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-
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
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.
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
A number of models in mathematical epidemiology have been developed to account for control measures such as vaccination or quarantine. However, COVID-19 has brought unprecedented social distancing measures, with a challenge on how to include these in a manner that can explain the data but avoid overfitting in parameter inference. We here develop a simple time-dependent model, where social distancing effects are introduced analogous to coarse-grained models of gene expression control in systems biology. We apply our approach to understand drastic differences in COVID-19 infection and fatality counts, observed between Hubei (Wuhan) and other Mainland China provinces. We find that these unintuitive data may be explained through an interplay of differences in transmissibility, effective protection, and detection efficiencies between Hubei and other provinces. More generally, our results demonstrate that regional differences may drastically shape infection outbursts. The obtained results demonstrate the applicability of our developed method to extract key infection parameters directly from publically available data so that it can be globally applied to outbreaks of COVID-19 in a number
With the completion of human genome mapping, the focus of scientists seeking to explain the biological complexity of living systems is shifting from analyzing the individual components (such as a particular gene or biochemical reaction) to understanding the set of interactions amongst the large number of components that results in the different functions of the organism. To this end, the area of systems biology attempts to achieve a "systems-level" description of biology by focusing on the network of interactions instead of the characteristics of its isolated parts. In this article, we briefly describe some of the emerging themes of research in "network" biology, looking at dynamical processes occurring at the two different length scales of within the cell and between cells, viz., the intra-cellular signaling network and the nervous system. We show that focusing on the systems-level aspects of these problems allows one to observe surprising and illuminating common themes amongst them.
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
Benchmarking the performance of complex systems such as rail networks, renewable generation assets and national economies is central to transport planning, regulation and macroeconomic analysis. Classical frontier methods, notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), estimate an efficient frontier in the observed input-output space and define efficiency as distance to this frontier, but rely on restrictive assumptions on the production set and only indirectly address heterogeneity and scale effects. We propose Geometric Manifold Analysis (GeMA), a latent manifold frontier framework implemented via a productivity-manifold variational autoencoder (ProMan-VAE). Instead of specifying a frontier function in the observed space, GeMA represents the production set as the boundary of a low-dimensional manifold embedded in the joint input-output space. A split-head encoder learns latent variables that capture technological structure and operational inefficiency. Efficiency is evaluated with respect to the learned manifold, endogenous peer groups arise as clusters in latent technology space, a quotient construction supports scale-invariant benchmarking, and
Cells in a fungal hyphae are separated by internal walls (septa). The septa have tiny pores that allow cytoplasm flowing between cells. Cells can close their septa blocking the flow if they are injured, preventing fluid loss from the rest of filament. This action is achieved by special organelles called Woronin bodies. Using the controllable pores as an inspiration we advance one and two-dimensional cellular automata into Elementary fungal cellular automata (EFCA) and Majority fungal automata (MFA) by adding a concept of Woronin bodies to the cell state transition rules. EFCA is a cellular automaton where the communications between neighboring cells can be blocked by the activation of the Woronin bodies (Wb), allowing or blocking the flow of information (represented by a cytoplasm and chemical elements it carries) between them. We explore a novel version of the fungal automata where the evolution of the system is only affected by the activation of the Wb. We explore two case studies: the Elementary Fungal Cellular Automata (EFCA), which is a direct application of this variant for elementary cellular automata rules, and the Majority Fungal Automata (MFA), which correspond to an appl
As the impending consequences of climate change loom over the Earth, it has become vital for researchers to understand the role microorganisms play in this process. In this paper, we examine how environmental factors, including moisture levels and temperature, affect the expression of certain fungal characteristics on a microscale, and how these in turn affect fungal biodiversity and ecosystem decomposition rates over time. We first present a differential equation model to understand how the distribution of different fungal isolates depends on regional moisture levels. We introduce both slow and sudden variations into the environment in order to represent the various ways climate change will impact fungal ecosystems. This model demonstrates that increased variability in moisture (both short-term and long-term) increases biodiversity and that fungal populations will shift towards more stress-tolerant fungi as aridity increases. The model further suggests the lack of any direct link between biodiversity and decomposition rates. To better describe fungal competition with respect to space, we develop a local agent-based model (ABM). Unlike the previous model, our ABM focuses on individ
Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring \emph{in vivo} biochemical parameters is difficult, and collectively fitting them to other data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a `sloppy' spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our m
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.
