Isolating and quantifying the role of developmental noise in generating phenotypic variation.

Genotypic variation, environmental variation, and their interaction may produce variation in the developmental process and cause phenotypic differences among individuals. Developmental noise, which arises during development from stochasticity in cellular and molecular processes when genotype and environment are fixed, also contributes to phenotypic variation. While evolutionary biology has long focused on teasing apart the relative contribution of genes and environment to phenotypic variation, our understanding of the role of developmental noise has lagged due to technical difficulties in directly measuring the contribution of developmental noise. The influence of developmental noise is likely underestimated in studies of phenotypic variation due to intrinsic mechanisms within organisms that stabilize phenotypes and decrease variation. Since we are just beginning to appreciate the extent to which phenotypic variation due to stochasticity is potentially adaptive, the contribution of developmental noise to phenotypic variation must be separated and measured to fully understand its role in evolution. Here, we show that variation in the component of the developmental process corresponding to environmental and genetic factors (here treated together as a unit called the LALI-type) versus the contribution of developmental noise, can be distinguished for leopard gecko (Eublepharis macularius) head color patterns using mathematical simulations that model the role of random variation (corresponding to developmental noise) in patterning. Specifically, we modified the parameters of simulations corresponding to variation in the LALI-type to generate the full range of phenotypic variation in color pattern seen on the heads of eight leopard geckos. We observed that over the range of these parameters, variation in color pattern due to LALI-type variation exceeds that due to developmental noise in the studied gecko cohort. However, the effect of developmental noise on patterning is also substantial. Our approach addresses one of the major goals of evolutionary biology: to quantify the role of stochasticity in shaping phenotypic variation.

Nanoscale high-content analysis using compositional heterogeneities of single proteoliposomes.

Proteoliposome reconstitution is a standard method to stabilize purified transmembrane proteins in membranes for structural and functional assays. Here we quantified intrareconstitution heterogeneities in single proteoliposomes using fluorescence microscopy. Our results suggest that compositional heterogeneities can severely skew ensemble-average proteoliposome measurements but also enable ultraminiaturized high-content screens. We took advantage of this screening capability to map the oligomerization energy of the ß2-adrenergic receptor using ∼10(9)-fold less protein than conventional assays.

Capturing and analyzing pattern diversity: an example using the melanistic spotted patterns of leopard geckos.

Animal color patterns are widely studied in ecology, evolution, and through mathematical modeling. Patterns may vary among distinct body parts such as the head, trunk or tail. As large amounts of photographic data is becoming more easily available, there is a growing need for general quantitative methods for capturing and analyzing the full complexity and details of pattern variation. Detailed information on variation in color pattern elements is necessary to understand how patterns are produced and established during development, and which evolutionary forces may constrain such a variation. Here, we develop an approach to capture and analyze variation in melanistic color pattern elements in leopard geckos. We use this data to study the variation among different body parts of leopard geckos and to draw inferences about their development. We compare patterns using 14 different indices such as the ratio of melanistic versus total area, the ellipticity of spots, and the size of spots and use these to define a composite distance between two patterns. Pattern presence/absence among the different body parts indicates a clear pathway of pattern establishment from the head to the back legs. Together with weak within-individual correlation between leg patterns and main body patterns, this suggests that pattern establishment in the head and tail may be independent from the rest of the body. We found that patterns vary greatest in size and density of the spots among body parts and individuals, but little in their average shapes. We also found a correlation between the melanistic patterns of the two front legs, as well as the two back legs, and also between the head, tail and trunk, especially for the density and size of the spots, but not their shape or inter-spot distance. Our data collection and analysis approach can be applied to other organisms to study variation in color patterns between body parts and to address questions on pattern formation and establishment in animals.

On the use of Ripley's K-function and its derivatives to analyze domain size.

Ripley's K-, H-, and L-functions are used increasingly to identify clustering of proteins in membrane microdomains. In this approach, aggregation (or clustering) is identified if the average number of proteins within a distance r of another protein is statistically greater than that expected for a random distribution. However, it is not entirely clear how the function may be used to quantitatively determine the size of domains in which clustering occurs. Here, we evaluate the extent to which the domain radius can be determined by different interpretations of Ripley's K-statistic in a theoretical, idealized context. We also evaluate the measures for noisy experimental data and use Monte Carlo simulations to separate the effects of different types of experimental noise. We find that the radius of maximal aggregation approximates the domain radius, while identifying the domain boundary with the minimum of the derivative of H(r) is highly accurate in idealized conditions. The accuracy of both measures is impacted by the noise present in experimental data; for example, here, the presence of a large fraction of particles distributed as monomers and interdomain interactions. These findings help to delineate the limitations and potential of Ripley's K in real-life scenarios.

