Mapping of redox state of mitochondrial cytochromes in live cardiomyocytes using Raman microspectroscopy

This paper presents a nonivasive approach to study redox state of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text] of complexes II and III in mitochondria of live cardiomyocytes by means of Raman microspectroscopy. For the first time with the proposed approach we perform studies of rod- and round-shaped cardiomyocytes, representing different morphological and functional states. Raman mapping and cluster analysis reveal that these cardiomyocytes differ in the amounts of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text]. The rod-shaped cardiomyocytes possess uneven distribution of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text] in cell center and periphery. Moreover, by means of Raman spectroscopy we demonstrated the decrease in the relative amounts of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text] in the rod-shaped cardiomyocytes caused by H(2)O(2)-induced oxidative stress before any visible changes. Results of Raman mapping and time-dependent study of reduced cytochromes of complexes II and III and cytochrome [Formula: see text] in cardiomyocytes are in a good agreement with our fluorescence indicator studies and other published data.     

Unifying Time to Contact Estimation and Collision Avoidance across Species

The [Formula: see text]-function and the [Formula: see text]-function are phenomenological models that are widely used in the context of timing interceptive actions and collision avoidance, respectively. Both models were previously considered to be unrelated to each other: [Formula: see text] is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, [Formula: see text] has a maximum before ttc. Furthermore, it is not clear how both functions could be implemented at the neuronal level in a biophysically plausible fashion. Here we propose a new framework - the corrected modified Tau function - capable of predicting both [Formula: see text]-type ("[Formula: see text]") and [Formula: see text]-type ("[Formula: see text]") responses. The outstanding property of our new framework is its resilience to noise. We show that [Formula: see text] can be derived from a firing rate equation, and, as [Formula: see text], serves to describe the response curves of collision sensitive neurons. Furthermore, we show that [Formula: see text] predicts the psychophysical performance of subjects determining ttc. Our new framework is thus validated successfully against published and novel experimental data. Within the framework, links between [Formula: see text]-type and [Formula: see text]-type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain.     

A Mathematical Model of Rift Valley Fever with Human Host

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold [Formula: see text] is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission [Formula: see text] and the endemic equilibrium are determined. Both [Formula: see text] and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d(m). The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, [Formula: see text] and [Formula: see text], respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level.     

Robustness and information propagation in attractors of random boolean networks

Attractors represent the long-term behaviors of Random Boolean Networks. We study how the amount of information propagated between the nodes when on an attractor, as quantified by the average pairwise mutual information ([Formula: see text]), relates to the robustness of the attractor to perturbations ([Formula: see text]). We find that the dynamical regime of the network affects the relationship between [Formula: see text] and [Formula: see text]. In the ordered and chaotic regimes, [Formula: see text] is anti-correlated with [Formula: see text], implying that attractors that are highly robust to perturbations have necessarily limited information propagation. Between order and chaos (for so-called "critical" networks) these quantities are uncorrelated. Finite size effects cause this behavior to be visible for a range of networks, from having a sensitivity of 1 to the point where [Formula: see text] is maximized. In this region, the two quantities are weakly correlated and attractors can be almost arbitrarily robust to perturbations without restricting the propagation of information in the network.     

Application of DFT methods to the study of the coordination environment of the VO2+ ion in V?proteins

