A novel procedure for the identification of chaos in complex biological systems

The molecular networks regulating basic physiological processes in a cell are generally converted into rate equations assuming the number of biochemical molecules as deterministic variables. At steady state these rate equations gives a set of differential equations that are solved using numerical methods. However, the stochastic cellular environment motivates us to propose a mathematical framework for analyzing such biochemical molecular networks. The stochastic simulators that solve a system of differential equations includes this stochasticity in the model, but suffer from simulation stiffness and require huge computational overheads. This paper describes a new markov chain based model to simulate such complex biological systems with reduced computation and memory overheads. The central idea is to transform the continuous domain chemical master equation (CME) based method into a discrete domain of molecular states with corresponding state transition probabilities and times. Our methodology allows the basic optimization schemes devised for the CME and can also be extended to reduce the computational and memory overheads appreciably at the cost of accuracy. The simulation results for the standard Enzyme-Kinetics and Transcriptional Regulatory systems show promising correspondence with the CME based methods and point to the efficacy of our scheme.

Despite significant effort on understanding complex biological systems, we lack a unified theory for modeling, inference, analysis, and efficient control of their dynamics in uncertain environments. These problems are made even more challenging when considering that only limited and noisy information is accessible for modeling, which can prove insufficient for explaining, and predicting the behavior of complex systems. For instance, missing information hampers the capabilities of analytical tools to uncover the true degrees of freedom and infer the model structure and parameters of complex biological systems. Toward this end, in this paper, we discuss several important mathematical challenges that could open new theoretical avenues in studying complex systems: (1) By understanding the universal laws characterizing the asymmetric statistics of magnitude increments and the complex space-time interdependency within one process and across many processes, we can develop a class of compact yet accurate mathematical models capable to potentially providing higher degree of predictability, and more efficient control strategies. (2) In order to better predict the onset of disease and their root cause, as well as potentially discover more efficient quality-of-life (QoL)-control strategies, we need to develop mathematical strategies that not only are capable to discover causal interactions and their corresponding mathematical expressions for space and time operators acting on biological processes, but also mathematical and algorithmic techniques to identify the number of unknown unknowns (UUs) and their interdependency with the observed variables. (3) Lastly, to improve the QoL of control strategies when facing intra- and inter-patient variability, the focus should not only be on specific values and ranges for biological processes, but also on optimizing/controlling knob variables that enforce a specific spatiotemporal multifractal behavior that corresponds to an initial healthy (patient specific) behavior. All in all, the modeling, analysis and control of complex biological collective systems requires a deeper understanding of the multifractal properties of high dimensional heterogeneous and noisy data streams and new algorithmic tools that exploit geometric, statistical physics, and information theoretic concepts to deal with these data challenges.

Given continuous improvements in industrial production and living standards, the analysis and detection of complex biological sample systems has become increasingly important. Common complex biological samples include blood, serum, saliva, and urine. At present, the main methods used to separate and recognize target analytes in complex biological systems are electrophoresis, spectroscopy, and chromatography. However, because biological samples consist of complex components, they suffer from the matrix effect, which seriously affects the accuracy, sensitivity, and reliability of the selected separation analysis technique. In addition to the matrix effect, the detection of trace components is challenging because the content of the analyte in the sample is usually very low. Moreover, reasonable strategies for sample enrichment and signal amplification for easy analysis are lacking. In response to the various issues described above, researchers have focused their attention on immuno-affinity technology with the aim of achieving efficient sample separation based on the specific recognition effect between antigens and antibodies. Following a long period of development, this technology is now widely used in fields such as disease diagnosis, bioimaging, food testing, and recombinant protein purification. Common immuno-affinity technologies include solid-phase extraction (SPE) magnetic beads, affinity chromatography columns, and enzyme linked immunosorbent assay (ELISA) kits. Immuno-affinity techniques can successfully reduce or eliminate the matrix effect; however, their applications are limited by a number of disadvantages, such as high costs, tedious fabrication procedures, harsh operating conditions, and ligand leakage. Thus, developing an effective and reliable method that can address the matrix effect remains a challenging endeavor. Similar to the interactions between antigens and antibodies as well as enzymes and substrates, biomimetic molecularly imprinted polymers (MIPs) exhibit high specificity and affinity. Furthermore, compared with many other biomacromolecules such as antigens and aptamers, MIPs demonstrate higher stability, lower cost, and easier fabrication strategies, all of which are advantageous to their application. Therefore, molecular imprinting technology (MIT) is frequently used in SPE, chromatographic separation, and many other fields. With the development of MIT, researchers have engineered different types of imprinting strategies that can specifically extract the target analyte in complex biological samples while simultaneously avoiding the matrix effect. Some traditional separation technologies based on MIP technology have also been studied in depth; the most common of these technologies include stationary phases used for chromatography and adsorbents for SPE. Analytical methods that combine MIT with highly sensitive detection technologies have received wide interest in fields such as disease diagnosis and bioimaging. In this review, we highlight the new MIP strategies developed in recent years, and describe the applications of MIT-based separation analysis methods in fields including chromatographic separation, SPE, diagnosis, bioimaging, and proteomics. The drawbacks of these techniques as well as their future development prospects are also discussed.

