A Model for the Action of Vinblastine in Vivo

A model for the action of vinblastine (VLB) on cells multiplying exponentially in vivo with a generation time, T_G, has been derived. It is based on the assumption that cells attempting to pass through mitosis in the presence of VLB lose their proliferative capacity and that this lethal effect occurs only when the cells are exposed to a concentration of VLB which is above a critical value, C_k. The model leads to two predictions. First, that the percentage of cells surviving at any time after exposure to a dose, D, of VLB is 100% if D < D_k and decreases to 0% after a time, T_G, following a dose D ≥ D_k·2^{T G/T1/2}, where D_k represents the dose of VLB required to produce the concentration C_k, and T_1/2 is the half-life of the VLB in vivo. Second, that the time, T_G, at which the percentage of cells surviving an exposure to VLB, at doses greater than D_k·2^{U G/T1/2}, decreases to zero should be equal to the generation time of the cells. Both of these predictions were confirmed experimentally which indicates that the model adequately explains the action of VLB in vivo.     

Cardiac chemical constant. Part I: Derivation of the characteristic phenomenological equation

A physiochemical parameter is derived and defined as the cardiac chemical equilibrium dissociation constant (K_D), K_D is based upon a phenomenological model in which the cardiac muscle chemical reaction kinetics describe the interconversion between long and short unils (i.e. the individual sarcomere is fully extended or fully contracted). K_D is defined as the ratio of the number of units in the long state to the number of units in the short state. The mathematical development proceeds through four stages: derivation of the governing differential equation during cardiac systole; simplification of the differential equation to describe the cardiac model; determination of the upper and lower limits and average value of Nt (the total number of units in a hypothetical mid-wall circumferential fibre); definition and calculation of the cardiac chemical constant (K_D). K_D is shown to describe a series of equilibrium points throughout cardiac systole. This requires that each mechanical equilibrium state (a series of static, steady-state intervals over time) is also associated with its own specific chemical equilibrium state.     

Variable affinity of the (Na+ + K+)-dependent adenosine triphosphatase for potassium: Studies using beryllium inactivation

Inactivation of the (Na⁺ + K⁺)-dependent ATPase by 50 μm BeCl₂ occurred during brief incubations in the presence of both Mg²⁺ and K⁺. Inactivation followed, initially, a first-order time course, with rate constants sensitive to the concentration of K⁺ (other components held constant). From these data dissociation constants can be calculated for K⁺ binding to sites controlling inactivation. Comparisons of relative affinities for K⁺ analogs (T1⁺ and NH₄⁺), and of sensitivity to reagents altering K⁺ activation (phlorizin and dimethylsulfoxide) indicate that the same K⁺ sites operate for both Be²⁺ inactivation and enzyme activation. With 3 mm MgCl₂ the dissociation constant, K_D, for K⁺ was 1.4 mm, but decreased 20-fold on addition of both Na⁺ and CTP. Alone, Na⁺ increased the apparent K_D for K⁺, either by direct competition or indirectly from its own site, with a K_D of 7 mm. The data suggest a model for K⁺ transport with K⁺ sites on the outer membrane surface that increase in affinity after formation of the phosphorylated enzyme intermediate, sufficiently to bind K⁺ in a high Na⁺ environment. Translocation may occur by an “oscillating pore” mechanism discharging K⁺ at the inner surface, while leaving demonstrable sites of moderate affinity at the outer end of the pore (which preclude attempts to document low-affinity discharge sites).     

Light dependence of the decay of the proton gradient in broken chloroplasts

The initial rates and steady-state values of proton uptake by broken chloroplasts have been measured as functions of light intensity at various concentrations of chlorophyll, pyocyanine, supporting electrolyte, buffer, as well as pH and temperature. Kinetic analysis of the data shows that the rate of decay of proton gradient due to backward leakage depends on light intensity. Under steady illumination, the decay constant k_L is equal to k_D + mR₀, where R₀ is the initial rate of proton uptake which is a function of light intensity, k_D is the decay constant in the dark and m is a parameter which is independent of light intensity. Treatment of chloroplasts with lysolecithin, neutral detergent, 2,4-dinitrophenol, or valinomycin in the presence of K⁺ increases k_D without affecting m. Treatment with N,N′-dicyclohexylcarbodiimide or adenylyl imidodiphosphate under appropriate conditions decreases m without affecting k_D. Treatment with glutaraldehyde makes k_L independent of light intensity and hence m = 0. These results suggest that the light-dependent part (mR₀) of k_L is due to leakage of protons through the coupling factor (CF₁-CF₀) complex which can open or close depending on light intensity and that the light-independent part (k_D) of the decay constant k_L is due to proton leakage elsewhere.     

Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency

We consider the relationship between the target affinity of a monoclonal antibody and its in vivo potency. The dynamics of the system is described mathematically by a target-mediated drug disposition model. As a measure of potency, we consider the minimum level of the free receptor following a single bolus injection of the ligand into the plasma compartment. From the differential equations, we derive two expressions for this minimum level in terms of the parameters of the problem, one of which is valid over the full range of values of the equilibrium dissociation constant K_D and the other which is valid only for a large drug dose or for a small value of K_D. Both of these formulae show that the potency achieved by increasing the association constant k_on can be very different from the potency achieved by decreasing the dissociation constant k_off. In particular, there is a saturation effect when decreasing k_off where the increase in potency that can be achieved is limited, whereas there is no such effect when increasing k_on. Thus, for certain monoclonal antibodies, an increase in potency may be better achieved by increasing k_on than by decreasing k_off.     

Impact of hapten presentation on antibody binding at lipid membrane interfaces

We report the effects of ligand presentation on the binding of aqueous proteins to solid supported lipid bilayers. Specifically, we show that the equilibrium dissociation constant can be strongly affected by ligand lipophilicity and linker length/structure. The apparent equilibrium dissociation constants (K_D) were compared for two model systems, biotin/anti-biotin and 2,4-dinitrophenyl (DNP)/anti-DNP, in bulk solution and at model membrane surfaces. The binding constants in solution were obtained from fluorescence anisotropy measurements. The surface binding constants were determined by microfluidic techniques in conjunction with total internal reflection fluorescence microscopy. The results showed that the bulk solution equilibrium dissociation constants for anti-biotin and anti-DNP were almost identical, K_D(bulk) = 1.7 ± 0.2 nM vs. 2.9 ± 0.1 nM. By contrast, the dissociation constant for anti-biotin antibody was three orders of magnitude tighter than for anti-DNP at a lipid membrane interface, K_D = 3.6 ± 1.1 nM vs. 2.0 ± 0.2 μM. We postulate that the pronounced difference in surface binding constants for these two similar antibodies is due to differences in the ligands’ relative lipophilicity, i.e., the more hydrophobic DNP molecules had a stronger interaction with the lipid bilayers, rendering them less available to incoming anti-DNP antibodies compared with the biotin/anti-biotin system. However, when membrane-bound biotin ligands were well screened by a poly(ethylene glycol) (PEG) polymer brush, the K_D value for the anti-biotin antibody could also be weakened by three orders of magnitude, 2.4 ± 1.1 μM. On the other hand, the dissociation constant for anti-DNP antibodies at a lipid interface could be significantly enhanced when DNP haptens were tethered to the end of very long hydrophilic PEG lipopolymers (K_D = 21 ± 10 nM) rather than presented on short lipid-conjugated tethers. These results demonstrate that ligand presentation strongly influences protein interactions with membrane-bound ligands.     

Formulation of a Universal First-Order Rate Constant for Enzymatic Reactions

It is a common practice to employ k _cat[E]₀/K _m as a first-order rate constant for the analysis of an enzymatic reaction, where [E]₀ is the total enzyme concentration. I describe in this report a serious shortcoming in analyzing enzymatic reactions when k _cat[E]₀/K _m is employed and show that k _cat[E]₀/K _m can only be applied under very limited conditions. I consequently propose the use of a more universal first-order rate constant, k _cat[ES]_K/[S]₀, where [ES]_K is the initial equilibrium concentration of the ES-complex derived from [E]₀, [S]₀ and K _m. Employing k _cat[ES]_K/[S]₀ as the first-order rate constant enables all enzymatic reactions to be reasonably simulated under a wide range of conditions, and the catalytic and binding contributions to the rate constant of any enzyme can be determined under any and all conditions.     

Thermodynamics and kinetics of co-operative protein-nucleic acid binding: II. Studies on the binding between protamine and calf thymus DNA

Unspecific binding of a protamine, namely fluorescein-labelled clupeine Z, to double-stranded calf thymus DNA was studied using fluorescence titration methods and chemical relaxation techniques. Both equilibrium and kinetic data have been analysed using general theoretical approaches discussed in the accompanying paper. The results agree well with the predictions made on the basis of a standard co-operative binding model.Basic parameters evaluated are the co-operative binding constant (K), the coefficient measuring co-operative interaction between nearest neighbours (q), the number of nucleotides occupied by one protamine molecule (n) and the rate constant of dissociation at the ends of bound ligand sequences (K_D). Values obtained at 20 °C, pH 7.5 and 0.4 m-NaCl were K = 5.8 × 10⁷m^?1, q = 1700, n = 20 and K_D = 0.29 s^?1. They have been found to be sensitive to the concentration of added salt (NaCl). This effect apparently reflects the essentially electrostatic nature of the binding process. The results can be satisfactorily described in terms of competitive binding of sodium ions.     

