David Zwicker

Tracking Single Particles and Elongated Filaments with Nanometer Precision

Recent developments in image processing have greatly advanced our understanding of biomolecular processes in vitro and in vivo. In particular, using Gaussian models to fit the intensity profiles of nanometer-sized objects have enabled their two-dimensional localization with a precision in the one-nanometer range. Here, we present an algorithm to precisely localize curved filaments whose structures are characterized by subresolution diameters and micrometer lengths. Using surface-immobilized microtubules, fluorescently labeled with rhodamine, we demonstrate positional precisions of ∼2 nm when determining the filament centerline and ∼9 nm when localizing the filament tips. Combined with state-of-the-art single particle tracking we apply the algorithm 1), to motor-proteins stepping on immobilized microtubules, 2), to depolymerizing microtubules, and 3), to microtubules gliding over motor-coated surfaces.

Robust circadian clocks from coupled protein-modification and transcription–translation cycles

The cyanobacterium Synechococcus elongatus uses both a protein phosphorylation cycle and a transcription–translation cycle to generate circadian rhythms that are highly robust against biochemical noise. We use stochastic simulations to analyze how these cycles interact to generate stable rhythms in growing, dividing cells. We find that a protein phosphorylation cycle by itself is robust when protein turnover is low. For high decay or dilution rates (and compensating synthesis rates), however, the phosphorylation-based oscillator loses its integrity. Circadian rhythms thus cannot be generated with a phosphorylation cycle alone when the growth rate, and consequently the rate of protein dilution, is high enough; in practice, a purely posttranslational clock ceases to function well when the cell doubling time drops below the 24-h clock period. At higher growth rates, a transcription–translation cycle becomes essential for generating robust circadian rhythms. Interestingly, although a transcription–translation cycle is necessary to sustain a phosphorylation cycle at high growth rates, a phosphorylation cycle can dramatically enhance the robustness of a transcription–translation cycle at lower protein decay or dilution rates. In fact, the full oscillator built from these two tightly intertwined cycles far outperforms not just each of its two components individually, but also a hypothetical system in which the two parts are coupled as in textbook models of coupled phase oscillators. Our analysis thus predicts that both cycles are required to generate robust circadian rhythms over the full range of growth conditions.

Centrosomes are autocatalytic droplets of pericentriolar material organized by centrioles

Significance How cells position their proteins is still an open question. Here, we propose a physical description of centrosomes, which are membraneless organelles involved in cell division. In our model, centrosome material occurs in a soluble form and a form that tends to form droplets by phase separation. We find that an autocatalytic chemical transition between these forms quantitatively accounts for our experimental data. Importantly, a catalytic activity of the centrioles, which are located inside centrosomes, can control centrosome nucleation and suppress Ostwald ripening to allow for two equal-sized centrosomes to coexist in the cell. Consequently, our example shows how the combination of chemical reactions and phase separation can be used to control the formation of liquid-like compartments in cells. Centrosomes are highly dynamic, spherical organelles without a membrane. Their physical nature and their assembly are not understood. Using the concept of phase separation, we propose a theoretical description of centrosomes as liquid droplets. In our model, centrosome material occurs in a form soluble in the cytosol and a form that tends to undergo phase separation from the cytosol. We show that an autocatalytic chemical transition between these forms accounts for the temporal evolution observed in experiments. Interestingly, the nucleation of centrosomes can be controlled by an enzymatic activity of the centrioles, which are present at the core of all centrosomes. This nonequilibrium feature also allows for multiple stable centrosomes, a situation that is unstable in equilibrium phase separation. Our theory explains the growth dynamics of centrosomes for all cell sizes down to the eight-cell stage of the Caenorhabditis elegans embryo, and it also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with perturbed centrioles. We also propose an interpretation of the molecular details of the involved proteins in the case of C. elegans. Our example suggests a general picture of the organization of membraneless organelles.

Growth and division of active droplets provides a model for protocells

It has been proposed that during the early steps in the origin of life, small droplets could have formed via the segregation of molecules from complex mixtures by phase separation. These droplets could have provided chemical reaction centres. However, whether these droplets could divide and propagate is unclear. Here we examine the behaviour of droplets in systems that are maintained away from thermodynamic equilibrium by an external supply of energy. In these systems, droplets grow by the addition of droplet material generated by chemical reactions. Surprisingly, we find that chemically driven droplet growth can lead to shape instabilities that trigger the division of droplets into two smaller daughters. Therefore, chemically active droplets can exhibit cycles of growth and division that resemble the proliferation of living cells. Dividing active droplets could serve as a model for prebiotic protocells, where chemical reactions in the droplet play the role of a prebiotic metabolism. Droplets are an appealing picture for protocells in origin-of-life studies, but it’s unclear how they would have propagated by growth and division. Theory suggests that chemically active droplets spontaneously split into equal daughter droplets.

