Reconstruction of endosomal organization and function by a combination of ODE and agent-based modeling strategies

Background

Reproducing cell processes using an in silico system is an essential tool for understanding the underlying mechanisms and emergent properties of this extraordinary complex biological machine. However, computational models are seldom applied in the field of intracellular trafficking. In a cell, numerous molecular interactions occur on the surface or in the interior of membrane-bound compartments that continually change position and undergo dynamic processes of fusion and fission. At present, the available simulation tools are not suitable to develop models that incorporate the dynamic evolution of the cell organelles.

Results

We developed a modeling platform combining Repast (Agent-Based Modeling, ABM) and COPASI (Differential Equations, ODE) that can be used to reproduce complex networks of molecular interactions. These interactions occur in dynamic cell organelles that change position and composition over the course of time. These two modeling strategies are fundamentally different and comprise of complementary capabilities. The ODEs can easily model the networks of molecular interactions, signaling cascades, and complex metabolic reactions. On the other hand, ABM software is especially suited to simulate the movement, interaction, fusion, and fission of dynamic organelles. We used the combined ABM-ODE platform to simulate the transport of soluble and membrane-associated cargoes that move along an endocytic route composed of early, sorting, recycling and late endosomes. We showed that complex processes that strongly depend on transport can be modeled. As an example, the hydrolysis of a GM2-like glycolipid was programmed by adding a trans-Golgi network compartment, lysosomal enzyme trafficking, endosomal acidification, and cholesterol processing to the simulation model.

Conclusions

The model captures the highly dynamic nature of cell compartments that fuse and divide, creating different conditions for each organelle. We expect that this modeling strategy will be useful to understand the logic underlying the organization and function of the endomembrane system.

Reviewers

This article was reviewed by Drs. Rafael Fernández-Chacón, James Faeder, and Thomas Simmen.

     

Three-dimensional geometric modeling of membrane-bound organelles in ventricular myocytes: bridging the gap between microscopic imaging and mathematical simulation

A general framework of image-based geometric processing is presented to bridge the gap between three-dimensional (3D) imaging that provides structural details of a biological system and mathematical simulation where high-quality surface or volumetric meshes are required. A 3D density map is processed in the order of image pre-processing (contrast enhancement and anisotropic filtering), feature extraction (boundary segmentation and skeletonization), and high-quality and realistic surface (triangular) and volumetric (tetrahedral) mesh generation. While the tool-chain described is applicable to general types of 3D imaging data, the performance is demonstrated specifically on membrane-bound organelles in ventricular myocytes that are imaged and reconstructed with electron microscopic (EM) tomography and two-photon microscopy (T-PM). Of particular interest in this study are two types of membrane-bound Ca²⁺-handling organelles, namely, transverse tubules (T-tubules) and junctional sarcoplasmic reticulum (jSR), both of which play an important role in regulating the excitation–contraction (E–C) coupling through dynamic Ca²⁺ mobilization in cardiomyocytes.     

Agent农业土地变化模型研究进展

农业土地变化是全球变化与可持续研究的热点,当前研究虽取得了长足进展,但仍存在诸多不足,集中表现在对农业土地系统复杂性与动态性的认识不够.近年来,基于Agent的农业土地变化研究(农业ABM/LUCC,Agent-based agricultural land change modeling)逐渐兴起,极大的丰富了传统研究的理论与方法,具体表现在:(1)农业ABM/LUCC将微观层面的人类个体行为整合进土地变化研究框架,有助于更加清楚的认识农业土地系统的“人类-自然”综合复杂性问题.(2)农业ABM/LUCC能够动态表达土地系统变化的内生反馈机制,有助于弥补传统的静态土地变化驱动机制分析的不足.(3)基于ABM/LUCC的农业土地利用格局动态研究是整合“人类-自然”综合研究的关键桥梁,农业ABM/LUCC能够与其他生物地球物理模型或经济模型动态嵌套,使多尺度、多维度综合模型研究成为可能.然而,农业ABM/LUCC研究也存在诸多挑战,如理论研究滞后于应用研究,大尺度应用难以开展,以及农户行为的模拟结果很难得到校验等.     

Constrained geometric simulation of diffusive motion in proteins

We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins. The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein. Using random moves, the available conformational phase space of a 100 residue protein can be well explored in approximately 10-100 min of computer time using a single processor. All of the covalent, hydrophobic and hydrogen bond constraints are maintained, and van der Waals overlaps are avoided, throughout the simulation. We illustrate the results of a FRODA simulation on barnase, and show that good agreement is obtained with nuclear magnetic resonance experiments. We additionally show how FRODA can be used to find a pathway from one conformation to another. This directed dynamics is illustrated with the protein dihydrofolate reductase.     