Vaccination strategies to control Ebola epidemics in the context of variable household inaccessibility levels.

Despite a very effective vaccine, active conflict and community distrust during the ongoing DRC Ebola epidemic are undermining control efforts, including a ring vaccination strategy that requires the prompt immunization of close contacts of infected individuals. However, in April 2019, it was reported 20% or more of close contacts cannot be reached or refuse vaccination, and it is predicted that the ring vaccination strategy would not be effective with such a high level of inaccessibility. The vaccination strategy is now incorporating a "third ring" community-level vaccination that targets members of communities even if they are not known contacts of Ebola cases. To assess the impact of vaccination strategies for controlling Ebola epidemics in the context of variable levels of community accessibility, we employed an individual-level stochastic transmission model that incorporates four sources of heterogeneity: a proportion of the population is inaccessible for contact tracing and vaccination due to lack of confidence in interventions or geographic inaccessibility, two levels of population mixing resembling household and community transmission, two types of vaccine doses with different time periods until immunity, and transmission rates that depend on spatial distance. Our results indicate that a ring vaccination strategy alone would not be effective for containing the epidemic in the context of significant delays to vaccinating contacts even for low levels of household inaccessibility and affirm the positive impact of a supplemental community vaccination strategy. Our key results are that as levels of inaccessibility increase, there is a qualitative change in the effectiveness of the vaccination strategy. For higher levels of vaccine access, the probability that the epidemic will end steadily increases over time, even if probabilities are lower than they would be otherwise with full community participation. For levels of vaccine access that are too low, however, the vaccination strategies are not expected to be successful in ending the epidemic even though they help lower incidence levels, which saves lives, and makes the epidemic easier to contain and reduces spread to other communities. This qualitative change occurs for both types of vaccination strategies: ring vaccination is effective for containing an outbreak until the levels of inaccessibility exceeds approximately 10% in the context of significant delays to vaccinating contacts, a combined ring and community vaccination strategy is effective until the levels of inaccessibility exceeds approximately 50%. More broadly, our results underscore the need to enhance community engagement to public health interventions in order to enhance the effectiveness of control interventions to ensure outbreak containment.

Modeling household and community transmission of Ebola virus disease: Epidemic growth, spatial dynamics and insights for epidemic control.

The mechanisms behind the sub-exponential growth dynamics of the West Africa Ebola virus disease epidemic could be related to improved control of the epidemic and the result of reduced disease transmission in spatially constrained contact structures. An individual-based, stochastic network model is used to model immediate and delayed epidemic control in the context of social contact networks and investigate the extent to which the relative role of these factors may be determined during an outbreak. We find that in general, epidemics quickly establish a dynamic equilibrium of infections in the form of a wave of fixed size and speed traveling through the contact network. Both greater epidemic control and limited community mixing decrease the size of an infectious wave. However, for a fixed wave size, epidemic control (in contrast with limited community mixing) results in lower community saturation and a wave that moves more quickly through the contact network. We also found that the level of epidemic control has a disproportionately greater reductive effect on larger waves, so that a small wave requires nearly as much epidemic control as a larger wave to end an epidemic.

A three-scale network model for the early growth dynamics of 2014 west Africa ebola epidemic.

BACKGROUND: In mid-October 2014, the number of cases of the West Africa Ebola virus epidemic in Guinea, Sierra Leone and Liberia exceeded 9,000 cases. The early growth dynamics of the epidemic has been qualitatively different for each of the three countries. However, it is important to understand these disparate dynamics as trends of a single epidemic spread over regions with similar geographic and cultural aspects, with likely common parameters for transmission rates and reproduction number R0. METHODS: We combine a discrete, stochastic SEIR model with a three-scale community network model to demonstrate that the different regional trends may be explained by different community mixing rates. Heuristically, the effect of different community mixing rates may be understood as the observation that two individuals infected by the same chain of transmission are more likely to share the same contacts in a less-mixed community. Local saturation effects occur as the contacts of an infected individual are more likely to already be exposed by the same chain of transmission. RESULTS: The effects of community mixing, together with stochastic effects, can explain the qualitative difference in the growth of Ebola virus cases in each country, and why the probability of large outbreaks may have recently increased. An increase in the rate of Ebola cases in Guinea in late August, and a local fitting of the transient dynamics of the Ebola cases in Liberia, suggests that the epidemic in Liberia has been more severe, and the epidemic in Guinea is worsening, due to discrete seeding events as the epidemic spreads into new communities. CONCLUSIONS: A relatively simple network model provides insight on the role of local effects such as saturation that would be difficult to otherwise quantify. Our results predict that exponential growth of an epidemic is driven by the exposure of new communities, underscoring the importance of limiting this spread.

