How to Measure Load-Dependent Kinetics of Individual Motor Molecules Without a Force-Clamp.

Single-molecule force spectroscopy techniques, including optical trapping, magnetic trapping, and atomic force microscopy, have provided unprecedented opportunities to understand biological processes at the smallest biological length scales. For example, they have been used to elucidate the molecular basis of muscle contraction and intracellular cargo transport along cytoskeletal filamentous proteins. Optical trapping is among the most sophisticated single-molecule techniques. With exceptionally high spatial and temporal resolutions, it has been extensively utilized to understand biological functions at the single molecule level, such as conformational changes and force-generation of individual motor proteins or force-dependent kinetics in molecular interactions. Here, we describe a new method, "Harmonic Force Spectroscopy (HFS)." With a conventional dual-beam optical trap and a simple harmonic oscillation of the sample stage, HFS can measure the load-dependent kinetics of transient molecular interactions, such as a human ß-cardiac myosin II interacting with an actin filament. We demonstrate that the ADP release rate of an individual human ß-cardiac myosin II molecule depends exponentially on the applied load, which provides a clue to understanding the molecular mechanism behind the force-velocity curve of a contracting cardiac muscle. The experimental protocol and the data analysis are simple, fast, and efficient. This chapter provides a practical guide to the method: basic concepts, experimental setup, step-by-step experimental protocol, theory, data analysis, and results.

How to Measure Separations and Angles Between Intramolecular Fluorescent Markers.

Structure and function of an individual biomolecule can be explored with minimum two fluorescent markers of different colors. Since the light of such markers can be spectrally separated and imaged simultaneously, the markers can be colocalized. Here, we describe the method used for such two-color colocalization microscopy. Then we extend it to fluorescent markers with fixed orientations and in intramolecular proximity. Our benchmarking of this extension produced two extra results: (a) we established short double-labeled DNA molecules as probes of 3D orientation of anything to which one can attach them firmly; (b) we established how to map with super-resolution between color-separated channels, which should be useful for all dual-color colocalization measurements with either fixed or freely rotating fluorescent molecules. Throughout, we use only simple means: from each color-separated microscope image in a time-lapse movie, we simultaneously determine both the relative (x,y)-separation of the fluorophores and their individual orientations in space, both with accuracy and precision. The relative positions and orientations of two domains of the same molecule are thus time-resolved. Using short double-stranded DNA (dsDNA) molecules internally labeled with two fixed fluorophores, we (i) demonstrate the accuracy and precision of our localization- and mapping-methods, using the known structure of dsDNA as benchmark; (ii) resolve 10 base pair differences in fluorophore separations; (iii) determine the unique 3D orientation of each DNA molecule.

Combining single-molecule optical trapping and small-angle x-ray scattering measurements to compute the persistence length of a protein ER/K alpha-helix.

A relatively unknown protein structure motif forms stable isolated single alpha-helices, termed ER/K alpha-helices, in a wide variety of proteins and has been shown to be essential for the function of some molecular motors. The flexibility of the ER/K alpha-helix determines whether it behaves as a force transducer, rigid spacer, or flexible linker in proteins. In this study, we quantify this flexibility in terms of persistence length, namely the length scale over which it is rigid. We use single-molecule optical trapping and small-angle x-ray scattering, combined with Monte Carlo simulations to demonstrate that the Kelch ER/K alpha-helix behaves as a wormlike chain with a persistence length of approximately 15 nm or approximately 28 turns of alpha-helix. The ER/K alpha-helix length in proteins varies from 3 to 60 nm, with a median length of approximately 5 nm. Knowledge of its persistence length enables us to define its function as a rigid spacer in a translation initiation factor, as a force transducer in the mechanoenzyme myosin VI, and as a flexible spacer in the Kelch-motif-containing protein.

Automatic differentiation of multichannel EEG signals.

Intention of movement of left or right index finger, or right foot is recognized in electroencephalograms (EEGs) from three subjects. We present a multichannel classification method that uses a "committee" of artificial neural networks to do this. The classification method automatically finds spatial regions on the skull relevant for the classification task. Depending on subject, correct recognition of intended movement was achieved in 75%-98% of trials not seen previously by the committee, on the basis of single EEGs of one-second duration. Frequency filtering did not improve recognition. Classification was optimal during the actual movement, but a first peak in the classification success rate was observed in all subjects already when they had been cued which movement later to perform.

Classification of movement-related EEG in a memorized delay task experiment.

