Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

NMR investigation of ferricytochrome c unfolding: Detection of an equilibrium unfolding intermediate and residual structure in the denatured state

Horse ferricytochrome c (cyt c) undergoes exchange of one of its axial heme ligands (Met-80) for one or more non-native ligands under denaturing conditions. We have used 1H NMR spectroscopy to detect two conformations of paramagnetic cyt c with non-native heme ligation through a range of urea concentrations. One non-native form is an equilibrium unfolding intermediate observed under partially denaturing conditions and is attributed to replacement of Met-80 with one or more Lys side chains. The second non-native form, in which the native Met ligand is replaced by a His, is observed under strongly denaturing conditions. Thermodynamic analysis of these data indicates a relatively small ΔG (17 kJ/mol) for the transition from native to the Lys-ligated intermediate and a significantly larger ΔG (47 kJ/mol) for the transition from native to the His-ligated species. Although CD and fluorescence data indicate that the equilibrium unfolding of cyt c is a two-state process, these NMR results implicate an intermediate with His-Lys ligation.

Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

Diverse roles of the tumor necrosis factor family member TRANCE in skeletal physiology revealed by TRANCE deficiency and partial rescue by a lymphocyte-expressed TRANCE transgene

Tumor necrosis factor-related, activation-induced cytokine (TRANCE), a tumor necrosis factor family member, mediates survival of dendritic cells in the immune system and is required for osteoclast differentiation and activation in the skeleton. We report the skeletal phenotype of TRANCE-deficient mice and its rescue by the TRANCE transgene specifically expressed in lymphocytes. TRANCE-deficient mice showed severe osteopetrosis, with no osteoclasts, marrow spaces, or tooth eruption, and exhibited profound growth retardation at several skeletal sites, including the limbs, skull, and vertebrae. These mice had marked chondrodysplasia, with thick, irregular growth plates and a relative increase in hypertrophic chondrocytes. Transgenic overexpression of TRANCE in lymphocytes of TRANCE-deficient mice rescued osteoclast development in two locations in growing long bones: excavation of marrow cavities permitting hematopoiesis in the marrow spaces, and remodeling of osteopetrotic woven bone in the shafts of long bones into histologically normal lamellar bone. However, osteoclasts in these mice failed to appear at the chondroosseous junction and the metaphyseal periosteum of long bones, nor were they present in tooth eruption pathways. These defects resulted in sclerotic metaphyses with persistence of club-shaped long bones and unerupted teeth, and the growth plate defects were largely unimproved by the TRANCE transgene. Thus, TRANCE-mediated regulation of the skeleton is complex, and impacts chondrocyte differentiation and osteoclast formation in a manner that likely requires local delivery of TRANCE.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

A Computer-Assisted Personalized Approach in an Undergraduate Plant Physiology Class1

We used Computer-Assisted Personalized Approach (CAPA), a networked teaching and learning tool that generates computer individualized homework problem sets, in our large-enrollment introductory plant physiology course. We saw significant improvement in student examination performance with regular homework assignments, with CAPA being an effective and efficient substitute for hand-graded homework. Using CAPA, each student received a printed set of similar but individualized problems of a conceptual (qualitative) and/or quantitative nature with quality graphics. Because each set of problems is unique, students were encouraged to work together to clarify concepts but were required to do their own work for credit. Students could enter answers multiple times without penalty, and they were able to obtain immediate feedback and hints until the due date. These features increased student time on task, allowing higher course standards and student achievement in a diverse student population. CAPA handles routine tasks such as grading, recording, summarizing, and posting grades. In anonymous surveys, students indicated an overwhelming preference for homework in CAPA format, citing several features such as immediate feedback, multiple tries, and on-line accessibility as reasons for their preference. We wrote and used more than 170 problems on 17 topics in introductory plant physiology, cataloging them in a computer library for general access. Representative problems are compared and discussed.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Partial molar volume, surface area, and hydration changes for equilibrium unfolding and formation of aggregation transition state: High-pressure and cosolute studies on recombinant human IFN-γ