Polo-like kinase phosphorylation determines Caenorhabditis elegans centrosome size and density by biasing SPD-5 toward an assembly-competent conformation

ABSTRACT Centrosomes are major microtubule-organizing centers composed of centrioles surrounded by an extensive proteinacious layer called the pericentriolar material (PCM). In Caenorhabditis elegans embryos, the mitotic PCM expands by Polo-like kinase 1 (PLK-1) phosphorylation-accelerated assembly of SPD-5 molecules into supramolecular scaffolds. However, how PLK-1 phosphorylation regulates SPD-5 assembly is not known. We found that a mutant version of SPD-5 that is insensitive to PLK-1 phosphorylation (SPD-54A) could localize to PCM but was unable to rescue the reduction in PCM size and density when wild-type SPD-5 levels were decreased. In vitro, purified SPD-54A self-assembled into functional supramolecular scaffolds over long time scales, suggesting that phosphorylation only controls the rate of SPD-5 scaffold assembly. Furthermore, the SPD-5 scaffold, once assembled, remained intact and supported microtubule nucleation in the absence of PLK-1 activity in vivo. We conclude that PLK-1 is required for rapid assembly of the PCM scaffold but not for scaffold maintenance or function. Based on this idea, we developed a theoretical model that adequately predicted PCM growth rates in different mutant conditions in vivo. We propose that PLK-1 phosphorylation-dependent conversion of SPD-5 into an assembly-competent form underlies PCM formation in vivo and that the rate of this conversion determines final PCM size and density. Summary: Polo-like kinase phosphorylation determines proper centrosome scaffold size and density, but not function or maintenance, in Caenorhabditis elegans embryos.

Receptor arrays optimized for natural odor statistics.

Significance Natural odors typically consist of many molecules at different concentrations, which together determine the odor identity. This information is collectively encoded by olfactory receptors and then forwarded to the brain. However, it is unclear how the receptor activity can encode both the composition of the odor and the concentrations of its constituents. We study a simple model of the olfactory receptors from which we derive design principles for optimally communicating odor information in a given natural environment. We use these results to discuss biological olfactory systems, and we propose how they can be used to improve artificial sensor arrays. Natural odors typically consist of many molecules at different concentrations. It is unclear how the numerous odorant molecules and their possible mixtures are discriminated by relatively few olfactory receptors. Using an information theoretic model, we show that a receptor array is optimal for this task if it achieves two possibly conflicting goals: (i) Each receptor should respond to half of all odors and (ii) the response of different receptors should be uncorrelated when averaged over odors presented with natural statistics. We use these design principles to predict statistics of the affinities between receptors and odorant molecules for a broad class of odor statistics. We also show that optimal receptor arrays can be tuned to either resolve concentrations well or distinguish mixtures reliably. Finally, we use our results to predict properties of experimentally measured receptor arrays. Our work can thus be used to better understand natural olfaction, and it also suggests ways to improve artificial sensor arrays.

Primacy coding facilitates effective odor discrimination when receptor sensitivities are tuned

The olfactory system faces the difficult task of identifying an enormous variety of odors independent of their intensity. Primacy coding, where the odor identity is encoded by the receptor types that respond earliest, is one possible representation that can facilitate this task. So far, it is unclear whether primacy coding facilitates typical olfactory tasks and what constraints it implies for the olfactory system. In this paper, we develop a simple model of primacy coding, which we simulate numerically and analyze using a statistical description. We show that the encoded information depends strongly on the number of receptor types included in the primacy representation, but only weakly on the size of the receptor repertoire. The representation is independent of the odor intensity and the transmitted information is useful to perform typical olfactory tasks, like detecting a target odor or discriminating similar mixtures, with close to experimentally measured performance. Interestingly, we find situations in which a smaller receptor repertoire is advantageous for identifying a target odor. The model also suggests that overly sensitive receptor types could dominate the entire response and make the whole array useless, which allows us to predict how receptor arrays need to adapt to stay useful during environmental changes. By quantifying the information transmitted using primacy coding, we can thus connect microscopic characteristics of the olfactory system to its overall performance. Author summary Humans can identify odors independent of their intensity. Experimental data suggest that this is accomplished by representing the odor identity by the earliest responding receptor types. Using theoretical modeling, we here show that such a primacy code allows discriminating odors with close to experimentally measured performance. This performance depends strongly on the number of receptors considered in the primacy code, but the receptor repertoire size is less important. The model also suggests a strong evolutionary pressure on the receptor sensitivities, which could explain observed receptor copy number adaptations. Taken together, the model connects detailed molecular measurements to large-scale psycho-physical measurements, which will contribute to our understanding of the olfactory system.

Physical and geometric constraints shape the labyrinth-like nasal cavity

Significance Although nasal cavities fulfill similar tasks across animals, their geometry varies widely. One such task is heating and humidifying the inhaled air, which works best if the nasal cavity is narrow. However, narrow geometries have a large resistance to flow. We show that these opposing geometrical requirements are critical for shaping the nasal cavity and strongly restrict the local gap width. In contrast, the overall shape has little influence on the resistance and air conditioning, so the observed labyrinth-like patterns could emerge from geometric constraints imposed by the head. Our theory predicts geometric parameters of nasal cavities quantitatively, and it suggests that the surprisingly small nasal cavities of humans force us to become oral breathers during heavy exercise. The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates. Despite this common function, the shapes of nasal cavities vary widely across animals. To understand this variability, we here connect nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, while their overall shape can adhere to the geometric constraints imposed by the head. Our theory explains the geometric variations of natural nasal cavities quantitatively, and we hypothesize that the trade-off between high exchange efficiency and low resistance to airflow is the main driving force shaping the nasal cavity. Our model further explains why humans, whose nasal cavities evolved to be smaller than expected for their size, become obligate oral breathers in aerobically challenging situations.

Positioning of Particles in Active Droplets

Chemically active droplets are nonequilibrium systems that combine phase separation with chemical reactions. We here investigate how the activity introduced by the chemical reactions influences solid particles inside such droplets. We find that passive particles are centered in active droplets governed by first-order reactions. In autocatalytic active droplets, only catalytically active particles can be centered. An example of such systems in biology are centrosomes. Our study can account for the observed positioning of centrioles and provides a general mechanism to control the position of particles within chemically active droplets.