Role for stromal heterogeneity in prostate tumorigenesis.

Prostate cancer develops through a stochastic mechanism whereby precancerous lesions on occasion progress to multifocal adenocarcinoma. Analysis of human benign and cancer prostate tissues revealed heterogeneous loss of TGF-ß signaling in the cancer-associated stromal fibroblastic cell compartment. To test the hypothesis that prostate cancer progression is dependent on the heterogeneous TGF-ß responsive microenvironment, a tissue recombination experiment was designed in which the ratio of TGF-ß responsive and nonresponsive stromal cells was varied. Although 100% TGF-ß responsive stromal cells supported benign prostate growth and 100% TGF-ß nonresponsive stromal cells resulted in precancerous lesions, only the mixture of TGF-ß responsive and nonresponsive stromal cells resulted in adenocarcinoma. A computational model was used to resolve a mechanism of tumorigenic progression in which proliferation and invasion occur in two independent steps mediated by distinct stromally derived paracrine signals produced by TGF-ß nonresponsive and responsive stromal cells. Complex spatial relationships of stromal and epithelial cells were incorporated into the model on the basis of experimental data. Informed by incorporation of experimentally derived spatial parameters for complex stromal-epithelial relationships, the computational model indicated ranges for the relative production of paracrine factors by each cell type and provided bounds for the diffusive range of the molecules. Because SDF-1 satisfied model predictions for an invasion-promoting paracrine factor, a more focused computational model was subsequently used to investigate whether SDF-1 was the invasion signal. Simulations replicating SDF-1 expression data revealed the requirement for cooperative SDF-1 expression, a prediction supported biologically by heterotypic stromal interleukin-1ß signaling between fibroblastic cell populations. The cancer stromal field effect supports a functional role for the unaltered fibroblasts as a cooperative mediator of cancer progression.

Cooperation of polarized cell intercalations drives convergence and extension of presomitic mesoderm during zebrafish gastrulation.

During vertebrate gastrulation, convergence and extension (C&E) movements narrow and lengthen the embryonic tissues, respectively. In zebrafish, regional differences of C&E movements have been observed; however, the underlying cell behaviors are poorly understood. Using time-lapse analyses and computational modeling, we demonstrate that C&E of the medial presomitic mesoderm is achieved by cooperation of planar and radial cell intercalations. Radial intercalations preferentially separate anterior and posterior neighbors to promote extension. In knypek;trilobite noncanonical Wnt mutants, the frequencies of cell intercalations are altered and the anteroposterior bias of radial intercalations is lost. This provides evidence for noncanonical Wnt signaling polarizing cell movements between different mesodermal cell layers. We further show using fluorescent fusion proteins that during dorsal mesoderm C&E, the noncanonical Wnt component Prickle localizes at the anterior cell edge, whereas Dishevelled is enriched posteriorly. Asymmetrical localization of Prickle and Dishevelled to the opposite cell edges in zebrafish gastrula parallels their distribution in fly, and suggests that noncanonical Wnt signaling defines distinct anterior and posterior cell properties to bias cell intercalations.

In silico characterization of resonance energy transfer for disk-shaped membrane domains.

Förster resonance energy transfer (FRET) has become an important tool to study the submicrometer distribution of proteins and lipids in membranes. Although resolving the two-dimensional distribution of fluorophores from FRET is generally underdetermined, a forward approach can be used to determine characteristic FRET "signatures" for interesting classes of microdomain organizations. As a first step toward this goal, we use a stochastic Monte Carlo approach to characterize FRET in the case of molecules randomly distributed within disk-shaped domains. We find that when donors and acceptors are confined within domains, FRET depends very generally on the density of acceptors within domains. An implication of this result is that two domain populations with the same acceptor density cannot be distinguished by this FRET approach even if the domains have different diameters or different numbers of molecules. In contrast, both the domain diameter and molecule number can be resolved by combining this approach with a segregation approach that measures FRET between donors confined in domains and acceptors localized outside domains. These findings delimit where the inverse problem is tractable for this class of distributions and reframe ways FRET can be used to characterize the structure of microdomains such as lipid rafts.