Density functional theory (DFT) methods were used to simulate the environment of vanadium in several V proteins, such as vanadyl-substituted carboxypeptidase (sites A and B), vanadyl-substituted chloroplast F(1)-ATPase (CF(1); site 3), the reduced inactive form of vanadium bromoperoxidase (VBrPO; low- and high-pH sites), and vanadyl-substituted imidazole glycerol phosphate dehydratase (IGPD; sites α, β, and γ). Structural, electron paramagnetic resonance, and electron spin echo envelope modulation parameters were calculated and compared with the experimental values. All the simulations were performed in water within the framework of the polarizable continuum model. The angular dependence of [Formula: see text] and [Formula: see text] on the dihedral angle θ between the V=O and N-C bonds and on the angle φ between the V=O and V-N bonds, where N is the coordinated aromatic nitrogen atom, was also found. From the results it emerges that it is possible to model the active site of a vanadium protein through DFT methods and determine its structure through the comparison between the calculated and experimental spectroscopic parameters. The calculations confirm that the donor sets of sites B and A of vanadyl-substituted carboxypeptidase are [[Formula: see text], H(2)O, H(2)O, H(2)O] and [N(His)(||), N(His)(⊥), [Formula: see text], H(2)O], and that the donor set of site 3 of CF(1)-ATPase is [[Formula: see text], OH(Thr), H(2)O, H(2)O, [Formula: see text]]. For VBrPO, the coordination modes [N(His)(||), N(His)(∠), OH(Ser), H(2)O, H(2)O(ax)] for the low-pH site and [N(His)(||), N(His)(∠), OH(Ser), OH(-), H(2)O(ax)] or [N(His)(||), N(His)(∠), [Formula: see text], H(2)O] for the high-pH site, with an imidazole ring of histidine strongly displaced from the equatorial plane, can be proposed. Finally, for sites α, β, and γ of IGPD, the subsequent deprotonation of one, two, and three imidazole rings of histidine and the participation of a carboxylate group of a glutamate residue ([N(His)(||), [Formula: see text], H(2)O, H(2)O], [N(His)(||), N(His)(||), [Formula: see text], H(2)O], and [N(His)(||), N(His)(||), [Formula: see text], OH(-), [Formula: see text]], respectively) seems to be the most plausible hypothesis.     

Fracture Faces in the Cell Envelope of Escherichia coli

Freeze-fracturing of Escherichia coli cells in the presence of 30% (v/v) glycerol resulted in a double cleavage of the cell envelope exposing two convex and two concave fracture faces ([Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text]) with characteristic patterns. Complementary replicas revealed the relationship of the fracture faces to their corresponding fracture planes. The inner fracture plane splits the plasma membrane at one particular level. Apparently the outer fracture plane was located in the outer part of the wall, as it was separated by a layer ([Formula: see text]) from the fractured profile (CW1) presumably corresponding to the murein layer. The outer fracture plane did alternate toward the cell periphery, exposing complementary smooth areas ([Formula: see text] and [Formula: see text]). When cells were freeze-fractured in the absence of glycerol, the outer cell surface appeared as an etching face rather than a fracture face. A schematic representation of the relative location of the different fracture faces in the E. coli cell envelope is given.     

Critical motor number for fractional steps of cytoskeletal filaments in gliding assays

In gliding assays, filaments are pulled by molecular motors that are immobilized on a solid surface. By varying the motor density on the surface, one can control the number [Formula: see text] of motors that pull simultaneously on a single filament. Here, such gliding assays are studied theoretically using Brownian (or Langevin) dynamics simulations and taking the local force balance between motors and filaments as well as the force-dependent velocity of the motors into account. We focus on the filament stepping dynamics and investigate how single motor properties such as stalk elasticity and step size determine the presence or absence of fractional steps of the filaments. We show that each gliding assay can be characterized by a critical motor number, [Formula: see text]. Because of thermal fluctuations, fractional filament steps are only detectable as long as [Formula: see text]. The corresponding fractional filament step size is [Formula: see text] where [Formula: see text] is the step size of a single motor. We first apply our computational approach to microtubules pulled by kinesin-1 motors. For elastic motor stalks that behave as linear springs with a zero rest length, the critical motor number is found to be [Formula: see text], and the corresponding distributions of the filament step sizes are in good agreement with the available experimental data. In general, the critical motor number [Formula: see text] depends on the elastic stalk properties and is reduced to [Formula: see text] for linear springs with a nonzero rest length. Furthermore, [Formula: see text] is shown to depend quadratically on the motor step size [Formula: see text]. Therefore, gliding assays consisting of actin filaments and myosin-V are predicted to exhibit fractional filament steps up to motor number [Formula: see text]. Finally, we show that fractional filament steps are also detectable for a fixed average motor number [Formula: see text] as determined by the surface density (or coverage) of the motors on the substrate surface.     

