Implications of different membrane compartmentalization models in particle-based in silico studies.

Studying membrane dynamics is important to understand the cellular response to environmental stimuli. A decisive spatial characteristic of the plasma membrane is its compartmental structure created by the actin-based membrane-skeleton (fences) and anchored transmembrane proteins (pickets). Particle-based reaction-diffusion simulation of the membrane offers a suitable temporal and spatial resolution to analyse its spatially heterogeneous and stochastic dynamics. Fences have been modelled via hop probabilities, potentials or explicit picket fences. Our study analyses the different approaches' constraints and their impact on simulation results and performance. Each of the methods comes with its own constraints; the picket fences require small timesteps, potential fences might induce a bias in diffusion in crowded systems, and probabilistic fences, in addition to carefully scaling the probability with the timesteps, induce higher computational costs for each propagation step.

Long-term stimulation with alternating electric fields modulates the differentiation and mineralization of human pre-osteoblasts.

Biophysical stimulation by electric fields can promote bone formation in bone defects of critical size. Even though, long-term effects of alternating electric fields on the differentiation of osteoblasts are not fully understood. Human pre-osteoblasts were stimulated over 31 days to gain more information about these cellular processes. An alternating electric field with 0.7 Vrms and 20 Hz at two distances was applied and viability, mineralization, gene expression, and protein release of differentiation factors were analyzed. The viability was enhanced during the first days of stimulation. A higher electric field resulted in upregulation of typical osteogenic markers like osteoprotegerin, osteopontin, and interleukin-6, but no significant changes in mineralization. Upregulation of the osteogenic markers could be detected with a lower electric field after the first days of stimulation. As a significant increase in the mineralized matrix was identified, an enhanced osteogenesis due to low alternating electric fields can be assumed.

Using a Digital Twin of an Electrical Stimulation Device to Monitor and Control the Electrical Stimulation of Cells in vitro.

Electrical stimulation for application in tissue engineering and regenerative medicine has received increasing attention in recent years. A variety of stimulation methods, waveforms and amplitudes have been studied. However, a clear choice of optimal stimulation parameters is still not available and is complicated by ambiguous reporting standards. In order to understand underlying cellular mechanisms affected by the electrical stimulation, the knowledge of the actual prevailing field strength or current density is required. Here, we present a comprehensive digital representation, a digital twin, of a basic electrical stimulation device for the electrical stimulation of cells in vitro. The effect of electrochemical processes at the electrode surface was experimentally characterised and integrated into a numerical model of the electrical stimulation. Uncertainty quantification techniques were used to identify the influence of model uncertainties on relevant observables. Different stimulation protocols were compared and it was assessed if the information contained in the monitored stimulation pulses could be related to the stimulation model. We found that our approach permits to model and simulate the recorded rectangular waveforms such that local electric field strengths become accessible. Moreover, we could predict stimulation voltages and currents reliably. This enabled us to define a controlled stimulation setting and to identify significant temperature changes of the cell culture in the monitored voltage data. Eventually, we give an outlook on how the presented methods can be applied in more complex situations such as the stimulation of hydrogels or tissue in vivo.

VPMBench: a test bench for variant prioritization methods.

BACKGROUND: Clinical diagnostics of whole-exome and whole-genome sequencing data requires geneticists to consider thousands of genetic variants for each patient. Various variant prioritization methods have been developed over the last years to aid clinicians in identifying variants that are likely disease-causing. Each time a new method is developed, its effectiveness must be evaluated and compared to other approaches based on the most recently available evaluation data. Doing so in an unbiased, systematic, and replicable manner requires significant effort. RESULTS: The open-source test bench "VPMBench" automates the evaluation of variant prioritization methods. VPMBench introduces a standardized interface for prioritization methods and provides a plugin system that makes it easy to evaluate new methods. It supports different input data formats and custom output data preparation. VPMBench exploits declaratively specified information about the methods, e.g., the variants supported by the methods. Plugins may also be provided in a technology-agnostic manner via containerization. CONCLUSIONS: VPMBench significantly simplifies the evaluation of both custom and published variant prioritization methods. As we expect variant prioritization methods to become ever more critical with the advent of whole-genome sequencing in clinical diagnostics, such tool support is crucial to facilitate methodological research.

