Multistability in a Model for CTL Response to HTLV-I Infection and Its Implications to HAM/TSP Development and Prevention

Human T-cell leukaemia/lymphoma virus type I (HTLV-I) is a retrovirus that has been identified as the causative agent of HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and other illnesses. HTLV-I infects primarily CD4⁺ T cells and the transmission occurs through direct cell-to-cell contact. HAM/TSP patients harbor higher proviral loads in peripheral blood lymphocytes than asymptomatic carriers. Also, HAM/TSP patients exhibit a remarkably high number of circulating HTLV-I-specific CD8⁺ cytotoxic T lymphocytes (CTLs) in the peripheral blood. While CTLs have a protective role by killing the infected cells and lowering the proviral load, a high level of CTLs and their cytotoxicity are believed to be a main cause of the development of HAM/TSP. A mathematical model for HTLV-I infection of CD4⁺ T cells that incorporates the CD8⁺ cytotoxic T-cell (CTL) response is investigated. Our mathematical analysis reveals that the system can stabilize at a carrier steady-state with persistent viral infection but no CTL response, or at a HAM/TSP steady-state at which both the viral infection and CTL response are persistent. We also establish two threshold parameters R ₀ and R ₁, the basic reproduction numbers for viral persistence and for CTL response, respectively. We show that the parameter R ₁ can be used to distinguish asymptomatic carriers from HAM/TSP patients, and as an important control parameter for preventing the development of HAM/TSP.     

Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth

Chronic hepatitis B virus (HBV) infection is a major cause of human suffering, and a number of mathematical models have examined within-host dynamics of the disease. Most previous HBV infection models have assumed that: (a) hepatocytes regenerate at a constant rate from a source outside the liver; and/or (b) the infection takes place via a mass action process. Assumption (a) contradicts experimental data showing that healthy hepatocytes proliferate at a rate that depends on current liver size relative to some equilibrium mass, while assumption (b) produces a problematic basic reproduction number. Here we replace the constant infusion of healthy hepatocytes with a logistic growth term and the mass action infection term by a standard incidence function; these modifications enrich the dynamics of a well-studied model of HBV pathogenesis. In particular, in addition to disease free and endemic steady states, the system also allows a stable periodic orbit and a steady state at the origin. Since the system is not differentiable at the origin, we use a ratio-dependent transformation to show that there is a region in parameter space where the origin is globally stable. When the basic reproduction number, R ₀, is less than 1, the disease free steady state is stable. When R ₀ > 1 the system can either converge to the chronic steady state, experience sustained oscillations, or approach the origin. We characterize parameter regions for all three situations, identify a Hopf and a homoclinic bifurcation point, and show how they depend on the basic reproduction number and the intrinsic growth rate of hepatocytes.     

Enantioselective hydrolysis of (R)-2, 2-dimethylcyclopropane carboxamide by immobilized cells of an R-amidase-producing bacterium, Delftia tsuruhatensis CCTCC M 205114, on an alginate capsule carrier

Immobilized cells of Delftia tsuruhatensis CCTCC M 205114 harboring R-amidase were applied in asymmetric hydrolysis of (R)-2, 2-dimethylcyclopropane carboxamide (R − 1) from racemic (R, S)-2, 2-dimethylcyclopropane carboxamide to accumulate (S)-2, 2-dimethylcyclopropane carboxamide (S − 1). Maximum R-amidase activity of 13.1 U/g wet cells (0.982 U/g beads) was obtained under conditions of 3% sodium alginate, 2.5% CaCl₂, 15 h crosslinking and 2 mm bead size, which was 53.9% of that of free cells (24.3 U/g wet cells). In addition, characterization of the immobilized cells was examined. The optimum R − 1 hydrolysis conditions were identified as follows: substrate concentration 10 mM, pH 8.5, temperature 35°C and time course 40 min. Under optimum conditions, the maximum yield and enantiomeric excess of (R)-2, 2-dimethylcyclopropanecarboxylic acid were 49.5% and >99%, respectively. This afforded S − 1 with a yield >49% and an e.e. of 97.7%. With good operational stability and excellent enanotioselectivity, the immobilized cells could be potentially utilized in industrial production of S − 1.     