Initiation of convergence and extension movements of lateral mesoderm during zebrafish gastrulation.

Embryonic morphogenesis is accomplished by cellular movements, rearrangements, and cell fate inductions. Vertebrate gastrulation entails morphogenetic processes that generate three germ layers, endoderm, mesoderm, and ectoderm, shaped into head, trunk, and tail. To understand how cell migration mechanistically contributes to tissue shaping during gastrulation, we examined migration of lateral mesoderm in the zebrafish. Our results illustrate that cell behaviors, different from mediolaterally oriented cell intercalation, also promote convergence and extension (C&E). During early gastrulation, upon internalization, individually migrating mesendodermal cells contribute to the elongation of the mesoderm by moving animally, without dorsal movement. Convergence toward dorsal starts later, by 70% epiboly (7.7 hpf). Depending on location along the Animal-Vegetal axis, an animal or vegetal bias is added to the dorsalward movement, so that paths fan out and the lateral mesoderm both converges and extends. Onset of convergence is independent of noncanonical Wnt signaling but is delayed when Stat3 signaling is compromised. To understand which aspects of motility are controlled by guidance cues, we measured turning behavior of lateral mesodermal cells. We show that cells exhibit directional preference, directionally-regulated speed, and turn toward dorsal when off-course. We estimate that ectoderm could supply from a fraction to all the dorsalward displacement seen in mesoderm cells. Using mathematical modeling, we demonstrate that directional preference is sufficient to account for mesoderm convergence and extension, and that, at minimum, two sources of guidance cues could orient cell paths realistically if located in the dorsal midline.

Role of streams in myxobacteria aggregate formation.

Cell contact, movement and directionality are important factors in biological development (morphogenesis), and myxobacteria are a model system for studying cell-cell interaction and cell organization preceding differentiation. When starved, thousands of myxobacteria cells align, stream and form aggregates which later develop into round, non-motile spores. Canonically, cell aggregation has been attributed to attractive chemotaxis, a long range interaction, but there is growing evidence that myxobacteria organization depends on contact-mediated cell-cell communication. We present a discrete stochastic model based on contact-mediated signaling that suggests an explanation for the initialization of early aggregates, aggregation dynamics and final aggregate distribution. Our model qualitatively reproduces the unique structures of myxobacteria aggregates and detailed stages which occur during myxobacteria aggregation: first, aggregates initialize in random positions and cells join aggregates by random walk; second, cells redistribute by moving within transient streams connecting aggregates. Streams play a critical role in final aggregate size distribution by redistributing cells among fewer, larger aggregates. The mechanism by which streams redistribute cells depends on aggregate sizes and is enhanced by noise. Our model predicts that with increased internal noise, more streams would form and streams would last longer. Simulation results suggest a series of new experiments.

Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning.

We present a stochastic cellular automaton model for the behavior of limb bud precartilage mesenchymal cells undergoing chondrogenic patterning. This "agent-oriented" model represents cells by points on a lattice that obey rules motivated by experimental findings. The "cells" follow these rules as autonomous agents, interacting with other cells and with the microenvironments cell activities produce. The rules include random cell motion, production and lateral deposition of a substrate adhesion molecule (SAM, corresponding to fibronectin), production and release of a diffusible growth factor ("activator," corresponding to TGF-beta) that stimulates production of the SAM, and another diffusible factor ("inhibitor") that suppresses the activity of the activator. We implemented the cellular automaton on a two-dimensional (2D) square lattice to emulate the quasi-2D micromass culture extensively used to study patterning in avian limb bud precartilage cells. We identified parameters that produce nodular patterns that resemble, in size and distribution, cell condensations in leg-cell cultures, thus establishing a correspondence between in vitro and in silico results. We then studied the in vitro and in silico micromass cultures experimentally. We altered the standard in vitro micromass culture by diluting the initial cell density, transiently exposing it to exogenous activator, suppressing the inhibitor, and constitutively activating fibronectin production. We altered the standard in silico micromass culture in each case by changing the corresponding parameter. In vitro and in silico experiments agreed well. We also used the model to test hypotheses for differences in the in vitro patterns of cells derived from chick embryo forelimb and hindlimb. We discuss the applicability of this model to limb development in vivo and to other organ development.