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Systems biology of plants offers myriad opportunities and many challenges in modeling. A number of technical challenges stem from paucity of computational methods for discovery of the most fundamental properties of complex dynamical systems. In systems engineering, eigen-mode analysis have proved to be a powerful approach. Following this philosophy, we introduce a new theory that has the benefits of eigen-mode analysis, while it allows investigation of complex dynamics prior to estimation of optimal scales and resolutions. Information Surfaces organizes the many intricate relationships among "eigen-modes" of gene networks at multiple scales and via an adaptable multi-resolution analytic approach that permits discovery of the appropriate scale and resolution for discovery of functions of genes in the model plant Arabidopsis. Applications are many, and some pertain developments of crops that sustainable agriculture requires.
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure or dynamics of specific subsystems in controlled conditions, compositional systems biology aims to connect these models, asking critical questions about the space between models: What variables should a submodel expose through its interface? How do coupled models connect and translate across scales? How do domain-specific models connect across biological and physical disciplines to drive the synthesis of new knowledge? This approach requires robust software to integrate diverse datasets and submodels, providing researchers with tools to flexibly recombine, iteratively refine, and collaboratively expand their models. This article offers a comprehensive framework to support this vision, including: a conceptual and graphical framework to define interfaces and composition patterns; standardized schemas that facilitate modular data and model assembly; biological templates that integrate detailed submodels that connect molecular processes to the emerg
Recent tumor genome sequencing confirmed that one tumor often consists of multiple cell subpopulations (clones) which bear different, but related, genetic profiles such as mutation and copy number variation profiles. Thus far, one tumor has been viewed as a whole entity in cancer functional studies. With the advances of genome sequencing and computational analysis, we are able to quantify and computationally dissect clones from tumors, and then conduct clone-based analysis. Emerging technologies such as single-cell genome sequencing and RNA-Seq could profile tumor clones. Thus, we should reconsider how to conduct cancer systems biology studies in the genome sequencing era. We will outline new directions for conducting cancer systems biology by considering that genome sequencing technology can be used for dissecting, quantifying and genetically characterizing clones from tumors. Topics discussed in Part 1 of this review include computationally quantifying of tumor subpopulations; clone-based network modeling, cancer hallmark-based networks and their high-order rewiring principles and the principles of cell survival networks of fast-growing clones.
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled systems, we enforce non-negativity of the solutions, aligning with realistic scenarios in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction in measurement/observation data due to averaging effects, the nonlinear coupling between multiple equations, and the nonlocality arising from fractional-type derivatives. These factors present significant challenges to our inverse problem, and such inverse problems have never been explored in previous literature. To address these challenges, we develop new and effective schemes. Our approach involves properly controlling the injection of different source terms to obtain multiple sets of mean flux data. This allows us to achieve unique identifiability results and accurately determine the unknown parameters. Finally, we establish a connection between our study and practical applications in biology, further highlighting the relevance of our work in real-
Phage lambda is one of the most studied biological models in modern molecular biology. Over the past 50 years quantitative experimental knowledge on this biological model has been accumulated at all levels: physics, chemistry, genomics, proteomics, functions, and more. All its components have been known to a great detail. The theoretical task has been to integrate its components to make the organism working quantitatively in a harmonic manner. This would test our biological understanding and would lay a solid fundamental for further explorations and applications, an obvious goal of systems biology. One of the outstanding challenges in doing so has been the so-called stability puzzle of lambda switch: the biologically observed robustness and its difficult mathematical reconstruction based on known experimental values. In this chapter we review the recent theoretical and experimental efforts on tackling this problem. An emphasis is put on the minimum quantitative modeling where a successful numerical agreement between experiments and modeling has been achieved. A novel method tentatively named stochastic dynamical structure analysis emerged from such study is also discussed within a
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects of biological systems. In this case, an appropriate simple model represents a universality class. The extraction of universal properties is supported by evolutionary robustness and the reduction of dimensionality in high-dimensional states. Integrating the data-driven omics approach with the universality approach is an important step in systems biology.