Mathematical modeling of malaria infection with innate and adaptive immunity in individuals and agent-based communities

Background

Agent-based modeling of Plasmodium falciparum infection offers an attractive alternative to the conventional Ross-Macdonald methodology, as it allows simulation of heterogeneous communities subjected to realistic transmission (inoculation patterns).

Methodology/Principal Findings

We developed a new, agent based model that accounts for the essential in-host processes: parasite replication and its regulation by innate and adaptive immunity. The model also incorporates a simplified version of antigenic variation by Plasmodium falciparum. We calibrated the model using data from malaria-therapy (MT) studies, and developed a novel calibration procedure that accounts for a deterministic and a pseudo-random component in the observed parasite density patterns. Using the parasite density patterns of 122 MT patients, we generated a large number of calibrated parameters. The resulting data set served as a basis for constructing and simulating heterogeneous agent-based (AB) communities of MT-like hosts. We conducted several numerical experiments subjecting AB communities to realistic inoculation patterns reported from previous field studies, and compared the model output to the observed malaria prevalence in the field. There was overall consistency, supporting the potential of this agent-based methodology to represent transmission in realistic communities.

Conclusions/Significance

Our approach represents a novel, convenient and versatile method to model Plasmodium falciparum infection.     

Facial patterns in Cercopithecoidea and Hominoidea: a geometric approach

The maxillofacial and orbital compartments of the primate skull contribute to the ontogenetic and phylogenetic variability of the viscerocranium and are of crucial evolutionary relevance. As the form of organisms changes depending on endo- and exogenous factors, metrical evaluation of specific adaptations and incorporation of the results into a biological framework could be helpful in identifying valid characters for separation of taxa (e.g. family, genus, and species) and in understanding divergence and convergence. During the last two decades a morphometric "revolution" heralded by Rohlf & Marcus (1993), Adams et al. (2004) and Oxnard (2004) brought about a synthesis of traditional quantitative-morphometrical with modern methods. This approach is called "Geometric Morphometrics (GM)" and constitutes the coremethod applied here. Based on standardized photographs (in Norma frontalis), landmarks (LM) were set and two-dimensional coordinates (X, Y) recorded for the facial cranium in selected representatives of the superfamilies Cercopithecoidea and Hominoidea. The comparison of two datasets by means of factor analysis and distance computation for the complete maxillofacial complex on the one hand, and circumorbital and orbital features on the other, indicate that morphological differences between super-families and genera are valid for separating them even in a heterogeneous sample like the one presented here. Including more landmarks and therewith capturing the morph in a more complex way optimizes separation within the sample.     

Fractal geometric analysis of lung cancer angiogenic patterns

For medical images, the fractal dimension D may be used as an index of irregularity. The angiogenesis patterns of lung cancer were analysed by means of the perimeter-area and box counting algorithms. The fractal nature of all images in the sense of the perimeter-area method and of 68% images in the sense of the box-counting method suggest the possibility to use the fractal dimension as a new non-morphometric parameter evaluating angiogenic processes in neoplasms.     

基于智能体模型的青岛市林地生态格局评价与优化

设计并在GIS平台上开发了基于智能体的生态格局评价模型,以青岛市及周边地区林地为研究对象,分析不同林地空间格局及生态网络保护框架对于物种生存与扩散的影响.结果表明,与现状相比,不同等级的生态网络框架对物种种群数量与物种迁移都有明显提升,且等级越高的生态网络框架提升作用越明显.然而仅仅依靠生态网络框架不足以使研究区域林地系统形成功能上的相互连通,因此,在分析研究区域现状土地利用格局基础上,提出与湿地系统结合,在胶州湾周围及大沽河干流地区增加林地的空间布局.通过模型模拟分析,发现优化后的林地空间格局结合生态网络框架能有效提升林地之间的物种扩散.基于模拟结果,为研究区林地生态格局构建提出如下建议:(1)保证现有的规模较大的林地不被破坏;(2)青岛市中部湿地系统可以作为新增林地的理想区域;(3)生态网络框架可作为青岛市建立城市组团间生态间隔的空间参考.     

Potential new therapeutic modality revealed through agent-based modeling of the neuromuscular junction and acetylcholinesterase inhibition

Background

One of the leading causes of death and illness within the agriculture industry is through unintentionally ingesting or inhaling organophosphate pesticides. OP intoxication directly inhibits acetylcholinesterase, resulting in an excitatory signaling cascade leading to fasciculation, loss of control of bodily fluids, and seizures.