OBJECTIVES: We studied the activation of cortical motor areas during a memorized delay task with a classification technique. METHODS: Multichannel EEG was recorded during the sequence of warning stimulus, visual cue, reaction stimulus, and actual execution of hand or foot movements. Two different approaches are presented: first, we trained a classifier on data from the time segments immediately preceding the actual movements, and analyzed the whole recordings in overlapping segments with this fixed classifier. The classification rates obtained as a function of experimental time reflect the activation of the same cortical areas that are active during the actual movements. In the second approach, we trained classifiers on data segments with the same latency in time as the data tested ('running classifiers'). By this, we checked whether we could detect event-related activity sufficiently marked to allow for correct classification. RESULTS: With the fixed classifier approach we found two maxima of classification: one maximum after processing of the visual cue corresponding to an activation of motor cortex without overt movement, and a second maximum at the time of the actual movement. The first maximum relates to a very short-lived brain state, in the order of 300 ms, while the broad second maximum (1.5 s) indicates a very stable and long-lasting activation. CONCLUSIONS: With the running classifier approach we found similar maxima as with the fixed classifier, indicating that only the activity of motor areas is relevant for classification. Possible implications of our findings for the development of a brain computer interface (BCI) are discussed.

Designing optimal spatial filters for single-trial EEG classification in a movement task.

We devised spatial filters for multi-channel EEG that lead to signals which discriminate optimally between two conditions. We demonstrate the effectiveness of this method by classifying single-trial EEGs, recorded during preparation for movements of the left or right index finger or the right foot. The classification rates for 3 subjects were 94, 90 and 84%, respectively. The filters are estimated from a set of multichannel EEG data by the method of Common Spatial Patterns, and reflect the selective activation of cortical areas. By construction, we obtain an automatic weighting of electrodes according to their importance for the classification task. Computationally, this method is parallel by nature, and demands only the evaluation of scalar products. Therefore, it is well suited for on-line data processing. The recognition rates obtained with this relatively simple method are as good as, or higher than those obtained previously with other methods. The high recognition rates and the method's procedural and computational simplicity make it a particularly promising method for an EEG-based brain-computer interface.

Microtubule's conformational cap.

The molecular mechanisms that allow elongation of the unstable microtubule lattice remain unclear. It is usually thought that the GDP-liganded tubulin lattice is capped by a small layer of GTP- or GDP-Pi-liganded molecules, the so called "GTP-cap". Here, we point-out that the elastic properties of the microtubule lattice cause a difference in stability between the elongating tubulin sheet and the completed microtubule wall. The implications of our observations for microtubule structure and dynamics are discussed.

Limited flexibility of the inter-protofilament bonds in microtubules assembled from pure tubulin.

The superposition of the regular arrangement of tubulin subunits in microtubules gives rise to moiré patterns in cryo-electron micrographs. The moiré period can be predicted from the dimensions of the tubulin subunits and their arrangement in the surface lattice. Although the average experimental moiré period is usually in good agreement with the theoretical one, there is variation both within and between microtubules. In this study, we addressed the origin of this variability. We examined different possibilities, including artefacts induced by the preparation of the vitrified samples, and variations of the parameters that describe the microtubule surface lattice. We show that neither flattening nor bending of the microtubules, nor changes in the subunit dimensions, can account for the moiré period variations observed in 12 and 14 protofilament microtubules. These can be interpreted as slight variations, in the range -0.5 A to +0.9 A, of the lateral interactions between tubulin subunits in adjacent protofilaments. These results indicate that the inter-protofilament bonds are precisely maintained in microtubules assembled in vitro from pure tubulin. The fact that the moiré period is not affected by bending indicates that the local interactions between tubulin subunits are sufficiently stiff to accommodate large deformations of the microtubule wall.

Modeling elastic properties of microtubule tips and walls.

Electron micrographs of tips of growing and shrinking microtubules are analyzed and interpreted. The many shapes observed are all consistent with a simple mechanical model, a flexible tube with competing intrinsic curvatures. Observations are also consistent with growing and shrinking microtubules having the same intrinsic curvature for protofilaments, the one observed in oligomers peeling off shrinking microtubules. If this is so, the lateral bonds between protofilaments are responsible for the difference between shapes of tips on growing and shrinking microtubules.

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.

Evolution as a self-organized critical phenomenon.

We present a simple mathematical model of biological macroevolution. The model describes an ecology of adapting, interacting species. The environment of any given species is affected by other evolving species; hence, it is not constant in time. The ecology as a whole evolves to a "self-organized critical" state where periods of stasis alternate with avalanches of causally connected evolutionary changes. This characteristic behavior of natural history, known as "punctuated equilibrium," thus finds a theoretical explanation as a self-organized critical phenomenon. The evolutionary behavior of single species is intermittent. Also, large bursts of apparently simultaneous evolutionary activity require no external cause. Extinctions of all sizes, including mass extinctions, may be a simple consequence of ecosystem dynamics. Our results are compared with data from the fossil record.