Receptor/Raft Ratio Is a Determinant for LRP6 Phosphorylation and WNT/ß-Catenin Signaling.

Microdomains or lipid rafts greatly affect the distribution of proteins and peptides in the membrane and play a vital role in the formation and activation of receptor/protein complexes. A prominent example for the decisive impact of lipid rafts on signaling is LRP6, whose localization to the same lipid rafts domain as the kinase CK1γ is crucial for its successful phosphorylation and the subsequent activation of the signalosome, hence WNT/ß-catenin signaling. However, according to various experimental measurements, approximately 25 to 35 % of the cell plasma membrane is covered by nanoscopic raft domains with diameters ranging between 10 to 200 nm. Extrapolating/Translating these values to the membrane of a "normal sized" cell yields a raft abundance, that, by far, outnumbers the membrane-associated pathway components of most individual signaling pathway, such as receptor and kinases. To analyze whether and how the quantitative ratio between receptor and rafts affects LRP6 phosphorylation and WNT/ß-catenin pathway activation, we present a computational modeling study, that for the first time employs realistic raft numbers in a compartment-based pathway model. Our simulation experiments indicate, that for receptor/raft ratios smaller than 1, i.e., when the number of raft compartments clearly exceeds the number of pathway specific membrane proteins, we observe significant decrease in LRP6 phosphorylation and downstream pathway activity. Our results suggest that pathway specific targeting and sorting mechanism are required to significantly narrow down the receptor/raft ratio and to enable the formation of the LRP6 signalosome, hence signaling.

Relating simulation studies by provenance-Developing a family of Wnt signaling models.

For many biological systems, a variety of simulation models exist. A new simulation model is rarely developed from scratch, but rather revises and extends an existing one. A key challenge, however, is to decide which model might be an appropriate starting point for a particular problem and why. To answer this question, we need to identify entities and activities that contributed to the development of a simulation model. Therefore, we exploit the provenance data model, PROV-DM, of the World Wide Web Consortium and, building on previous work, continue developing a PROV ontology for simulation studies. Based on a case study of 19 Wnt/ß-catenin signaling models, we identify crucial entities and activities as well as useful metadata to both capture the provenance information from individual simulation studies and relate these forming a family of models. The approach is implemented in WebProv, a web application for inserting and querying provenance information. Our specialization of PROV-DM contains the entities Research Question, Assumption, Requirement, Qualitative Model, Simulation Model, Simulation Experiment, Simulation Data, and Wet-lab Data as well as activities referring to building, calibrating, validating, and analyzing a simulation model. We show that most Wnt simulation models are connected to other Wnt models by using (parts of) these models. However, the overlap, especially regarding the Wet-lab Data used for calibration or validation of the models is small. Making these aspects of developing a model explicit and queryable is an important step for assessing and reusing simulation models more effectively. Exposing this information helps to integrate a new simulation model within a family of existing ones and may lead to the development of more robust and valid simulation models. We hope that our approach becomes part of a standardization effort and that modelers adopt the benefits of provenance when considering or creating simulation models.

ROS Dependent Wnt/ß-Catenin Pathway and Its Regulation on Defined Micro-Pillars-A Combined In Vitro and In Silico Study.

