Hybrid approaches to molecular simulation

Molecular dynamics (MD) simulation is an established method for studying the conformational changes that are important for protein function. Recent advances in hardware and software have allowed MD simulations over the same timescales as experiment, improving the agreement between theory and experiment to a large extent. However, running such simulations are costly, in terms of resources, storage, and trajectory analysis. There is still a place for techniques that involve short MD simulations. In order to overcome the sampling paucity of short time-scales, hybrid methods that include some form of MD simulation can exploit certain features of the system of interest, often combining experimental information in surprising ways. Here, we review some recent hybrid approaches to the simulation of proteins.     

Dynamic cellular automata: an alternative approach to cellular simulation

A wide variety of approaches, ranging from Petri nets to systems of partial differential equations, have been used to model very specific aspects of cellular or biochemical functions. Here we describe how an agent-based or dynamic cellular automata (DCA) approach can be used as a very simple, yet very general method to model many different kinds of cellular or biochemical processes. Specifically, using simple pairwise interaction rules coupled with random object moves to simulate Brownian motion, we show how the DCA approach can be used to easily and accurately model diffusion, viscous drag, enzyme rate processes, metabolism (the Kreb's cycle), and complex genetic circuits (the repressilator). We also demonstrate how DCA approaches are able to accurately capture the stochasticity of many biological processes. The success and simplicity of this technique suggests that many other physical properties and significantly more complicated aspects of cellular behavior could be modeled using DCA methods. An easy-to-use, graphically-based computer program, called SimCell, was developed to perform the DCA simulations described here. It is available at http://wishart.biology.ualberta.ca/SimCell/.     

Laminin 332 processing impacts cellular behavior

Laminin 332, composed of the α3, β3 and γ2 chains, is an epithelial-basement membrane specific laminin variant. Its main role in normal tissues is the maintenance of epithelial-mesenchymal cohesion in tissues exposed to external forces, including skin and stratified squamous mucosa. After being secreted and deposited in the extracellular matrix, laminin 332 undergoes physiological maturation processes consisting in the proteolytic processing of domains located within the α3 and the γ2 chains. These maturation events are essential for laminin 332 integration into the basement membrane where it plays an important function in the nucleation and maintenance of anchoring structures. Studies in normal and pathological situations have revealed that laminin 332 can trigger distinct cellular events depending on the level of its proteolytic cleavages. In this review, the biological and structural characteristics of laminin 332 domains are presented and we discuss whether they trigger specific functions.     

Computer simulation of Paramecium chemokinesis behavior

A computer program was designed to simulate the distribution of paramecia in a T-maze assay for chemo-accumulation and dispersal. Simulated values of chemokinesis are compared to experimental values for normal and mutant paramecia. The roles of components of swimming behavior (turning frequency and swimming speed), adaptation, and reaction at the border of solutions are examined.     

Hybrid liposomes affect cellular lipid constituents and caveolae structures

We examined alterations of lipid constituents induced by hybrid liposomes (HLs) in cancer cells. As early as 1h after HL treatment, amounts of the raft/caveolae lipids sphingomyelin, ceramide, and ether-type PC were altered. In addition, the structures of caveolae on the cytoplasmic surface of the cell membrane were significantly changed. Our results suggest that alterations of lipid composition in caveolae mediate HL signaling for apoptosis.     

The behavior of adaptive bone-remodeling simulation models

The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset value for the strain energy per unit bone mass, by adapting the density. If an element in the structure cannot achieve that, it either turns to its maximal density (cortical bone) or resorbs completely.

It is found that the solution obtained in generally a discontinuous patchwork. For a two-dimensional proximal femur model this patchwork shows a good resemblance with the density distribution of a real proximal femur.

It is shown that the discontinuous end configuration is dictated by the nature of the differential equations describing the remodeling process. This process can be considered as a nonlinear dynamical system with many degrees of freedom, which behaves divergent relative to the objective, leading to many possible solutions. The precise solution is dependent on the parameters in the remodeling rule, the load and the initial conditions. The feedback mechanism in the process is self-enhancing; denser bone attracts more strain energy, whereby the bone becomes even more dense. It is suggested that this positive feedback of the attractor state (the strain energy field) creates order in the end configuration. In addition, the process ensures that the discontinuous end configuration is a structure with a relatively low mass, perhaps a minimal-mass structure, although this is no explicit objective in the optimization process.

It is hypothesized that trabecular bone is a chaotically ordered structure which can be considered as a fractal with characteristics of optimal mechanical resistance and minimal mass, of which the actual morphology depends on the local (internal) loading characteristics, the sensor-cell density and the degree of mineralization.     