Methods

Our model was developed using a discrete, rules-based modeling approach in NetLogo. This model includes acetylcholinesterase, the nicotinic acetylcholine receptor responsible for signal transduction, a single release of acetylcholine, organophosphate inhibitors, and a theoretical novel medical countermeasure. We have parameterized the system considering the molecular reaction rate constants in an agent-based approach, as opposed to apparent macroscopic rates used in differential equation models.

Results

Our model demonstrates how the cholinergic crisis can be mitigated by therapeutic intervention with an acetylcholinesterase activator. Our model predicts signal rise rates and half-lives consistent with in vitro and in vivo data in the absence and presence of inhibitors. It also predicts the efficacy of theoretical countermeasures acting through three mechanisms: increasing catalytic turnover of acetylcholine, increasing acetylcholine binding affinity to the enzyme, and decreasing binding rates of inhibitors.

Conclusion

We present a model of the neuromuscular junction confirming observed acetylcholine signaling data and suggesting that developing a countermeasure capable of reducing inhibitor binding, and not activator concentration, is the most important parameter for reducing organophosphate (OP) intoxication.

     

Emergent patterns of social organization in captive Cercocebus torquatus: Testing the GrooFiWorld agent-based model

We empirically applied the GrooFiWorld agent-based model (Puga-Gonzalez et al. 2009) in a group of captive redcapped mangabeys (Cercocebus torquatus). We analysed several measurements related to aggression and affiliative patterns. The group adopted a combination of despotic and egalitarian behaviours resulting from the behavioural flexibility observed in the Cercopithecinae subfamily. Our study also demonstrates that the GrooFiWorld agent-based model can be extended to other members of the Cercopithecinae subfamily generating parsimonious hypotheses related to the social organization.     

The development of locomotor kinematics in neonatal rats: an agent-based modeling analysis in group and individual contexts

An agent-based model of infant rat (pup) locomotion and aggregation was developed by modifying a previous model of pup aggregation [Schank, J.C., Alberts, J.R., 2000a. The developmental emergence of coupled activity as cooperative aggregation in rat pups. Proc. R. Soc. London B 267, 2307-2315]. The main difference between the earlier and current models is the incorporation of whole-body kinematics of directional locomotion. Data on locomotion and aggregation are presented for individuals and groups of 7- and 10-day-old pups and the data were used to evolve models (with a genetic algorithm) that fit these data. Aggregation between 7- and 10-day-old pups was considerably different and could be explained by agent-based models, in particular, models with directional-kinematic matrices specifying the probabilities of moving to adjacent cells. The directional kinematics of whole-body movement differed between the two age classes and differed between group and individual contexts for 10-day-old pups. This may indicate a developmental transition (by day 10) to more central control of behavior and the ability to change patterns of movement based on social context. The behavior analyzed with agent-based models may provide a precise way to measure motor and nervous system development in rats and other rodents.     

Mathematical modeling and simulation of seated stability

Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight, and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications.     

The role of simulation in biomathematical modeling

This paper is a general introduction to the field of biomathematical modeling. Biomathematical modeling is divided into three parts: the derivation of models, the fitting of models to data, and the simulation of data from models. This paper focuses on the simulation of data from models. The uses of simulation, the potential users of simulation, and simulation software are described.     

Analysis of Delta-Notch interaction by molecular modeling and molecular dynamic simulation studies

Notch is a single-pass transmembrane receptor protein. Delta (member of the DSL protein family), a Notch ligand, is also single-pass transmembrane protein that can interact with Notch to form the Delta-Notch complex. It has been demonstrated that of the 36 Epidermal Growth Factor (EGF) repeats of Notch, 11th and 12th are sufficient to mediate interactions with Delta. Crystal structure of mammalian Notch1 extracellular ligand binding domain shows the presence of 11th and 12th EGF-like repeats. Here a portion of the Drosophila Delta protein, known to interact with Notch extracellular domain, has been modeled using homology modeling. The structure of the Delta-Notch complex was subsequently modeled by protein-docking method using GRAMM. Molecular dynamic simulations of the modeled structures were performed. The probable structures for Delta-Notch complex have been proposed based on interaction energy parameter and planarity studies.     

