An examination of the forms of scatchard plots of binding results outside domains of sigmoidality

General expressions are formulated for the first and second derivatives of the Scatchard function, r/[S], with respect to the binding function, r, from an equation that describes the binding of a ligand to a two-state acceptor system (either isomerizing or polymerizing). The expressions are utilized to determine the sign of the second derivative for particular systems under conditions where the first derivative is negative for all r. The work therefore correlates with previous studies, which stressed conditions of existence of critical points in Scatchard plots, by examining more fully possible forms of binding curves outside such domains of sigmoidality. Particular attention is given to the condition, d(r/[S])/dr < 0 and d²(r/[S])/dr² > 0 for all r (which defines a Scatchard plot convex to the r-axis). In agreement with previous findings it is proven that the isomerizing acceptor model cannot give rise to this form of plot and is therefore distinguished from negatively co-operative allosteric models. On the other hand, the polymerizing acceptor model may yield such a Scatchard plot, a feature demonstrated by formulating explicit conditions for its manifestation when ligand binding is exclusive to the polymeric state, and illustrated numerically for a system in which ligand binds to both oligomeric states. Distinction between such systems and those exhibiting negative co-operativity is possible on the basis of the Scatchard plots, which exhibit dependence on acceptor concentration in the case of a polymerizing acceptor; indeed, an example is provided where variation of acceptor concentration for a system characterized by fixed interaction parameters effects a conversion from sigmoidal binding behaviour to that typified by a Scatchard plot convex to the r-axis.     

Quantitative considerations of the consequences of an interplay between ligand binding and reversible adsorption of a macromolecular solute

Explicit expressions are derived which determine the equilibrium composition of mixtures comprising a multivalent, insoluble matrix, a multivalent, macromolecular solute (acceptor) and a univalent ligand. With three-reactant mixtures of this type a range of combinations of interactions is possible wherein the ligand interacts with either the acceptor or the matrix, in either event perturbing the acceptor-matrix equilibria. Theory encompassing this range of possibilities is written in terms of a single site-binding constant for each type of interaction to account, in general terms, for both multiple binding and crosslinking effects. These explicit thermodynamic relationships are discussed, with the use of reported findings on several biological systems, in two frameworks. First, it is established that the theory is applicable to the quantitative interpretation of affinity chromatography experiments designed to elucidate the thermodynamic interaction parameters governing the various types of interacting system. Second, it is emphasized that the relationships are also relevant to metabolite-induced changes in the subcellular distribution of macromolecular species.     

Synthesis and separation of tritium-labeled intermediates of the shikimate pathway

[5-³H]Shikimate (sp radioact 2000 Ci/mol) has been synthesized by reduction of the methyl ester of 5-dehydroshikimate with NaB³H₄ and subsequent hydrolysis of the ester group (M. M. Leduc, P. M. Dansette, and R. G. Azerad (1970) Eur. J. Biochem.15, 428–435). The [5-³H]shikimate has been converted enzymatically to [5-³H]chorismate and [5-³H]prephenate of similar high specific radioactivity by using a cell-free extract of Aerobacter aerogenes 62-1. In addition, a chromatograhic procedure, which utilizes polyethyleneimine-cellulose thin-layer chromatograms, has been developed for the separation of intermediates along the shikimate pathway between shikimate and hydroxyphenylpyruvate or phenylpyruvate. Since the method allows quantitative measurement of tritium-labeled intermediates, it provides the basis for sensitive radioassays of the individual enzymes and allows study of the reaction flux along the overall pathway. The same intermediates can be separated on a large scale by use of a column of DEAE-Sephacel.     

Stability constants of metal complexes of phosphonoacetic acid

The antiviral drug, phosphonoacetic acid (PAA), forms stable complexes with Mg²⁺, Ca²⁺, Cu²⁺ and Zn²⁺. Stability constants of these complexes were determined in aqueous solution (0.15 M in KNO₃, 37°) by potentiometric titration. Mixed ligand complex formation of Cu²⁺ and Zn²⁺ with PAA and glycinate ion, and with PAA and histidinate ion, was studied. In a theoretical model for blood plasma, PAA affects the distribution of Mg²⁺ and, to a lesser extent, Ca²⁺.     