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R ₀ for each system. When R ₀<1, only the trivial equilibrium exists and is stable; when R ₀>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system’s qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach).     

Assessment of rabbit hemorrhagic disease in controlling the population of red fox: A measure to preserve endangered species in Australia

Predator's management requires a detailed understanding of the ecological circumstances associated with predation. Predation by foxes has been a significant contributor to the Australian native animal reduction. This paper mainly focuses on the dissemination of rabbit hemorrhagic disease in the rabbit population and its subsequences on red fox (Vulpes vulpes) population, by qualitative and quantitative analyses of a designed eco-epidemiological model with simple law of mass action and sigmoid functional response.Existence of solution has been analyzed and shown to be uniformly bounded. The basic reproduction number (R₀) is obtained and the occurrence of a backward bifurcation at R₀ = 1 is shown to be possible using central manifold theory. Global stability of endemic equilibrium is established by geometric approach. Criteria for diffusion-driven ecological instability caused by local random movements of European rabbits and red fox are obtained. Detailed analyses of Turing patterns formation selected by reaction-diffusion system under zero flux boundary conditions are presented. We found that transmission rate, self and cross-diffusion coefficients have appreciable influence on spatial spread of epidemics. Numerical simulation results confirm the analytical finding and generate patterns which indicate that population of red foxes might be controlled if rabbit hemorrhagic disease (RHD) is introduced into the rabbit population and thus ecological balance can be maintained.     

Dynamics of an epidemic model with non-local infections for diseases with latency over a patchy environment

In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a simple demographic structure for the population living in an n-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the latency and a non-local term caused by the mobility of the individuals during the latent period. Assuming irreducibility of the travel matrices of the infection related classes, an expression for the basic reproduction number R₀{\mathcal{R}_0} is derived, and it is shown that the disease free equilibrium is globally asymptotically stable if R₀ < 1{\mathcal{R}_0 < 1} , and becomes unstable if ${\mathcal{R}_0 > 1}${\mathcal{R}_0 > 1} . In the latter case, there is at least one endemic equilibrium and the disease will be uniformly persistent. When n = 2, two special cases allowing reducible travel matrices are considered to illustrate joint impact of the disease latency and population mobility on the disease dynamics. In addition to the existence of the disease free equilibrium and interior endemic equilibrium, the existence of a boundary equilibrium and its stability are discussed for these two special cases.     

Measurement of net ecosystem production and ecosystem respiration in a Zoysia japonica grassland,central Japan,by the chamber method

Measuring light, temperature, soil moisture, and growth provides a better understanding of net ecosystem production (NEP), ecosystem respiration (R _eco), and their response functions. Here, we studied the variations in NEP and R _eco in a grassland dominated by a perennial warm-season C₄ grass, Zoysia japonica. We used the chamber method to measure NEP and R _eco from August to September 2007. Biomass and leaf area index (LAI) were also measured to observe their effects on NEP and R _eco. Diurnal variations in NEP and R _eco were predicted well by light intensity (PPFD) and by soil temperature, respectively. Maximum NEP (NEP_max) values on days of year 221, 233, 247, and 262, were 2.44, 2.55, 3.90, and 4.17 μmol m⁻² s⁻¹, respectively. Throughout the growing period, the apparent quantum yield (α) increased with increasing NEP_max that ranged from 0.0154 to 0.0515, and NEP responded to the soil temperature changes by 44% and R _eco changes by 48%, and R _eco responded from 88 to 94% with the soil temperature diurnally. NEP’s light response and R _eco’s temperature response were affected by soil water content; more than 27% of the variation in NEP and 67% of the variation in R _eco could be explained by this parameter. NEP was strongly correlated with biomass and LAI, but R _eco was not, because environmental variables affected R _eco more strongly than growth parameters. Using the light response of NEP, the temperature response of R _eco, and meteorological data, daily NEP and R _eco were estimated at 0.67, 0.81, 1.17, and 1.56 g C m⁻², and at 2.88, 2.50, 3.51, and 3.04 g C m⁻², respectively, on days of year 221, 233, 247, and 262. The corresponding daily gross primary production (NEP + R _eco) was 3.5, 3.3, 4.6, and 4.6 g C m⁻².     