Shaker pore structure as predicted by annealed atomic simulation using symmetry and novel geometric restraints

Recent studies making use of channel-blocking peptides as molecular calipers have revealed the architecture of the pore-forming region of Shaker-type potassium channels. Here we show that the low-resolution, experimentally derived geometric information can be incorporated as restraints within the context of an annealed molecular dynamics simulation to predict an atomic structure for the channel pore which, by virtue of restraints, conforms to the experimental evidence. The simulation is reminiscent of the computational method employed by nuclear magnetic resonance (NMR) spectroscopists to resolve solution structures of biological macromolecules, but in lieu of restraints conventionally derived from NMR spectra, novel restraints are developed that include side-chain orientation of amino acid residues and assumed symmetry of protein subunits. The method presented here offers the possibility of expanding cooperation between simulation and experiment in developing structural models, especially for systems such as ion channels whose three-dimensional structures may not be amenable to determination by direct methods at the present time.     

Modulation of melanocytic activity by acetylcholine

Acetylcholine esterase (AChE) activity is lowered in vitiliginous skin. The AChE activity in 52 cases of vitiligo during repigmentation and depigmentation has been observed in this study. The cases with marginal dendritic melanocytes show that AChE is negative in these cells during depigmentation but positive on repigmentation. There is little variation in activity in the cases showing nondendritic marginal melanocytes. Acetylcholine (ACh) has an inhibitory effect on dopa oxidase activity in both types of marginal melanocytes in vitiligo. ACh modulates pigment production by the melanocytes, its role being inhibitory. From the present results, it is evident that a fall in AChE activity in the melanocytes leads to greater inhibition by ACh aggravating the process of depigmentation in vitiligo.     

An agent-based modeling approach to represent infestation dynamics of the emerald ash borer beetle

Agent-based modeling (ABM) is a bottom-up approach capable of operationalizing complex systems. The approach can be used to reproduce the spatio-temporal patterns in ecological processes such as insect infestation by representing individual dynamics and interactions between “agents” and their environment from which complex behavior emerges. The emerald ash borer (Agrilus planipennis; EAB) is an invasive species native to south-east Asia which has infested and killed millions of ash trees (Fraxinus sp.) across the eastern United States as well as Ontario and Quebec in Canada. Efforts to model the insect's behavior are ongoing, but current models are limited to approaches that do not address the complexity that emerges from the dynamics between individual beetles and their varying spatial environments. The objective of this study is to develop an ABM to represent the interactions of the EAB and the emerging spatio-temporal pattern of the insect spread. The model is implemented on real datasets from the Town of Oakville, Ontario, Canada from 2008 to 2010. Tree inventory and land use data acquired from the Town of Oakville were used to represent the spatial environment of the EAB agents. The EAB interactions are implemented in the model as subroutines, each representing a stage in the EAB life cycle using a temporal resolution of one day. Model verification was performed based on the literature documenting the life cycle processes of the EAB to represent EAB behavior. The model is calibrated using the rate of spread observed in the Town of Oakville from 2008 to 2009 and is validated using datasets delimiting the spatial extent and severity of EAB infestation in 2009. When comparing simulated and observed data, there is a 72% agreement for the locations of the infestation. This indicates that the developed ABM approach offers a model able to capture the complex behavior of EAB where both the spatial extent and severity of infestation are simulated realistically. The model generates insights about the underlying processes governing EAB behavior, highlights areas of uncertainty in modeling the complex spatio-temporal patterns of EAB infestation, and is a useful tool for forest and pest management.     

An agent-based model of sleeping sickness: simulation trials of a forest focus in southern Cameroon

An agent-based model (AMB) used to simulate the spread of Human African Trypanosomiasis is presented together with the results of simulations of a focus of the disease. This model is a completely spatialized approach taking into account a series of often overlooked parameters such as human behaviour (activity-related movements), the density and mobility of the disease vectors--tsetse flies (Glossina spp.)--and the influence of other tsetse feeding hosts (livestock and wild animal populations). The agents that represent humans and tsetse flies move in a spatially structured environment managed by specialized location agents. Existing compartmental mathematical models governed by differential equations fail to incorporate the spatial dimension of the disease transmission. Furthermore, on a small scale, transmission is unrealistically represented by entities less than one. This ABM was tested with data from one village of the Bipindi sleeping sickness focus (southern Cameroon) and with obtained realistic simulations of stable transmission involving an animal reservoir. In varying different spatial configurations, we observe that the stability of spread is linked to the spatial complexity (number of heterogeneous locations). The prevalence is very sensitive to the human densities and to the number of tsetse flies initially infected in a given location. A relatively low and durable prevalence is obtained with shortening the phase I. In addition, we discuss some upgrading possibilities, in particular the linkage to a Geographical Information System (GIS). The agent-based approach offers new ways to understanding the spread of the disease and a tool to evaluate risk and test control strategies.