Copper(I)-alkyl sulfide and -cysteine tri-nuclear clusters as models for metallo proteins: a structural density functional analysis

After having set up the computational methodology for Cu(I)-sulfur systems as models for copper proteins, namely using the simple ligands H(2)S, HS(-), CH(3)SH, and CH(3)S(-), the Cu(I)-Cysteine systems have been investigated: [Cu(I)( S -H(2)Cys) (n) ](+) (H(2)Cys, cysteine, NH(2),SH,COOH) [Cu(I)( S -HCys) (n) ](1-) (n) (NH(2),S(-),COOH). Finally, the structures for bi-nuclear [Formula: see text] (Et, CH(2)CH(3)), [Formula: see text] and tri-nuclear [Cu(I)( S -SH)](3), [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] (NH(2),SH,COOH), [Formula: see text] (NH(2),S(-),COOH, and NH(2),SH,COO(-)), as well as [Formula: see text] (NH(2),S(-),COO(-)), were also optimized to mimic the active center for a metallo-chaperone copper transport protein (CopZ). The X-ray structures for the biomolecules were matched fairly well as regards the Cu-S bond distances and Cu…Cu contact distances in the case the model cysteine S atom is deprotonated. Upon protonation of ligand S atoms, the conformation of clusters is altered and might bring about the di- and tri-nuclear core breakage. These findings suggest that subtle protonation/deprotonation steps, i.e. small and/or local pH changes play a significant role for copper transport processes.     

Complete determination of the Pin1 catalytic domain thermodynamic cycle by NMR lineshape analysis

The phosphorylation-specific peptidyl-prolyl isomerase Pin1 catalyzes the isomerization of the peptide bond preceding a proline residue between cis and trans isomers. To best understand the mechanisms of Pin1 regulation, rigorous enzymatic assays of isomerization are required. However, most measures of isomerase activity require significant constraints on substrate sequence and only yield rate constants for the cis isomer, [Formula: see text] and apparent Michaelis constants, [Formula: see text]. By contrast, NMR lineshape analysis is a powerful tool for determining microscopic rates and populations of each state in a complex binding scheme. The isolated catalytic domain of Pin1 was employed as a first step towards elucidating the reaction scheme of the full-length enzyme. A 24-residue phosphopeptide derived from the amyloid precurser protein intracellular domain (AICD) phosphorylated at Thr668 served as a biologically-relevant Pin1 substrate. Specific (13)C labeling at the Pin1-targeted proline residue provided multiple reporters sensitive to individual isomer binding and on-enzyme catalysis. We have performed titration experiments and employed lineshape analysis of phosphopeptide (13)C-(1)H constant time HSQC spectra to determine [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for the catalytic domain of Pin1 acting on this AICD substrate. The on-enzyme equilibrium value of [E·trans]/[E·cis]?=?3.9 suggests that the catalytic domain of Pin1 is optimized to operate on this substrate near equilibrium in the cellular context. This highlights the power of lineshape analysis for determining the microscopic parameters of enzyme catalysis, and demonstrates the feasibility of future studies of Pin1-PPIase mutants to gain insights on the catalytic mechanism of this important enzyme.     

(13)C NMR Reveals No Evidence of n-π* Interactions in Proteins

An [Formula: see text] interaction between neighboring carbonyl groups has been postulated to stabilize protein structures. Such an interaction would affect the [Formula: see text]C chemical shielding of the carbonyl groups, whose paramagnetic component is dominated by [Formula: see text] and [Formula: see text] excitations. Model compound calculations indicate that both the interaction energetics and the chemical shielding of the carbonyl group are instead dominated by a classical dipole-dipole interaction. A set of high-resolution protein structures with associated carbonyl [Formula: see text]C chemical shift assignments verifies this correlation and provides no evidence for an inter-carbonyl [Formula: see text] interaction.     

