Stochastic Chlamydia Dynamics and Optimal Spread.

Chlamydia trachomatis is an important bacterial pathogen that has an unusual developmental switch from a dividing form (reticulate body or RB) to an infectious form (elementary body or EB). RBs replicate by binary fission within an infected host cell, but there is a delay before RBs convert into EBs for spread to a new host cell. We developed stochastic optimal control models of the Chlamydia developmental cycle to examine factors that control the number of EBs produced.

Regulatory feedback on receptor and non-receptor synthesis for robust signaling.

Elaborate regulatory feedback processes are thought to make biological development robust, that is, resistant to changes induced by genetic or environmental perturbations. How this might be done is still not completely understood. Previous numerical simulations on reaction-diffusion models of Dpp gradients in Drosophila wing imaginal disc have showed that feedback (of the Hill function type) on (signaling) receptors and/or non-(signaling) receptors are of limited effectiveness in promoting robustness.

Replication-dependent size reduction precedes differentiation in Chlamydia trachomatis.

Chlamydia trachomatis is the most common cause of bacterial sexually transmitted infection. It produces an unusual intracellular infection in which a vegetative form, called the reticulate body (RB), replicates and then converts into an elementary body (EB), which is the infectious form. Here we use quantitative three-dimensional electron microscopy (3D EM) to show that C.

Optimal Proliferation and Differentiation of .

is a bacterium that causes eye infection and blindness in humans. It has an unusual life cycle involving two developmental forms. Within a cytoplasmic inclusion, the reticulate body (RB) repeatedly divides by binary fission and asynchronously differentiates into the infectious elementary body (EB).

TRANSIENT FEEDBACK AND ROBUST SIGNALING GRADIENTS.

Robust development of biological organisms in the presence of genetic and epi-genetic perturbations is important for time spans short relative to evolutionary time. Gradients of receptor bound signaling morphogens are responsible for patterning formation and development. A variety of inhibitors for reducing ectopic signaling activities are known to exist and their specific role in down-regulating the undesirable ectopic activities reasonably well understood.

Robust and precise morphogen-mediated patterning: trade-offs, constraints and mechanisms.

The patterning of many developing tissues is organized by morphogens. Genetic and environmental perturbations of gene expression, protein synthesis and ligand binding are among the sources of unreliability that limit the accuracy and precision of morphogen-mediated patterning. While it has been found that the robustness of morphogen gradients to the perturbation of morphogen synthesis can be enhanced by particular mechanisms, how such mechanisms affect robustness to other perturbations, such as to receptor synthesis for the same morphogen, has been little explored.

Fastest time to cancer by loss of tumor suppressor genes.

Genetic instability promotes cancer progression (by increasing the probability of cancerous mutations) as well as hinders it (by imposing a higher cell death rate for cells susceptible to cancerous mutation). With the loss of tumor suppressor gene function known to be responsible for a high percentage of breast and colorectal cancer (and a good fraction of lung cancer and other types as well), it is important to understand how genetic instability can be orchestrated toward carcinogenesis. In this context, this paper gives a complete characterization of the optimal (time-varying) cell mutation rate for the fastest time to a target cancerous cell population through the loss of both copies of a tumor suppressor gene.

Cell-Surface Bound Nonreceptors and Signaling Morphogen Gradients.

The patterning of many developing tissues is orchestrated by gradients of signaling morphogens. Included among the molecular events that drive the formation of morphogen gradients are a variety of elaborate regulatory interactions. Such interactions are thought to make gradients robust, i.

ROBUSTNESS OF MORPHOGEN GRADIENTS WITH "BUCKET BRIGADE" TRANSPORT THROUGH MEMBRANE-ASSOCIATED NON-RECEPTORS.

Robust multiple-fate morphogen gradients are essential for embryo development. Here, we analyze mathematically a model of morphogen gradient (such as Dpp in Drosophila wing imaginal disc) formation in the presence of non-receptors with both diffusion of free morphogens and the movement of morphogens bound to non-receptors. Under the assumption of rapid degradation of unbound morphogen, we introduce a method of functional boundary value problem and prove the existence, uniqueness and linear stability of a biologically acceptable steady-state solution.

ROBUSTNESS OF SIGNALING GRADIENT IN DROSOPHILA WING IMAGINAL DISC.

Quasi-stable gradients of signaling protein molecules (known as morphogens or ligands) bound to cell receptors are known to be responsible for differential cell signaling and gene expressions. From these follow different stable cell fates and visually patterned tissues in biological development. Recent studies have shown that the relevant basic biological processes yield gradients that are sensitive to small changes in system characteristics (such as expression level of morphogens or receptors) or environmental conditions (such as temperature changes).

Spatial dynamics of multistage cell lineages in tissue stratification.

In developing and self-renewing tissues, terminally differentiated (TD) cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit-amplifying) cell stages, which ultimately give rise to TD cells. As the tissue reaches a tightly controlled steady-state size, cells at different lineage stages assume distinct spatial locations within the tissue.

The measure of success: constraints, objectives, and tradeoffs in morphogen-mediated patterning.

A large, diverse, and growing number of strategies have been proposed to explain how morphogen gradients achieve robustness and precision. We argue that, to be useful, the evaluation of such strategies must take into account the constraints imposed by competing objectives and performance tradeoffs. This point is illustrated through a mathematical and computational analysis of the strategy of self-enhanced morphogen clearance.

Feedback regulation in multistage cell lineages.

Studies of developing and self-renewing tissues have shown that differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit amplifying; TA) cell stages, which ultimately give rise to terminally differentiated (TD) cells. In several cases, self-renewal and differentiation of stem and progenitor cells within such lineages have been shown to be under feedback regulation.