We present the GPU-powered simulators that we designed and implemented to accelerate the simulation and analysis of reaction-based models of biological systems (cuTauLeaping [1], cupSODA [2], LASSIE [3]), which can rely either on numerical integration methods or stochastic simulation algorithms. In particular, we present both coarse-grain and fine-grain methods, which allow to execute a large number of parallel simulations of the same model, and to parallelize all calculations required by a single simulation run, respectively. These methods were developed to carry out either stochastic or deterministic simulations of both small and large-scale models, providing a relevant reduction of the running time, up to two orders of magnitude with respect to a classic CPU-bound execution. Three models of biological systems characterized by an increasing complexity: the Michaelis-Menten (MM) enzymatic kinetics; a model of gene expression in prokaryotic organisms (PGN); the Ras/cAMP/PKA signaling pathway in the yeast S. cerevisiae, are used as test cases to show the speed-up obtained by GPU-based tools. [1] M. S. Nobile, P. Cazzaniga, D. Besozzi, D. Pescini, G. Mauri. cuTauLeaping: A GPU–Powered Tau–Leaping Stochastic Simulator for Massive Parallel Analyses of Biological Systems. PLoS ONE 9(3), 2014: e91963 [2] M. S. Nobile, P. Cazzaniga, D. Besozzi, G.Mauri. GPU–accelerated simulations of mass–action kinetics models with cupSODA . J of Supercomputing 69(1), 2014, 17–24 [3] A. Tangherloni, M. S. Nobile, P. Cazzaniga, D. Besozzi, G.Mauri. LASSIE: A GPU-based deterministic simulator for large-scale models. In preparation

Information plays a critical role in complex biological systems. Complex systems like immune systems and ant colonies co-ordinate heterogeneous components in a decentralized fashion. How do these distributed decentralized systems function? One key component is how these complex systems efficiently process information. These complex systems have an architecture for integrating and processing information coming in from various sources and points to the value of information in the functioning of different complex biological systems. This article proposes a role for information processing in questions around the origin of life and suggests how computational simulations may yield insights into questions related to the origin of life. Such a computational model of the origin of life would unify thermodynamics with information processing and we would gain an appreciation of why proteins and nucleotides evolved as the substrate of computation and information processing in living systems that we see on Earth. Answers to questions like these may give us insights into non-carbon based forms of life that we could search for outside Earth. We hypothesize that carbon-based life forms are only one amongst a continuum of systems in the universe. Investigations into the role of computational substrates that allow information processing is important and could yield insights into: 1) novel non-carbon based computational substrates that may have life-like properties, and 2) how life may have actually originated from non-life on Earth. Life may exist as a continuum between non-life and life and we may have to revise our notion of life and how common it is in the universe. Looking at life or phenomenon through the lens of information theory may yield a broader view of life.

