Necessary conditions for the method of inferring phylogeny by linear invariants.

It is known that if all the Markov transition matrices that govern the substitution of one nucleotide for another satisfy six linear constraints, then equations can be derived that permit one to infer evolutionary trees from nucleic acid sequences by the method of linear invariants. These sufficient conditions are also necessary. Any relaxation of them results in the loss of all linear invariants. Necessary conditions for any given set of linear invariants can be derived by examining conditions a matrix must satisfy to map a certain set of matrices into itself. To the extent that necessary conditions are incorrect, a method is not reliable. In a world where different parts of molecules evolve at different rates, the two-parameter model of Kimura may not be empirically distinguishable from the more general one treated here.     

Structure and kinetic behavior of linear multicompartment systems

The general kinetic behavior of a multicompartment system is shown to depend upon certain general structural features, including its connectivity, whether it is open, and whether it contains cyclic pathways. Structural influences are clarified by putting the system matrix in a certain form. For systems not strongly connected, a distinction is drawn between partially and completely open systems. Necessary and sufficient conditions are given for non-singularity of the system matrix and for asymptotic stability of the system. Sufficient conditions are given for non-overshooting and monotonic transitions. A system is demonstrated whose solution may contain a prolonged series of damped oscillations; but the oscillations are very slow and small; and it seems unlikely that oscillations could be detected experimentally in any biological system. This work was supported by U.S. Public Health Service Research Grant NS 08710 from the National Institute of Neurological Diseases and Stroke.     

The community matrix in three species community models

The explicit function of the community matrix of a three dimensional Lotka-Volterra model is delineated by a set of necessary and sufficient conditions for a positive equilibrium to be asymptotically stable. In the special case that the community matrix is quasi weakly diagonally dominant, it is shown that a positive determinant for the community matrix is not only necessary but is also sufficient for stability. The results are specific to three dimensional models and do not extend to communities of dimension greater than three.     

Ambipolarity condition and possibility of multivalued steady-state solutions to transport equations in stellarators

The possibility of steady-state multivalued solutions to transport equations in stellarators is considered. It is shown that the ambipolarity condition is necessary but not sufficient to find the ambipolar electric field, because the functions entering into it (the plasma density and temperature, as well as their spatial derivatives) depend on the ambipolar field. To do this correctly, it is necessary to solve the full set of time-independent transport equations (including diffusion and heat conduction equations). The possible existence of multivalued solutions to this set of equations is analyzed numerically. It is shown that, under certain conditions that depend on the form and magnitude of particle and heat sources, such solutions can exist. Their form is determined by the initial value of the ambipolar field, the source magnitudes, and the boundary conditions. Discontinuous solutions in which the radial profile of the ambipolar field undergoes jumps are found. In this case, however, the particle and energy fluxes remain continuous, because the discontinuities of the electric field are balanced by the discontinuities of the density and temperature gradients.     

Ab initio prediction of thermodynamically feasible reaction directions from biochemical network stoichiometry

Analysis of the stoichiometric structure of metabolic networks provides insights into the relationships between structure, function, and regulation of metabolic systems. Based on knowledge of only reaction stoichiometry, certain aspects of network functionality and robustness can be predicted. Current theories focus on breaking a metabolic network down into non-decomposable pathways able to operate in steady state. The physics underlying these theories is based on mass balance and the laws of thermodynamics. However, due to the inherent nonlinearity of the thermodynamic constraints on metabolic fluxes, computational analysis of large-scale biochemical systems can be expensive. In this study, it is shown how the feasible reaction directions may be determined by either computing the allowable ranges under the mass-balance and thermodynamic constraints or by analyzing the stoichiometric structure of the network. The computed reaction directions translate into a set of linear constraints necessary for thermodynamic feasibility. This set of necessary linear constraints is shown to be sufficient to guarantee feasibility in certain cases, thus translating the nonlinear thermodynamic constraints to linear. We show that for a reaction network of 44 internal reactions representing energy metabolism, the computed linear inequality constraints represent necessary and sufficient conditions for thermodynamic feasibility.     

Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size

We study an SIR epidemic model with a variable host population size. We prove that if the model parameters satisfy certain inequalities then competition between n pathogens for a single host leads to exclusion of all pathogens except the one with the largest basic reproduction number. It is shown that a knowledge of the basic reproduction numbers is necessary but not sufficient for determining competitive exclusion. Numerical results illustrate that these inequalities are sufficient but not necessary for competitive exclusion to occur. In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur.     

An integrating sphere leaf chamber

Abstract. A combination of an optical integrating sphere and leaf chamber is described, and some principles of its design are given. It is shown that the number of quanta absorbed by the leaf inside the sphere can be found from measurements of the quantum flux density inside the sphere with and without the leaf present, when certain constant parameters of the sphere are known. Methods for finding these are given. It is not necessary to know leaf area or absorptivity for the quantum yield for photosynthesis to be derived from additional measurement of CO₂, fixation.     

Qualitative analysis of an HIV transmission model.

In 1988, a multiple-group model for HIV transmission with preferred mixing was proposed by Jacquez and coworkers. In the present paper, the work done by Jacquez et al. is extended. It is shown that the stability modulus of the Jacobian matrix at the no-disease equilibrium is a threshold for this model. Furthermore, if the no-disease equilibrium is unstable, the number of infected individuals will remain above a certain positive level regardless of initial levels; that is, the disease will persist uniformly. The stability of the endemic equilibrium in the case of restricted mixing is also studied. A series of sufficient conditions for local and global asymptotic stability of the endemic equilibrium are stated.     

Reconstitution of the transition matrix from experimental data

The identification of a linear compartment model, which may describe a chemical or biological process, is a difficult task, since the available data is generally limited. In this paper we propose a method for determining the state transition matrix by minimizing a given quadratic criterion. To solve the resulting matrix equation, an assumption has to be made which constitutes a necessary condition for the identifiability of the model. Moreover when this assumption is satisfied, it is shown that the knowledge of one line or one column of the transition matrix is sufficient to define it completely.     

Power series expansion and structural analysis for life cycle assessment

Goal, Scope and Background The usefulness of power series expansion for an LCA system has often been doubted, as those systems may not possess the unique properties that enable power series expansion and analyses based on the power series. This paper surveys the existing literature on power series expansion of monetary input-output system and discusses how the power series expansion can be utilized for more general systems including the LCA model. Methods The inherent properties of matrices that are capable of producing power series forms for their inverse and, further, can utilize structural path analysis are analyzed. Using these analyses, the way how a matrix that is not eligible for structural analyses is converted into an eligible form is investigated. A numerical example is presented to demonstrate the findings. Results The necessary and sufficient condition for an indecomposable, real square technology matrix can be expressed using power series was identified. Two additional conditions for a technology matrix to be utilized for structural analyses using power series expansion are discussed as well. It was also shown that an LCA system that fulfills the Hawkins-Simon condition can be easily converted into the form that is eligible for structural analysis by rescaling the columns and rows. Discussion As a numerical example, an application of accumulative structural path analysis for an LCA system is shown. The implications of the results are discussed in a more plain language as well. Conclusions The survey presented in this paper provides not only the conditions under which a linear system is expressed using a power series form but also the way to appropriately convert a system to utilize the rich analytical tools using power series expansion for structural analyses. Recommendations and Perspectives Widely used LCA databases and software tools have employed the linear systems approach as the basis. Much of these developments in the domain of LCA have been made, however, in isolation of the rich findings of IOA. There will be much to benefit LCA through an active dialogue between the two disciplines. There are rich analytical tools available through the use of power series expansion. The current survey will help software developers and LCA practitioners to apply such tools in LCA.     