Cell cycle control at the first restriction point and its effect on tissue growth

Cell cycle is controlled at two restriction points, R ₁ and R ₂. At both points the cell will commit apoptosis if it detects irreparable damage. But at R ₁ an undamaged cell also decides whether to proceed to the S phase or go into a quiescent mode, depending on the environmental conditions (e.g., overpopulation, hypoxia). We consider the effect of this decision at the population level in a spherical tissue {r < R(t)}. We prove that if the cells have full control at R ₁, they can manipulate the size of R(t) to ensure that 0 < c ≤ R(t) ≤ C < ∞; simulations further show that R(t) can be made nearly stationary. In the absence of such control, R(t) will either increase to ∞ or decrease to 0. The mathematical model and analysis involve a system of PDEs in {r < R(t)}.     

Three stage semelparous Leslie models

Nonlinear Leslie matrix models have a long history of use for modeling the dynamics of semelparous species. Semelparous models, as do nonlinear matrix models in general, undergo a transcritical equilibrium bifurcation at inherent net reproductive number R ₀ = 1 where the extinction equilibrium loses stability. Semelparous models however do not fall under the purview of the general theory because this bifurcation is of higher co-dimension. This mathematical fact has biological implications that relate to a dichotomy of dynamic possibilities, namely, an equilibration with over lapping age classes as opposed to an oscillation in which age classes are periodically missing. The latter possibility makes these models of particular interest, for example, in application to the well known outbreaks of periodical insects. While the nature of the bifurcation at R ₀ = 1 is known for two-dimensional semelparous Leslie models, only limited results are available for higher dimensional models. In this paper I give a thorough accounting of the bifurcation at R ₀ = 1 in the three-dimensional case, under some monotonicity assumptions on the nonlinearities. In addition to the bifurcation of positive equilibria, there occurs a bifurcation of invariant loops that lie on the boundary of the positive cone. I describe the geometry of these loops, classify them into three distinct types, and show that they consist of either one or two three-cycles and heteroclinic orbits connecting (the phases of) these cycles. Furthermore, I determine stability and instability properties of these loops, in terms of model parameters, as well as those of the positive equilibria. The analysis also provides the global dynamics on the boundary of the cone. The stability and instability conditions are expressed in terms of certain measures of the strength and the symmetry/asymmetry of the inter-age class competitive interactions. Roughly speaking, strong inter-age class competitive interactions promote oscillations (not necessarily periodic) with separated life-cycle stages, while weak interactions promote stable equilibration with overlapping life-cycle stages. Methods used include the theory of planar monotone maps, average Lyapunov functions, and bifurcation theory techniques.      

Combined gas exchange characteristics,chlorophyll fluorescence and response curves as selection traits for temperature tolerance in maize genotypes