Specificity of Hpa II and Hae III DNA methylases

The methylases M.HaeIII and M.HpaII recognize the tetranucleotide sequences [Formula: see text] and [Formula: see text] respectively, in DNA, and transfer a methyl group from S-adenosylmethionine to the 5-position of cytosine on each strand as indicated by the asterisks. Restriction endonuclease R.HaeIII does not cleave the methylated sequence [Formula: see text] but can cleave [Formula: see text] in which methylation is introduced on the unnatural external cytosine positions. Similarly, R.HpaII does not cleave [Formula: see text] but can cleave [Formula: see text].Images     

The IspA protease's involvement in the regulation of the sporulation process of Bacillus thuringiensis is revealed by proteomic analysis

We have observed that the process of sporulation of the ispA-deficient mutant was delayed under phase-contrast microscopy. The protein profiles of the ispA-deficient mutant have been analyzed using two-dimensional gel electrophoresis. The results of a proteomic analysis using MALDI-TOF MS indicated that a sporulation-associated protein, pro- [Formula: see text], was upregulated, while two other sporulation-associated proteins, SpoVD and SpoVR, were downregulated in the ispA-deficient mutant. It has been known that pro- [Formula: see text] is a precursor of [Formula: see text] and is required for gene expression related to the late stage of sporulation. Moreover, SpoVD and SpoVR are known to be involved in the formation of the spore cortex. Based on these observations, we propose that the delay in the sporulation process observed in the ispA-deficient mutant may be due to a failure of [Formula: see text] to signal sporulation. This phenomenon may be further enhanced by insufficient amount of SpoVD and SpoVR for cortex formation. In this study, we have revealed for the first time a possible pathway for the regulation of sporulation-associated proteins via IspA.     

Species-specific allometric scaling under self-thinning: evidence from long-term plots in forest stands

Experimental plots covering a 120 years' observation period in unthinned, even-aged pure stands of common beech (Fagus sylvatica), Norway spruce (Picea abies), Scots pine (Pinus sylvestris), and common oak (Quercus Petraea) are used to scrutinize Reineke's (1933) empirically derived stand density rule [see text], N=tree number per unit area, [see text]=mean stem diameter), Yoda's (1963) self-thinning law based on Euclidian geometry ([see text] [see text]=mean biomass per tree), and basic assumptions of West, Brown and Enquist's (1997, 1999) fractal scaling rules ([see text] [see text] w=biomass per tree, d=stem diameter). RMA and OLS regression provides observed allometric exponents, which are tested against the exponents, expected by the considered rules. Hope for a consistent scaling law fades away, as observed exponents significantly correspond with the considered rules only in a minority of cases: (1) exponent r of [see text] varies around Reineke's constant -1.605, but is significantly different from r=-2, supposed by Euclidian or fractal scaling, (2) Exponent c of the self-thinning line [see text] roams roughly about the Euclidian scaling constant -3/2, (3) Exponent a of [see text] tends to follow fractal scaling 8/3. The unique dataset's evaluation displays that (4) scaling exponents and their oscillation are species-specific, (5) Euclidian scaling of one relation and fractal scaling of another are coupled, depending on species. Ecological implications of the results in respect to self-tolerance (common oak>Norway spruce>Scots pine>common beech) and efficiency of space occupation (common beech>Scots pine>Norway spruce>common oak) are stressed and severe consequences for assessing, regulating and scheduling stand density are discussed.     

Uptake of Different Species of Iodine by Water Spinach and Its Effect to Growth

A hydroponic experiment has been carried out to study the influence of iodine species [iodide (I(-)), iodate ([Formula: see text]), and iodoacetic acid (CH(2)ICOO(-))] and concentrations on iodine uptake by water spinach. Results show that low levels of iodine in the nutrient solution can effectively stimulate the growth of biomass of water spinach. When iodine levels in the nutrient solution are from 0 to 1.0 mg/l, increases in iodine levels can linearly augment iodine uptake rate by the leafy vegetables from all three species of iodine, and the uptake effects are in the following order: [Formula: see text]. In addition, linear correlation was observed between iodine content in the roots and shoots of water spinach, and their proportion is 1:1. By uptake of I(-), vitamin C (Vit C) content in water spinach increased, whereas uptake of [Formula: see text] and CH(2)ICOO(-) decreased water spinach Vit C content. Furthermore, through uptake of I(-) and [Formula: see text], the nitrate content in water spinach was increased by different degrees.     

