Extension of the thermodynamics of small systems to open metastable states: An example

By using a simplified model of small open liquid-like clusters with surface effects, in the gas phase, it is shown how the statistical thermodynamics of small systems can be extended to include metastable supersaturated gaseous states not too far from the gas–liquid equilibrium transition point. To accomplish this, one has to distinguish between mathematical divergence and physical convergence of the open-system partition function.

A double-hexamer archaeal minichromosome maintenance protein is an ATP-dependent DNA helicase

The minichromosome maintenance (MCM) proteins are essential for DNA replication in eukaryotes. Thus far, all eukaryotes have been shown to contain six highly related MCMs that apparently function together in DNA replication. Sequencing of the entire genome of the thermophilic archaeon Methanobacterium thermoautotrophicum has allowed us to identify only a single MCM-like gene (ORF Mt1770). This gene is most similar to MCM4 in eukaryotic cells. Here we have expressed and purified the M. thermoautotrophicum MCM protein. The purified protein forms a complex that has a molecular mass of ≈850 kDa, consistent with formation of a double hexamer. The protein has an ATP-independent DNA-binding activity, a DNA-stimulated ATPase activity that discriminates between single- and double-stranded DNA, and a strand-displacement (helicase) activity that can unwind up to 500 base pairs. The 3′ to 5′ helicase activity requires both ATP hydrolysis and a functional nucleotide-binding site. Moreover, the double hexamer form is the active helicase. It is therefore likely that an MCM complex acts as the replicative DNA helicase in eukaryotes and archaea. The simplified replication machinery in archaea may provide a simplified model for assembly of the machinery required for initiation of eukaryotic DNA replication.

Gamma rhythms and beta rhythms have different synchronization properties

Experimental and modeling efforts suggest that rhythms in the CA1 region of the hippocampus that are in the beta range (12–29 Hz) have a different dynamical structure than that of gamma (30–70 Hz). We use a simplified model to show that the different rhythms employ different dynamical mechanisms to synchronize, based on different ionic currents. The beta frequency is able to synchronize over long conduction delays (corresponding to signals traveling a significant distance in the brain) that apparently cannot be tolerated by gamma rhythms. The synchronization properties are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are used for higher level interactions involving more distant structures.

Electrostatic interactions between rotor and stator in the bacterial flagellar motor

Bacterial flagellar motors rotate, obtaining power from the membrane gradient of protons or, in some species, sodium ions. Torque generation in the flagellar motor must involve interactions between components of the rotor and components of the stator. Sites of interaction between the rotor and stator have not been identified. Mutational studies of the rotor protein FliG and the stator protein MotA showed that both proteins contain charged residues essential for motor rotation. This suggests that functionally important electrostatic interactions might occur between the rotor and stator. To test this proposal, we examined double mutants with charged-residue substitutions in both the rotor protein FliG and the stator protein MotA. Several combinations of FliG mutations with MotA mutations exhibited strong synergism, whereas others showed strong suppression, in a pattern that indicates that the functionally important charged residues of FliG interact with those of MotA. These results identify a functionally important site of interaction between the rotor and stator and suggest a hypothesis for electrostatic interactions at the rotor–stator interface.

Intrastriatal injection of an adenoviral vector expressing glial-cell-line-derived neurotrophic factor prevents dopaminergic neuron degeneration and behavioral impairment in a rat model of Parkinson disease

Glial-cell-line-derived neurotrophic factor (GDNF) is a potent neurotrophic factor for adult nigral dopamine neurons in vivo. GDNF has both protective and restorative effects on the nigro-striatal dopaminergic (DA) system in animal models of Parkinson disease. Appropriate administration of this factor is essential for the success of its clinical application. Since it cannot cross the blood–brain barrier, a gene transfer method may be appropriate for delivery of the trophic factor to DA cells. We have constructed a recombinant adenovirus (Ad) encoding GDNF and injected it into rat striatum to make use of its ability to infect neurons and to be retrogradely transported by DA neurons. Ad-GDNF was found to drive production of large amounts of GDNF, as quantified by ELISA. The GDNF produced after gene transfer was biologically active: it increased the survival and differentiation of DA neurons in vitro. To test the efficacy of the Ad-mediated GDNF gene transfer in vivo, we used a progressive lesion model of Parkinson disease. Rats received injections unilaterally into their striatum first of Ad and then 6 days later of 6-hydroxydopamine. We found that mesencephalic nigral dopamine neurons of animals treated with the Ad-GDNF were protected, whereas those of animals treated with the Ad-β-galactosidase were not. This protection was associated with a difference in motor function: amphetamine-induced turning was much lower in animals that received the Ad-GDNF than in the animals that received Ad-β-galactosidase. This finding may have implications for the development of a treatment for Parkinson disease based on the use of neurotrophic factors.