Thermodynamic compensation process in interacting protein systems: definition of thermodynamic compensatory temperature, (Tc).

In our thermodynamic analysis of the non-linear Van't Hoff expression as applied to several self-associating systems -- specifically in the cases of bovine liver L-glutamate dehydrogenase (GDH), glucagon and S-carboxymethylated apo A-II protein from human high density lipoprotein -- we have examined the interrelationships of a number of thermodynamic temperatures as they affect the association process. We found the principal determinants of the linear thermodynamic compensation process to be delta S0(T)/delta C0p(T) = (delta T'C)/(Texp), where (delta T'C) = Texp). We have defined the unique compensatory temperature, (TC), for any interacting system, at which the contributions of enthalpy and entropy to the association process are balanced.     

Similarity between 5'- and 3'-terminal nucleotide sequences and double-stranded RNA-derived sequences of eukaryotic mRNA

It has been reported recently that parts of the nucleotide sequences present in the 5′- and 3′-terminal regions of cytoplasmic mRNA are derived from double-stranded hairpin structures of heterogeneous nuclear RNA—a putative mRNA precursor (Naora, 1979). In order to explore the nature of double-stranded hairpin structures, using the sequencing data of human and rabbit globin mRNA and hen ovalbumin mRNA, we examined the following possibility: that certain regions of both the 5′- and 3′-terminal nucleotide sequences of mature mRNA were present in double-stranded hairpin structures covalently linked to both sides of the message sequence in the precursor mRNA molecule and that these double-stranded hairpin structures are similar to each other. The results support the above possibility by showing substantial similarity of nucleotide sequences between the 5′- and 3′-terminal regions of these mRNAs in terms of the formation of similar double-stranded hairpin structures.     

Scanning molecular sieve chromatography of interacting protein systems. IV. The difference profile method as applied to the Gibbs-Duhem expression in the analysis of the dimer-tetramer equilibria of oxyhemoglobin A

The recently-developed large zone difference profile method in scanning molecular sieve chromatography is applied to the analysis of the Gibbs-Duhem expression in the tetramer-dimer equilibrium of human oxyhemoglobin A. The preferential binding term and solvation parameters of the Hofmeister anion phosphate are examined. Results indicate that as the concentration of phosphate ions increase, a hydrated phosphate is formed which enhances the association by perturbing the solvation layer of the hemoglobin molecules. The standard free energy change at a given Hofmeister anion activity of InA(x) = -3.2476 is 9.4 +/- 0.2 kcal mole . DeltaG degrees at InA(x) = -1.2711 is 10.90 +/- 0.05 kcal mole , suggesting that approximately 11 kcal are required to dissociate one mole of tetramer into dimer.     

Scanning molecular sieve chromatography of interacting protein systems. II. Determination of large zone transport parameters by the difference profile method at low solute concentration

The experimental determination of difference profiles for the study of large zone transport processes by scanning molecular sieve chromatography is described. Using the difference profile method, the progesterone-induced purple glycoprotein of the porcine uterus was found to exist as monomeric units in high ionic environment, with a partition coefficient of 0.269, partition cross-section of 0.488, partition radius of 25 A and a molecular weight of 33500 g mole . The technique was further applied in examining the association-dissociation properties of oxyhemoglobin. In a high tonic environment, the partition coefficient was found to be 0.365 for dimer and the partition cross-section, 0.419; for the tetramer in low ionic strength solution, the partition coefficient was 0.275 and the partition cross-section 0.377, with a dissociation constant of 1.03 x 10(-6) mole/1. This new technique should prove applicable in (1) readily locating the centroid positions of transport boundary profiles at the lowest practicable protein concentration limits, (2) demonstrating the characteristic boundary shape and concentration-dependent centroid position for an interacting solute, (3) determining the axial dispersion coefficient characteristic of solute turbulence within the gel matrix, and (4) distinguishing the boundary between low and high ionic strength solvent phases in the gel column.     