Maize is a low-temperature (LT)-sensitive plant and its physiological responses towards LT of temperate regions developed is an adaptive trait. To further our understanding about the response of maize to LT at the physiological and photosynthesis level, we conducted Infrared Gas Analysis (IRGA using LICOR6400-XT in 45-day-old grown two maize genotypes, one from temperate region (Gurez-Kashmir Himalayas), viz., Gurez local (Gz local), and another from tropics (Gujarat), viz., GM6. This study was carried out to evaluate the underlying physiological mechanisms in the two differentially temperature-tolerant maize genotypes. Net photosynthetic rate (A/P_N), 18.253 in Gz local and 25.587 (µmol CO₂ m^?2 s^?1) in GM6; leaf conductance (gs), 0.0102 in Gz local and 0.0566 (mmol H₂O m^?2 s^?1) in GM6; transpiration rate (E), 0.5371 in Gz local and 2.9409 (mmol H₂O m^?2 s^?1) in GM6; and water use efficiency (WUE), 33.9852 in Gz local and 8.7224 (µmol CO₂ mmol H₂O^?1) in GM6, were recorded under ambient conditions. Also, photochemical efficiency of photosystem II (PSII) (F_v/F_m), 0.675 in Gz local and 0.705 in GM6; maximum photochemical efficiency (F_v′/F_m′), 0.310234 in Gz local and 0.401391 in GM6; photochemical quenching (qP), 0.2375 in Gz local and 0.2609 in GM6; non-photochemical quenching (NPQ), 2.0036 in Gz local and 1.1686 in GM6; effective yield of PSII (ФPSII), 0.0789 in Gz local and 0.099 in GM6; and electron transport rate (ETR), 55.3152 in Gz local and 68.112 in GM6, were also evaluated in addition to various response curves, like light intensities and temperature. We observed that light response curves show the saturation light intensity requirement of 1600 µmol for both the genotypes, whereas temperature response curves showed the optimum temperature requirement for Gz local as 20 °C and for GM6 it was found to be 35 °C. The results obtained for each individual parameter and other correlational studies indicate that IRGA forms a promising route for quick and reliable screening of various stress-tolerant valuable genotypes, forming the first study of its kind.

     

Predicting ecosystem carbon balance in a warming Arctic: the importance of long‐term thermal acclimation potential and inhibitory effects of light on respiration

The carbon balance of Arctic ecosystems is particularly sensitive to global environmental change. Leaf respiration (R), a temperature‐dependent key process in determining the carbon balance, is not well‐understood in Arctic plants. The potential for plants to acclimate to warmer conditions could strongly impact future global carbon balance. Two key unanswered questions are (1) whether short‐term temperature responses can predict long‐term respiratory responses to growth in elevated temperatures and (2) to what extent the constant daylight conditions of the Arctic growing season inhibit leaf respiration. In two dominant Arctic species E riophorum vaginatum (tussock grass) and B etula nana (woody shrub), we assessed the extent of respiratory inhibition in the light (R _L/R _D), respiratory response to short‐term temperature change, and respiratory acclimation to long‐term warming treatments. We found that R of both species is strongly inhibited by light (averaging 35% across all measurement temperatures). In E . vaginatum both R _L and R _D acclimated to the long‐term warming treatment, reducing the magnitude of respiratory response relative to the short‐term response to temperature increase. In B . nana, both R _L and R _D responded to short‐term temperature increase but showed no acclimation to the long‐term warming. The ability to predict plant respiratory response to global warming with short‐term temperature responses will depend on species‐specific acclimation potential and the differential response of R _L and R _D to temperature. With projected woody shrub encroachment in Arctic tundra and continued warming, changing species dominance between these two functional groups, may impact ecosystem respiratory response and carbon balance.     

Novel biosynthesis of (R)-ethyl-3-hydroxyglutarate with (R)-enantioselective hydrolysis of racemic ethyl 4-cyano-3-hydroxybutyate by Rhodococcus erythropolis

(R)-ethyl-3-hydroxyglutarate with highly optical purity (≥99%) can be used as a novel precursor for synthesis of chiral side chain of rosuvastatin. In this study, a novel synthesis route of (R)-ethyl-3-hydroxyglutarate by whole microorganism cells from racemic ethyl 4-cyano-3-hydroxybutyate was created. A strain ZJB-0910 capable of transforming racemic β-hydroxy aliphatic nitrile was isolated by employing a screening method based on a colorimetric reaction of Co²⁺ ion with ammonia, and identified as Rhodococcus erythropolis based on its morphology, physiological tests, Biolog, and the 16S rDNA sequence. After cultivation in a sterilized medium with composition of 20 g glucose, 5 g yeast extract, 0.5 g KH₂PO₄, 0.5 g K₂HPO₄, 0.2 g MgSO₄·7H₂O per liter at 30°C and 150 rpm for 48 h, the whole cells of R. erythropolis ZJB-0910 were prepared as a catalyst in (R)-enantioselective hydrolysis of racemic ethyl 4-cyano-3-hydroxybutyate for synthesis of (R)-ethyl-3-hydroxyglutarate, without bearing hydrolase activity for the ester bond of ethyl 4-cyano-3-hydroxybutyate. Under the optimized biotransformation conditions of pH 7.5, 30°C, and 20 mM substrate concentration, (R)-ethyl-3-hydroxyglutarate with 46.2% yield (ee > 99%) was afforded, and its chemical structure was determined by ESI-MS, NMR, and IR. The apparent Michaelis constant K _m and maximum rate V _max for this biocatalytic reaction were 0.01 M and 85.6 μmol min⁻¹ g⁻¹, respectively.     

