Experiments,measurements, and mathematical modeling to decipher time signals in development

Good progress has been made in identifying key signaling molecules and explaining how they are used to generate spatial patterns during embryonic development. In contrast, little is known about the control of timing or how cells use time signals in the developing embryo. In this review, I describe how direct measurements from the embryo combined with mathematical modeling could bring new insights. To illustrate this point, I discuss three examples: the Dpp gradient during growth of the Drosophila wing imaginal disc; the Polycomb‐based epigenetic silencing during vernalization in plants; and the Notch‐dependent somite segmentation clock. Birth Defects Research (Part C) 96:121–131, 2012. © 2012 Wiley Periodicals, Inc.     

Plasmodium development in the mosquito: biology bottlenecks and opportunities for mathematical modeling

Quantitative analyses of malaria parasite development are necessary to assess the efficacy of control measures. Such analyses in the mammalian host have been difficult to implement, lagging behind the use of antiparasitic drugs, vaccine development and transmission-blocking strategies. Even less is known about the genetic, environmental and other factors that impact sporogony in the mosquito host. Here, we summarize current knowledge and review a first attempt to model sporogonic development quantitatively.     

Mlab--a mathematical modeling tool

An interactive interpreter called Mlab is described. One uses Mlab by typing commands. In this sense, Mlab is a programming language. It has various mathematical and graphical facilities which make it a useful tool for mathematical modeling. The curve fitting capabilities of Mlab are augmented with differential-equation-handling and matrix-manipulation capabilities which provide a powerful and civilized facility for curve fitting. Many people are engaged in this activity, and, in general, they use programs which are neither sufficiently general nor easy to use. (Some conventional programming is usually required, for example.) Mlab purports to be easier than alternate approaches. The nature of Mlab is discussed with accompanying examples. The main example is the use of curve fitting to determine molecular weight from ultracentrifuge data. This example was chosen because it exhibits a special feature of Mlab, namely the root operator, which appears in the definition of the model function.     

Roles of endothelin signaling in melanocyte development and melanoma

Endothelin (Edn) signaling via the G-coupled, Edn receptor type B (Ednrb) is essential for the development of melanocytes from the neural crest (NC) and has been associated with melanoma progression. Edn3 plays varying roles during melanocyte development, promoting the proliferation and self-renewal of NC-derived multi- and bi-potential precursors as well as the survival, proliferation, differentiation and migration of committed melanocyte precursors. Melanocyte differentiation is achieved via the interaction of Ednrb and Kit signaling, with Ednrb being specifically required in the final differentiation step, rather than in the initial specification of melanocytic fate. Ednrb has also been implicated in the de-differentiation of mature melanocytes, a process that takes place during the malignant transformation of these cells. Ednrb was found to be upregulated in melanoma metastases and was shown to alter tumor–host interactions leading to melanoma progression. Antagonists to this receptor were shown to inhibit melanoma cell growth and increase the apoptotic rate of these cells, and to lead to disease stabilization in melanoma patients. Thus, Edn signaling inhibition may prove useful in the treatment of certain types of melanoma.     

Mechanism and mathematical modeling of electro-enzymatic denitrification

In this study, a novel nitrate reduction method using an electro-enzymatic system was investigated to treat an aqueous solution containing high concentrations of nitrate. This system was comprised of working electrodes and their counter electrodes, where enzymes for nitrate removal were located inside the microorganisms. A nitrate reduction mechanism for the electro-enzymatic system was proposed and a mathematical model was developed. The modeling results were compared to the experimental results and all the experimental results fit well with the model; thus, the derived mathematical model can be used for reactor control and effluent prediction.     

展望数学生态学与生态模型的未来

首先简要回顾了２０世纪数学生态学发展的历史,特别是半２个世纪以来在中国的发展。然后指出了生物学的进步为数学生态学的发展提供了机遇。作者列出了当前数学生态学和生态模型研究的几个热点：⑴非线性动力学;⑵种群的时空动态：包括异质种群动态,源－汇理论以及种群对时、空变化的响应等;⑶多样性和稳定性的关系;⑷行为的动态模型;⑸基于个体的模型。最后指出,生态学中混沌现象,可能表明多年来理论生态学家寻找的种群动态     

Biological adaptation and the mathematical theory of information

Adaptation is viewed as a tendency maximizing the Shannon entropy of an ecosystem, where the ecosystem is considered as two interacting subsystems, namely, the biota and its environment. We derive theadapted structures starting from three fundamental hypotheses and we apply this result to an ecological topic: the cryptic and aposematic behaviour.     