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a ‘wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This ‘wave-like’ profile contradicts experimental observations. In our study we investigate the conditions, under which such profile appears in the solution. Those conditions are determined in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system. The stability analysis was carried out for the reduced system of PDE’s, of which we prove, that it is equivalent to the original system of equations, with respect to the stability properties of constant solutions. The conclusions, derived from the linear stability analysis, are extended for the case of large perturbations. If the constant solution is unstable, then the solution of the system never converges to this constant solution. The analytical results are validated with finite element simulations. The simulations show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.     

Optimum design of a series of CSTRs performing reversible Michaelis-Menten kinetics: a rigorous mathematical study

The optimum design of a given number of CSTRs in series performing reversible Michaelis-Menten kinetics in the liquid phase assuming constant activity of the enzyme is studied. In this study, the presence of product in the feed stream to the first reactor, as well as the effect of the product intermediate concentrations in the downstream reactors on the reaction rate are investigated. For a given number of N CSTRs required to perform a certain degree of substrate conversion and under steady state operation and constant volumetric flow rate, the reactor optimization problem is posed as a constrained nonlinear programming problem (NLP). The reactor optimization is based on the minimum overall residence time (volume) of N reactors in series. When all the reactors in series operate isothermally, the constrained NLP is solved as an unconstrained NLP. And an analytical expression for the optimum overall residence time is obtained. Also, the necessary and sufficient conditions for the minimum overall residence time of N CSTRs are derived analytically. In the presence of product in the feed stream, the reversible Michaelis-Menten kinetics shows competitive product inhibition. And this is, because of the increase in the apparent rate constant K^' _m that results in a reduction of the overall reaction rate. The optimum total residence time is found to increase as the ratio (‚₀) of product to substrate concentrations in the feed stream increases. The isomerization of glucose to fructose, which follows a reversible Michaelis-Menten kinetics, is chosen as a model for the numerical examples.     

On the visibility of leading eigenvalues in compartmental models

The system matrix eigenvalue with the largest real part (leading eigenvalue) of any input-output (IO) connectable compartmental model is real and visible (appears explicitly) in the impulse response, and thus it governs the asymptotic response of the model. Its visible multiplicity is calculated here by decomposing the model into strongly connected components and applying the Perron-Frobenius theorem. Cascade models and fully visible eigenvalues are defined, and it is shown that for any cascade model the leading eigenvalue is fully visible in the impulse response. A necessary and sufficient condition is given for full visibility of the leading eigenvalue of any IO-connectable model. As a corollary, if an IO-connectable compartmental model has one or more traps, the leading eigenvalue λ₁ = 0 always has visible multiplicity one.     

Modelling HIV/AIDS in the presence of an HIV testing and screening campaign

Preventing and managing the HIV/AIDS epidemic in South Africa will dominate the next decade and beyond. Reduction of new HIV infections by implementing a comprehensive national HIV prevention programme at a sufficient scale to have real impact remains a priority. In this paper, a deterministic HIV/AIDS model that incorporates condom use, screening through HIV counseling and testing (HCT), regular testing and treatment as control strategies is proposed with the objective of quantifying the effectiveness of HCT in preventing new infections and predicting the long-term dynamics of the epidemic. It is found that a backward bifurcation occurs if the rate of screening is below a certain threshold, suggesting that the classical requirement for the basic reproduction number to be below unity though necessary, is not sufficient for disease control in this case. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number R₀. Numerical simulations are performed and the model is fitted to data on HIV prevalence in South Africa. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long-term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed.     

