Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.     

In vitro Approach to Bacterial Chemotaxis

An in vitro approach to study bacterial motility and chemotaxis is described. The approach is based on a preparation of flagellated cell envelopes. The envelopes are prepared from bacteria by a penicillin treatment and subsequent osmotic lysis. When the envelopes are energized, their flagella rotate. The direction of rotation in wild type envelopes is counterclockwise. Inclusion of the CheY protein within the envelopes may restore clockwise rotation. The advantages and disadvantages of this approach are pointed out.     

The Study of Bacterial Chemotaxis to Naphthalene

The chemotaxis of two pseudomonads,Pseudomonas putida AZ (Naph⁺) and P. putida AZ (Naph^–), differing in their ability to metabolize naphthalene was studied by the known capillary method of Adler and the densitometric method devised in our laboratory. The migration of P. putida AZ (Naph⁺) cells toward increasing levels of naphthalene was accompanied by the formation of a migrating front of converted naphthalene. P. putida AZ (Naph^–) cells also exhibited positive chemotaxis to naphthalene, but they did not form the front of converted naphthalene. The analysis of experimental data in terms of a kinetic model of bacterial chemotaxis showed that the densitometric method is a potential tool for studying bacterial chemotaxis to hydrophobic organic substances.     

Autocatalytic Loop,Amplification and Diffusion: A Mathematical and Computational Model of Cell Polarization in Neural Chemotaxis

The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.     

单细胞RNA测序数据分析方法研究进展

单细胞RNA测序(Single cell RNA sequencing,scRNA-Seq)已经广泛应用于细胞分化、肿瘤微环境及多种疾病病因学研究。目前,由于scRNA-Seq具有低捕获率、高噪声、高变异性等特点,通过优化数据分析方法提高测序结果准确性已经成为测序领域的研究热点。对近年来数据分析过程中利用的数学方法进行了总结,讨论了数据分析的优势及存在的问题,以期为新算法的开发和应用提供参考,逐步提高测序结果的可靠性。     

Cell Growth and Division: I. A Mathematical Model with Applications to Cell Volume Distributions in Mammalian Suspension Cultures

A mathematical model is formulated for the development of a population of cells in which the individual members may grow and divide or die. A given cell is characterized by its age and volume, and these parameters are assumed to determine the rate of volume growth and the probability per unit time of division or death. The initial value problem is formulated, and it is shown that if cell growth rate is proportional to cell volume, then the volume distribution will not converge to a time-invariant shape without an added dispersive mechanism. Mathematical simplications which are possible for the special case of populations in the exponential phase or in the steady state are considered in some detail. Experimental volume distributions of mammalian cells in exponentially growing suspension cultures are analyzed, and growth rates and division probabilities are deduced. It is concluded that the cell volume growth rate is approximately proportional to cell volume and that the division probability increases with volume above a critical threshold. The effects on volume distribution of division into daughter cells of unequal volumes are examined in computer models.     

木材横断面六棱规则细胞数学描述理论研究

本文采用微观力学和细胞学理论,在横观各向同性的假设下,提出了一种木材规则细胞主方向截面形状描述的理论方法。应用本文提出的理论,可以根据纤维、木质素、细胞直径和排列的程度,绘出理想状态下木材的主方向规则细胞结构形状,为木材学运用数学手术深入到细胞结构研究的深度提供了一种新的数学方法,并且可以为定量解释木材规则细胞变异后材性与性能提高的原因提供定量解释的数学手段。     

Single Cell Genomics of the Brain: Focus on Neuronal Diversity and Neuropsychiatric Diseases

Single cell genomics has made increasingly significant contributions to our understanding of the role that somatic genome variations play in human neuronal diversity and brain diseases. Studying intercellular genome and epigenome variations has provided new clues to the delineation of molecular mechanisms that regulate development, function and plasticity of the human central nervous system (CNS). It has been shown that changes of genomic content and epigenetic profiling at single cell level are involved in the pathogenesis of neuropsychiatric diseases (schizophrenia, mental retardation (intellectual/leaning disability), autism, Alzheimer’s disease etc.). Additionally, several brain diseases were found to be associated with genome and chromosome instability (copy number variations, aneuploidy) variably affecting cell populations of the human CNS. The present review focuses on the latest advances of single cell genomics, which have led to a better understanding of molecular mechanisms of neuronal diversity and neuropsychiatric diseases, in the light of dynamically developing fields of systems biology and “omics”.     