Scanning molecular sieve chromatography of interacting protein systems. III. Effect of kinetic parameters on the large zone boundary profiles for local equilibration between mobile and stationary phases

Large zone reaction boundary profiles for molecular sieve chromatography as affected by kinetic parameters have been simulated for local equilibration between the mobile and stationary phases. Our studies of monomer-dimer and monomer-tetramer systems indicate that in a slowly equilibrating system, the kinetic controls operating between the mobile and stationary phases contribute most significantly to the overall boundary profile. In a rapidly equilibrating system, however, the kinetic parameters k(ij) and k(ji) operating in the mobile phase are the principal determinants of the reaction boundary, while the kinetic effects of k(ii) and k-(ii) between the mobile and stationary phases are minimal.     

The concept of a changing receptor concentration: implications for the theory of drug action

Drugs are considered to produce their effects on biological tissues either by altering some physical property of cells or by interacting with specific cellular components, called receptors. Most drugs and endogenous neurotransmitters act on highly selective receptors located on the outer surface membrane of cells. These receptors were believed, until recently, to be stationary on the cell surface and to be present in unvarying numbers. Consequently, most early theorists modeled the drug-receptor interaction on the basis of stationary and static receptor molecules. The substantial advances in our understanding of drug action based on these models have partly justified this view. However, recent electron microscopic studies have revealed the presence of structures, including "coated" pits and vesicles, that appear to provide a mechanism by which cell surface receptors might be internalized in a process of endocytosis. The precise intracellular fate of these internalized receptors is unknown, but based on present understanding, it seems reasonable to believe that some are destroyed intracellularly whereas others are recycled to the cell surface. The importance of such processes to pharmacologic theory is a new awareness of a cellular pathway that is capable of internalizing drugs, receptors, or both. The implications of such a process to the theory of drug action extends to some unexplained drug phenomena such as down regulation, drug tolerance, tachyphyllaxis, and partial agonism. We present herein the theoretical framework for a model of drug action that incorporates the possibility of receptor internalization and subsequent degradation, recycling, or replacement.     

Crystal and molecular structure of piperidinium μ-acetato-di-μ-1,2-benzenediolato-bis-1,2-benzenediolatoferrate(III), (C5H12N)3 [(CH3COO){Fe(C6H4O2)2}2]: a compound of relevance to the 2Fe-active site of the respiratory protein hemerythrin

The title compound is readily prepared as chunky purple-black crystals with the space group P$\text{4}$. The crystal structure was determined to a conventional R value of 0.088. The two FeO₆ octahedra in the anion share a common edge using oxygens of two equatorially disposed catechol dianions and one pair of adjacent coordination sites is bridged by the acetate moiety. Bidentate catecholates complete the coordination array. The Fe-O distances range from 1.95(3) to 2.03(3)Å with chelate bite angles of 82.3(9)° and 84.0(4)°. The basal Fe₂O₂ ring is folded about the O-O vector with dihedral angles of 150.0° and 149.4°. For the two dimers pres per asymmetric unit, Fe-Fe separations are 3.137(4) and 3.172(4)Å. Extensive hydrogen bonding creates rosettes of four anions and eight cations alternating about inversion centers. These structural data together with magnetic and spectroscopic properties of the dimer strongly suggest that such a (near) confacial bioctahedral structure is not an appropriate model for the active site of the respiratory protein hemerythrin.     

Hemin-mediated para-hydroxylation of aniline: A potential model for oxygen activation and insertion reactions of mixed function oxidases