Implications of cytoskeletal interactions for cellular architecture and behavior

The three major filamentous components of the cytoskeleton (microfilaments, microtubules and intermediate filaments) do not just coexist in the cell, but interact with each other in various ways. This paper discusses some examples of structural interactions visualized in critical-point-dried cells by stereoscopic high-voltage electron microscopy. The relative contribution of two classes of interactions to the consolidation of different cytoskeletal domains is considered. One class is represented by T-junctions (end-to-side contacts) of actin filaments with other filaments, and the other by 3 nm links. Attention is then turned to what may be called the behavioural consequences of cytoskeletal interactions. As an example of a coordinated interplay between events at the cell membrane and the cytoskeleton, we discuss changes in cytoskeletal organization of polymorphonuclear leucocytes upon stimulation with a chemotactic factor. These changes culminate in some cells in centriole separation and the establishment of two microtubule asters, each centred around a single centriole.     

Cortical control of motor behavior at the cellular level

The studies reviewed in this paper describe the relations of single-cell activity in central motor structures to complex visuomotor tasks and document the fact that various cortical areas process visuomotor information in parallel. Moreover, the studies provide clear evidence that the map in the motor cortex is modifiable and dynamically maintained.     

Analysing dynamical behavior of cellular networks via stochastic bifurcations

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.     

基于元胞自动机的喀斯特石漠化格局模拟研究

西南喀斯特山区的石漠化问题是目前我国西部地区最为突出的地域环境问题之一,其迅速发展已经严重影响到当地人们的生产生活。以导致石漠化发生发展的自然、人文因子为切入点,通过模拟影响喀斯特系统地表覆被变化的基本生态过程(如植物定居、植物死亡、水蚀风蚀引起的土地退化以及岩石成土过程等),利用随机元胞自动机具有的简单邻域规则产生复杂空间格局的特点,使喀斯特系统地表覆被植被-裸土-裸岩状态在一定概率下发生状态转换,并结合RS和GIS技术,构建了简单、有效的喀斯特石漠化模拟及预测模型(KarstCA)。以典型喀斯特石漠化地区关岭县为研究区,在自然、人文驱动因素共同影响以及只考虑自然驱动因素情景下,KarstCA模型模拟的研究区2007年石漠化空间分布格局的差异主要分布在中部和南部,其主要是不同空间范围上人类活动作用方式和强度差异所致。在16a中(1992—2007年)喀斯特地区地物(植被-裸土-裸岩)丰度变化成非线性关系,当植被覆达到54%以上并继续增加时,裸岩发展趋势与之呈明显的负相关(P<0.01)。在模拟期内人类活动对研究区石漠化的发展起到抑制作用,人类活动的正效应(植树造林等)与负效应(乱砍滥伐、过度放牧等)在一定程度上抵消了植被总面积的剧烈变化趋势。将地表过程耦合进元胞自动机模型,突破了以往该类研究只通过概率考虑状态转换,而对其机理认识的不足;同时本研究考虑了自然、人文驱动因素在不同空间尺度上作用于石漠化现象的复杂性,对于探索这些因素是如何作用于地表过程及其贡献率等研究具有一定的参考价值。     

DEVS modelling and simulation of the cellular metabolism by mitochondria

We present a method for modelling and simulating metabolic pathways in the cells (namely, the glycolysis and Krebs' cycle), using the discrete event system specification (DEVS) formalism. The hierarchical nature of DEVS makes it ideal for describing naturally hierarchical systems as the Cell, while its discrete-event approach improves performance due to the asynchronous nature of the events involved. DEVS time-based nature can adequately represent the timing of the chemical reactions. We show how this methodology enables creating a precise and easy way to model and simulate biological systems, including advanced visualisation of the experiments. The results presented, which focus on the simulation of the cellular metabolism pathways in mitochondria, show the potential of our approach.     

Mathematical simulation and analysis of cellular metabolism and regulation.

MOTIVATION: A better understanding of the biological phenomena observed in cells requires the creation and analysis of mathematical models of cellular metabolism and physiology. The formulation and study of such models must also be simplified as far as possible to cope with the increasing complexity demanded and exponential accumulation of the metabolic reconstructions computed from sequenced genomes. RESULTS: A mathematical simulation workbench, DBsolve, has been developed to simplify the derivation and analysis of mathematical models. It combines: (i) derivation of large-scale mathematical models from metabolic reconstructions and other data sources; (ii) solving and parameter continuation of non-linear algebraic equations (NAEs), including metabolic control analysis; (iii) solving the non-linear stiff systems of ordinary differential equations (ODEs); (iv) bifurcation analysis of ODEs; (v) parameter fitting to experimental data or functional criteria based on constrained optimization. The workbench has been successfully used for dynamic metabolic modeling of some typical biochemical networks (Dolgacheva et al., Biochemistry (Moscow), 6, 1063-1068, 1996; Goldstein and Goryanin, Mol. Biol. (Moscow), 30, 976-983, 1996), including microbial glycolytic pathways, signal transduction pathways and receptor-ligand interactions. AVAILABILITY: DBsolve 5. 00 is freely available from http://websites.ntl.com/ approximately igor.goryanin. CONTACT: gzz78923@ggr.co.uk     

Linking chordate gene networks to cellular behavior in ascidians

Embryos of simple chordates called ascidians (sea squirts) have few cells, develop rapidly, and are transparent, enabling the in vivo fluorescent imaging of labeled cell lineages. Ascidians are also simple genetically, with limited redundancy and compact regulatory regions. This cellular and genetic simplicity is now being exploited to link comprehensive gene networks to the cellular events underlying morphogenesis.     