Characterization of binding of [3H]PD 128907, A selective Dopamine D3 receptor agonist ligand,to CHO-K1 cells

PD 128907 [4a R, 10 b R-(+)-trans- 3, 4, 4a, 10 b - tetrahydro - 4- n-propy12 H,5H-[1] benzopyrano[4,3-b]1,4-oxazin-9-ol.], a selective dopamine (DA) D3 receptor agonist ligand exhibits about a 1000-fold selectivity for human D3 receptors (K_i, 1 nM) versus human D₂ receptors (K_i, 1183 nM) and a 10000-fold selectivity versus human D₄ receptors (K_i, 7000 nM) using [³H]spiperone as the radioligand in CHO-K1-cells. Studies with [³H]PD 128907, showed saturable, high affinity binding to human D₃ receptors expressed in CHO-K1 cells (CHO-K1-D₃) with an equilibrium dissociation constant (K_d) of 0.99 nM and a binding density (B_max) of 475 fmol/mg protein. Under the same conditions, there was no significant specific binding in CHO-K1-cells expressing human D₂ receptors (CHO-K1-D₂). The rank order of potency for inhibition of [³H]PD 128907 binding with reference DA agents was consistent with reported values for D₃ receptors. These results indicate that [³H]PD 128907 is a new, highly selective D₃ receptor ligand with high specific activity, high specific binding and low non-specific binding and therefore should be useful for further characterizing the DA D₃ receptors.     

Concentration-dependent hydrogen exchange kinetics of 3H-labeled S-peptide in ribonuclease S.

The hydrogen exchange kinetics of the S-peptide in ribonuclease S can be measured by first tritiating the S-peptide in the absence of S-protein and then allowing it to recombine rapidly with S-protein. Afterwards the exchange reactions of this specific segment of ribonuclease S can be studied. The exchange kinetics of bound S-peptide are complex, indicating that different protons exchange at markedly different rates. The terminal exchange reaction, involving at least five highly protected protons, has been studied as a function of pH.At low concentrations of ribonuclease S the exchange kinetics become concentration-dependent, owing to the dissociation of the S-peptide. Although the fraction of free S-peptide is always very small, its rate of exchange is several orders of magnitude faster than that of bound S-peptide, and the concentration dependence of the exchange kinetics is readily measurable. It provides a highly sensitive method for determining small dissociation constants (K_D). Values of K_D ranging from 10^?6m at pH 2.7, 0 °C, to 2 × 10^?10m at pH 7.0, 0 °C, are reported here. Our value for K_D at pH 7.0, 0 °C, confirms the data and extrapolation to 0 °C of Hearn et al. (1971).At high concentrations of ribonuclease S the terminal exchange reaction is independent of concentration. It probably results from a local unfolding reaction of the bound S-peptide. Above pH 4 the strong pH dependence of K_D closely resembles that of the apparent equilibrium constant for this local unfolding reaction. The latter may be one step in the dissociation process and we present such a model for ribonuclease S dissociation.Measurement of concentration-dependent exchange kinetics should provide a useful method of determining small dissociation constants in other systems: for example, in studies of protein-nucleic acid interactions.     

Transient Phases of the Isometric Tetanus in Frog's Striated Muscle

In an isometric tetanus in frog's sartorius muscle tension approaches the plateau exponentially with rate constant α. α a depends on sarcomere length, s, and temperature, T, according to the Arrhenius equation See PDF for Equation for temperatures between 1 and 20°C and for sarcomere lengths 2.0–2.8 µm. The energy of activation, E, does not vary significantly with s; E = 13.9 ± 2.4 kcal/mole. A(s) decreases monotonically with s; A(2.1 µm) is about three times greater than A(2.8 µm). Late in relaxation active tension approaches zero exponentially with rate constant r. r decreases exponentially with increasing duration of tetanus, D, from r₀ in a twitch to r_∞ for large D. The rate constant for decrease of r with D increases with s and with T. r₀ and r_∞ obey the Arrhenius equation and decrease with increasing s.     