The Bacterial Cell Cycle: DNA Replication,Nucleoid Segregation,and Cell Division

Data on the bacterial cell cycle published in the last 10–15 years are considered, with a special stress on studies of nucleoid segregation between dividing cells. The degree of similarity between the eukaryotic mitotic apparatus and the apparatus performing nucleoid separation is discussed.__________Translated from Mikrobiologiya, Vol. 74, No. 4, 2005, pp. 437–451.Original Russian Text Copyright © 2005 by Prozorov.     

A Mathematical Model of the Cerebellar-Olivary System I: Self-Regulating Equilibrium of Climbing Fiber Activity

We use a mathematical model to investigate how climbing fiber-dependent plasticity at granule cell to Purkinje cell (grPkj) synapses in the cerebellar cortex is influenced by the synaptic organization of the cerebellar-olivary system. Based on empirical studies, grPkj synapses are assumed to decrease in strength when active during a climbing fiber input (LTD) and increase in strength when active without a climbing fiber input (LTP). Results suggest that the inhibition of climbing fibers by cerebellar output combines with LTD/P to self-regulate spontaneous climbing fiber activity to an equilibrium level at which LTP and LTD balance and the expected net change in grPkj synaptic weights is zero. The synaptic weight vector is asymptotically confined to an equilibrium hyperplane defining the set of all possible combinations of synaptic weights consistent with climbing fiber equilibrium. Results also suggest restrictions on LTP/D at grPkj synapses required to produce synaptic weights that do not drift spontaneously.     

Single cell oil production from low-cost substrates: The possibility and potential of its industrialization

Currently, single cell oils (SCO) attract much attention because of their bi-function as a supplier of functional oils and feedstock for biodiesel production. However, high fermentation costs prevent their further application, and the possibility and potential of their industrialization is suspected. Therefore, various low-cost, hydrophilic and hydrophobic substrates were utilized for SCO production. Of these substrates, lignocellulosic biomass, which is the most available and renewable source in nature, might be an ideal raw material for SCO production. Although many reviews on SCO have been published, few have focused on SCO production from low-cost substrates or evaluated the possibility and potential of its industrialization. Therefore, this review mainly presents information on SCO and its production using low-cost substrates and mostly focuses on lignocellulosic biomass. Finally, the possibility and potential of SCO industrialization is evaluated.     

细胞分化模型在细胞生物学实验教学中的应用与实践

生命活动包括细胞分化、生长、衰老、死亡等一系列变化,是一个连续发展的过程,而在当前的细胞生物学实验教学中,针对独立、单个知识点的实验设计仍占多数,这不利于学生系统、有机地理解生命现象。该研究以U-937细胞分化过程为对象,设计了3个相互联系的实验,分别为:(1)分化对细胞形态影响的观察;(2)分化对细胞周期影响的观察;(3)分化对细胞吞噬功能影响的观察。通过对实验结果的观察,学生发现分化后,(1)细胞由悬浮生长转变为贴壁生长,细胞形态由圆形变为不规则多边形,并伸出伪足;(2)细胞周期则会发生G1/S期阻滞,停留在G1期;(3)分化后的细胞对细菌的吞噬能力明显增强。该教学设计巧妙地将3个知识点有机整合在一起,旨在通过细胞分化这一生命现象,让学生深入理解细胞在发育成熟过程中形态学、分裂增殖及吞噬功能的变化,帮助学生充分理解生命活动是动态发展这一本质,且能很好地培养学生全面思考、分析及解决问题的能力,进而提升学生对教学实验的兴趣,发挥学习的主观能动性。     

Cell traction in collective cell migration and morphogenesis: The chase and run mechanism

Directional collective cell migration plays an important role in development, physiology, and disease. An increasing number of studies revealed key aspects of how cells coordinate their movement through distances surpassing several cell diameters. While physical modeling and measurements of forces during collective cell movements helped to reveal key mechanisms, most of these studies focus on tightly connected epithelial cultures. Less is known about collective migration of mesenchymal cells. A typical example of such behavior is the migration of the neural crest cells, which migrate large distances as a group. A recent study revealed that this persistent migration is aided by the interaction between the neural crest and the neighboring placode cells, whereby neural crest chase the placodes via chemotaxis, but upon contact both populations undergo contact inhibition of locomotion and a rapid reorganization of cellular traction. The resulting asymmetric traction field of the placodes forces them to run away from the chasers. We argue that this chase and run interaction may not be specific only to the neural crest system, but could serve as the underlying mechanism for several morphogenetic processes involving collective cell migration.     