This article frames the relation between biology and physics by characterizing the former as a subdiscipline rather than a special case of the latter. To do this, we posit biological physics as the science of living matter in contrast to classic biophysics, the study of organismal properties by physical techniques. At the scale of the individual cell, living matter is nonunitary, i.e., not composed of aggregated subunits, and has features (e.g., intracellular organizational arrangements and biomolecular condensates) that are unlike any materials of the nonliving world. In transiently or constitutively multicellular forms (social microorganisms, animals, plants), living matter sustains physical processes that are generic (shared with nonliving matter, e.g., subunit communication by molecular diffusion in cellular slime molds), biogeneric (analogous to nonliving matter but realized through cellular activities, e.g., subunit demixing in animal embryos) or nongeneric (pertaining to sui generis materials, e.g., budding of active solids in plants). This "forms of matter" perspective is philosophically situated in the dialectical materialism of Engels and Hessen and the multilevel physica
A tumor often consists of multiple cell subpopulations (clones). Current chemo-treatments often target one clone of a tumor. Although the drug kills that clone, other clones overtake it and the tumor reoccurs. Genome sequencing and computational analysis allows to computational dissection of clones from tumors, while singe-cell genome sequencing including RNA-Seq allows to profiling of these clones. This opens a new window for treating a tumor as a system in which clones are evolving. Future cancer systems biology studies should consider a tumor as an evolving system with multiple clones. Therefore, topics discussed in Part 2 of this review include evolutionary dynamics of clonal networks, early-warning signals for formation of fast-growing clones, dissecting tumor heterogeneity, and modeling of clone-clone-stroma interactions for drug resistance. The ultimate goal of the future systems biology analysis is to obtain a whole-system understanding of a tumor and therefore provides a more efficient and personalized management strategies for cancer patients.
Understanding the biological mechanisms of disease is crucial for medicine, and in particular, for drug discovery. AI-powered analysis of genome-scale biological data holds great potential in this regard. The increasing availability of single-cell RNA sequencing data has enabled the development of large foundation models for disease biology. However, existing foundation models only modestly improve over task-specific models in downstream applications. Here, we explored two avenues for improving single-cell foundation models. First, we scaled the pre-training data to a diverse collection of 116 million cells, which is larger than those used by previous models. Second, we leveraged the availability of large-scale biological annotations as a form of supervision during pre-training. We trained the \model family of models comprising six transformer-based state-of-the-art single-cell foundation models with 70 million, 160 million, and 400 million parameters. We vetted our models on several downstream evaluation tasks, including identifying the underlying disease state of held-out donors not seen during training, distinguishing between diseased and healthy cells for disease conditions and
We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdos-Renyi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data. We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs, characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labeled and unlabeled graphs and prove that the Kolmogorov complexity of a labeled graph is a good approximation of its unlabeled Kolmogorov complexity and thus a robust definition of graph complexity.
We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The potential candidate logics should have a traditional proof theoretic pedigree (including a sequent calculus presentation enjoying cut-elimination and focusing), and should come with (certified) proof tools. Beyond providing a reliable framework, this allows the adequate encodings of our biological systems. We present two candidate logics (two modal extensions of linear logic, called HyLL and SELL), along with biological examples. The examples we have considered so far are very simple ones-coming with completely formal (interactive) proofs in Coq. Future works includes using automatic provers, which would extend existing automatic provers for linear logic. This should enable us to specify and study more realistic examples in systems biology, biomedicine (diagnosis and prognosis), and eventually neuroscience.
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown remarkable ability in approximating complex distributions in various domains. However, their application in systems biology for approximating intractable likelihood functions remains unexplored. Here, we elucidate a framework for leveraging normalizing flows to approximate complex likelihood functions inherent to systems biology models. By using normalizing flows in the Simulation-based inference setting, we demonstrate a method that not only approximates a likelihood function but also allows for model inference in the model selection setting. We showcase the effectiveness of this approach on real-world systems biology problems, providing practical guidance for implementation and highlighting its advantages over traditional computational methods.