Minority rule supertrees? MRP,Compatibility, and Minimum Flip may display the least frequent groups

New examples are presented, showing that supertree methods such as matrix representation with parsimony, minimum flip trees, and compatibility analysis of the matrix representing the input trees, produce supertrees that cannot be interpreted as displaying the groups present in the majority of the input trees. These methods may produce a supertree displaying some groups present in the minority of the trees, and contradicted by the majority. Of the three methods, compatibility analysis is the least used, but it seems to be the one that differs the least from majority rule consensus. The three methods are similar in that they choose the supertree(s) that best fit the set of input trees (quantified as some measure of the fit to the matrix representation of the input trees); in the case of complete trees, it is argued that, for a supertree method to be equivalent to majority rule or frequency difference consensus, two necessary (but not sufficient) conditions must be met. First, the measure of fit between a supertree and an input tree must be symmetrical. Second, the fit for a character representing a group must be measured as absolute: either it fits or it does not fit. In the restricted case of complete and equally resolved input trees, compatibility analysis (unlike MRP and minimum flipping) fulfils these two conditions: it is symmetrical (i.e., as long as the trees have the same taxon sets and are equally resolved, the number of characters in the matrix representation of tree A that require homoplasy in tree B is always the same as the number of characters in the matrix representation of tree B that require homoplasy in tree A) and it measures fit as all‐or‐none. In the case of just two complete and equally resolved input trees, the two conditions (symmetry and absolute fit) are necessary and sufficient, which explains why the compatibility analysis of such trees behaves as majority consensus. With more than two such trees, these conditions are still necessary but no longer sufficient for the equivalence; in such cases, the compatibility supertree may differ significantly from the majority rule consensus, even when these conditions apply (as shown by example). MRP and minimum flipping are asymmetric and measure various degrees of fit for each character, which explains why they often behave very differently from majority rule procedures, and why they are very likely to have groups contradicted by each of the input trees, or groups supported by a minority of the input trees. © The Willi Hennig Society 2005.     

The reaction mechanism of bovine kidney biliverdin reductase

The steady-state kinetics of biliverdin reductase can be studied in detail at pH 9 as under these conditions the Km for biliverdin is high enough to obtain reliable measurements of the initial rate in the absence of any biliverdin binding proteins. The initial rate kinetics and the product-inhibition studies are consistent with an ordered sequential mechanism provided the biliverdin concentration was below 20 microM. Above this concentration significant flux occurs through a substrate inhibition pathway involving an enzyme-NAD(P)-biliverdin complex. Chloride is shown to cause a significant activation of the enzyme under certain conditions and this is shown to result from an inability of biliverdin to bind to an enzyme-NAD-chloride complex.     

Mouse germ cell mutation tests in genetic risk evaluation of chemical mutagens

That certain environmental chemicals can induce transmissible mutations in germ cells of experimental mammal is clear. The assumption that under certain conditions these chemicals are also likely to be mutagenic to human germ cells is not detectable. However, it is a difficult challenge to determine the level of human exposure at which such chemicals can be produced and used economically without significantly harming human health. Data on transmitted genetic effects in mice are necessary, not only as a measure of endpoints that are considered directly in genetic risk assessment, but also as the standard for evaluating the usefulness of non-germ-cell effects as predictors in genetic risk assessment. To carry out a "real world" genetic risk assessment exercise, in vivo mouse data are being obtained for two model chemicals--ethylene oxide and acrylamide. Both chemicals are capable of inducing transmissible genetic effects in mice; their production and use involve measurable human exposures; and, because they are socially and economically important, they are not likely to be banned altogether despite their mutagenicity. For both chemicals, data are not sufficient for accurate low-dose and low-dose-rate extrapolations.     

Matrix metalloproteinase 13 (MMP13) and tissue inhibitor of matrix metalloproteinase 1 (TIMP1), regulated by the MAPK pathway, are both necessary for Madin-Darby canine kidney tubulogenesis