The physico-chemical surface design of implants influences the surrounding cells. Osteoblasts on sharp-edged micro-topographies revealed an impaired cell phenotype, function and Ca2+ mobilization. The influence of edges and ridges on the Wnt/ß-catenin pathway in combination with the cells' stress response has not been clear. Therefore, MG-63 osteoblasts were studied on defined titanium-coated micro-pillars (5 × 5 × 5 µm) in vitro and in silico. MG-63s on micro-pillars indicated an activated state of the Wnt/ß-catenin pathway. The ß-catenin protein accumulated in the cytosol and translocated into the nucleus. Gene profiling indicated an antagonism mechanism of the transcriptional activity of ß-catenin due to an increased expression of inhibitors like ICAT (inhibitor of ß-catenin and transcription factor-4). Cells on pillars produced a significant reactive oxygen species (ROS) amount after 1 and 24 h. In silico analyses provided a detailed view on how transcriptional activity of Wnt signaling is coordinated in response to the oxidative stress induced by the micro-topography. Based on a coordinated expression of regulatory elements of the Wnt/ß-catenin pathway, MG-63s are able to cope with an increased accumulation of ß-catenin on micro-pillars and suppress an unintended target gene expression. Further, ß-catenin may be diverted into other signaling pathways to support defense mechanisms against ROS.

Exploring the mechanistic and temporal regulation of LRP6 endocytosis in canonical WNT signaling.

Endocytosis plays a pivotal regulatory role in canonical WNT signaling. Internalization of the low-density lipoprotein receptor-related protein 6 (LRP6) receptor complex can either promote or attenuate canonical WNT signaling, depending on the employed internalization pathway. Detailed analysis of the mechanism of LRP6 internalization and its temporal regulation is crucial for understanding the different cellular responses to WNT stimulation under varying conditions and in various cell types. Here, we elucidate the mechanisms involved in the internalization of LRP6 and re-evaluate existing, partly contradicting, theories on the regulation of LRP6 receptor internalization. We utilize a computational approach that aims at finding a set of mechanisms that accounts for the temporal dynamics of LRP6 receptor internalization upon WNT stimulation. Starting with a simple simulation model, we successively extend and probe the model's behavior based on quantitative measurements. The final model confirms that LRP6 internalization is clathrin independent in vertebrates, is not restricted to microdomains, and that signalosome formation delays LRP6 internalization within the microdomains. These findings partly revise the current understanding of LRP6 internalization in vertebrates.

Potential based, spatial simulation of dynamically nested particles.

BACKGROUND: To study cell biological phenomena which depend on diffusion, active transport processes, or the locations of species, modeling and simulation studies need to take space into account. To describe the system as a collection of discrete objects moving and interacting in continuous space, various particle-based reaction diffusion simulators for cell-biological system have been developed. So far the focus has been on particles as solid spheres or points. However, spatial dynamics might happen at different organizational levels, such as proteins, vesicles or cells with interrelated dynamics which requires spatial approaches that take this multi-levelness of cell biological systems into account. RESULTS: Based on the perception of particles forming hollow spheres, ML-Force contributes to the family of particle-based simulation approaches: in addition to excluded volumes and forces, it also supports compartmental dynamics and relating dynamics between different organizational levels explicitly. Thereby, compartmental dynamics, e.g., particles entering and leaving other particles, and bimolecular reactions are modeled using pair-wise potentials (forces) and the Langevin equation. In addition, forces that act independently of other particles can be applied to direct the movement of particles. Attributes and the possibility to define arbitrary functions on particles, their attributes and content, to determine the results and kinetics of reactions add to the expressiveness of ML-Force. Its implementation comprises a rudimentary rule-based embedded domain-specific modeling language for specifying models and a simulator for executing models continuously. Applications inspired by cell biological models from literature, such as vesicle transport or yeast growth, show the value of the realized features. They facilitate capturing more complex spatial dynamics, such as the fission of compartments or the directed movement of particles, and enable the integration of non-spatial intra-compartmental dynamics as stochastic events. CONCLUSIONS: By handling all dynamics based on potentials (forces) and the Langevin equation, compartmental dynamics, such as dynamic nesting, fusion and fission of compartmental structures are handled continuously and are seamlessly integrated with traditional particle-based reaction-diffusion dynamics within the cell. Thereby, attributes and arbitrary functions allow to flexibly describe diverse spatial phenomena, and relate dynamics across organizational levels. Also they prove crucial in modeling intra-cellular or intra-compartmental dynamics in a non-spatial manner, and, thus, to abstract from spatial dynamics, on demand which increases the range of multi-compartmental processes that can be captured.

