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.

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.

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.

A synthetic oscillatory network of transcriptional regulators.

Networks of interacting biomolecules carry out many essential functions in living cells, but the 'design principles' underlying the functioning of such intracellular networks remain poorly understood, despite intensive efforts including quantitative analysis of relatively simple systems. Here we present a complementary approach to this problem: the design and construction of a synthetic network to implement a particular function. We used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli. The network periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells. The resulting oscillations, with typical periods of hours, are slower than the cell-division cycle, so the state of the oscillator has to be transmitted from generation to generation. This artificial clock displays noisy behaviour, possibly because of stochastic fluctuations of its components. Such 'rational network design may lead both to the engineering of new cellular behaviours and to an improved understanding of naturally occurring networks.

From molecular to modular cell biology.

Cellular functions, such as signal transmission, are carried out by 'modules' made up of many species of interacting molecules. Understanding how modules work has depended on combining phenomenological analysis with molecular studies. General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences such as engineering and computer science, from stronger interactions between experiment and theory in cell biology, and from an appreciation of evolutionary constraints.

Robustness in bacterial chemotaxis.

Networks of interacting proteins orchestrate the responses of living cells to a variety of external stimuli, but how sensitive is the functioning of these protein networks to variations in their biochemical parameters? One possibility is that to achieve appropriate function, the reaction rate constants and enzyme concentrations need to be adjusted in a precise manner, and any deviation from these 'fine-tuned' values ruins the network's performance. An alternative possibility is that key properties of biochemical networks are robust; that is, they are insensitive to the precise values of the biochemical parameters. Here we address this issue in experiments using chemotaxis of Escherichia coli, one of the best-characterized sensory systems. We focus on how response and adaptation to attractant signals vary with systematic changes in the intracellular concentration of the components of the chemotaxis network. We find that some properties, such as steady-state behaviour and adaptation time, show strong variations in response to varying protein concentrations. In contrast, the precision of adaptation is robust and does not vary with the protein concentrations. This is consistent with a recently proposed molecular mechanism for exact adaptation, where robustness is a direct consequence of the network's architecture.

Protein mobility in the cytoplasm of Escherichia coli.

The rate of protein diffusion in bacterial cytoplasm may constrain a variety of cellular functions and limit the rates of many biochemical reactions in vivo. In this paper, we report noninvasive measurements of the apparent diffusion coefficient of green fluorescent protein (GFP) in the cytoplasm of Escherichia coli. These measurements were made in two ways: by photobleaching of GFP fluorescence and by photoactivation of a red-emitting fluorescent state of GFP (M. B. Elowitz, M. G. Surette, P. E. Wolf, J. Stock, and S. Leibler, Curr. Biol. 7:809-812, 1997). The apparent diffusion coefficient, Da, of GFP in E. coli DH5alpha was found to be 7.7 +/- 2.5 microm2/s. A 72-kDa fusion protein composed of GFP and a cytoplasmically localized maltose binding protein domain moves more slowly, with Da of 2.5 +/- 0.6 microm2/s. In addition, GFP mobility can depend strongly on at least two factors: first, Da is reduced to 3.6 +/- 0.7 microm2/s at high levels of GFP expression; second, the addition to GFP of a small tag consisting of six histidine residues reduces Da to 4.0 +/- 2.0 microm2/s. Thus, a single effective cytoplasmic viscosity cannot explain all values of Da reported here. These measurements have implications for the understanding of intracellular biochemical networks.

Response regulator output in bacterial chemotaxis.

Chemotaxis responses in Escherichia coli are mediated by the phosphorylated response-regulator protein P-CheY. Biochemical and genetic studies have established the mechanisms by which the various components of the chemotaxis system, the membrane receptors and Che proteins function to modulate levels of CheY phosphorylation. Detailed models have been formulated to explain chemotaxis sensing in quantitative terms; however, the models cannot be adequately tested without knowledge of the quantitative relationship between P-CheY and bacterial swimming behavior. A computerized image analysis system was developed to collect extensive statistics on freeswimming and individual tethered cells. P-CheY levels were systematically varied by controlled expression of CheY in an E.coli strain lacking the CheY phosphatase, CheZ, and the receptor demethylating enzyme CheB. Tumbling frequency was found to vary with P-CheY concentration in a weakly sigmoidal fashion (apparent Hill coefficient approximately 2.5). This indicates that the high sensitivity of the chemotaxis system is not derived from highly cooperative interactions between P-CheY and the flagellar motor, but rather depends on nonlinear effects within the chemotaxis signal transduction network. The complex relationship between single flagella rotation and free-swimming behavior was examined; our results indicate that there is an additional level of information processing associated with interactions between the individual flagella. An allosteric model of the motor switching process is proposed which gives a good fit to the observed switching induced by P-CheY. Thus the level of intracellular P-CheY can be estimated from behavior determinations: approximately 30% of the intracellular pool of CheY appears to be phosphorylated in fully adapted wild-type cells.

