are based on standard expressions for transmural transport and on solute and water conservation. Model results suggest that the preferential interactions among tubules enhance the urine concentration capacity of short medullary cones by reducing the diluting effect of the descending limbs on the region of the interstitium where the collecting ducts are located; however, the effects on longer cones are unclear.     

Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism

This paper establishes some results for the existence and uniqueness of solutions to a previously published mathematical model of the mammalian urine concentrating mechanism [H.E. Layton, Distribution of Henle's loops may enhance urine concentrating capability, Biophys. J. 49:1033-1040 (1986)]. In particular, the contraction mapping principle is used to show that for sufficiently small and sufficiently large values of a positive parameter β there exist unique solutions to the model, whether it be endowed with first-order kinetics or Michaelis-Menten kinetics. Large or small β corresponds to large or small rates of active transport of NaCl from the ascending limbs. The Schauder principle is used to show that there exist solutions to the model for physiologically reasonable reabsorption kinetics, including first-order and Michaelis-Menten kinetics for all values of β.     

An improved method for concentrating rotavirus from water samples

A modified adsorption-elution method for the concentration of seeded rotavirus from water samples was used to determine various factors which affected the virus recovery. An enzyme-linked immunosorbent assay was used to detect the rotavirus antigen after concentration. Of the various eluents compared, 0.05M glycine, pH 11.5 gave the highest rotavirus antigen recovery using negatively charged membrane filtration whereas 2.9% tryptose phosphate broth containing 6% glycine; pH 9.0 was found to give the greatest elution efficiency when a positively charged membrane was used. Reconcentration of water samples by a speedVac concentrator showed significantly higher rotavirus recovery than polyethylene glycol precipitation through both negatively and positively charged filters (p-value <0.001). In addition, speedVac concentration using negatively charged filtration resulted in greater rotavirus recovery than that using positively charged filtration (p-value = 0.004). Thirty eight environmental water samples were collected from river, domestic sewage, canals receiving raw sewage drains, and tap water collected in containers for domestic use, all from congested areas of Bangkok. In addition, several samples of commercial drinking water were analyzed. All samples were concentrated and examined for rotavirus antigen. Coliforms and fecal coliforms (0->1,800 MPN/100 ml) were observed but rotavirus was not detected in any sample. This study suggests that the speedVac reconcentration method gives the most efficient rotavirus recovery from water samples.     

An improved numerical method for strong coupling of excitation and contraction models in the heart

Quantifying the interactions between excitation and contraction is fundamental to furthering our understanding of cardiac physiology. To date simulating these effects in strongly coupled excitation and contraction tissue models has proved computationally challenging. This is in part due to the numerical methods implemented to maintain numerical stability in previous simulations, which produced computationally intensive problems. In this study, we analytically identify and quantify the velocity and length dependent sources of instability in the current established coupling method and propose a new method which addresses these issues. Specifically, we account for the length and velocity dependence of active tension within the finite deformation equations, such that the active tension is updated at each intermediate Newton iteration, within the mechanics solution step. We then demonstrate that the model is stable and converges in a three-dimensional rod under isometric contraction. Subsequently, we show that the coupling method can produce stable solutions in a cube with many of the attributes present in the heart, including asymmetrical activation, an inhomogeneous fibre field and a nonlinear constitutive law. The results show no instabilities and quantify the error introduced by discrete length updates. This validates our proposed coupling framework, demonstrating significant improvement in the stability of excitation and contraction simulations.     