A model of excitation and adaptation in bacterial chemotaxis

Bacterial chemotaxis is widely studied because of its accessibility and because it incorporates processes that are important in a number of sensory systems: signal transduction, excitation, adaptation, and a change in behavior, all in response to stimuli. Quantitative data on the change in behavior are available for this system, and the major biochemical steps in the signal transduction/processing pathway have been identified. We have incorporated recent biochemical data into a mathematical model that can reproduce many of the major features of the intracellular response, including the change in the level of chemotactic proteins to step and ramp stimuli such as those used in experimental protocols. The interaction of the chemotactic proteins with the motor is not modeled, but we can estimate the degree of cooperativity needed to produce the observed gain under the assumption that the chemotactic proteins interact directly with the motor proteins.

Kinesin’s processivity results from mechanical and chemical coordination between the ATP hydrolysis cycles of the two motor domains

Kinesin is a processive motor protein: A single molecule can walk continuously along a microtubule for several micrometers, taking hundreds of 8-nm steps without dissociating. To elucidate the biochemical and structural basis for processivity, we have engineered a heterodimeric one-headed kinesin and compared its biochemical properties to those of the wild-type two-headed molecule. Our construct retains the functionally important neck and tail domains and supports motility in high-density microtubule gliding assays, though it fails to move at the single-molecule level. We find that the ATPase rate of one-headed kinesin is 3–6 s−1 and that detachment from the microtubule occurs at a similar rate (3 s−1). This establishes that one-headed kinesin usually detaches once per ATP hydrolysis cycle. Furthermore, we identify the rate-limiting step in the one-headed hydrolysis cycle as detachment from the microtubule in the ADP⋅Pi state. Because the ATPase and detachment rates are roughly an order of magnitude lower than the corresponding rates for two-headed kinesin, the detachment of one head in the homodimer (in the ADP⋅Pi state) must be accelerated by the other head. We hypothesize that this results from internal strain generated when the second head binds. This idea accords with a hand-over-hand model for processivity in which the release of the trailing head is contingent on the binding of the forward head. These new results, together with previously published ones, allow us to propose a pathway that defines the chemical and mechanical cycle for two-headed kinesin.

A neuronal model of a global workspace in effortful cognitive tasks

A minimal hypothesis is proposed concerning the brain processes underlying effortful tasks. It distinguishes two main computational spaces: a unique global workspace composed of distributed and heavily interconnected neurons with long-range axons, and a set of specialized and modular perceptual, motor, memory, evaluative, and attentional processors. Workspace neurons are mobilized in effortful tasks for which the specialized processors do not suffice. They selectively mobilize or suppress, through descending connections, the contribution of specific processor neurons. In the course of task performance, workspace neurons become spontaneously coactivated, forming discrete though variable spatio-temporal patterns subject to modulation by vigilance signals and to selection by reward signals. A computer simulation of the Stroop task shows workspace activation to increase during acquisition of a novel task, effortful execution, and after errors. We outline predictions for spatio-temporal activation patterns during brain imaging, particularly about the contribution of dorsolateral prefrontal cortex and anterior cingulate to the workspace.

