Complex mathematical analysis of photobioreactor system

Modeling as a tool solves extremely difficult tasks in life sciences. Recently, schemes of culturing of microalgae have received special attention because of its unique features and possible uses in many industrial applications for renewable energy production and high value products isolation. The goal of this review is to present the use of system analysis theory applied to microalgae culturing modeling and process development. The review mainly focuses on the modeling of the key steps of autotrophic growth under the integral biorefinery concept of the microalgae biomass. The system approach follows systematically a procedure showing the difficulties by modeling of sub‐systems. The development of microalgae kinetics and computational fluid dynamics (CFD) studies were analyzed in details as sub‐systems in advanced design of photobioreactor (PBR). This review logically follows the trends of the modeling procedure and clarifies how this approach may save time and money during the research efforts. The result of this work is a successful development of a complex PBR mathematical analysis in the frame of the integral biorefinery concept.     

From ABC genes to regulatory networks,epigenetic landscapes and flower morphogenesis: Making biological sense of theoretical approaches

The ABC model postulates that expression combinations of three classes of genes (A, B and C) specify the four floral organs at early stages of flower development. This classic model provides a solid framework to study flower development and has been the foundation for multiple studies in different plant species, as well as for new evolutionary hypotheses. Nevertheless, it has been shown that in spite of being necessary, these three gene classes are not sufficient for flower organ specification. Rather, flower organ specification depends on complex interactions of several genes, and probably other non-genetic factors. Being useful to study systems of complex interactions, mathematical and computational models have enlightened the origin of the A, B and C stereotyped and robust expression patterns and the process of early flower morphogenesis. Here, we present a brief introduction to basic modeling concepts and techniques and review the results that these models have rendered for the particular case of the Arabidopsis thaliana flower organ specification. One of the main results is the uncovering of a robust functional module that is sufficient to recover the gene configurations characterizing flower organ primordia. Another key result is that the temporal sequence with which such gene configurations are attained may be recovered only by modeling the aforementioned functional module as a noisy or stochastic system. Finally, modeling approaches enable testable predictions regarding the role of non-genetic factors (noise, mechano-elastic forces, etc.) in development. These predictions, along with some perspectives for future work, are also reviewed and discussed.     

Modeling how soluble microbial products (SMP) support heterotrophic bacteria in autotroph-based biofilms

Multi-species biofilm modeling has been used for many years to understand the interactions between species in different biofilm systems, but the complex symbiotic relationship between species is sometimes overlooked, because models do not always include all relevant species and components. In this paper, we develop and use a mathematical model to describe a model biofilm system that includes autotrophic and heterotrophic bacteria and the key products produced by the bacteria. The model combines the methods of earlier multi-species models with a multi-component biofilm model in order to explore the interaction between species via exchange of soluble microbial products (SMP). We show that multiple parameter sets are able to describe the findings of experimental studies, and that heterotrophs growing on autotrophically produced SMP may pursue either r- or K-strategies to sustain themselves when SMP is their only substrate. We also show that heterotrophs can colonize some distance from the autotrophs and still be sustained by autotrophically produced SMP. This work defines the feasible range of parameters for utilization of SMP by heterotrophs and the nature of the interactions between autotrophs and heterotrophs in multi-species, multi-component biofilms.     

Mathematical modeling as a tool for investigating cell cycle control networks

Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.     

Simple network motifs can capture key characteristics of the floral transition in Arabidopsis

The floral transition is a key decision during plant development. While different species have evolved diverse pathways to respond to different environmental cues to flower in the correct season, key properties such as irreversibility and robustness to fluctuating signals appear to be conserved. We have used mathematical modeling to demonstrate how minimal regulatory networks of core components are sufficient to capture these behaviors. Simplified models inevitably miss finer details of the biological system, yet they provide a tractable route to understanding the overall system behavior. We combined models with experimental data to qualitatively reproduce characteristics of the floral transition and to quantitatively scale the network to fit with available leaf numbers. Our study highlights the value of pursuing an iterative approach combining modeling with experimental work to capture key features of complex systems.     

Modeling microbial community structure and functional diversity across time and space

Microbial communities exhibit exquisitely complex structure. Many aspects of this complexity, from the number of species to the total number of interactions, are currently very difficult to examine directly. However, extraordinary efforts are being made to make these systems accessible to scientific investigation. While recent advances in high-throughput sequencing technologies have improved accessibility to the taxonomic and functional diversity of complex communities, monitoring the dynamics of these systems over time and space - using appropriate experimental design - is still expensive. Fortunately, modeling can be used as a lens to focus low-resolution observations of community dynamics to enable mathematical abstractions of functional and taxonomic dynamics across space and time. Here, we review the approaches for modeling bacterial diversity at both the very large and the very small scales at which microbial systems interact with their environments. We show that modeling can help to connect biogeochemical processes to specific microbial metabolic pathways.     

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.     

Modeling and simulation of biological systems with stochasticity

Mathematical modeling is a powerful approach for understanding the complexity of biological systems. Recently, several successful attempts have been made for simulating complex biological processes like metabolic pathways, gene regulatory networks and cell signaling pathways. The pathway models have not only generated experimentally verifiable hypothesis but have also provided valuable insights into the behavior of complex biological systems. Many recent studies have confirmed the phenotypic variability of organisms to an inherent stochasticity that operates at a basal level of gene expression. Due to this reason, development of novel mathematical representations and simulations algorithms are critical for successful modeling efforts in biological systems. The key is to find a biologically relevant representation for each representation. Although mathematically rigorous and physically consistent, stochastic algorithms are computationally expensive, they have been successfully used to model probabilistic events in the cell. This paper offers an overview of various mathematical and computational approaches for modeling stochastic phenomena in cellular systems.     