Hybrid dynamic/static method for large-scale simulation of metabolism

Background  

Many computer studies have employed either dynamic simulation or metabolic flux analysis (MFA) to predict the behaviour of biochemical pathways. Dynamic simulation determines the time evolution of pathway properties in response to environmental changes, whereas MFA provides only a snapshot of pathway properties within a particular set of environmental conditions. However, owing to the large amount of kinetic data required for dynamic simulation, MFA, which requires less information, has been used to manipulate large-scale pathways to determine metabolic outcomes.     

On the dynamics of controlled metabolic network and cellular behavior

The existence of elaborate control mechanisms for the various biochemical processes inside and within living cells is responsible for the coherent behaviour observed in its spatio-temporal organisation. Stability and sensitivity are both necessary properties of living systems and these are achieved through negetive and positive feedback loops as in other control systems. We have studied a three-step reaction scheme involving a negative and a positive feedback loop in the form of end-product inhibition and allosteric activation. The variety of behaviour exhibited by this system, under different conditions, includes steady state, simple limit cycle oscillations, complex oscillations and period bifurcations leading to random oscillations or chaos. The system also shows the existence of two distinct chaotic regimes under the variation of a single parameter. These results, in comparison with single biochemical control loops, show that new behaviours can be exhibited in a more complex network which are not seen in the single control loops. The results are discussed in the light of a diverse variety of cellular functions in normal and altered cells indicating the role of controlled metabolic network as the underlying basis for cellular behaviour.     

Computer simulation of cellular movements: cell-sorting, cellular migration through a mass of cells and contact inhibition

The motility rules for cellular movement proposed earlier by Goel &; Rogers for engulfment of two or more intact embryonic tissues have been used to simulate on a computer the phenomena of cell-sorting, migration of individual cells through a mass of cells and contact inhibition of overlapping. These simulations in the most part are found to be consistent with the observations with real cells.     

基于元胞自动机的城市空间动态模拟

城市空间动态的模拟与预测可以为城市可持续发展规划与管理提供重要的参考依据。SLEUTH元胞自动机模型在城市空间模拟中较强的适用性和可移植性,该模型通过对历史数据的蒙特卡洛迭代自动寻找城市增长误差最小的参数组合,解决了传统元胞自动机模型中转换规则不易确定的问题。以武汉市为研究案例,运用SLEUTH模型进行了城市空间动态模拟与情景预测。2007年至2011年的城市空间模拟结果显示,模拟结果与实际历史数据可以获得良好的空间匹配度,Lee-Sallee形状指数均在0.6以上,显示SLEUTH元胞自动机模型经过本地化校正后具有较强的适用性和满意的模拟精度。进而,设置了现状趋势、基本保护、严格保护等3种情景对武汉2025年城市空间动态进行了预测,结果显示,各情景模式下城市居住用地均明显增长,农业用地、林地、水域等均有所减少;现状趋势情景和基本保护情景下农田、林地、水域减少的幅度较大,会加剧区域的生境破碎、耕地功能下降、水资源匮乏、湖滨湿地萎缩等生态问题,说明这两种情景不能有效满足城市生态系统健康和可持续发展的需要。严格保护情景下,城市居住用地扩张的程度得到了明显的控制,水域和林地得到了有效的保护,对于重要的自然生态系统组分保护及其服务能力维持可以起到显著作用。     

Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs

Mathematic models help interpret experimental results and accelerate tissue engineering developments. We develop in this paper a hybrid cellular automata model that combines the differential nutrient transport equation to investigate the nutrient limited cell construct development for cartilage tissue engineering. Individual cell behaviors of migration, contact inhibition and cell collision, coupled with the cell proliferation regulated by oxygen concentration were carefully studied. Simplified two-dimensional simulations were performed. Using this model, we investigated the influence of cell migration speed on the overall cell growth within in vitro cell scaffolds. It was found that intense cell motility can enhance initial cell growth rates. However, since cell growth is also significantly modulated by the nutrient contents, intense cell motility with conventional uniform cell seeding method may lead to declined cell growth in the final time because concentrated cell population has been growing around the scaffold periphery to block the nutrient transport from outside culture media. Therefore, homogeneous cell seeding may not be a good way of gaining large and uniform cell densities for the final results. We then compared cell growth in scaffolds with various seeding modes, and proposed a seeding mode with cells initially residing in the middle area of the scaffold that may efficiently reduce the nutrient blockage and result in a better cell amount and uniform cell distribution for tissue engineering construct developments.