Multi-Level Modeling and Simulation of Cellular Systems: An Introduction to ML-Rules.

ML-Rules is a rule-based language for multi-level modeling and simulation. ML-Rules supports dynamic nesting of entities and applying arbitrary functions on entity attributes and content, as well as for defining kinetics of reactions. This allows describing and simulating complex cellular dynamics operating at different organizational levels, e.g., to combine intra-, inter-, and cellular dynamics, like the proliferation of cells, or to include compartmental dynamics like merging and splitting of mitochondria or endocytosis. The expressiveness of the language is bought with additional efforts in executing ML-Rules models. Therefore, various simulators have been developed from which the user and automatic procedures can select. The experiment specification language SESSL facilitates design, execution, and reuse of simulation experiments. The chapter illuminates the specific features of ML-Rules as a rule-based modeling language, the implications for an efficient execution, and shows ML-Rules at work.

Requirements for Documenting Electrical Cell Stimulation Experiments for Replicability and Numerical Modeling∗.

Thorough documentation of biological experiments is necessary for their replicability. This becomes even more evident when individual steps of in vitro wet-lab experiments are to be incorporated into computer simulation models. In the highly interdisciplinary field of electrical stimulation of biological cells, not only biological but also physical aspects play a crucial role. Simulations may help to identify parameters that influence cells and thereby reveal new insights into mechanisms of the cell biological system. However, missing or misleading documentation of the electrical stimulation step within wet-lab experiments may lead to discrepancies between reported and simulated electrical quantities. In addition, this threatens the replicability of electrical stimulation experiments. Thus, we argue that a minimal set of information is needed to enable a translation of electrical stimulation experiments of biological cells into computer simulation experiments and to support replicability. This set includes detailed information about the electronic devices and components, their set-up as well as the applied stimulus and shall be integrated into an existing guideline for cell biological experiments. Ideally, the documentation should also contain measured properties of the cellular and experimental environment. Furthermore, a realization of our proposed documentation requirements within electronic lab notebooks may provide a crucial step toward a more seamless integration of wet-lab data into simulations. Based on two exemplary studies, we demonstrate the relevance of our claim.

Modelling and simulating decision processes of linked lives: An approach based on concurrent processes and stochastic race.

Individuals' decision processes play a central role in understanding modern migration phenomena and other demographic processes. Their integration into agent-based computational demography depends largely on suitable support by a modelling language. We are developing the Modelling Language for Linked Lives (ML3) to describe the diverse decision processes of linked lives succinctly in continuous time. The context of individuals is modelled by networks the individual is part of, such as family ties and other social networks. Central concepts, such as behaviour conditional on agent attributes, age-dependent behaviour, and stochastic waiting times, are tightly integrated in the language. Thereby, alternative decisions are modelled by concurrent processes that compete by stochastic race. Using a migration model, we demonstrate how this allows for compact description of complex decisions, here based on the Theory of Planned Behaviour. We describe the challenges for the simulation algorithm posed by stochastic race between multiple concurrent complex decisions.

Non-canonical pathway induced by Wnt3a regulates ß-catenin via Pyk2 in differentiating human neural progenitor cells.