EmrE dimerization depends on membrane environment

The small multi-drug resistant (SMR) transporter EmrE functions as a homodimer. Although the small size of EmrE would seem to make it an ideal model system, it can also make it challenging to work with. As a result, a great deal of controversy has surrounded even such basic questions as the oligomeric state. Here we show that the purified protein is a homodimer in isotropic bicelles with a monomer–dimer equilibrium constant (K_MD^2D) of 0.002–0.009 mol% for both the substrate-free and substrate-bound states. Thus, the dimer is stabilized in bicelles relative to detergent micelles where the K_MD^2D is only 0.8–0.95 mol% (Butler et al. 2004). In dilauroylphosphatidylcholine (DLPC) liposomes K_MD^2D is 0.0005–0.0008 mol% based on Förster resonance energy transfer (FRET) measurements, slightly tighter than bicelles. These results emphasize the importance of the lipid membrane in influencing dimer affinity.     

Tetra(β-phenothiazinyl) zinc phthalocyanine: An easily prepared D4-A system for efficient photoinduced electron transfer

Four identical electron donor (D) moieties, phenothiazines (PTZs), were covalently attached onto the same acceptor (A), zinc phthalocyanine (ZnPc), to form ZnPc(β-PTZ)₄, i.e. D₄-A. The symmetrical D₄-A was synthesized by the condensation method to examine intra-molecular photoinduced electron transfer (PET). The common electron donor-spacer-acceptor (D-A) photosynthetic models, which involve the asymmetrical synthesis of a mono-substituted porphyrin or its analogs, suffer from a low yield and arduous isolation, since D-A is only one of several products (D_n-A or A_n-D, n = 0, 2-4). The D₄-A preparation, however, can be carried out without the problem. The steady state and time-resolved fluorescence of the D₄-A were measured and compared with that of ZnPc(β-R)₄ (R = H, OPh). The result showed that the excited singlet state of phthalocyanine moiety in the D₄-A molecule was efficiently quenched by phenothiazine units owing to intra-molecular PET. The rate constant of PET (k_et) was calculated and the value is much higher than the rate constant of fluorescence emission, intersystem crossing and internal conversion of ZnPc moiety. The laser flash photolysis study revealed the presence of a long-lived charge-separated state due to PET. The results suggest that a D₄-A system can be a more efficient artificial photosynthetic model than D-A towards the practical commercial use.     

Dynamic light-scattering studies of internal motions in DNA. I. Applicability of the rouse-zimm model

The intermediate scattering function G(K,t) for any polymer model obeying a linear separable Langevin equation can be expressed in terms of the eigenvalues and eigenvectors of its normal coordinate transformation. An algorithm for the extract numerical evaluation of G(K,t) for linear Rouse-Zimm chains in the presence of hydrodynamic interaction has been developed. The computed G(K,t)² were fit to C(t) = A exp(?t/τA) + B, and apparent diffusion coefficients calculated according to D_app ≡ 1/(2τ_AK²). G(K,t)² was surprisingly well-fit by single-exponential decays, especially at both small and large values of Kb, where K is the scattering vector and b the root-mean-squared subunit extension. Plots of D_app vs K² in-variably showed a sigmoidal rise from D₀ at K² = O up to a constant plateau value at large K²b². Analytical expression for G(K,t), exact in the limit of short times, were obtained for circular Rouse-Zimm chains with and without hydrodynamic interaction, and also for free-draining linear chains, and in addition for the independent-segment-mean-force (ISMF) model. The predicted behaviors for G(K,t) at large Kb (or KR_G) was found in all cases to be single-exponential with 1/τ ∝ K² at large Kb, in agreement with the computational results. A simple procedure for estamating all parameter of the Rouse-Zimm model from a plot of D_app vs K² is proposed. Experimental data for both native and pH-denatured calf-thymus DNA in 1.0M Nacl with and without EDTA clearly plateau behavior of D_app at large values of K, in harmony with the present Rouse-Zimm and ISMF theories, and in sharp contrast to previous predictions based on the Rouse-Zimm model.     

Resurveying the Tris buffer solution: the specific interaction between tris(hydroxymethyl)aminomethane and lysozyme

An unusual phenomenon, the specific interaction between tris(hydroxymethyl)aminomethane (Tris) and lysozyme (LZM), was demonstrated for the first time by rapid screen analysis of interactions using a quartz crystal microbalance (QCM) biosensor. This phenomenon was also observed in a surface plasmon resonance (SPR) system. Further study using high-performance affinity chromatography (HPAC) confirmed this specific interaction between LZM and immobilized Tris with an apparent dissociation constant (K_D) of 6.7 × 10⁻⁵ M. Molecular docking was carried out to identify possible modes of binding between LZM and Tris linked to a binding arm. The estimated binding free energy was −6.34 kcal mol⁻¹, corresponding to a K_D of 2.3 × 10⁻⁵ M, which correlated well with the experimental value. Based on the docking model, the three hydroxyl groups of Tris form intermolecular H bonds with Asp52, Glu35, and Ala107 in LZM. This study reinforces the importance of buffer selection in quantitative biochemical investigations. For a lysozyme ligand binding study, it is better to avoid using Tris when the ligands under study are weak binders.     