Autotrophic and heterotrophic respiration in needle fir and Quercus-dominated stands in a cool-temperate forest, central Korea

To investigate annual variation in soil respiration (R _S) and its components [autotrophic (R _A) and heterotrophic (R _H)] in relation to seasonal changes in soil temperature (ST) and soil water content (SWC) in an Abies holophylla stand (stand A) and a Quercus-dominated stand (stand Q), we set up trenched plots and measured R _S, ST and SWC for 2 years. The mean annual rate of R _S was 436 mg CO₂ m⁻² h⁻¹, ranging from 76 to 1,170 mg CO₂ m⁻² h⁻¹, in stand A and 376 mg CO₂ m⁻² h⁻¹, ranging from 82 to 1,133 mg CO₂ m⁻² h⁻¹, in stand Q. A significant relationship between R _S and its components and ST was observed over the 2 years in both stands, whereas a significant correlation between R _A and SWC was detected only in stand Q. On average over the 2 years, R _A accounted for approximately 34% (range 17–67%) and 31% (15–82%) of the variation in R _S in stands A and Q, respectively. Our results suggested that vegetation type did not significantly affect the annual mean contributions of R _A or R _H, but did affect the pattern of seasonal change in the contribution of R _A to R _S.     

Viral dynamics model with CTL immune response incorporating antiretroviral therapy

We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected $\text{ CD4}^+$ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.     

Production of (R)-mandelic acid by immobilized cells of Saccharomyces cerevisiae on chitosan carrier

The asymmetric microbial reduction of phenylglyoxylic acid (PGA) to (R)-mandelic acid ((R)-MA) with immobilized Saccharomyces cerevisiae cells on globular chitosan was studied. The immobilization conditions and characterization of the immobilized cells were carried out. Chitosan–acetic acid solution was injected into a mixture of 20% NaOH and 30% CH₃OH aqueous solution to obtain globular chitosan, and then the globular chitosan was treated with 1% solution of glutaraldehyde to immobilize yeast cells, which were used to synthesize (R)-MA. The optimum conditions were identified as the substrate concentration of 10 mmol L⁻¹, pH of 6.5 and reaction temperature of 30 °C with the yield of 62% for (R)-MA and the enantiomeric excess (e.e.) of 98% for (R)-MA. The immobilized cells showed good operation and storage stability.     

Influence of stand density on soil CO2 efflux for a Pinus densiflora forest in Korea

We investigated the influence of stand density [938 tree ha⁻¹ for high stand density (HD), 600 tree ha⁻¹ for medium stand density (MD), and 375 tree ha⁻¹ for low stand density (LD)] on soil CO₂ efflux (R _S) in a 70-year-old natural Pinus densiflora S. et Z. forest in central Korea. Concurrent with R _S measurements, we measured litterfall, total belowground carbon allocation (TBCA), leaf area index (LAI), soil temperature (ST), soil water content (SWC), and soil nitrogen (N) concentration over a 2-year period. The R _S (t C ha⁻¹ year⁻¹) and leaf litterfall (t C ha⁻¹ year⁻¹) values varied with stand density: 6.21 and 2.03 for HD, 7.45 and 2.37 for MD, and 6.96 and 2.23 for LD, respectively. In addition, R _S was correlated with ST (R ² = 0.77–0.80, P < 0.001) and SWC (R ² = 0.31–0.35, P < 0.001). It appeared that stand density influenced R _S via changes in leaf litterfall, LAI and SWC. Leaf litterfall (R ² = 0.71), TBCA (R ² = 0.64–0.87), and total soil N contents in 2007 (R ² = 0.94) explained a significant amount of the variance in R _S (P < 0.01). The current study showed that stand density is one of the key factors influencing R _S due to the changing biophysical and environmental factors in P. densiflora.     