Wnt/ß-catenin and Wnt/Ca2+ pathways are involved in cellular processes during embryonic development and the interaction between them in the same cell decides the outcome of cellular functions. In this study, we showed that Wnt3a triggers the Wnt/Ca2+ signaling pathway, indicated by an increase of cytosolic free calcium ([Ca2+]i) and activation of calmodulin dependent kinase II (CaMKII) during the differentiation of human neuronal progenitor cells (hNPCs). Wnt3a via the increase of [Ca2+]i activates proline-rich tyrosine kinase 2 (Pyk2), which subsequently regulates phosphorylation of glycogen synthase kinase 3ß (GSK3ß) and ß-catenin stabilization. Our findings suggest that Pyk2 plays an important role in the coordination of stabilization of ß-catenin in the crosstalk between Wnt/ß-catenin and Wnt/Ca2+ signaling pathways upon Wnt3a stimulation in differentiating hNPCs.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

Spatio-temporal model of endogenous ROS and raft-dependent WNT/beta-catenin signaling driving cell fate commitment in human neural progenitor cells.

Canonical WNT/ß-catenin signaling is a central pathway in embryonic development, but it is also connected to a number of cancers and developmental disorders. Here we apply a combined in-vitro and in-silico approach to investigate the spatio-temporal regulation of WNT/ß-catenin signaling during the early neural differentiation process of human neural progenitors cells (hNPCs), which form a new prospect for replacement therapies in the context of neurodegenerative diseases. Experimental measurements indicate a second signal mechanism, in addition to canonical WNT signaling, being involved in the regulation of nuclear ß-catenin levels during the cell fate commitment phase of neural differentiation. We find that the biphasic activation of ß-catenin signaling observed experimentally can only be explained through a model that combines Reactive Oxygen Species (ROS) and raft dependent WNT/ß-catenin signaling. Accordingly after initiation of differentiation endogenous ROS activates DVL in a redox-dependent manner leading to a transient activation of down-stream ß-catenin signaling, followed by continuous auto/paracrine WNT signaling, which crucially depends on lipid rafts. Our simulation studies further illustrate the elaborate spatio-temporal regulation of DVL, which, depending on its concentration and localization, may either act as direct inducer of the transient ROS/ß-catenin signal or as amplifier during continuous auto-/parcrine WNT/ß-catenin signaling. In addition we provide the first stochastic computational model of WNT/ß-catenin signaling that combines membrane-related and intracellular processes, including lipid rafts/receptor dynamics as well as WNT- and ROS-dependent ß-catenin activation. The model's predictive ability is demonstrated under a wide range of varying conditions for in-vitro and in-silico reference data sets. Our in-silico approach is realized in a multi-level rule-based language, that facilitates the extension and modification of the model. Thus, our results provide both new insights and means to further our understanding of canonical WNT/ß-catenin signaling and the role of ROS as intracellular signaling mediator.

Membrane related dynamics and the formation of actin in cells growing on micro-topographies: a spatial computational model.

BACKGROUND: Intra-cellular processes of cells at the interface to an implant surface are influenced significantly by their extra-cellular surrounding. Specifically, when growing osteoblasts on titanium surfaces with regular micro-ranged geometry, filaments are shorter, less aligned and they concentrate at the top of the geometric structures. Changes to the cytoskeleton network, i. e., its localization, alignment, orientation, and lengths of the filaments, as well as the overall concentration and distribution of key-actors are induced. For example, integrin is distributed homogeneously, whereas integrin in activated state and vinculin, both components of focal adhesions, have been found clustered on the micro-ranged geometries. Also, the concentration of Rho, an intracellular signaling protein related to focal adhesion regulation, was significantly lower. RESULTS: To explore whether regulations associated with the focal adhesion complex can be responsible for the changed actin filament patterns, a spatial computational model has been developed using ML-Space, a rule-based model description language, and its associated Brownian-motion-based simulator. The focus has been on the deactivation of cofilin in the vicinity of the focal adhesion complex. The results underline the importance of sensing mechanisms to support a clustering of actin filament nucleations on the micro-ranged geometries, and of intracellular diffusion processes, which lead to spatially heterogeneous distributions of active (dephosphorylated) cofilin, which in turn influences the organization of the actin network. We find, for example, that the spatial heterogeneity of key molecular actors can explain the difference in filament lengths in cells on different micro-geometries partly, but to explain the full extent, further model assumptions need to be added and experimentally validated. In particular, our findings and hypothesis referring to the role, distribution, and amount of active cofilin have still to be verified in wet-lab experiments. CONCLUSION: Letting cells grow on surface structures is a possibility to shed new light on the intricate mechanisms that relate membrane and actin related dynamics in the cell. Our results demonstrate the need for declarative expressive spatial modeling approaches that allow probing different hypotheses, and the central role of the focal adhesion complex not only for nucleating actin filaments, but also for regulating possible severing agents locally.