Cell lineages and the logic of proliferative control.

It is widely accepted that the growth and regeneration of tissues and organs is tightly controlled. Although experimental studies are beginning to reveal molecular mechanisms underlying such control, there is still very little known about the control strategies themselves. Here, we consider how secreted negative feedback factors ("chalones") may be used to control the output of multistage cell lineages, as exemplified by the actions of GDF11 and activin in a self-renewing neural tissue, the mammalian olfactory epithelium (OE).

The role of feedback in the formation of morphogen territories.

In this paper, we consider a mathematical model for the formation of spatial morphogen territories of two key morphogens: Wingless (Wg) and Decapentaplegic (DPP), involved in leg development of Drosophila. We define a gene regulatory network (GRN) that utilizes autoactivation and cros-sinhibition (modeled by Hill equations) to establish and maintain stable boundaries of gene expression. By computational analysis we find that in the presence of a general activator, neither autoactivation, nor cross-inhibition alone are sufficient to maintain stable sharp boundaries of morphogen production in the leg disc.

Compact integration factor methods in high spatial dimensions.

The dominant cost for integration factor (IF) or exponential time differencing (ETD) methods is the repeated vector-matrix multiplications involving exponentials of discretization matrices of differential operators. Although the discretization matrices usually are sparse, their exponentials are not, unless the discretization matrices are diagonal. For example, a two-dimensional system of N × N spatial points, the exponential matrix is of a size of N(2) × N(2) based on direct representations.

Selective pressures for and against genetic instability in cancer: a time-dependent problem.

Genetic instability in cancer is a two-edge sword. It can both increase the rate of cancer progression (by increasing the probability of cancerous mutations) and decrease the rate of cancer growth (by imposing a large death toll on dividing cells). Two of the many selective pressures acting upon a tumour, the need for variability and the need to minimize deleterious mutations, affect the tumour's 'choice' of a stable or unstable 'strategy'.

EFFECTS OF SOG ON DPP-RECEPTOR BINDING.

Concentration gradients of morphogens are known to be instrumental in cell signaling and tissue patterning. Of interest here is how the presence of a competitor of BMP ligands affects cell signaling. The effects of Sog on the binding of Dpp with cell receptors are analyzed for dorsal-ventral morphogen gradient formation in vertebrate and Drosophila embryos.

Wingless directly represses DPP morphogen expression via an armadillo/TCF/Brinker complex.

Background: Spatially restricted morphogen expression drives many patterning and regeneration processes, but how is the pattern of morphogen expression established and maintained? Patterning of Drosophila leg imaginal discs requires expression of the DPP morphogen dorsally and the wingless (WG) morphogen ventrally. We have shown that these mutually exclusive patterns of expression are controlled by a self-organizing system of feedback loops that involve WG and DPP, but whether the feedback is direct or indirect is not known.

Methods/findings: By analyzing expression patterns of regulatory DNA driving reporter genes in different genetic backgrounds, we identify a key component of this system by showing that WG directly represses transcription of the dpp gene in the ventral leg disc.

Formation of the BMP activity gradient in the Drosophila embryo.

The dorsoventral axis of the Drosophila embryo is patterned by a gradient of bone morphogenetic protein (BMP) ligands. In a process requiring at least three additional extracellular proteins, a broad domain of weak signaling forms and then abruptly sharpens into a narrow dorsal midline peak. Using experimental and computational approaches, we investigate how the interactions of a multiprotein network create the unusual shape and dynamics of formation of this gradient.

Spatially distributed morphogen production and morphogen gradient formation.

Partial diferential equations and auxiliary conditions governing the activities of the morphogen Dpp in Drosophila wing imaginal discs were formulated and analyzed as Systems B, R, and C in [7] [9] [10]. All had morphogens produced at the border of anterior and posterior chamber of the wing disc idealized as a point, line, or plane in a one-, two-, or three-dimensional model. In reality, morphogens are synthesized in a narrow region of finite width (possibly of only a few cells) between the two chambers in which diffusion and reversible binding with degradable receptors may also take place.

On the behavior of solutions in viral dynamical models.

We consider simple mathematical models for the early population dynamics of the human immunodefficiency type 1 virus (HIV-1). Although these systems of differential equations may be solved by numerical methods, few general theoretical results are available due to nonlinearities. We analyze a model whose components are plasma densities of uninfected CD4+ T-cells and infected cells (assumed in this model to be proportional to virion density).

Determination of firing times for the stochastic Fitzhugh-Nagumo neuronal model.

We present for the first time an analytical approach for determining the time of firing of multicomponent nonlinear stochastic neuronal models. We apply the theory of first exit times for Markov processes to the Fitzhugh-Nagumo system with a constant mean gaussian white noise input, representing stochastic excitation and inhibition. Partial differential equations are obtained for the moments of the time to first spike.

Do morphogen gradients arise by diffusion?

Many patterns of cell and tissue organization are specified during development by gradients of morphogens, substances that assign different cell fates at different concentrations. Gradients form by morphogen transport from a localized site, but whether this occurs by simple diffusion or by more elaborate mechanisms is unclear. We attempt to resolve this controversy by analyzing recent data in ways that appropriately capture the complexity of systems in which transport, receptor interaction, endo- and exocytosis, and degradation occur together.

A spatial stochastic neuronal model with Ornstein-Uhlenbeck input current.

We consider a spatial neuron model in which the membrane potential satisfies a linear cable equation with an input current which is a dynamical random process of the Ornstein-Uhlenbeck (OU) type. This form of current may represent an approximation to that resulting from the random opening and closing of ion channels on a neuron's surface or to randomly occurring synaptic input currents with exponential decay. We compare the results for the case of an OU input with those for a purely white-noise-driven cable model.