The activation of molecular oxygen by alkaline hemin (ferriprotoporphyrin IX) has been studied. In the presence of reductant nicotineamide adenine dinucleotide (NADH) or nicotineamide adenine dinucleotide phosphate (NADPH) and organic substrate, aniline, hemin activates oxygen to the hydroperoxide anion (HO₂^?) and subsequently mediates insertion of active oxygen into the benzene ring of the substrate to form p-aminophenol, with a high degree of regiospecificity. Oxygen activation does not occur in the absence of aniline. Stoichiometry of the reaction indicates that two electrons are required per molecule of oxygen activated or atom of oxygen inserted into the substrate aromatic ring system. Direct measurements of H₂O₂ and of the pK_a for maximum rate of p-aminophenol formation (11.7 ± 0.1) indicate participation of the hydroperoxide anion as the active oxygen species in the rate-determining step of the insertion reaction. Powerful scavengers of the hydroxyl radical (OH′) have little effect on the formation of H₂O₂ or p-aminophenol by the system. Superoxide dismutase (10^?7 mol dm^?3) inhibited both p-aminophenol and H₂O₂ formation, when added to the system immediately prior to initiation of the reaction. Studies involving N-phenylhydroxylamine indicate that aromatic ring hydroxylation is occurring directly and not by rearrangement of an N-hydroxylated intermediate. Implications of hemin-mediated hydroxylation reactions for those of enzymatic mixed function oxidase activity are discussed.     

Maintenance of the shore-level size gradient in the marine snail Tegula funebralis (A. Adams): Importance of behavioral responses to light and sea star predators

The intertidal gastropod, Tegula funebralis (A. Adams) exhibits a shore-level size gradient with mean shell size increasing in a down-shore direction. Snails transferred to zones where they do not usually occur migrated back towards their original zone, thus re-establishing a size gradient and implying differential movement among size classes. Both large (≥2.1 cm shell width) and small (≤ 1.77 cm) snails were photonegative on a horizontal surface and geonegative in the laboratory; there were no statistical differences between size classes. Light, however, inhibited upward, or caused downward, movement of large snails on vertical surfaces. Small snails were unaffected, ranging higher on illuminated vertical surfaces than large snails. Both sizes exhibited similar distributions in the dark. In an experimental chamber providing both emersed and immersed surfaces, T. funebralis established vertical size gradients when the chamber was illuminated from above. It is suggested that light is an important factor in the formation and maintenance of Tegula's shore-level size gradient.In response to water-borne chemicals derived from the sea star Pisaster ochraceus (Brandt), large snails moved up vertical surfaces in greater proportion than small. In response to contact with the predator, large snails moved away faster than small and individuals collected from crevices in the field moved away slower than those collected from open rock faces. Although predation may select for a size gradient in Tegulafunebralis, it is unlikely that responses to predatory sea stars directly and proximally cause or maintain them over the short term.     

Precision Medicine with Imprecise Therapy: Computational Modeling for Chemotherapy in Breast Cancer

Medical oncology is in need of a mathematical modeling toolkit that can leverage clinically-available measurements to optimize treatment selection and schedules for patients. Just as the therapeutic choice has been optimized to match tumor genetics, the delivery of those therapeutics should be optimized based on patient-specific pharmacokinetic/pharmacodynamic properties. Under the current approach to treatment response planning and assessment, there does not exist an efficient method to consolidate biomarker changes into a holistic understanding of treatment response. While the majority of research on chemotherapies focus on cellular and genetic mechanisms of resistance, there are numerous patient-specific and tumor-specific measures that contribute to treatment response. New approaches that consolidate multimodal information into actionable data are needed. Mathematical modeling offers a solution to this problem. In this perspective, we first focus on the particular case of breast cancer to highlight how mathematical models have shaped the current approaches to treatment. Then we compare chemotherapy to radiation therapy. Finally, we identify opportunities to improve chemotherapy treatments using the model of radiation therapy. We posit that mathematical models can improve the application of anticancer therapeutics in the era of precision medicine. By highlighting a number of historical examples of the contributions of mathematical models to cancer therapy, we hope that this contribution serves to engage investigators who may not have previously considered how mathematical modeling can provide real insights into breast cancer therapy.     

The reduction of trimethylarsine oxide to trimethylarsine by thiols: a mechanistic model for the biological reduction of arsenicals

Trimethylarsine oxide is reduced to trimethylarsine in aqueous solution by a variety of thiols and dithiols including cysteine, glutathione, and lipoic acid. Kinetic results and other observations suggest that the rate-determining step is the production of [Me₃AsSR]⁺ from an initially formed Me₃As(SR)OH species, and that the reduction occurs via a two-electron transfer from Me₃As(SR)₂ affording Me₃As and RS-SR. A simple model for the biological methylation of arsenic is proposed based on oxidative methylation of arsenic(III) by S-adenosylmethionine and reduction by a thiol such as lipoic acid.     