Sensitivity Analysis of an ENteric Immunity SImulator (ENISI)-Based Model of Immune Responses to Helicobacter pylori Infection

Agent-based models (ABM) are widely used to study immune systems, providing a procedural and interactive view of the underlying system. The interaction of components and the behavior of individual objects is described procedurally as a function of the internal states and the local interactions, which are often stochastic in nature. Such models typically have complex structures and consist of a large number of modeling parameters. Determining the key modeling parameters which govern the outcomes of the system is very challenging. Sensitivity analysis plays a vital role in quantifying the impact of modeling parameters in massively interacting systems, including large complex ABM. The high computational cost of executing simulations impedes running experiments with exhaustive parameter settings. Existing techniques of analyzing such a complex system typically focus on local sensitivity analysis, i.e. one parameter at a time, or a close “neighborhood” of particular parameter settings. However, such methods are not adequate to measure the uncertainty and sensitivity of parameters accurately because they overlook the global impacts of parameters on the system. In this article, we develop novel experimental design and analysis techniques to perform both global and local sensitivity analysis of large-scale ABMs. The proposed method can efficiently identify the most significant parameters and quantify their contributions to outcomes of the system. We demonstrate the proposed methodology for ENteric Immune SImulator (ENISI), a large-scale ABM environment, using a computational model of immune responses to Helicobacter pylori colonization of the gastric mucosa.     

Translational systems biology of inflammation

Inflammation is a complex, multi-scale biologic response to stress that is also required for repair and regeneration after injury. Despite the repository of detailed data about the cellular and molecular processes involved in inflammation, including some understanding of its pathophysiology, little progress has been made in treating the severe inflammatory syndrome of sepsis. To address the gap between basic science knowledge and therapy for sepsis, a community of biologists and physicians is using systems biology approaches in hopes of yielding basic insights into the biology of inflammation. “Systems biology” is a discipline that combines experimental discovery with mathematical modeling to aid in the understanding of the dynamic global organization and function of a biologic system (cell to organ to organism). We propose the term translational systems biology for the application of similar tools and engineering principles to biologic systems with the primary goal of optimizing clinical practice. We describe the efforts to use translational systems biology to develop an integrated framework to gain insight into the problem of acute inflammation. Progress in understanding inflammation using translational systems biology tools highlights the promise of this multidisciplinary field. Future advances in understanding complex medical problems are highly dependent on methodological advances and integration of the computational systems biology community with biologists and clinicians.     

Systems biology and cancer: promises and perils

Systems biology uses systems of mathematical rules and formulas to study complex biological phenomena. In cancer research there are three distinct threads in systems biology research: modeling biology or biophysics with the goal of establishing plausibility or obtaining insights, modeling based on statistics, bioinformatics, and reverse engineering with the goal of better characterizing the system, and modeling with the goal of clinical predictions. Using illustrative examples we discuss these threads in the context of cancer research.     

Review and application of group theory to molecular systems biology

In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C ₆ network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.     

Mathematical Models Light Up Plant Signaling

Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis thaliana, have revealed many of the mechanisms by which these responses are actuated. In recent years, mathematical modeling has become a complementary tool to the experimental approach that has furthered our understanding of biological mechanisms. In this review, we present modeling examples encompassing a range of different biological processes, in particular those regulated by light. Current issues and future directions in the modeling of plant systems are discussed.     

Using induced pluripotent stem cell neuronal models to study neurodegenerative diseases

Current application of human induced pluripotent stem cells (hiPSCs) technology in patient-specific models of neurodegenerative disorders recapitulate some of key phenotypes of diseases, representing disease-specific cellular modeling and providing a unique platform for therapeutics development. We review recent efforts toward advancing hiPSCs-derived neuronal cell types and highlight their potential use for the development of more complex in vitro models of neurodegenerative diseases by focusing on Alzheimer's disease, Parkinson's disease, Huntington's disease and Amyotrophic lateral sclerosis. We present evidence from previous works on the important phenotypic changes of various neuronal types in these neurological diseases. We also summarize efforts on conducting low- and high-throughput screening experiments with hiPSCs toward developing potential therapeutics for treatment of neurodegenerative diseases. Lastly, we discuss the limitations of hiPSCs culture system in studying neurodegenerative diseases and alternative strategies to overcome these hurdles.     

Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis

Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis.     

Plant Metabolic Modeling: Achieving New Insight into Metabolism and Metabolic Engineering

Models are used to represent aspects of the real world for specific purposes, and mathematical models have opened up new approaches in studying the behavior and complexity of biological systems. However, modeling is often time-consuming and requires significant computational resources for data development, data analysis, and simulation. Computational modeling has been successfully applied as an aid for metabolic engineering in microorganisms. But such model-based approaches have only recently been extended to plant metabolic engineering, mainly due to greater pathway complexity in plants and their highly compartmentalized cellular structure. Recent progress in plant systems biology and bioinformatics has begun to disentangle this complexity and facilitate the creation of efficient plant metabolic models. This review highlights several aspects of plant metabolic modeling in the context of understanding, predicting and modifying complex plant metabolism. We discuss opportunities for engineering photosynthetic carbon metabolism, sucrose synthesis, and the tricarboxylic acid cycle in leaves and oil synthesis in seeds and the application of metabolic modeling to the study of plant acclimation to the environment. The aim of the review is to offer a current perspective for plant biologists without requiring specialized knowledge of bioinformatics or systems biology.