Metabolic networks: biology meets engineering sciences

Synthetic biology is an emerging field blending approaches and concepts derived from classic engineering disciplines with modern biological approaches. Concepts of modularity and orthogonality, i.e. the transfer of simple building blocks between unrelated chassis (host organisms), are guiding principles for the design and construction of artificial biological systems, which in their ultimate implementation can be artificial organisms. Synthetic biology is not only leading the way towards the engineering of useful organisms that serve human purposes, it is also a new way of approaching basic scientific questions to understand complex biological systems. The classic reductionist methodology by which scientists have dissected complex systems to understand their properties through understanding the functionality of isolated components, finds its counterpart in synthetic biology. If we can build complex biological processes, systems, and ultimately organisms from simple, fully understood functional modules using a set of defined rules, we must fully understand the system. At first this approach may sound almost naïve as with near certainty scientists will encounter spectacular 'failures' on the way to building complex biological systems. Undoubtedly, the result of synthetic biology efforts will be more than the sum of the individual components giving rise to complex systems with novel emergent properties, many of which are unexpected or even undesired. However, the process of learning from those 'failures' often through predictive modeling and simulation studies in parallel to the actual assembly and testing of artificial biological systems, will lead to novel insights into the function of complex biological systems in general. Plant and algal cells are complex with their extra organelle, the plastid, and are highly sophisticated in their metabolism enabling them to convert light, CO2 and minerals into the building blocks of cells, produce all oxygen in the atmosphere, thousands of specialized chemicals including drugs, and energy-rich compounds that fuel life on earth. While engineers have been dabbling for many years in the redesign of bacterial and yeast chassis with novel properties, the application of synthetic biology to photosynthetic organisms is just beginning. Therefore, it seems timely to provide an overview of the state of the art of 'Synthetic Biology for Basic and Applied Plant Research' in this special issue of The Plant Journal. Next Generation Sequencing has given us a nearly unlimited number of genomic blueprints for photosynthetic bacteria, algae and plants and this provides the raw material for synthetic biology. Tools for recombining of genes and introducing them into an increasing number of photosynthetic chassis including organelles such as chloroplasts, are available and no longer an impediment to the application of synthetic biology to plants. One revolutionary technique, the introduction of the CRISPR/CAS system for genome editing is now being applied to edit not only the plant genome, but also the transcriptome and epigenome as discussed by Puchta (2016). Bacterial microcompartments, first discovered as carboxysomes in cyanobacteria, provide an important platform for the engineering of synthetic modules. They can encapsulate enzymes, concentrate substrates, and help in the avoidance of toxic products as Gonzalez-Esquer et al. (2016) describe. Cyanobacteria address one key problem that all photosynthetic organisms encounter, the natural inefficiency of the carbon-fixing enzyme RubBisCO, by encapsulating this enzyme in carboxysomes, which increases the local concentration of CO2 around the enzyme. Plants do not have a carboxysome-based carbon concentration mechanism to overcome the limitation of photosynthesis through RubBisCO's inefficiency. The solution could be to introduce this bacterial microcompartment into chloroplasts of crop plants and synthetic biology efforts towards this aim are well under way as described by Hanson et al. (2016). A subset of plants has evolved their own way of overcoming this problem by prefixing carbon using a more efficient enzyme than RubBisCO. This carbon concentration mechanism requires the compartmentalization of different sets of enzymes in different cells of the leaf, and this overall approach is referred to as C4-syndrome of C4 plants, because the CO2 is first fixed into a four-carbon compound rather than the three-carbon compound produced first by RuBisCO in C3 plants. Some of the important crop plants that feed the world are C4 plants, such as maize, but many are not, including wheat and rice. The solution is to engineer C4 photosynthesis in a C3 chassis and as Schuler et al. (2016) describe, efforts are well underway by applying synthetic biology. Introduction of orthogonal biosynthetic pathways into photosynthetic organelles and bacteria to enhance their synthetic repertoires requires a deep knowledge of the regulation of photosynthesis, as the balance of ATP/and NADPH and the nature of the carbon sink are critical for the efficiency of photosynthesis. Nielson and coworkers describe how optimization of carbon flux and reductant are critical elements in engineering cyanobacteria and chloroplasts to sustainably produce novel chemicals (Nielsen et al., 2015). Plants are capable of making a seemingly unlimited number of specialized compounds to defend themselves against pathogens or herbivores and many of these compounds have been used by humans for thousands of years, e.g. as drugs. One particular compound class, the terpenoids, provides an example of the amazing natural combinatorial chemistry that plants are capable of. Applying synthetic biology principles of modularity and orthogonality, plant engineers are now capable of recombining different modules of terpenoid biosynthesis from different sources into new chassis to engineer plants that produce new-to-nature compounds as Arendt et al. (2016) describe. Another spectacular success in recombining modules of genes derived from different plants, algae, and fungi into a new chassis, the industrial crop Camelina, is the production of oils with a near natural composition of healthy oils found in fish as summarized by Haslam et al. (2016). With this accomplishment, important sustainability and human health questions can be addressed. These include improving the sustainability of the aquaculture industry for the production of fish rich in omega-3 oils with well-known health benefits when part of the human diet. Another example of addressing pressing problems for humankind is the generation of sustainable feed-stocks for energy production, independent of fossil fuels. For this reason, many scientists are currently pursuing the engineering of dedicated biofuel crops through the application of synthetic biology principles as summarized by Shih et al. (2016). Plant signaling pathways are highly interconnected and redundant, and hence often hard to dissect using the classical reductionistic approaches. Synthetic Biology offers a new way to explore individual signaling pathways by reassembling them bottom up from modules in non-interfering backgrounds of new chassis. Braguy and Zurbriggen (2016) describe this approach in detail. Ultimately, understanding how signaling pathways feed into programmable plant genetic circuits will be essential for the engineering of plants to be more efficient or to produce novel compounds. Medford and Prasad (2016) explain how genetic parts such as promoters and other regulatory elements can be tested and their assembly into genetic circuits simulated. The list of examples and approaches described in this special issue of The Plant Journal is comprehensive. Our intention is that this special issue will explain key principles and areas of plant synthetic biology to guide the reader and future contributors of The Plant Journal in embracing these approaches for both fundamental and applied plant science. Other areas of interest not covered here include synthetic consortia, the synthetic interaction of photosynthetic and heterotrophic organisms beyond naturally occurring symbioses. As we learn to understand how the microbiome affects plant growth, synthetic biology approaches may be key in learning more about these complex interactions, a topic that certainly falls with in the scope of The Plant Journal. With the expansion of the current field of plant synthetic biology, The Plant Journal welcomes the submission of basic research papers applying synthetic biology to further our understanding of the full biological complexity of photosynthetic organisms and their complex biotic and abiotic interaction with the environment.