A quantitative analysis of ipsilateral tectal unit responses to moving stimuli in frogs

Ipsilateral retino-tecto-tectal (IRTT) units were recorded extracellularly in the rostral optic tectum of the frog (Rana esculenta). The activity of 79 superficial units (II type) was quantified in response to black disks of various sizes, moved vertically at various angular velocities and against a white background. The contrast ¦C¦ was constant during the experiments. Neuronal activity was analysed by two methods, yielding identical results:

Backward bifurcation,equilibrium and stability phenomena in a three-stage extended BRSV epidemic model

In this paper we consider the phenomenon of backward bifurcation in epidemic modelling illustrated by an extended model for Bovine Respiratory Syncytial Virus (BRSV) amongst cattle. In its simplest form, backward bifurcation in epidemic models usually implies the existence of two subcritical endemic equilibria for R ₀ < 1, where R ₀ is the basic reproductive number, and a unique supercritical endemic equilibrium for R ₀ > 1. In our three-stage extended model we find that more complex bifurcation diagrams are possible. The paper starts with a review of some of the previous work on backward bifurcation then describes our three-stage model. We give equilibrium and stability results, and also provide some biological motivation for the model being studied. It is shown that backward bifurcation can occur in the three-stage model for small b, where b is the common per capita birth and death rate. We are able to classify the possible bifurcation diagrams. Some realistic numerical examples are discussed at the end of the paper, both for b small and for larger values of b.      

Highly enantioselective reduction of 4-(trimethylsilyl)-3-butyn-2-one to enantiopure (R)-4-(trimethylsilyl)-3-butyn-2-ol using a novel strain Acetobacter sp. CCTCC M209061

The biocatalytic reduction of 4-(trimethylsilyl)-3-butyn-2-one to enantiopure (R)-4-(trimethylsilyl)-3-butyn-2-ol was successfully conducted with high enantioselectivity using immobilized whole cells of a novel strain Acetobacter sp. CCTCC M209061, newly isolated from kefir. Compared with other microorganisms that were investigated, Acetobacter sp. CCTCC M209061 was shown to be more effective for the bioreduction reaction, and afforded much higher yield and product enantiomeric excess (e.e.). The optimal buffer pH, co-substrate concentration, reaction temperature, substrate concentration and shaking rate were 5.0, 130.6 mM, 30 °C, 6.0 mM and 180 r/min, respectively. Under the optimized conditions, the maximum yield and the product e.e. were 71% and >99%, respectively, which are much higher than those reported previously. Additionally, the established biocatalytic system proved to be efficient for the bioreduction of acetyltrimethylsilane to (R)-1-trimethylsilylethanol with excellent yield and product e.e. The immobilized cells manifested a good operational stability under the above reaction conditions since they retained 70% of their catalytic activity after ten cycles of use.     

Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation

We generalize the Dogterom–Leibler model for microtubule dynamics (Dogterom and Leibler in Phys Rev Lett 70(9):1347–1350, 1993) to the case where the rates of elongation as well as the lifetimes of the elongating shortening phases are a function of GTP-tubulin concentration. We analyze also the effect of nucleation rate in the form of a damping term which leads to new steady-states. For this model, we study existence and stability of steady states satisfying the boundary conditions at x = 0. Our stability analysis introduces numerical and analytical Evans function computations as a new mathematical tool in the study of microtubule dynamics.