Osmotic response element-binding protein (OREBP) is an essential regulator of the urine concentrating mechanism

OREBP (osmotic response element-binding protein), also called TonEBP or NFAT5, is thought to induce the expression of genes that increase the accumulation of organic osmolytes to protect cells against a hypertonic environment. To investigate the consequences of lacking OREBP activity, transgenic (Tg) mice that overexpress OREBPdn (dominant negative form of OREBP) specifically in the epithelial cells of the renal collecting tubules were generated. These mice showed impairment in their urine concentrating mechanism, most likely due to reduced expression of the aquaporin AQP2 and the urea transporter UT-A1 and UT-A2 mRNAs. When deprived of water or after the administration of a vasopressin analogue, urine osmolality of the Tg mice was significantly increased but not to the same extent as that of the wild type mice. The expression of AQP2 and UT-A1, but not UT-A2 mRNAs, was increased to the same level as that of the wild type mice in the water deprivation state, indicating that the vasopressin regulatory mechanism was not affected by OREBPdn. These data indicate that in addition to vasopressin, OREBP is another essential regulator of the urine concentrating mechanism. Furthermore, the OREBPdn Tg mice developed progressive hydronephrosis soon after weaning, confirming the osmoprotective function of OREBP implicated by the in vitro experiments.     

A dynamic numerical method for models of renal tubules

We show that an explicit method for solving hyperbolic partial differential equations can be applied to a model of a renal tubule to obtain both dynamic and steady-state solutions. Appropriate implementation of this method eliminates numerical instability arising from reversal of intratubular flow direction. To obtain second-order convergence in space and time, we employ the recently developed ENO (Essentially Non-Oscillatory) methodology. We present examples of computed flows and concentration profiles in representative model contexts. Finally, we indicate briefly how model tubules may be coupled to construct large-scale simulations of the renal counterflow system.     

An efficient method for the sequence analysis of oligodeoxyribonucleotides

Modifications of the chemical method of DNA sequence analysis that permit rapid and reliable sequence determination of single-stranded oligodeoxyribonucleotides as short as 4 nucleotides in length are reported. The principal changes made were increasing the level of chemical modification and optimizing the conditions for recovery of the chemically modified oligodeoxyribonucleotides. This method includes two approaches to the removal of [γ-³²P]ATP from ³²P-labeled oligodeoxyribonucleotides and is especially useful in the determination of the sequence of chemically synthesized oligodeoxyribonucleotides, which are generally between 4 and 20 nucleotides in length.     

A simple and efficient method for obtaining urine samples from rats

A method for collection of urine from rats was developed that is simple, reliable, and efficient. A 5 ml. polystyrene beaker is placed over the urethra and the base of the tail is stimulated with the fingers of one hand. Depending on the quality and quantity of urine needed the perineal area may be shaved and the beaker may be held by hand or attached with tape.     

An efficient mutational method for photosynthetic bacteria

The pigment and auxotrophic mutants of Rhodobacter sphaeroides Y6 were obtained by treatment with ethyl methanesulfonate (EMS) followed by lithium chloride (LiCI). Treatment with 0.081 M EPS and subsequent treatment with 0.071 M LiCI resulted in 12% higher frequency of pigment mutations than application of 0.081 M EMS alone; the frequency of auxotrophic mutations increased 2.5-fold when treatment with lithium chloride was applied. A blue shift 10 nm was recorded in the absorption spectrum of carotenoids form YM5-3 green mutant; considerable accumulation of neurosporine was revealed by HPLC and mass spectrometry. The method is efficient for isolating mutants of photosynthetic bacteria.     

Mathematical analysis of a model for the renal concentrating mechanism

A system of ordinary differential equations, designed to model the counterflow system in the renal medulla, is studied. An existence theorem for solutions of the model equations is obtained. An exact solution of the system is obtained in the limiting case of infinite water permeability. If there is diffusion in the core, evaluation of the exact solution leads to multiple stable solutions of the model equations. One solution has a large concentration ratio, which tends to a finite asymptotic limit as the pump strength tends to infinity.     