The biology of melanocyte and melanocyte stem cell

The melanocyte stem cells of the hair follicle provide an attractive system for the study of the stem cells. Successful regeneration of a functional organ relies on the organized and timely orchestration of molecular events among dis- tinct stem/progenitor cell populations. The stem cells are regulated by communication with their specialized microenvironment known as the niche. Despite remarkable progress in understanding stem cell-intrinsic behavior, the molecular nature of the extrinsic factors provided to the stem cells by the niche microenvironment remains poorly understood. In this regard, the bulge niche of the mammalian hair follicle offers an excellent model for study. It holds two resident populations of SCs： epidermal stem cells and melanocyte stem cells. While their behavior is tightly coordinated, very little of the crosstaik involved is known. This review summarized the recent development in trying to understand the regulation of melanocyte and melanocyte stem cells. A better understanding of the normal regulation and behaviors of the melanocytes and the melanocyte stem cells will help to improve the clinical applications in regenerative medicine, cancer therapy, and aging.     

Perturbation analysis analyzed—mathematical modeling of intact and perturbed gene regulatory circuits for animal development

Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development.     

A framework for whole-cell mathematical modeling

The default framework for modeling biochemical processes is that of a constant-volume reactor operating under steady-state conditions. This is satisfactory for many applications, but not for modeling growth and division of cells. In this study, a whole-cell modeling framework is developed that assumes expanding volumes and a cell-division cycle. A spherical newborn cell is designed to grow in volume during the growth phase of the cycle. After 80% of the cycle period, the cell begins to divide by constricting about its equator, ultimately affording two spherical cells with total volume equal to twice that of the original. The cell is partitioned into two regions or volumes, namely the cytoplasm (Vcyt) and membrane (Vmem), with molecular components present in each. Both volumes change during the cell cycle; Vcyt changes in response to osmotic pressure changes as nutrients enter the cell from the environment, while Vmem changes in response to this osmotic pressure effect such that membrane thickness remains invariant. The two volumes change at different rates; in most cases, this imposes periodic or oscillatory behavior on all components within the cell. Since the framework itself rather than a particular set of reactions and components is responsible for this behavior, it should be possible to model various biochemical processes within it, affording stable periodic solutions without requiring that the biochemical process itself generates oscillations as an inherent feature. Given that these processes naturally occur in growing and dividing cells, it is reasonable to conclude that the dynamics of component concentrations will be more realistic than when modeled within constant-volume and/or steady-state frameworks. This approach is illustrated using a symbolic whole cell model.     

The mathematical modeling of entrained biological oscillators

In this paper perturbation methods are used for the mathematical analysis of coupled relaxation oscillators. This study covers entrainment by an external periodic stimulus as well as mutual entrainment of coupled oscillators with different limit cycles. The oscillators are of a type one meets in the modeling of biological oscillators by chemical reactions and electronic circuits. Special attention is given to entrainment different from 1∶1. The results relate to phenomena occurring in physiological experiments, such as the periodic stimulation of neural and cardiac cells, and in the non-regular functioning of organs and organisms, such as the AV-block in the heart.     

Cancer immunotherapy, mathematical modeling and optimal control

Clinical immunologists, among other problems, routinely face a question: what is the best time and dose for a certain therapeutic agent to be administered to the patient in order to decrease/eradicate the pathological condition? In cancer immunotherapies the therapeutic agent is something able to elicit an immune response against cancer. The immune response has its own dynamics that depends on the immunogenicity of the therapeutic agent and on the duration of the immune response. The question then is "how can we decide when and how much of the drug to inject so to have a prolonged and effective immune response to the cancer?". This question can be addressed in mathematical terms in two stages: first one construct a mathematical model describing the cancer-immune interaction and secondly one applies the theory of optimal control to determine when and to which extent to stimulate the immune system by means of an immunotherapeutic agent administered in discrete variable doses within the therapeutic period. The solution of this mathematical problem is described and discussed in this article. We show that the method employed can be applied to find the optimal protocol in a variety of clinical problems where the kinetics of the drug or treatment and its influence on the physiologic/pathologic functions have been described by a system of ordinary differential equations.