Exploiting magnetic resonance angiography imaging improves model estimation of BOLD signal

The change of BOLD signal relies heavily upon the resting blood volume fraction ([Formula: see text]) associated with regional vasculature. However, existing hemodynamic data assimilation studies pretermit such concern. They simply assign the value in a physiologically plausible range to get over ill-conditioning of the assimilation problem and fail to explore actual [Formula: see text]. Such performance might lead to unreliable model estimation. In this work, we present the first exploration of the influence of [Formula: see text] on fMRI data assimilation, where actual [Formula: see text] within a given cortical area was calibrated by an MR angiography experiment and then was augmented into the assimilation scheme. We have investigated the impact of [Formula: see text] on single-region data assimilation and multi-region data assimilation (dynamic cause modeling, DCM) in a classical flashing checkerboard experiment. Results show that the employment of an assumed [Formula: see text] in fMRI data assimilation is only suitable for fMRI signal reconstruction and activation detection grounded on this signal, and not suitable for estimation of unobserved states and effective connectivity study. We thereby argue that introducing physically realistic [Formula: see text] in the assimilation process may provide more reliable estimation of physiological information, which contributes to a better understanding of the underlying hemodynamic processes. Such an effort is valuable and should be well appreciated.     

Architecture of the Outer Membrane of Escherichia coli III. Protein-Lipopolysaccharide Complexes in Intramembraneous Particles

In a previous paper (A. Verkleij, L. van Alphen, J. Bijvelt, and B. Lugtenberg, Biochim. Biophys. Acta 466:269-282, 1977) we have hypothesized that particles on the outer fracture face of the outer membrane ([Formula: see text]), with corresponding pits on the inner fracture face of the outer membrane ([Formula: see text]), consist of lipopolysaccharide (LPS) aggregates stabilized by divalent cations and that they might contain protein and/or phospholipid. In the present paper the roles of LPS, cations, and proteins in these [Formula: see text] particles are described more extensively, using a strain that lacks the major outer membrane proteins, b, c, and d (b(-) c(-) d(-)), and has a reduction in the number of [Formula: see text] particles of 75%. To study the role of divalent cations in the formation of [Formula: see text] particles, these b(-) c(-) d(-) cells were grown or incubated with Ca(2+), Mg(2+), or putrescine. The presence of Ca(2+) resulted in the appearance of many [Formula: see text] particles and [Formula: see text] pits. Mg(2+) and putrescine were less effective than Ca(2+). Introduction of these particles was not accompanied by alterations in the relative amounts of LPS and cell envelope proteins. Ca(2+) treatment of a heptoseless derivative of a b(-) c(-) d(-) strain did not result in morphological changes. Incubation of Ca(2+)-treated cells with ethylenediaminetetraacetate caused the disappearance of the introduced particles as well as the release of more than 60% of the cellular LPS. These results strongly support the hypothesis that LPS is involved in the formation of [Formula: see text] particles and [Formula: see text] pits. The roles of various outer membrane proteins in the formation of [Formula: see text] particles were studied by comparing the freeze-fracture morphology of b(-) c(-) d(-) cells with that of cells which contain one of the outer membrane proteins b, c, d, and e or the receptor protein for bacteriophage lambda. The results showed that the presence of any of these five proteins in a b(-) c(-) d(-) background resulted in a large increase in the number of [Formula: see text] particles and [Formula: see text] pits, indicating that these proteins are, independent of each other, involved in the formation of [Formula: see text] particles and [Formula: see text] pits. The simplest explanation for the results is that in wild-type cells each particle consists of LPS complexed with some molecules of a single protein species, stabilized by either divalent cations or polyamines. It is hypothesized that the outer membrane of the wild-type cell contains a heterogeneous population of particles, of which 75% consists of protein b-LPS, protein c-LPS, and protein d-LPS particles. A function of these particles as aqueous pores is proposed.     