A model of long-term memory storage in the cerebellar cortex: A possible role for plasticity at parallel fiber synapses onto stellate/basket interneurons

By evoking changes in climbing fiber activity, movement errors are thought to modify synapses from parallel fibers onto Purkinje cells (pf*Pkj) so as to improve subsequent motor performance. Theoretical arguments suggest there is an intrinsic tradeoff, however, between motor adaptation and long-term storage. Assuming a baseline rate of motor errors is always present, then repeated performance of any learned movement will generate a series of climbing fiber-mediated corrections. By reshuffling the synaptic weights responsible for any given movement, such corrections will degrade the memories for other learned movements stored in overlapping sets of synapses. The present paper shows that long-term storage can be accomplished by a second site of plasticity at synapses from parallel fibers onto stellate/basket interneurons (pf*St/Bk). Plasticity at pf*St/Bk synapses can be insulated from ongoing fluctuations in climbing fiber activity by assuming that changes in pf*St/Bk synapses occur only after changes in pf*Pkj synapses have built up to a threshold level. Although climbing fiber-dependent plasticity at pf*Pkj synapses allows for the exploration of novel motor strategies in response to changing environmental conditions, plasticity at pf*St/Bk synapses transfers successful strategies to stable long-term storage. To quantify this hypothesis, both sites of plasticity are incorporated into a dynamical model of the cerebellar cortex and its interactions with the inferior olive. When used to simulate idealized motor conditioning trials, the model predicts that plasticity develops first at pf*Pkj synapses, but with additional training is transferred to pf*St/Bk synapses for long-term storage.

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.

A test of the "jigsaw puzzle" model for protein folding by multiple methionine substitutions within the core of T4 lysozyme.

To test whether the structure of a protein is determined in a manner akin to the assembly of a jigsaw puzzle, up to 10 adjacent residues within the core of T4 lysozyme were replaced by methionine. Such variants are active and fold cooperatively with progressively reduced stability. The structure of a seven-methionine variant has been shown, crystallographically, to be similar to wild type and to maintain a well ordered core. The interaction between the core residues is, therefore, not strictly comparable with the precise spatial complementarity of the pieces of a jigsaw puzzle. Rather, a certain amount of give and take in forming the core structure is permitted. A simplified hydrophobic core sequence, imposed without genetic selection or computer-based design, is sufficient to retain native properties in a globular protein.

Motor learning by field approximation.

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.

The neck region of the myosin motor domain acts as a lever arm to generate movement.

The myosin head consists of a globular catalytic domain that binds actin and hydrolyzes ATP and a neck domain that consists of essential and regulatory light chains bound to a long alpha-helical portion of the heavy chain. The swinging neck-level model assumes that a swinging motion of the neck relative to the catalytic domain is the origin of movement. This model predicts that the step size, and consequently the sliding velocity, are linearly related to the length of the neck. We have tested this point by characterizing a series of mutant Dictyostelium myosins that have different neck lengths. The 2xELCBS mutant has an extra binding site for essential light chain. The delta RLCBS mutant myosin has an internal deletion that removes the regulatory light chain binding site. The delta BLCBS mutant lacks both light chain binding sites. Wild-type myosin and these mutant myosins were subjected to the sliding filament in vitro motility assay. As expected, mutants with shorter necks move slower than wild-type myosin in vitro. Most significantly, a mutant with a longer neck moves faster than the wild type, and the sliding velocities of these myosins are linearly related to the neck length, as predicted by the swinging neck-lever model. A simple extrapolation to zero speed predicts that the fulcrum point is in the vicinity of the SH1-SH2 region in the catalytic domain.

ncd and kinesin motor domains interact with both alpha- and beta-tubulin.

Motor domains of the Drosophila minus-end-directed microtubule (MT) motor protein ncd, were found to saturate microtubule binding sites at a stoichiometry of approximately one motor domain per tubulin dimer. To determine the tubulin subunit(s) involved in binding to ncd, mixtures of ncd motor domain and MTs were treated with the zero-length cross-linker 1-ethyl-3-(3-dimethylaminopropyl-carbodiimide) (EDC). EDC treatment generated covalently cross-linked products of ncd and alpha-tubulin and of ncd and beta-tubulin, indicating that the ncd motor domain interacts with both alpha- and beta-tubulin. When the Drosophila kinesin motor domain protein was substituted for the ncd motor domain, cross-linked products of kinesin and alpha-tubulin and of kinesin and beta-tubulin were produced. EDC treatment of mixtures of ncd motor domain and unassembled tubulin dimers or of kinesin motor domain and unassembled tubulin dimers produced the same motor-tubulin products generated in the presence of MTs. These results indicate that kinesin family motors of opposite polarity interact with both tubulin monomers and support a model in which some portion of each protein's motor domain overlaps adjacent alpha- and beta-tubulin subunits.