Porters versus rowers: a unified stochastic model of motor proteins.

We present a general phenomenological theory for chemical to mechanical energy transduction by motor enzymes which is based on the classical "tight-coupling" mechanism. The associated minimal stochastic model takes explicitly into account both ATP hydrolysis and thermal noise effects. It provides expressions for the hydrolysis rate and the sliding velocity, as functions of the ATP concentration and the number of motor enzymes. It explains in a unified way many results of recent in vitro motility assays. More importantly, the theory provides a natural classification scheme for the motors: it correlates the biochemical and mechanical differences between "porters" such as cellular kinesins or dyneins, and "rowers" such as muscular myosins or flagellar dyneins.

Control of microtubule dynamics and length by cyclin A- and cyclin B-dependent kinases in Xenopus egg extracts.

In eukaryotic cells, the onset of mitosis involves cyclin molecules which interact with proteins of the cdc2 family to produce active kinases. In vertebrate cells, cyclin A dependent kinases become active in S- and pro-phases, whereas a cyclin B-dependent kinase is mostly active in metaphase. It has recently been shown that, when added to Xenopus egg extracts, bacterially produced A- and B-type cyclins associate predominantly with the same kinase catalytic subunit, namely p34cdc2, and induce its histone H1 kinase activity with different kinetics. Here, we show that in the same cell free system, both the addition of cyclin A and cyclin B changes microtubule behavior. However, the cyclin A-dependent kinase does not induce a dramatic shortening of centrosome-nucleated microtubules whereas the cyclin B-dependent kinase does, as previously reported. Analysis of the parameters of microtubule dynamics by fluorescence video microscopy shows that the dramatic shortening induced by the cyclin B-dependent kinase is correlated with a several fold increase in catastrophe frequency, an effect not observed with the cyclin A-dependent kinase. Using a simple mathematical model, we show how the length distributions of centrosome-nucleated microtubules relate to the four parameters that describe microtubule dynamics. These four parameters define a threshold between unlimited microtubule growth and the establishment of steady-state dynamics, which implies that well defined steady-state length distributions can be produced by regulating precisely the respective values of the dynamical parameters. Moreover, the dynamical model predicts that increasing catastrophe frequency is more efficient than decreasing the rescue frequency to reduce the average steady state length of microtubules. These theoretical results are quantitatively confirmed by the experimental data.

Influence of M-phase chromatin on the anisotropy of microtubule asters.

In many eukaryotic cells going through M-phase, a bipolar spindle is formed by microtubules nucleated from centrosomes. These microtubules, in addition to being "captured" by kinetochores, may be stabilized by chromatin in two different ways: short-range stabilization effects may affect microtubules in close contact with the chromatin, while long-range stabilization effects may "guide" microtubule growth towards the chromatin (e.g., by introducing a diffusive gradient of an enzymatic activity that affects microtubule assembly). Here, we use both meiotic and mitotic extracts from Xenopus laevis eggs to study microtubule aster formation and microtubule dynamics in the presence of chromatin. In "low-speed" meiotic extracts, in the presence of salmon sperm chromatin, we find that short-range stabilization effects lead to a strong anisotropy of the microtubule asters. Analysis of the dynamic parameters of microtubule growth show that this anisotropy arises from a decrease in the catastrophe frequency, an increase in the rescue frequency and a decrease in the growth velocity. In this system we also find evidence for long-range "guidance" effects, which lead to a weak anisotropy of the asters. Statistically relevant results on these long-range effects are obtained in "high-speed" mitotic extracts in the presence of artificially constructed chromatin stripes. We find that aster anisotropy is biased in the direction of the chromatin and that the catastrophe frequency is reduced in its vicinity. In this system we also find a surprising dependence of the catastrophe and the rescue frequencies on the length of microtubules nucleated from centrosomes: the catastrophe frequency increase and the rescue frequency decreases with microtubule length.

Computer simulations of self-assembled membranes.

Molecular dynamics simulations in three dimensions of particles that self-assemble to form two-dimensional, membrane-like objects are presented. Anisotropic, multibody forces, chosen so as to mimic real interactions between amphiphilic molecules, generate a finite rigidity and compressibility of the assembled membranes, as well as a finite line tension at their free edges. This model and its generalizations can be used to study a large class of phenomena taking place in fluctuating membranes. For instance, both fluid and solid-like phases, separated by a phase transition, are obtained and some of the large-scale properties of these membranes studied. In particular, thermal undulations of quasi-spherical fluid vesicles are analyzed, in a manner similar to recent experiments in lipid systems.

Physical properties determining self-organization of motors and microtubules.

In eukaryotic cells, microtubules and their associated motor proteins can be organized into various large-scale patterns. Using a simplified experimental system combined with computer simulations, we examined how the concentrations and kinetic parameters of the motors contribute to their collective behavior. We observed self-organization of generic steady-state structures such as asters, vortices, and a network of interconnected poles. We identified parameter combinations that determine the generation of each of these structures. In general, this approach may become useful for correlating the morphogenetic phenomena taking place in a biological system with the biophysical characteristics of its constituents.

An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells.

Understanding biology at the single-cell level requires simultaneous measurements of biochemical parameters and behavioral characteristics in individual cells. Here, the output of individual flagellar motors in Escherichia coli was measured as a function of the intracellular concentration of the chemotactic signaling protein. The concentration of this molecule, fused to green fluorescent protein, was monitored with fluorescence correlation spectroscopy. Motors from different bacteria exhibited an identical steep input-output relation, suggesting that they actively contribute to signal amplification in chemotaxis. This experimental approach can be extended to quantitative in vivo studies of other biochemical networks.

Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria.

The recent advances in large-scale monitoring of gene expression raise the challenge of mapping systems on the basis of kinetic expression data in living cells. To address this, we measured promoter activity in the flagellar system of Escherichia coli at high accuracy and temporal resolution by means of reporter plasmids. The genes in the pathway were ordered by analysis algorithms without dependence on mutant strains. The observed temporal program of transcription was much more detailed than was previously thought and was associated with multiple steps of flagella assembly.

Photoactivation turns green fluorescent protein red.

In the few years since its gene was first cloned, the Aequorea victoria green fluorescent protein (GFP) has become a powerful tool in cell biology, functioning as a marker for gene expression, protein localization and protein dynamics in living cells. GFP variants with improved fluorescence intensity and altered spectral characteristics have been identified, but additional GFP variants are still desirable for multiple labeling experiments, protein interaction studies and improved visibility in some organisms. In particular, long-wavelength (red) fluorescence has remained elusive. Here we describe a red-emitting, green-absorbing fluorescent state of GFP that is generated by photoactivation with blue light. GFP can be switched to its red-emitting state easily with a laser or fluorescence microscope lamp under conditions of low oxygen concentration. This previously unnoticed ability enables regional, non-invasive marking of proteins in vivo. In particular, we report here the use of GFP photoactivation to make the first direct measurements of protein diffusion in the cytoplasm of living bacteria.

Precise domain specification in the developing Drosophila embryo.

A simple morphogen gradient based on the protein bicoid is insufficient to explain the precise (i.e., similar in all embryos) setting of anteroposterior gene expression domains in the early Drosophila embryo. We present here an alternative model, based on quantitative data, which accounts for all of our observations. The model also explains the robustness of hunchback boundary setting in unnatural environments such as published recently [Luccheta, Nature 434, 1134 (2005)]. The model is based on the existence of a secondary gradient correlated to bicoid through protein degradation by the same agent.