The equilibrium dissociation of recombinant human IFN-γ was monitored as a function of pressure and sucrose concentration. The partial molar volume change for dissociation was −209 ± 13 ml/mol of dimer. The specific molar surface area change for dissociation was 12.7 ± 1.6 nm2/molecule of dimer. The first-order aggregation rate of recombinant human IFN-γ in 0.45 M guanidine hydrochloride was studied as a function of sucrose concentration and pressure. Aggregation proceeded through a transition-state species, N*. Sucrose reduced aggregation rate by shifting the equilibrium between native state (N) and N* toward the more compact N. Pressure increased aggregation rate through increased solvation of the protein, which exposes more surface area, thus shifting the equilibrium away from N toward N*. The changes in partial molar volume and specific molar surface area between the N* and N were −41 ± 9 ml/mol of dimer and 3.5 ± 0.2 nm2/molecule, respectively. Thus, the structural change required for the formation of the transition state for aggregation is small relative to the difference between N and the dissociated state. Changes in waters of hydration were estimated from both specific molar surface area and partial molar volume data. From partial molar volume data, estimates were 25 and 128 mol H2O/mol dimer for formation of the aggregation transition state and for dissociation, respectively. From surface area data, estimates were 27 and 98 mol H2O/mol dimer. Osmotic stress theory yielded values ≈4-fold larger for both transitions.

Effects of Oxygen on Nodule Physiology and Expression of Nodulins in Alfalfa1

Early nodulin 2 (ENOD2) transcripts and protein are specifically found in the inner cortex of legume nodules, a location that coincides with the site of a barrier to O2 diffusion. The extracellular glycoprotein that binds the monoclonal antibody MAC236 has also been localized to this site. Thus, it has been proposed that these proteins function in the regulation of nodule permeability to O2 diffusion. It would then be expected that the levels of ENOD2 mRNA/protein and MAC236 antigen would differ in nodules with different permeabilities to O2. We examined the expression of ENOD2 and other nodule-expressed genes in Rhizobium meliloti-induced alfalfa nodules grown under 8, 20, or 50% O2. Although there was a change in the amount of MAC236 glycoprotein, the levels of ENOD2 mRNA and protein did not differ significantly among nodules grown at the different [O2], suggesting that neither ENOD2 transcription nor synthesis is involved in the long-term regulation of nodule permeability. Moreover, although nodules from all treatments reduced their permeability to O2 as the partial pressure of O2 (pO2) was increased to 100%, the levels of extractable ENOD2 and MAC236 proteins did not differ from those measured at the growth pO2, further suggesting that if these proteins are involved in a short-term regulation of the diffusion barrier, they must be involved in a way that does not require increased transcription or protein synthesis.

Phosphorylation by protein kinase C of serine-23 of the alpha-1 subunit of rat Na+,K(+)-ATPase affects its conformational equilibrium.

Phosphorylation of the alpha-1 subunit of rat Na+,K(+)-ATPase by protein kinase C has been shown previously to decrease the activity of the enzyme in vitro. We have now undertaken an investigation of the mechanism by which this inhibition occurs. Analysis of the phosphorylation of recombinant glutathione S-transferase fusion proteins containing putative cytoplasmic domains of the protein, site-directed mutagenesis, and two-dimensional peptide mapping indicated that protein kinase C phosphorylated the alpha-1 subunit of the rat Na+,K(+)-ATPase within the extreme NH2-terminal domain, on serine-23. The phosphorylation of this residue resulted in a shift in the equilibrium toward the E1 form, as measured by eosin fluorescence studies, and this was associated with a decrease in the apparent K+ affinity of the enzyme, as measured by ATPase activity assays. The rate of transition from E2 to E1 was apparently unaffected by phosphorylation by protein kinase C. These results, together with previous studies that examined the effects of tryptic digestion of Na+,K(+)-ATPase, suggest that the NH2-terminal domain of the alpha-1 subunit, including serine-23, is involved in regulating the activity of the enzyme.

Targeted deletion in astrocyte intermediate filament (Gfap) alters neuronal physiology.

Glial fibrillary acidic protein (GFAP) is a member of the family of intermediate filament structural proteins and is found predominantly in astrocytes of the central nervous system (CNS). To assess the function of GFAP, we created GFAP-null mice using gene targeting in embryonic stem cells. The GFAP-null mice have normal development and fertility, and show no gross alterations in behavior or CNS morphology. Astrocytes are present in the CNS of the mutant mice, but contain a severely reduced number of intermediate filaments. Since astrocyte processes contact synapses and may modulate synaptic function, we examined whether the GFAP-null mice were altered in long-term potentiation in the CA1 region of the hippocampus. The GFAP-null mice displayed enhanced long-term potentiation of both population spike amplitude and excitatory post-synaptic potential slope compared to control mice. These data suggest that GFAP is important for astrocyte-neuronal interactions, and that astrocyte processes play a vital role in modulating synaptic efficacy in the CNS. These mice therefore represent a direct demonstration that a primary defect in astrocytes influences neuronal physiology.