Chromophore-assisted light inactivation and self-organization of microtubules and motors.

Chromophore-assisted light inactivation (CALI) offers the only method capable of modulating specific protein activities in localized regions and at particular times. Here, we generalize CALI so that it can be applied to a wider range of tasks. Specifically, we show that CALI can work with a genetically inserted epitope tag; we investigate the effectiveness of alternative dyes, especially fluorescein, comparing them with the standard CALI dye, malachite green; and we study the relative efficiencies of pulsed and continuous-wave illumination. We then use fluorescein-labeled hemagglutinin antibody fragments, together with relatively low-power continuous-wave illumination to examine the effectiveness of CALI targeted to kinesin. We show that CALI can destroy kinesin activity in at least two ways: it can either result in the apparent loss of motor activity, or it can cause irreversible attachment of the kinesin enzyme to its microtubule substrate. Finally, we apply this implementation of CALI to an in vitro system of motor proteins and microtubules that is capable of self-organized aster formation. In this system, CALI can effectively perturb local structure formation by blocking or reducing the degree of aster formation in chosen regions of the sample, without influencing structure formation elsewhere.

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.

Self-organization of microtubules and motors.

Cellular structures are established and maintained through a dynamic interplay between assembly and regulatory processes. Self-organization of molecular components provides a variety of possible spatial structures: the regulatory machinery chooses the most appropriate to express a given cellular function. Here we study the extent and the characteristics of self-organization using microtubules and molecular motors as a model system. These components are known to participate in the formation of many cellular structures, such as the dynamic asters found in mitotic and meiotic spindles. Purified motors and microtubules have previously been observed to form asters in vitro. We have reproduced this result with a simple system consisting solely of multi-headed constructs of the motor protein kinesin and stabilized microtubules. We show that dynamic asters can also be obtained from a homogeneous solution of tubulin and motors. By varying the relative concentrations of the components, we obtain a variety of self-organized structures. Further, by studying this process in a constrained geometry of micro-fabricated glass chambers, we demonstrate that the same final structure can be reached through different assembly 'pathways.

Robustness in simple biochemical networks.

Cells use complex networks of interacting molecular components to transfer and process information. These "computational devices of living cells" are responsible for many important cellular processes, including cell-cycle regulation and signal transduction. Here we address the issue of the sensitivity of the networks to variations in their biochemical parameters. We propose a mechanism for robust adaptation in simple signal transduction networks. We show that this mechanism applies in particular to bacterial chemotaxis. This is demonstrated within a quantitative model which explains, in a unified way, many aspects of chemotaxis, including proper responses to chemical gradients. The adaptation property is a consequence of the network's connectivity and does not require the 'fine-tuning' of parameters. We argue that the key properties of biochemical networks should be robust in order to ensure their proper functioning.

Assembly and positioning of microtubule asters in microfabricated chambers.

Intracellular organization depends on a variety of molecular assembly processes; while some of these have been studied in simplified cell-free systems, others depend on the confined geometry of cells and cannot be reconstructed using bulk techniques. To study the latter processes in vitro, we fabricated microscopic chambers that simulate the closed environment of cells. We used these chambers to study the positioning of microtubule asters. Microtubule assembly alone, without the action of molecular motors, is sufficient to position asters. Asters with short microtubules move toward the position expected from symmetry; however, once the microtubules become long enough to buckle, symmetry is broken. Calculations and experiments show that the bending-energy landscape has multiple minima. Microtubule dynamic instability modifies the landscape over time and allows asters to explore otherwise inaccessible configurations.

Motor protein mechanics: a stochastic model with minimal mechanochemical coupling.

A stochastic model for the action of motor proteins such as kinesin is presented. The mechanical components of the enzyme are 1) two identical head domains that bind to discrete sites on a microtubule and that are capable of undergoing a conformational change; and 2) an elastic element that connects each head to the rest of the molecule. We investigate the situation in which the strain dependence of the chemical reaction rates is minimal and the heads have independent biochemical cycles. The enzyme advances stochastically along a filament when one head detaches and diffuses to a new binding site, while the other head remains bound to the microtubule. We also investigate the case in which the chemical cycles of the heads are correlated so that the molecule shifts each head alternately. The predictions of the model are found to be in agreement with experimentally measured force-velocity relationships for kinesin-both when the force is applied externally and when the enzyme is loaded by a viscous drag. For reasonable values of the parameters, this agreement is quantitative. The molecular stepping characteristics observed in recent motility assays are also reproduced. A number of experiments are suggested that would provide a more stringent test of the model and help determine whether this simple picture is an appropriate description of motor proteins or whether models that include strain-dependent reaction rates or more complicated types of cooperation of the two heads need to be considered.

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.