This paper studied the relationship between the decomposition rate of fungi and temperature, humidity, fungus elongation, moisture tolerance and fungus density in a given volume in the presence of a variety of fungi, and established a series of models to describe the decomposition of fungi in different states. Since the volume of soil was given in this case, the latter two characteristics could be attributed to the influence of the number of fungal population on the decomposition rate. Based on the Logistic model, the relationship between the number of population and time was established, and finally the number of fungi in the steady state was obtained The interaction between different species of fungi was analyzed by Lotka-Volterra model, and the decomposition rate of various fungal combinations in different environments was obtained. After studying the one and two cases, we can extrapher from one to the other, and the community consisting of n fungal populations will be similar to the community consisting of n+1 fungal populations. After the study, we substituted the collected data into the model and found that the fungal community composed of two kinds of fungi had a lower decom
Fungal Biosynthetic Gene Clusters (BGCs) of secondary metabolites are clusters of genes capable of producing natural products, compounds that play an important role in the production of a wide variety of bioactive compounds, including antibiotics and pharmaceuticals. Identifying BGCs can lead to the discovery of novel natural products to benefit human health. Previous work has been focused on developing automatic tools to support BGC discovery in plants, fungi, and bacteria. Data-driven methods, as well as probabilistic and supervised learning methods have been explored in identifying BGCs. Most methods applied to identify fungal BGCs were data-driven and presented limited scope. Supervised learning methods have been shown to perform well at identifying BGCs in bacteria, and could be well suited to perform the same task in fungi. But labeled data instances are needed to perform supervised learning. Openly accessible BGC databases contain only a very small portion of previously curated fungal BGCs. Making new fungal BGC datasets available could motivate the development of supervised learning methods for fungal BGCs and potentially improve prediction performance compared to data-driv
The last decade has witnessed a rapid growth in understanding of the pivotal roles of mechanical stresses and physical forces in cell biology. As a result an integrated view of cell biology is evolving, where genetic and molecular features are scrutinized hand in hand with physical and mechanical characteristics of cells. Physics of liquid crystals has emerged as a burgeoning new frontier in cell biology over the past few years, fueled by an increasing identification of orientational order and topological defects in cell biology, spanning scales from subcellular filaments to individual cells and multicellular tissues. Here, we provide an account of most recent findings and developments together with future promises and challenges in this rapidly evolving interdisciplinary research direction.
Systems Biology has emerged in the last years as a new holistic approach based on the global understanding of cells instead of only being focused on their individual parts (genes or proteins), to better understand the complexity of human cells. Since the Systems Biology still does not provide the most accurate answers to our questions due to the complexity of cells and the limited quality of available information to perform a good gene/protein map analysis, we have created simpler models to ensure easier analysis of the map that represents the human cell. Therefore, a virtual organism has been designed according to the main physiological rules for humans in order to replicate the human organism and its vital functions. This toy model was constructed by defining the topology of its genes/proteins and the biological functions associated to it. There are several examples of these toy models that emulate natural processes to perform analysis of the virtual life in order to design the best strategy to understand real life. The strategy applied in this study combines topological and functional analysis integrating the knowledge about the relative position of a node among the others in th
A fungal skin is a thin flexible sheet of a living homogeneous mycelium made by a filamentous fungus. The skin could be used in future living architectures of adaptive buildings and as a sensing living skin for soft self-growing/adaptive robots. In experimental laboratory studies we demonstrate that the fungal skin is capable for recognising mechanical and optical stimulation. The skin reacts differently to loading of a weight, removal of the weight, and switching illumination on and off. These are the first experimental evidences that fungal materials can be used not only as mechanical `skeletons' in architecture and robotics but also as intelligent skins capable for recognition of external stimuli and sensorial fusion.
The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them. This invalidates the assumptions behind standard statistical methods such as linear regression, and often the methods used to parameterise biological models from data are ad hoc. In this perspective, I will argue for an approach to model fitting in mathematical biology that incorporates modern statistical methodology without losing the insights gained through non-linear dynamic models, and will call such an approach principled model fitting. Principled model fitting therefore involves defining likelihoods of observing real data on the basis of models that capture key biological mechanisms.
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.