Rare events such as genetic mutations or cell-cell interactions are important contributors to dynamics in complex biological systems, eg, in drug-resistant infections. Computational approaches can help analyze rare events that are difficult to study experimentally. However, analyzing the frequency and dynamics of rare events in computational models can also be challenging due to high computational resource demands, especially for high-fidelity stochastic computational models. To facilitate analysis of rare events in complex biological systems, we present a multifidelity analysis approach that uses medium-fidelity analysis (Monte Carlo simulations) and/or low-fidelity analysis (Markov chain models) to analyze high-fidelity stochastic model results. Medium-fidelity analysis can produce large numbers of possible rare event trajectories for a single high-fidelity model simulation. This allows prediction of both rare event dynamics and probability distributions at much lower frequencies than high-fidelity models. Low-fidelity analysis can calculate probability distributions for rare events over time for any frequency by updating the probabilities of the rare event state space after each discrete event of the high-fidelity model. To validate the approach, we apply multifidelity analysis to a high-fidelity model of tuberculosis disease. We validate the method against high-fidelity model results and illustrate the application of multifidelity analysis in predicting rare event trajectories, performing sensitivity analyses and extrapolating predictions to very low frequencies in complex systems. We believe that our approach will complement ongoing efforts to enable accurate prediction of rare event dynamics in high-fidelity computational models.

Organoids are three-dimensional structures derived from stem cells that mimic the organization and function of specific organs, making them valuable tools for studying complex systems in biology. This paper explores the application of complex systems theory to understand and characterize organoids as exemplars of intricate biological systems. By identifying and analyzing common design principles observed across diverse natural, technological, and social complex systems, we can gain insights into the underlying mechanisms governing organoid behavior and function. This review outlines general design principles found in complex systems and demonstrates how these principles manifest within organoids. By acknowledging organoids as representations of complex systems, we can illuminate our understanding of their normal physiological behavior and gain valuable insights into the alterations that can lead to disease. Therefore, incorporating complex systems theory into the study of organoids may foster novel perspectives in biology and pave the way for new avenues of research and therapeutic interventions to improve human health and wellbeing.