Interpolation method for accurate affinity ranking of arrayed ligand–analyte interactions

The values of the affinity constants (k_d, k_a, and K_D) that are determined by label-free interaction analysis methods are affected by the ligand density. This article outlines a surface plasmon resonance (SPR) imaging method that yields high-throughput globally fitted affinity ranking values using a 96-plex array. A kinetic titration experiment without a regeneration step has been applied for various coupled antibodies binding to a single antigen. Globally fitted rate (k_d and k_a) and dissociation equilibrium (K_D) constants for various ligand densities and analyte concentrations are exponentially interpolated to the K_D at R_max = 100 RU response level (K_D^R100).     

Impact of protein binding on receptor occupancy: A two-compartment model

In this paper we analyse the impact of protein-, lipid- and receptor-binding on receptor occupancy in a two-compartment system, with proteins in both compartments and lipids and receptors in the peripheral compartment only. We do this for two manners of drug administration: a bolus administration and a constant rate infusion, both into the central compartment. We derive explicit approximations for the time-curves of the different compounds valid for a wide range of realistic values of rate constants and initial concentrations of proteins, lipids, receptors and the drug. These approximations are used to obtain both qualitative and quantitative insight into such critical properties as the distribution of the drug over the two compartments, the maximum receptor occupancy and the area under the drug-receptor complex curve. In particular we focus on assessing the impact of the dissociation constants, K_P, K_L and K_R of the drug with, respectively, the proteins, the lipids and the receptors, the permeability and the surface area of the membrane between compartments, and the rate the drug is eliminated from the system.     

A Modified Lumry–Eyring Analysis for the Determination of the Predominant Mechanism Underlying the Diminution of Protein Aggregation by Glycerol

Aggregation of aspartate-β-semialdehyde dehydrogenase (ASD) was analyzed by applying modified Lumry–Eyring with nucleated polymerization (LENP) model. Intrinsic nucleation time scales were determined. In absence of glycerol, ASD undergoes concentration and time-dependent polymerization into low-molecular weight soluble aggregates and thereafter condensation into insoluble aggregates. In the presence of increasing solvent glycerol concentration, the aggregation becomes more and more nucleation dominated, with slower polymerization to low-molecular weights soluble aggregates, without any condensation into insoluble aggregates. Effective nucleus size as well as the number of monomers in each irreversible growth event were sensitive to the changes in solvent glycerol concentration. Glycerol-directed diminution of aggregation appears to be largely due to the inhibition of rearrangement (decreased nucleation rearrangement rate coefficient, K _r,x ) because of compaction induced due to preferential hydration, thus, preventing the soluble aggregates from locking into irreversible soluble nuclei. Appreciably decreased K _r,x (as compared to nucleation dissociation constant, K _d,x ), appears to be responsible for increased nucleus size at higher solvent glycerol concentration. This study explains how modified LENP model can be applied to determine the predominant mechanism responsible for the diminution of aggregation by polyhydric alcohols (glycerol).     

Concentration distribution around a growing gas bubble in tissue

This paper presents the concentration distribution around a growing nitrogen gas bubble in the blood and other tissues of divers who surface too quickly, when the ambient pressure through the decompression process is variable and constant. This effort is a modification of Sirinivasan et al. model (1999) [9]. The mathematical model is solved analytically to find the growth rate of a gas bubble in a tissue after decompression in the ambient pressure. Moreover, the concentration distribution around the growing bubble is introduced. The growth process is affected by ascent rate , tissue diffusivity D_T, initial concentration difference ΔC₀, surface tension σ and void fraction ?₀.     

Dimerization constants of water-soluble porphyrins in aqueous alkali

Spectrophotometric analysis of changes in absorption spectra on dilution of different 2,4-disubstituted derivatives of deuteroporphyrin yielded dimerization constants (K_D) for each porphyrin in aqueous alkali. The K_D values appear to be related to the hydrophobic/hydrophilic interactions of the system such that K_D for proto- > meso- > deutero- > hemato- > coproporphyrin. The effects of alcohol, temperature, and ionic strength on the K_D were examined. A simple approach to the graphic analysis of the dilution curves is presented for use when absorbance readings at A₁₀₀ and A₀ cannot be reliably determined, and the use of soluble porphyrins as model systems for studying hydrophobic/hydrophilic interactions in aqueous media is discussed.