Composing problem solvers for simulation experimentation: a case study on steady state estimation.

Simulation experiments involve various sub-tasks, e.g., parameter optimization, simulation execution, or output data analysis. Many algorithms can be applied to such tasks, but their performance depends on the given problem. Steady state estimation in systems biology is a typical example for this: several estimators have been proposed, each with its own (dis-)advantages. Experimenters, therefore, must choose from the available options, even though they may not be aware of the consequences. To support those users, we propose a general scheme to aggregate such algorithms to so-called synthetic problem solvers, which exploit algorithm differences to improve overall performance. Our approach subsumes various aggregation mechanisms, supports automatic configuration from training data (e.g., via ensemble learning or portfolio selection), and extends the plugin system of the open source modeling and simulation framework James II. We show the benefits of our approach by applying it to steady state estimation for cell-biological models.

Studying the role of lipid rafts on protein receptor bindings with cellular automata.

It is widely accepted that lipid rafts promote receptor clustering and thereby facilitate signaling transduction. The role of lipid rafts in inducing and promoting receptor accumulation within the cell membrane has been explored by several computational and experimental studies. However, it remains unclear whether lipid rafts influence the recruitment and binding of proteins from the cytosol as well. To provide an answer to this question a spatial membrane model has been developed based on cellular automata. Our results indicate that lipid rafts indeed influence protein receptor bindings. In particular processes with slow dissociation and binding kinetics are promoted by lipid rafts, whereas fast binding processes are slightly hampered. However, the impact depends on a variety of parameters, such as the size and mobility of the lipid rafts, the induced slow down of receptors within rafts, and also the dissociation and binding kinetics of the cytosolic proteins. Thus, for any individual signaling pathway the influence of lipid rafts on protein binding might be different. To facilitate analyzing this influence given a specific pathway, our approach has been generalized into LiRaM, a modeling and simulation tool for lipid rafts models.

Elucidating the sources of ß-catenin dynamics in human neural progenitor cells.

Human neural progenitor cells (hNPCs) form a new prospect for replacement therapies in the context of neurodegenerative diseases. The Wnt/ß-catenin signaling pathway is known to be involved in the differentiation process of hNPCs. RVM cells form a common cell model of hNPCs for in vitro investigation. Previous observations in RVM cells raise the question of whether observed kinetics of the Wnt/ß-catenin pathway in later differentiation phases are subject to self-induced signaling. However, a concern when investigating RVM cells is that experimental results are possibly biased by the asynchrony of cells w.r.t. the cell cycle. In this paper, we present, based on experimental data, a computational modeling study on the Wnt/ß-catenin signaling pathway in RVM cell populations asynchronously distributed w.r.t. to their cell cycle phases. Therefore, we derive a stochastic model of the pathway in single cells from the reference model in literature and extend it by means of cell populations and cell cycle asynchrony. Based on this, we show that the impact of the cell cycle asynchrony on wet-lab results that average over cell populations is negligible. We then further extend our model and the thus-obtained simulation results provide additional evidence that self-induced Wnt signaling occurs in RVM cells. We further report on significant stochastic effects that directly result from model parameters provided in literature and contradict experimental observations.

Rule-based multi-level modeling of cell biological systems.

BACKGROUND: Proteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax. RESULTS: Multi-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II. CONCLUSIONS: Rule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.