Measuring Molecular Diffusion in Self-Organizing Xenopus Extracts by Fluorescence Correlation Spectroscopy.

The cytoplasm is densely packed with macromolecules and organelles, displaying viscoelastic properties at various scales. How biochemical reactions function efficiently enough in a seemingly jammed environment remains elusive. Cell-free Xenopus laevis extracts represent a powerful system for investigating the biochemistry and biophysics of living systems. Here we present a protocol for characterizing macromolecular diffusion in self-organizing cytoplasmic extracts using fluorescence correlation spectroscopy (FCS), which measures the motions on a distance scale of ~200 nm. The method can also be used to characterize diffusion in the cytoplasm as it progresses through different phases of the cell cycle.

Cytoplasmic organization promotes protein diffusion in Xenopus extracts.

The cytoplasm is highly organized. However, the extent to which this organization influences the dynamics of cytoplasmic proteins is not well understood. Here, we use Xenopus laevis egg extracts as a model system to study diffusion dynamics in organized versus disorganized cytoplasm. Such extracts are initially homogenized and disorganized, and self-organize into cell-like units over the course of tens of minutes. Using fluorescence correlation spectroscopy, we observe that as the cytoplasm organizes, protein diffusion speeds up by about a factor of two over a length scale of a few hundred nanometers, eventually approaching the diffusion time measured in organelle-depleted cytosol. Even though the ordered cytoplasm contained organelles and cytoskeletal elements that might interfere with diffusion, the convergence of protein diffusion in the cytoplasm toward that in organelle-depleted cytosol suggests that subcellular organization maximizes protein diffusivity. The effect of organization on diffusion varies with molecular size, with the effects being largest for protein-sized molecules, and with the time scale of the measurement. These results show that cytoplasmic organization promotes the efficient diffusion of protein molecules in a densely packed environment.

Xenopus laevis Egg Extract Preparation and Live Imaging Methods for Visualizing Dynamic Cytoplasmic Organization.

Traditionally used for bulk biochemical assays, Xenopus laevis egg extracts have emerged as a powerful imaging-based tool for studying cytoplasmic phenomena, such as cytokinesis, mitotic spindle formation and assembly of the nucleus. Building upon early methods that imaged fixed extracts sampled at sparse time points, recent approaches image live extracts using time-lapse microscopy, revealing more dynamical features with enhanced temporal resolution. These methods usually require sophisticated surface treatments of the imaging vessel. Here we introduce an alternative method for live imaging of egg extracts that require no chemical surface treatment. It is simple to implement and utilizes mass-produced laboratory consumables for imaging. We describe a system that can be used for both wide-field and confocal microscopy. It is designed for imaging extracts in a 2-dimensional (2D) field, but can be easily extended to imaging in 3D. It is well-suited for studying spatial pattern formation within the cytoplasm. With representative data, we demonstrate the typical dynamic organization of microtubules, nuclei and mitochondria in interphase extracts prepared using this method. These image data can provide quantitative information on cytoplasmic dynamics and spatial organization.

Spontaneous emergence of cell-like organization in Xenopus egg extracts.

Every daughter cell inherits two things from its mother: genetic information and a spatially organized complement of macromolecular complexes and organelles. The extent to which de novo self-organization, as opposed to inheritance of an already organized state, can suffice to yield functional cells is uncertain. We used Xenopus laevis egg extracts to show that homogenized interphase egg cytoplasm self-organizes over the course of ~30 minutes into compartments 300 to 400 micrometers in length that resemble cells. Formation of these cell-like compartments required adenosine triphosphate and microtubule polymerization but did not require added demembranated sperm nuclei with their accompanying centrosomes or actin polymerization. In cycling extracts with added sperm, the compartments underwent multiple cycles of division and reorganization, with mother compartments giving rise to two daughters at the end of each mitotic cycle. These results indicate that the cytoplasm can generate much of the spatial organization and cell cycle function of the early embryo.

Apoptosis propagates through the cytoplasm as trigger waves.

