Kinetics of self-assembling microtubules: an "inverse problem" in biochemistry.

Experimental time series for a nonequilibrium reaction may in some cases contain sufficient data to determine a unique kinetic model for the reaction by a systematic mathematical analysis. As an example, a kinetic model for the self-assembly of microtubules is derived here from turbidity time series for solutions in which microtubules assemble. The model may be seen as a generalization of Oosawa's classical nucleation-polymerization model. It reproduces the experimental data with a four-stage nucleation process and a critical nucleus of 15 monomers.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Isolation and Characterization of Glutathione S-Transferase Isozymes from Sorghum1

Two glutathione S-transferase (GST) isozymes, A1/A1 and B1/B2, were purified from etiolated, O-1,3-dioxolan-2-yl-methyl-2,2,2,-trifluoro-4′-chloroacetophenone-oxime-treated sorghum (Sorghum bicolor L. Moench) shoots. GST A1/A1, a constitutively expressed homodimer, had a subunit molecular mass of 26 kD and an isoelectric point of 4.9. GST A1/A1 exhibited high activity with 1-chloro-2, 4,dinitrobenzene (CDNB) but low activity with the chloroacetanilide herbicide metolachlor. For GST A1/A1, the random, rapid-equilibrium bireactant kinetic model provided a good description of the kinetic data for the substrates CDNB and glutathione (GSH). GST B1/B2 was a heterodimer with subunit molecular masses of 26 kD (designated the B1 subunit) and 28 kD (designated the B2 subunit) and a native isoelectric point of 4.8. GST B1/B2 exhibited low activity with CDNB and high activity with metolachlor as the substrate. The kinetics of GST B1/B2 activity with GSH and metolachlor fit a model describing a multisite enzyme having two binding sites with different affinities for these substrates. Both GST A1/A1 and GST B1/B2 exhibited GSH-conjugating activity with ethacrynic acid and GSH peroxidase activity with cumene hydroperoxide, 9-hydroperoxy-trans-10,cis-12-octadecadienoic acid and 13-hydroperoxy-cis-9,trans-11-octadecadienoic acid. Both GST A1/A1 and GST B1/B2 are glycoproteins, as indicated by their binding of concanavalin A. Polyclonal antibodies raised against GST A1/A1 exhibited cross-reactivity with the B1 subunit of GST B1/B2. Comparisons of the N-terminal amino acid sequences of the GST A1, B1, and B2 subunits with other type I θ-GSTs indicated a high degree of homology with the maize GST I subunit and a sugarcane GST.

A constant radius of curvature model for the organization of DNA in toroidal condensates.

Toroidal DNA condensates have received considerable attention for their possible relationship to the packaging of DNA in viruses and in general as a model of ordered DNA condensation. A spool-like model has primarily been supported for DNA organization within toroids. However, our observations suggest that the actual organization may be considerably different. We present an alternate model in which DNA for a given toroid is organized within a series of equally sized contiguous loops that precess about the toroid axis. A related model for the toroid formation process is also presented. This kinetic model predicts a distribution of toroid sizes for DNA condensed from solution that is in good agreement with experimental data.

Muscle protein synthesis by positron-emission tomography with l-[methyl-11C]methionine in adult humans

Existing methods for assessing protein synthetic rates (PSRs) in human skeletal muscle are invasive and do not readily provide information about individual muscle groups. Recent studies in canine skeletal muscle yielded PSRs similar to results of simultaneous stable isotope measurements using l-[1-13C, methyl-2H3]methionine, suggesting that positron-emission tomography (PET) with l-[methyl-11C]methionine could be used along with blood sampling and a kinetic model to provide a less invasive, regional assessment of PSR. We have extended and refined this method in an investigation with healthy volunteers studied in the postabsorptive state. They received ≈25 mCi of l-[methyl-11C]methionine with serial PET imaging of the thighs and arterial blood sampling for a period of 90 min. Tissue and metabolite-corrected arterial blood time activity curves were fitted to a three-compartment model. PSR (nmol methionine⋅min−1⋅g muscle tissue−1) was calculated from the fitted parameter values and the plasma methionine concentrations, assuming equal rates of protein synthesis and degradation. Pooled mean PSR for the anterior and posterior sites was 0.50 ± 0.040. When converted to a fractional synthesis rate for mixed proteins in muscle, assuming a protein-bound methionine content of muscle tissue, the value of 0.125 ± 0.01%⋅h−1 compares well with estimates from direct tracer incorporation studies, which generally range from ≈0.05 to 0.09%⋅h−1. We conclude that PET can be used to estimate skeletal muscle PSR in healthy human subjects and that it holds promise for future in vivo, noninvasive studies of the influences of physiological factors, pharmacological manipulations, and disease states on this important component of muscle protein turnover and balance.