An efficient mutational method for photosynthetic bacteria

The pigment and auxotrophic mutants of Rhodobacter sphaeroides Y6 were obtained by treatment with ethyl methanesulfonate (EMS) followed by lithium chloride (LiCl). Treatment with 0.081 MEMS and subsequent treatment with 0.071 M LiCl resulted in 12% higher frequency og than that by 0.081 mol/L EMS alone, and the same frequency of pigment mutations than application of 0.081 M EMS alone; the frequency of auxotrophic mutations increased 2.5-fold when treatment with lithium chloride was applied. A blue shift by 10 nm was recorded in the absorption spectrum of carotenoids form YM5-3 green mutant; considerable accumulation of neurosporine was revealed by HPLC and mass spectrometry. The method is efficient for isolating the mutants of photosynthetic bacteria. Published in Russian in Mikrobiologiya, 2006, Vol. 75, No. 6, pp. 758–764. The text was submitted by the authors in English.     

An efficient method for multi-locus molecular haplotyping

Many methods exist for genotyping—revealing which alleles an individual carries at different genetic loci. A harder problem is haplotyping—determining which alleles lie on each of the two homologous chromosomes in a diploid individual. Conventional approaches to haplotyping require the use of several generations to reconstruct haplotypes within a pedigree, or use statistical methods to estimate the prevalence of different haplotypes in a population. Several molecular haplotyping methods have been proposed, but have been limited to small numbers of loci, usually over short distances. Here we demonstrate a method which allows rapid molecular haplotyping of many loci over long distances. The method requires no more genotypings than pedigree methods, but requires no family material. It relies on a procedure to identify and genotype single DNA molecules, and reconstruction of long haplotypes by a ‘tiling’ approach. We demonstrate this by resolving haplotypes in two regions of the human genome, harbouring 20 and 105 single-nucleotide polymorphisms, respectively. The method can be extended to reconstruct haplotypes of arbitrary complexity and length, and can make use of a variety of genotyping platforms. We also argue that this method is applicable in situations which are intractable to conventional approaches.     

General method for the derivation and numerical solution of epithelial transport models

Summary A general method is presented for the formulation and numerical evaluation of mathematical models describing epithelial transport. The method is based on the principles of conservation of mass, and maintenance of electroneutrality within the cells and bathing solutions. It is therefore independent of the specific membrane transport mechanisms, and can be used to evaluate different models describing arbitrary transport processes (including passive, active and cotransport processes). Detailed numerical methods are presented that allow computation of steady-state and transient responses under open-circuit, current-clamp and voltage-clamp conditions, using a general-purpose laboratory minicomputer. To evaluate the utility of this approach, a specific model is presented that is consistent with the Koefoed-Johnson and Ussing hypothesis of sodium transport in tight epithelia (Acta Physiol. Scand. 42:298–308, 1958). This model considers passive transport of an arbitrary number of permeant solutes, active transport of sodium and potassium, and osmotically induced water transport across the apical and basolateral membranes. Results of the model are compared to published experimental measurements in rabbit urinary bladder epithelium.     

The effect of solution non-ideality on membrane transport in three-dimensional models of the renal concentrating mechanism

Previous models of the renal concentrating mechanism employ ideal approximations of solution thermodynamics for membrane transport calculation. In three-dimensional models of the renal medulla, predicted urine concentrations reach levels where there idealized approximations begin to break down. In this paper we derive equations that govern membrane transport for non-dilute solutions and use these equations in a three-dimensional model of the concentrating mechanism. New numerical methods were employed that are more stable than those employed previously. Compared to ideal solution models, the urea non-ideality tends to increase predicted osmolarities, whereas NaCl non-ideality decreases predictions.     

An efficient method for the preparation of protoplasts fromTrichoderma viride

Conditions for an efficient high-yield procedure for the preparation of protoplasts fromTrichoderma viride have been determined. The optimum yield of protoplasts was obtained using 15–18-h-old unbranched mycelia, 0.7 mol/L KCl in phosphate buffer (pH 6), and 5 % (W/V) of lyophilized snail gut-juice enzyme. The conversion of mycelia to protoplasts was complete within 40–60 min incubation at 30 °C.