Hydroxylation of p-substituted phenols by tyrosinase: further insight into the mechanism of tyrosinase activity

A study of the monophenolase activity of tyrosinase by measuring the steady state rate with a group of p-substituted monophenols provides the following kinetic information: k(cat)(m) and the Michaelis constant, K(M)(m). Analysis of these data taking into account chemical shifts of the carbon atom supporting the hydroxyl group (δ) and σ(p)(+), enables a mechanism to be proposed for the transformation of monophenols into o-diphenols, in which the first step is a nucleophilic attack on the copper atom on the form E(ox) (attack of the oxygen of the hydroxyl group of C-1 on the copper atom) followed by an electrophilic attack (attack of the hydroperoxide group on the ortho position with respect to the hydroxyl group of the benzene ring, electrophilic aromatic substitution with a reaction constant ρ of -1.75). These steps show the same dependency on the electronic effect of the substituent groups in C-4. Furthermore, a study of a solvent deuterium isotope effect on the oxidation of monophenols by tyrosinase points to an appreciable isotopic effect. In a proton inventory study with a series of p-substituted phenols, the representation of [Formula: see text] / [Formula: see text] against n (atom fractions of deuterium), where [Formula: see text] is the catalytic constant for a molar fraction of deuterium (n) and [Formula: see text] is the corresponding kinetic parameter in a water solution, was linear for all substrates. These results indicate that only one of the proton transfer processes from the hydroxyl groups involved the catalytic cycle is responsible for the isotope effects. We suggest that this step is the proton transfer from the hydroxyl group of C-1 to the peroxide of the oxytyrosinase form (E(ox)). After the nucleophilic attack, the incorporation of the oxygen in the benzene ring occurs by means of an electrophilic aromatic substitution mechanism in which there is no isotopic effect.     

The biosynthesis of 4-hydroxycoumarin and dicoumarol by Aspergillus fumigatus Fresenius

A strain of Aspergillus fumigatus Fresenius, isolated from spoiled hay, converts melilotic acid (o-hydroxyphenylpropionic acid) and o-coumaric acid into 4-hydroxycoumarin and dicoumarol. The sequence is shown to be melilotic acid (I) [Formula: see text] coumaric acid (IV) [Formula: see text] beta-hydroxymelilotic acid (II) [Formula: see text] beta-oxomelilotic acid (III) [Formula: see text] 4-hydroxycoumarin (VI), on the basis of (1) studies on the formation of postulated intermediates, (2) experiments with isotopically labelled materials and (3) sequential enzyme induction. In the presence of semicarbazide, o-coumaraldehyde is formed from o-coumaric acid: there is no evidence, however, that this lies on the normal metabolic pathway.     

Cholera Models with Hyperinfectivity and Temporary Immunity

A mathematical model for cholera is formulated that incorporates hyperinfectivity and temporary immunity using distributed delays. The basic reproduction number [Formula: see text] is defined and proved to give a sharp threshold that determines whether or not the disease dies out. The case of constant temporary immunity is further considered with two different infectivity kernels. Numerical simulations are carried out to show that when [Formula: see text], the unique endemic equilibrium can lose its stability and oscillations occur. Using cholera data from the literature, the quantitative effects of hyperinfectivity and temporary immunity on oscillations are investigated numerically.     

Trans-Theta Logistics: A New Family of Population Growth Sigmoid Functions

Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ([Formula: see text] L). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population (N) is divided into reproducing (P) and non-reproducing/quiescent (Q) sub-populations. The modes of the rate of change of ratio P/N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P/N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic (T [Formula: see text] L) since they exist when the [Formula: see text] L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid (TS). The [Formula: see text] L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T [Formula: see text] L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T [Formula: see text] L versus [Formula: see text] L for model growth curves.