Efficiency of DNA replication in the polymerase chain reaction

A detailed quantitative kinetic model for the polymerase chain reaction (PCR) is developed, which allows us to predict the probability of replication of a DNA molecule in terms of the physical parameters involved in the system. The important issue of the determination of the number of PCR cycles during which this probability can be considered to be a constant is solved within the framework of the model. New phenomena of multimodality and scaling behavior in the distribution of the number of molecules after a given number of PCR cycles are presented. The relevance of the model for quantitative PCR is discussed, and a novel quantitative PCR technique is proposed.

Sensitive detection of DNA polymorphisms by the serial invasive signal amplification reaction

The invasive signal amplification reaction has been previously developed for quantitative detection of nucleic acids and discrimination of single-nucleotide polymorphisms. Here we describe a method that couples two invasive reactions into a serial isothermal homogeneous assay using fluorescence resonance energy transfer detection. The serial version of the assay generates more than 107 reporter molecules for each molecule of target DNA in a 4-h reaction; this sensitivity, coupled with the exquisite specificity of the reaction, is sufficient for direct detection of less than 1,000 target molecules with no prior target amplification. Here we present a kinetic analysis of the parameters affecting signal and background generation in the serial invasive signal amplification reaction and describe a simple kinetic model of the assay. We demonstrate the ability of the assay to detect as few as 600 copies of the methylene tetrahydrofolate reductase gene in samples of human genomic DNA. We also demonstrate the ability of the assay to discriminate single base differences in this gene by using 20 ng of human genomic DNA.

Implications of macromolecular crowding for signal transduction and metabolite channeling

The effect of different total enzyme concentrations on the flux through the bacterial phosphoenolpyruvate:carbohydrate phosphotransferase system (PTS) in vitro was determined by measuring PTS-mediated carbohydrate phosphorylation at different dilutions of cell-free extract of Escherichia coli. The dependence of the flux on the protein concentration was more than linear but less than quadratic. The combined flux–response coefficient of the four enzymes constituting the glucose PTS decreased slightly from values of ≈1.8 with increasing protein concentrations in the assay. Addition of the macromolecular crowding agents polyethylene glycol (PEG) 6000 and PEG 35000 led to a sharper decrease in the combined flux–response coefficient, in one case to values of ≈1. PEG 6000 stimulated the PTS flux at lower protein concentrations and inhibited the flux at higher protein concentrations, with the transition depending on the PEG 6000 concentration. This suggests that macromolecular crowding decreases the dissociation rate constants of enzyme complexes. High concentrations of the microsolute glycerol did not affect the combined flux–response coefficient. The data could be explained with a kinetic model of macromolecular crowding in a two-enzyme group-transfer pathway. Our results suggest that, because of the crowded environment in the cell, the different PTS enzymes form complexes that live long on the time-scale of their turnover. The implications for the metabolic behavior and control properties of the PTS, and for the effect of macromolecular crowding on nonequilibrium processes, are discussed.

The relaxation dynamics of the excited electronic states of retinal in bacteriorhodopsin by two-pump-probe femtosecond studies

We present the results of two-pump and probe femtosecond experiments designed to follow the relaxation dynamics of the lowest excited state (S1) populated by different modes. In the first mode, a direct (S0 → S1) radiative excitation of the ground state is used. In the second mode, an indirect excitation is used where the S1 state is populated by the use of two femtosecond laser pulses with different colors and delay times between them. The first pulse excites the S0 → S1 transition whereas the second pulse excites the S1 → Sn transition. The nonradiative relaxation from the Sn state populates the lowest excited state. Our results suggest that the S1 state relaxes faster when populated nonradiatively from the Sn state than when pumped directly by the S0 → S1 excitation. Additionally, the Sn → S1 nonradiative relaxation time is found to change by varying the delay time between the two pump pulses. The observed dependence of the lowest excited state population as well as its dependence on the delay between the two pump pulses are found to fit a kinetic model in which the Sn state populates a different surface (called S′1) than the one being directly excited (S1). The possible involvement of the Ag type states, the J intermediate, and the conical intersection leading to the S0 or to the isomerization product (K intermediate) are discussed in the framework of the proposed model.

