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. Spatial nonuniformity of the feedback processes has also been shown theoretically to lead to serious shape distortion and a principal cause for ineffectiveness. Through mathematical modeling and analysis, the present article shows that spatially uniform nonlocal feedback mechanisms typically modify gradient shape through a shape parameter (that does not change with location). This in turn enables us to uncover new multi-feedback instrument for effective promotion of robust signaling gradients

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.e. insensitive to change in the face of genetic or environmental perturbations. But just how this is accomplished is a major unanswered question. Recently extensive numerical simulations suggest that robustness of signaling gradients can be achieved through morphogen degradation mediated by cell surface bound non-signaling receptor molecules (or nonreceptors for short) such as heparan sulfate proteoglycans (HSPG). The present paper provides a mathematical validation of the results from the aforementioned numerical experiments. Extension of a basic extracellular model to include reversible binding with nonreceptors synthesized at a prescribed rate and mediated morphogen degradation shows that the signaling gradient diminishes with increasing concentration of cell-surface nonreceptors. Perturbation and asymptotic solutions obtained for i) low (receptor and nonreceptor) occupancy, and ii) high nonreceptor concntration permit more explicit delineation of the effects of nonreceptors on signaling gradients and facilitate the identification of scenarios in which the presence of nonreceptors may or may not be effective in promoting robustness

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.e. insensitive to change in the face of genetic or environmental perturbations. But just how this is accomplished is a major unanswered question. Recently extensive numerical simulations suggest that robustness of signaling gradients can be achieved through morphogen degradation mediated by cell surface bound non-signaling receptor molecules (or nonreceptors for short) such as heparan sulfate proteoglycans (HSPG). The present paper provides a mathematical validation of the results from the aforementioned numerical experiments. Extension of a basic extracellular model to include reversible binding with nonreceptors synthesized at a prescribed rate and mediated morphogen degradation shows that the signaling gradient diminishes with increasing concentration of cell-surface nonreceptors. Perturbation and asymptotic solutions obtained for i) low (receptor and nonreceptor) occupancy, and ii) high nonreceptor concntration permit more explicit delineation of the effects of nonreceptors on signaling gradients and facilitate the identification of scenarios in which the presence of nonreceptors may or may not be effective in promoting robustness

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. However, how a developing organism manages to adjust inhibition/stimulation in response to genetic and/or environmental changes remains to be uncovered. The need to adjust for ectopic signaling activities requires the presence of one or more feedback mechanisms to stimulate the needed adjustment. As the ultimate effect of many inhibitors (including those of the nonreceptor type) is to reduce the availability of signaling morphogens for binding with signaling receptors, a negative feedback on signaling morphogen synthesis rate based on a root-mean-square measure of the spatial distribution of signaling concentration offers a simple approach to robusness and has been demonstrated to be effective in a proof-of-concept implementation. In this paper, we complement the previous investigation of feedback in steady state by examining the effect of one or more feedback adjustments during the transient phase of the biological development

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. However, how a developing organism manages to adjust inhibition/stimulation in response to genetic and/or environmental changes remains to be uncovered. The need to adjust for ectopic signaling activities requires the presence of one or more feedback mechanisms to stimulate the needed adjustment. As the ultimate effect of many inhibitors (including those of the nonreceptor type) is to reduce the availability of signaling morphogens for binding with signaling receptors, a negative feedback on signaling morphogen synthesis rate based on a root-mean-square measure of the spatial distribution of signaling concentration offers a simple approach to robusness and has been demonstrated to be effective in a proof-of-concept implementation. In this paper, we complement the previous investigation of feedback in steady state by examining the effect of one or more feedback adjustments during the transient phase of the biological development

Optimal Proliferation and Differentiation of Chlamydia Trachomatis.

Chlamydia trachomatis 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). Upon the death of the mammalian cell that host many such inclusions, only the EB form of the bacteria survive and proceed to infect other cells. Given the bacteria's fast spreading infection, conventional wisdom would have the few initial EB turn into RB, divide and proliferate first, and then eventually start converting in order to maximize the terminal EB population upon host cell lysis. Several biological processes are seen as possible mechanisms for implementing such a conversion strategy. However, the optimality of an instinctual strategy with a period of proliferate without conversion prior to the onset of differentiation has never been substantiated theoretically or justified mathematically. This paper formulates three relatively simple models that capture the essential features of the Chlamydia life cycle. When the initial infection is caused by the endocytosis of a small EB population well below the carrying capacity of the host cell, the Maximum Principle requires for these models an optimal conversion strategy that confirms and rigorously justifies the prevailing view of no conversion at the early stage of the host cell infection. However, the conventional supposition is found to be inappropriate for an initial EB (-to-RB) population near or above the carrying capacity. Previously suggested and new biological mechanisms are examined for their role in implementing the different optimal conversion strategies associated with models investigated herein

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. We find that diffusive mechanisms of morphogen transport are much more plausible-and nondiffusive mechanisms much less plausible-than has generally been argued. Moreover, we show that a class of experiments, endocytic blockade, thought to effectively distinguish between diffusive and nondiffusive transport models actually fails to draw useful distinctions

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. We find that diffusive mechanisms of morphogen transport are much more plausible-and nondiffusive mechanisms much less plausible-than has generally been argued. Moreover, we show that a class of experiments, endocytic blockade, thought to effectively distinguish between diffusive and nondiffusive transport models actually fails to draw useful distinctions

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). Additional biological activities must play an important role in the high level of robustness observed in embryonic patterning for example. It is natural to attribute observed robustness to various type of feedback control mechanisms. However, our own simulation studies have shown that feedback control is neither necessary nor sufficient for robustness of the morphogen decapentaplegic (Dpp) gradient in wing imaginal disc of Drosophilas. Furthermore, robustness can be achieved by substantial binding of the signaling morphogen Dpp with nonsignaling cell surface bound molecules (such as heparan sulfate proteoglygans) and degrading the resulting complexes at a sufficiently rapid rate. The present work provides a theoretical basis for the results of our numerical simulation studies

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. The results suggest that the usefulness of this strategy comes less from its ability to increase robustness to morphogen source fluctuations per se, than from its ability to overcome specific kinds of noise, and to increase the fraction of a morphogen gradient within which robust threshold positions may be established. This work also provides new insights into the longstanding question of why morphogen gradients show a maximum range in vivo