Proteasomal Degradation of Nod2 Protein Mediates Tolerance to Bacterial Cell Wall Components

The innate immune system serves as the first line of defense by detecting microbes and initiating inflammatory responses. Although both Toll-like receptor (TLR) and nucleotide binding domain and leucine-rich repeat (NLR) proteins are important for this process, their excessive activation is hazardous to hosts; thus, tight regulation is required. Endotoxin tolerance is refractory to repeated lipopolysaccharide (LPS) stimulation and serves as a host defense mechanism against septic shock caused by an excessive TLR4 response during Gram-negative bacterial infection. Gram-positive bacteria as well as their cell wall components also induce shock. However, the mechanism underlying tolerance is not understood. Here, we show that activation of Nod2 by its ligand, muramyl dipeptide (MDP) in the bacterial cell wall, induces rapid degradation of Nod2, which confers MDP tolerance in vitro and in vivo. Nod2 is constitutively associated with a chaperone protein, Hsp90, which is required for Nod2 stability and protects Nod2 from degradation. Upon MDP stimulation, Hsp90 rapidly dissociates from Nod2, which subsequently undergoes ubiquitination and proteasomal degradation. The SOCS-3 protein induced by Nod2 activation further facilitates this degradation process. Therefore, Nod2 protein stability is a key factor in determining responsiveness to MDP stimulation. This indicates that TLRs and NLRs induce a tolerant state through distinct molecular mechanisms that protect the host from septic shock.     

Some Aspects of the Cell Biology of the Bacterial Stationary Phase: Programmed Cell Death and Its Regulation by Guanosine Tetraphosphate

This paper discusses (1) programmed cell death, a phenomenon typical of the stationary phase of bacteria occurring under unfavorable conditions, (2) its pleiotropic regulation by guanosine tetraphosphate, and (3) the conception of addiction module, a specific genetic system responsible for the cell choice between survival and death under unfavorable conditions. The shortcomings of the proposed interpretation of the problem at hand are considered and the necessity of their further investigation is substantiated.     

Caco-2 Cell Line Used as an In Vitro Model to Study Cadmium Accumulation in Intestinal Epithelial Cells

¹⁰⁹Cd uptake was studied using the highly differentiated TC7 clone of Caco-2 cells as a model of human enterocyte function. Intracellular accumulation of 0.3 μm ¹⁰⁹Cd involved a rapid and a slow uptake phase, which resulted in complete equilibration (t _?= 17.3 ± 1.3 min) with an apparent in-to-out distribution ratio (α _e ) of 11.6 ± 0.8. The amplitude of the rapid phase (U ₀) and the rate of the slow phase (V) were similarly reduced in the less differentiated PF11 clone, but comparable α _e values were observed at equilibrium. In both clones, the t _? and α _e values increased and decreased, respectively, upon addition of unlabeled Cd to the uptake media. In TC7 cells, ¹⁰⁹Cd uptake at 1 min (U ₁) was unaffected by Ca concentrations four order of magnitude in excess, but both U ₀ and V demonstrated similar sensitivities to unlabeled Cd, Zn and sulfhydryl-reactive agents. Only U ₀ disappeared when EDTA was present in the wash solutions. U ₁ showed saturation kinetics and the data were found compatible with a model assuming rapid initial Cd binding and transport through a unique transport protein (K _m = 3.8 ± 0.7 μm). Cd efflux kinetics demonstrated partial reversibility in EDTA-containing solutions, suggesting that the taken up Cd might be both tightly and loosely bound to intracellular binding sites. However, the displacement of ¹⁰⁹Cd measured at 65 min failed to reveal this heterogeneity: the data were found compatible with a model equation assuming the presence of one class of high-capacity high-affinity binding sites. We conclude that a slow-transport fast-intracellular binding mechanism of Cd uptake best accounts for these results and that Cd transport most likely involves a carrier-type of protein unrelated to Ca absorption. Received: 19 January 1996/Revised: 23 January 1997     

成年绒山羊皮肤干细胞克隆定向诱导分化为成骨细胞

成年绒山羊皮肤经0.02%中性蛋白酶4℃过夜消化,分离表皮,37℃消化30min,经100μg/mlIV型胶原处理的培养皿黏附10min筛选干细胞,培养到第二代时采用有限稀释法进行单细胞克隆纯化,角蛋白15、角蛋白19免疫荧光染色部分细胞强阳性,添加成骨细胞诱导液定向诱导分化,经碱性磷酸酶、茜素红染色鉴定为阳性,表明分离的细胞是皮肤干细胞且有能力诱导分化为成骨细胞。