Excited-state dynamics in photosystem II: Insights from the x-ray crystal structure

The heart of oxygenic photosynthesis is photosystem II (PSII), a multisubunit protein complex that uses solar energy to drive the splitting of water and production of molecular oxygen. The effectiveness of the photochemical reaction center of PSII depends on the efficient transfer of excitation energy from the surrounding antenna chlorophylls. A kinetic model for PSII, based on the x-ray crystal structure coordinates of 37 antenna and reaction center pigment molecules, allows us to map the major energy transfer routes from the antenna chlorophylls to the reaction center chromophores. The model shows that energy transfer to the reaction center is slow compared with the rate of primary electron transport and depends on a few bridging chlorophyll molecules. This unexpected energetic isolation of the reaction center in PSII is similar to that found in the bacterial photosystem, conflicts with the established view of the photophysics of PSII, and may be a functional requirement for primary photochemistry in photosynthesis. In addition, the model predicts a value for the intrinsic photochemical rate constant that is 4 times that found in bacterial reaction centers.

Responses of the phototransduction cascade to dim light.

The biochemistry of visual excitation is kinetically explored by measuring the activity of the cGMP phosphodiesterase (PDE) at light levels that activate only a few tens of rhodopsin molecules per rod. At 23 degrees C and in the presence of ATP, the pulse of PDE activity lasts 4 s (full width at half maximum). Complementing the rod outer segments (ROS) with rhodopsin kinase (RK) and arrestin or its splice variant p44 does not significantly shorten the pulse. But when the ROS are washed, the duration of the signal doubles. Adding either arrestin or p44 back to washed ROS approximately restores the pulse width to its initial value, with p44 being 10 times more efficient than arrestin. This supports the idea that, in vivo, capping of phosphorylated R* is mostly done by p44. When myristoylated (14:0) recoverin is added to unwashed ROS, the pulse duration and amplitude increase by about 50% if the free calcium is 500 nM. This effect increases further if the calcium is raised to 1 microM. Whenever R* deactivation is changed--when RK is exogenously enriched or when ATP is omitted from the buffer--there is no impact on the rising slope of the PDE pulse but only on its amplitude and duration. We explain this effect as due to the unequal competition between transducin and RK for R*. The kinetic model issued from this idea fits the data well, and its prediction that enrichment with transducin should lengthen the PDE pulse is successfully validated.

Peptide interfacial adsorption is kinetically limited by the thermodynamic stability of self association

We present a study of the adsorption of two peptides at the octane–water interface. The first peptide, Lac21, exists in mixed monomer–tetramer equilibrium in bulk solution with an appreciable monomer concentration. The second peptide, Lac28, exists as a tetramer in solution, with minimal exposed hydrophobic surface. A kinetic limitation to interfacial adsorption exists for Lac28 at moderate to high surface coverage that is not observed for Lac21. We estimate the potential energy barrier for Lac28 adsorption to be 42 kJ/mol and show that this is comparable to the expected free energy barrier for tetramer dissociation. This finding suggests that, at moderate to high surface coverage, adsorption is kinetically limited by the availability of interfacially active monomeric “domains” in the subinterfacial region. We also show how the commonly used empirical equation for protein adsorption dynamics can be used to estimate the potential energy barrier for adsorption. Such an approach is shown to be consistent with a formal description of diffusion–adsorption, provided a large potential energy barrier exists. This work demonstrates that the dynamics of interfacial adsorption depend on protein thermodynamic stability, and hence structure, in a quantifiable way.

Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

A statistical mechanical model for β-hairpin kinetics

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here, we describe a simple statistical mechanical model for the formation of a β-hairpin, the minimal structural element of the antiparallel β-pleated sheet. The model accurately describes the thermodynamic and kinetic behavior of a 16-residue, β-hairpin-forming peptide, successfully explaining its two-state behavior and apparent negative activation energy for folding. The model classifies structures according to their backbone conformation, defined by 15 pairs of dihedral angles, and is further simplified by considering only the 120 structures with contiguous stretches of native pairs of backbone dihedral angles. This single sequence approximation is tested by comparison with a more complete model that includes the 215 possible conformations and 15 × 215 possible kinetic transitions. Finally, we use the model to predict the equilibrium unfolding curves and kinetics for several variants of the β-hairpin peptide.