Macrophage activation for tumor cytotoxicity: Control of cytotoxic activity by the time interval effector and target cells are exposed to lymphokines

Macrophages continuously exposed to lymphokines (LK) and target cells throughout a 48-hr cytotoxicity assay exhibit 3-fold more tumoricidal activity than do cells optimally treated with LK before addition of tumor cells. Increased cytotoxic activity induced by continuous LK treatment was not due to direct toxic effects of LK on tumor target cells or to alterations in target cell susceptibility to cytopathic effects of LK-activated macrophages. Moreover, sensitivities of responsive macrophages to LK activation signals and time courses for onset and loss of tumoricidal activity during continuous exposure or LK pulse were identical. Analysis of macrophage or LK dose responses and time courses for development of cytotoxicity each suggest that differences in tumoricidal activity between macrophages continuously exposed or pulsed with LK were quantitative: the number of cytotoxic events was increased 2.7 ± 0.2-fold (mean ± SEM for 11 experiments) during continuous LK treatment. Optimal levels of macrophage tumoricidal activity then occur only if effector cells, target cells and activation stimuli are simultaneously present for a defined time interval: tumor cells need not be present during the initial 2 to 3 hr of culture; LK can be removed after 8 hr with little or no loss of cytotoxic activity. However, removal of LK or target cells during the critical 4- to 8-hr interval decreased levels of cytotoxicity 3-fold. Thus, nonspecific effector function by LK-activated macrophages in controlled by both the physicochemical nature of the LK mediator and the time interval effector and target cells are exposed to LK.     

Autophagy: A New Mechanism of Prosurvival and Drug Resistance in Multiple Myeloma

Autophagy is an intracellular self-degradative process that balances cell energy source and regulates tissue homeostasis. In physiological condition, autophagy funnels cytoplasmic constituents to autophagolysosomes for degradation and is an alternative way for cell-death behavior. Here, we inspected autophagy as a prosurvival mechanism essential for drug resistance in multiple myeloma (MM). Accordingly, autophagy inhibitors used in association to conventional anti-MM drugs might enforce the effect against resistant MM plasma cells and render autophagy a new therapeutic target.     

DKK1 and Kremen Expression Predicts the Osteoblastic Response to Bone Metastasis

Bone metastasis is a complication of advanced breast and prostate cancer. Tumor-secreted Dickkopf homolog 1 (DKK1), an inhibitor of canonical Wnt signaling and osteoblast differentiation, was proposed to regulate the osteoblastic response to metastatic cancer in bone. The objectives of this study were to compare DKK1 expression with the in vivo osteoblastic response in a panel of breast and prostate cancer cell lines, and to discover mechanisms that regulate cancer DKK1 expression. DKK1 expression was highest in MDA-MB-231 and PC3 cells that produce osteolytic lesions, and hence a suppressed osteoblastic response, in animal models of bone metastasis. LnCaP, C4-2B, LuCaP23.1, T47D, ZR-75-1, MCF-7, ARCaP and ARCaP_M cancer cells that generate osteoblastic, mixed or no bone lesions had the lowest DKK1 expression. The cell lines with negligible expression, LnCaP, C4-2B and T47D, exhibited methylation of the DKK1 promoter. Canonical Wnt signaling activity was then determined and found in all cell lines tested, even in the MDA-MB-231 and PC3 cell lines despite sizeable amounts of DKK1 protein expression expected to block canonical Wnt signaling. A mechanism of DKK1 resistance in the osteolytic cell lines was investigated and determined to be at least partially due to down-regulation of the DKK1 receptors Kremen1 and Kremen2 in the MDA-MB-231 and PC3 cell lines. Combined DKK1 and Kremen expression in cancer cells may serve as predictive markers of the osteoblastic response of breast and prostate cancer bone metastasis.