Apoptosis is an evolutionarily conserved form of programmed cell death critical for development and tissue homeostasis in animals. The apoptotic control network includes several positive feedback loops that may allow apoptosis to spread through the cytoplasm in self-regenerating trigger waves. We tested this possibility in cell-free Xenopus laevis egg extracts and observed apoptotic trigger waves with speeds of ~30 micrometers per minute. Fractionation and inhibitor studies implicated multiple feedback loops in generating the waves. Apoptotic oocytes and eggs exhibited surface waves with speeds of ~30 micrometers per minute, which were tightly correlated with caspase activation. Thus, apoptosis spreads through trigger waves in both extracts and intact cells. Our findings show how apoptosis can spread over large distances within a cell and emphasize the general importance of trigger waves in cell signaling.

Regulatory logic and pattern formation in the early sea urchin embryo.

We model the endomesoderm tissue specification process in the vegetal half of the early sea urchin embryo using Boolean models with continuous-time updating to represent the regulatory network that controls gene expression. Our models assume that the network interaction rules remain constant over time and the dynamics plays out on a predetermined program of cell divisions. An exhaustive search of two-node models, in which each node may represent a module of several genes in the real regulatory network, yields a unique network architecture that can accomplish the pattern formation task at hand--the formation of three latitudinal tissue bands from an initial state with only two distinct cell types. Analysis of an eight-gene model constructed from available experimental data reveals that it has a modular structure equivalent to the successful two-node case. Our results support the hypothesis that the gene regulatory network provides sufficient instructions for producing the correct pattern of tissue specification at this stage of development (between the fourth and tenth cleavages in the urchin embryo).

Delayed transition to new cell fates during cellular reprogramming.

In many embryos specification toward one cell fate can be diverted to a different cell fate through a reprogramming process. Understanding how that process works will reveal insights into the developmental regulatory logic that emerged from evolution. In the sea urchin embryo, cells at gastrulation were found to reprogram and replace missing cell types after surgical dissections of the embryo. Non-skeletogenic mesoderm (NSM) cells reprogrammed to replace missing skeletogenic mesoderm cells and animal caps reprogrammed to replace all endomesoderm. In both cases evidence of reprogramming onset was first observed at the early gastrula stage, even if the cells to be replaced were removed earlier in development. Once started however, the reprogramming occurred with compressed gene expression dynamics. The NSM did not require early contact with the skeletogenic cells to reprogram, but the animal cap cells gained the ability to reprogram early in gastrulation only after extended contact with the vegetal halves prior to that time. If the entire vegetal half was removed at early gastrula, the animal caps reprogrammed and replaced the vegetal half endomesoderm. If the animal caps carried morpholinos to either hox11/13b or foxA (endomesoderm specification genes), the isolated animal caps failed to reprogram. Together these data reveal that the emergence of a reprogramming capability occurs at early gastrulation in the sea urchin embryo and requires activation of early specification components of the target tissues.

Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

Autonomous Boolean modelling of developmental gene regulatory networks.

During early embryonic development, a network of regulatory interactions among genes dynamically determines a pattern of differentiated tissues. We show that important timing information associated with the interactions can be faithfully represented in autonomous Boolean models in which binary variables representing expression levels are updated in continuous time, and that such models can provide a direct insight into features that are difficult to extract from ordinary differential equation (ODE) models. As an application, we model the experimentally well-studied network controlling fly body segmentation. The Boolean model successfully generates the patterns formed in normal and genetically perturbed fly embryos, permits the derivation of constraints on the time delay parameters, clarifies the logic associated with different ODE parameter sets and provides a platform for studying connectivity and robustness in parameter space. By elucidating the role of regulatory time delays in pattern formation, the results suggest new types of experimental measurements in early embryonic development.

Characteristics of three-phase internal loop airlift bioreactors with complete gas recirculation for non-Newtonian fluids.

Hydrodynamic and gas-liquid mass transfer characteristics, such as liquid velocity, gas holdup, solid holdup and gas-liquid volumetric mass transfer coefficient, in the riser and downcomer of the gas-liquid-solid three-phase internal loop airlift bioreactors with complete gas recirculation for non-Newtonian fluids, were investigated. A mathematical model for the description of flow behavior and gas-liquid mass transfer of these bioreactors was developed. The predicted results of this model agreed well with the experimental data.