A classic model of tubulogenesis utilizes Madin-Darby canine kidney (MDCK) cells. MDCK cells form monoclonal cysts in three-dimensional collagen and tubulate in response to hepatocyte growth factor, which activates multiple signaling pathways, including the mitogen-activated protein kinase (MAPK) pathway. It was shown previously that MAPK activation is necessary and sufficient to induce the first stage of tubulogenesis, the partial epithelial to mesenchymal transition (p-EMT), whereas matrix metalloproteinases (MMPs) are necessary for the second redifferentiation stage. To identify specific MMP genes, their regulators, tissue inhibitors of matrix metalloproteinases (TIMPs), and the molecular pathways by which they are activated, we used two distinct MAPK inhibitors and a technique we have termed subtraction pathway microarray analysis. Of the 19 MMPs and 3 TIMPs present on the Canine Genome 2.0 Array, MMP13 and TIMP1 were up-regulated 198- and 169-fold, respectively, via the MAPK pathway. This was confirmed by two-dimensional and three-dimensional real time PCR, as well as in MDCK cells inducible for the MAPK gene Raf. Knockdown of MMP13 using short hairpin RNA prevented progression past the initial phase of p-EMT. Knockdown of TIMP1 prevented normal cystogenesis, although the initial phase of p-EMT did occasionally occur. The MMP13 knockdown phenotype is likely because of decreased collagenase activity, whereas the TIMP1 knockdown phenotype appears due to increased apoptosis. These data suggest a model, which may also be important for development of other branched organs, whereby the MAPK pathway controls both MDCK p-EMT and redifferentiation, in part by activating MMP13 and TIMP1.     

ACID PHOSPHATASE LOCALIZATION IN RABBIT EOSINOPHILS

Eosinophil (and heterophil) leukocytes of glycogen-induced rabbit peritoneal exudates were fixed for 1½ min in 2% glutaraldehyde and examined for acid phosphatase activity both biochemically and cytochemically. Biochemical assays showed that enzymatic activity had been inhibited by only ~10% under these conditions. The cytochemical reaction in the eosinophil was confined to the granules in which the reaction product appeared in the matrix, not in the crystalline core (or in the core region after the latter's extraction). Granules wherein the matrix was disrupted and the crystalline core degraded or extracted showed the most intense deposition of reaction product, whereas well preserved granules with morphologically intact matrix and crystals were unreactive. Yet, not all disrupted granules gave a positive reaction, indicating that disruption was a necessary but not sufficient condition for reactivity. In many eosinophil leukocytes, most if not all granules were acid phosphatase-positive, provided they had become disrupted to a certain degree. Factors possibly involved in converting the granules from an unreactive to a reactive state are discussed.     

On the mechanism of topoisomerase I inhibition by camptothecin: evidence for binding to an enzyme-DNA complex

Camptothecin, a cytotoxic antitumor compound, has been shown to produce protein-linked DNA breaks mediated by mammalian topoisomerase I. We have investigated the mechanism by which camptothecin disrupts DNA processing by topoisomerase I and have examined the effect of certain structurally related compounds on the formation of a DNA-topoisomerase I covalent complex. Enzyme-mediated cleavage of supercoiled plasmid DNA in the presence of camptothecin was completely reversed upon the addition of exogenous linear DNA or upon dilution of the reaction mixture. Camptothecin and topoisomerase I produced the same amount of cleavage from supercoiled DNA or relaxed DNA. In addition, the alkaloid decreased the initial velocity of supercoiled DNA relaxation mediated by catalytic quantities of topoisomerase I. Inhibition occurred under conditions favoring processive catalysis as well as under conditions favoring distributive catalysis. By use of [3H]camptothecin and an equilibrium dialysis assay, the alkaloid was shown to bind reversibly to a DNA-topoisomerase I complex, but not to isolated enzyme or isolated DNA. These results are consistent with a model in which camptothecin reversibly traps an intermediate involved in DNA unwinding by topoisomerase I and thereby perturbs a set of equilibria, resulting in increased DNA cleavage. By examining certain compounds that are structurally related to camptothecin, it was found that the 20-hydroxy group, which has been shown to be essential for antitumor activity, was also necessary for stabilization of the covalent complex between DNA and topoisomerase I. In contrast, no such correlation existed for UV-light-induced cleavage of DNA by Cu(II)-camptothecin derivatives.