Fluorescein diacetate (FDA) should not be used to study human carboxylesterase 2 (CES2) in complex biological systems without validation.

Proteomics is generally defined as the simultaneous and high-throughput study of protein expression profiles in cells, tissues, organs and organisms. It is a relatively new scientific discipline which has developed highly significantly over the last decade and is now recognised as one of the most important tools used in the identification and characterisation of proteins or genes of interest. The researchers have turned to proteomics to study gene products and validate their predicted functions because the availability of the complete genome sequences of a variety of organisms itself is not sufficient to find out biological function. Proteomic data for an experiment includes quantitative expression profiles, profiles of posttranslational modifications (PTMs) and protein interaction networks and linking these towards the understanding of molecular mechanisms associated with endogenous and exogenous cues. The major application of proteomics technologies is to advance our knowledge in crop plant for their development, abiotic and biotic stress tolerance, PTMs and unravelling signal transduction cascades. Further, an in-depth comparative proteome study of subcellular organelles could provide more detailed information about the intrinsic mechanism of developmental or stress response. The success in proteomics research is attributed to advances in various technology platforms associated with MS-based techniques. The accurate quantitation of proteins and peptides in complex biological systems is one of the most challenging areas of proteomics. The discoveries aimed at improving sensitivity, and throughput of both mass analysers and fragmentation technology enabled mass spectrometry (MS)-based proteomics to become the mainstream method for the large-scale analysis of complex proteomes. Along with recent and ongoing improvements in liquid separation technologies and algorithms for protein/peptide identification, MS-based proteomics has become a powerful and valuable analytical tool to study highly complex and dynamic biological systems. In this chapter, we describe the recent progress in plant proteomics and highlight the achievements made in understanding the proteomes of major research area of plant biology.

Colliding Dynamical Complex Network Models: Biological Attractors versus Attractors from Material Physics

Towards a general theory of adaptive walks on rugged landscapes

The detection and characterization of low-level protein modifications in a complex system without a methodology for modification enrichment is a very challenging task. This study describes a high-resolution LC/MS-based background subtraction methodology for the unbiased detection and identification of acetaminophen-bound proteins formed in incubations with mouse liver microsomes. The microsomal incubations were conducted using both acetaminophen and [(13)C2,(15)N]acetaminophen at a drug concentration of 200 μM. After tryptic digestion and high-resolution LC/MS analysis, data from the two drug treatment groups were each background-subtracted against the other. Thus, peptide signals that were identical in both groups were effectively canceled out, and drug-bound peptide peaks, differing in masses between the groups because of the isotopic mass shift, were retained after background subtraction and became highlighted in the resultant base peak ion chromatograms. Follow-up MS/MS experiments with these drug-bound peptides led to the identification of three acetaminophen-bound proteins: microsomal glutathione S-transferase, oligosaccharyltransferase subunit ribophorin I, and argininosuccinate synthetase. These initial findings demonstrate the utility of the methodology and may shed new light on the mechanism of acetaminophen-induced hepatotoxicity. The approach is potentially applicable to similar tasks of identification of protein modifications in other complex biological systems.

It is very difficult to use exact mathematical models to study complexity systems. As the units beside complex systems can interact to bring forth its complexity, it is completely true for the mammal body, a classic kind of biological complex system. As singular biological complexity systems, including the mammal body, are considered in a series of new research fields, a few passivity or biological control studies have been carried out up to now. In this research, the single-chamber model of the environmental hormone formaldehyde which is flowing in the mammal body has been set up according to the corresponding physiological rules with the model passivity described in detail. Under the strict passivity station, the feedback controller for this singular mammal body complexity system has been designed with a controller example also given as a model instantiation. Both passivity study and feedback controller design of the mammal body complex system can be applied to biological complexity systems and lay a useful foundation for singular system research.