We developed a theory showing that under appropriate normalizations and rescalings, temperature response curves show a remarkably regular behavior and follow a general, universal law. The impressive universality of temperature response curves remained hidden due to various curve-fitting models not well-grounded in first principles. In addition, this framework has the potential to explain the origin of different scaling relationships in thermal performance in biology, from molecules to ecosystems. Here, we summarize the background, principles and assumptions, predictions, implications, and possible extensions of this theory.
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Results: Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embedded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources
In a recent paper, Wilmes et al. demonstrated a qualitative integration of omics data streams to gain a mechanistic understanding of cyclosporine A toxicity. One of their major conclusions was that cyclosporine A strongly activates the nuclear factor (erythroid-derived 2)-like 2 pathway (Nrf2) in renal proximal tubular epithelial cells exposed in vitro. We pursue here the analysis of those data with a quantitative integration of omics data with a differential equation model of the Nrf2 pathway. That was done in two steps: (i) Modeling the in vitro pharmacokinetics of cyclosporine A (exchange between cells, culture medium and vial walls) with a minimal distribution model. (ii) Modeling the time course of omics markers in response to cyclosporine A exposure at the cell level with a coupled PK-systems biology model. Posterior statistical distributions of the parameter values were obtained by Markov chain Monte Carlo sampling. Data were well simulated, and the known in vitro toxic effect EC50 was well matched by model predictions. The integration of in vitro pharmacokinetics and systems biology modeling gives us a quantitative insight into mechanisms of cyclosporine A oxidative-stress
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis o
Recently, microRNAs (miRNAs) have emerged as central posttranscriptional regulators of gene expression. miRNAs regulate many key biological processes, including cell growth, death, development and differentiation. This discovery is challenging the central dogma of molecular biology. Genes are working together by forming cellular networks. It has become an emerging concept that miRNAs could intertwine with cellular networks to exert their function. Thus, it is essential to understand how miRNAs take part in cellular processes at a systems-level. In this review, I will first introduce basic knowledge of miRNAs and their relations to heart disaeses and cancer, highlight recently dicovered functions such as filtering out gene expression noise by miRNAs. I will aslo introduce basic concepts of cellular networks and interpret their biological meaning in such a way that the network concepts are digested in a biological context and are understandable for biologists. Finally, I will summarize the most recent progress in understanding of miRNA biology at a systems-level: the principles of miRNA regulation of the major cellular networks including signaling, metabolic, protein interaction and
Although reproducibility is a core tenet of the scientific method, it remains challenging to reproduce many results. Surprisingly, this also holds true for computational results in domains such as systems biology where there have been extensive standardization efforts. For example, Tiwari et al. recently found that they could only repeat 50% of published simulation results in systems biology. Toward improving the reproducibility of computational systems research, we identified several resources that investigators can leverage to make their research more accessible, executable, and comprehensible by others. In particular, we identified several domain standards and curation services, as well as powerful approaches pioneered by the software engineering industry that we believe many investigators could adopt. Together, we believe these approaches could substantially enhance the reproducibility of systems biology research. In turn, we believe enhanced reproducibility would accelerate the development of more sophisticated models that could inform precision medicine and synthetic biology.
This paper introduces a cost-effective robotic handwriting system designed to replicate human-like handwriting with high precision. Combining a Raspberry Pi Pico microcontroller, 3D-printed components, and a machine learning-based handwriting generation model implemented via TensorFlow, the system converts user-supplied text into realistic stroke trajectories. By leveraging lightweight 3D-printed materials and efficient mechanical designs, the system achieves a total hardware cost of approximately \$56, significantly undercutting commercial alternatives. Experimental evaluations demonstrate handwriting precision within $\pm$0.3 millimeters and a writing speed of approximately 200 mm/min, positioning the system as a viable solution for educational, research, and assistive applications. This study seeks to lower the barriers to personalized handwriting technologies, making them accessible to a broader audience.
Modeling and topological analysis of networks in biological and other complex systems, must venture beyond the limited consideration of very few network metrics like degree, betweenness or assortativity. A proper identification of informative and redundant entities from many different metrics, using recently demonstrated techniques, is essential. A holistic comparison of networks and growth models is best achieved only with the use of such methods.