150 years of the mass action law

Pyrolysis mechanism study on xylose by combining experiments, chemical reaction neural networks and density functional theory

Chemical reaction neural networks (CRNN) and density functional theory (DFT) are gaining attention in biomass pyrolysis mechanism research. Reaction pathways are often speculated based on a single method, influenced by expert knowledge. To address this, the pyrolysis mechanism of xylose, a hemicellulose model compound, is studied using thermogravimetric-Fourier transform infrared spectroscopy (TG-FTIR), CRNN, and DFT. Based on the TG-FTIR measured products, seven main pyrolysis products of xylose are applied. A CRNN model of 8 species (7 + 1) and 10 reactions, including kinetic parameters, is established, achieving an MAE below 2 × 10-2. Furthermore, the detailed reaction pathways and potential energy surfaces of evolution into each species are studied through DFT calculations. The activation energy for the xylose ring-opening, ring-condensation, and dehydration reactions, as obtained from the CRNN model, are 152.78 kJ/mol, 485.81 kJ/mol, and 320.01 kJ/mol, respectively. The deviations from the theoretical DFT calculations are less than 37 %, demonstrating good agreement. Compared to dehydration and ring condensation reactions, xylose is most susceptible to ring-opening reactions to form d-xylose. d-xylose easily undergoes hemi-acetalization, isomerization and dehydration at the 3-OH + 2-H, 5-OH + 4-H and 4-OH + 3-H sites. Xylose is most susceptible to dehydration reactions at the 1-OH + 2-H and 2-OH + 3-H sites to generate dehydrated xylose. Finally, xylose can also generate furfural through a cyclic condensation reaction. The conclusion can promote the improvement and development of hemicellulose pyrolysis kinetics models, and the research process can provide experience for the pyrolysis mechanism of other materials.

The Dawn of High-Throughput and Genome-Scale Kinetic Modeling: Recent Advances and Future Directions

Researchers have invested much effort into developing kinetic models due to their ability to capture dynamic behaviors, transient states, and regulatory mechanisms of metabolism, providing a detailed and realistic representation of cellular processes. Historically, the requirements for detailed parametrization and significant computational resources created barriers to their development and adoption for high-throughput studies. However, recent advancements, including the integration of machine learning with mechanistic metabolic models, the development of novel kinetic parameter databases, and the use of tailor-made parametrization strategies, are reshaping the field of kinetic modeling. In this Review, we discuss these developments and offer future directions, highlighting the potential of these advances to drive progress in systems and synthetic biology, metabolic engineering, and medical research at an unprecedented scale and pace.

Analysis of systemic effects of dioxin on human health through template-and-anchor modeling

Dioxins are persistent environmental pollutants known for their multiple health effects, from skin rashes to liver dysfunction, reproductive toxicity and cancer. While the hazards of dioxins have been well documented, the challenge of developing a comprehensive understanding of the overall health impact of dioxins remains. We propose to address this challenge with a new approach methodology (NAM) consisting of a novel adaptation of the Template-and-Anchor (T&A) modeling paradigm. Generically, the template model is defined as a high-level coarse-grained model capturing the main physiological processes of the system. The variables of this template model are anchor models, which represent component sub-systems in greater detail at lower biological levels. For the case of dioxin, we design the template to capture the systemic effects of dioxin on the body's handling of cholesterol. Two new anchor models within this template elucidate the effects of dioxin on cholesterol transport in the bloodstream and on sex hormone steroidogenesis and the menstrual cycle. A third anchor model, representing dioxin-mediated effects on cholesterol biosynthesis via the mevalonate pathway, had been developed previously. The T&A modeling paradigm enables a holistic evaluation of the impact of toxicants, which in the future may be translated into a powerful tool for comprehensive computational health risk assessments, personalized medicine, and the development of virtual clinical trials.

Identify structures underlying out-of-equilibrium reaction networks with random graph analysis

Network measures have proven very successful in identifying structural patterns in complex systems (e.g., a living cell, a neural network, the Internet). How such measures can be applied to understand the rational and experimental design of chemical reaction networks (CRNs) is unknown. Here, we develop a procedure to model CRNs as a mathematical graph on which network measures and a random graph analysis can be applied. We used an enzymatic CRN (for which a mass-action model was previously developed) to show that the procedure provides insights into its network structure and properties. Temporal analyses, in particular, revealed when feedback interactions emerge in such a network, indicating that CRNs comprise various reactions that are being added and removed over time. We envision that the procedure, including the temporal network analysis method, could be broadly applied in chemistry to characterize the network properties of many other CRNs, promising data-driven analysis of future molecular systems of ever greater complexity.

MVSLLnc: LncRNA subcellular localization prediction based on multi-source features and two-stage voting strategy

The subcellular localization of long non-coding RNAs (lncRNAs) is crucial for understanding the function of lncRNAs. Since the traditional biological experimental methods are time-consuming and some existing computational methods rely on high computing power, we are committed to finding a simple and easy-to-implement method to achieve more efficient prediction of the subcellular localization of lncRNAs. In this work, we proposed a model based on multi-source features and two-stage voting strategy for predicting the subcellular localization of lncRNAs (MVSLLnc). The multi-source features include k-mer frequency, features based on the coordinate values of Chaos Game Representation (CGR) and features based on physicochemical property (PhyChe). We feed the multi-source features into the traditional machine learning classifiers RF, SVM and XGBoost, respectively, and perform the final prediction task with two-stage voting strategy. Experimental results on three benchmark datasets show that the accuracy can reach 0.829, 0.793 and 0.968, respectively. The accuracy on three independent test sets is 0.642, 0.737 and 0.518, respectively, which are competitive with the existing methods. Our ablation analyses show that the two-stage voting strategy can make full use of the advantages of multi-source features and multiple classifiers, and obtain more robust results.

Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models

Compartmental models with exponentially distributed lifetime stages assume a constant hazard rate, limiting their scope. This study develops a theoretical framework for systems with general lifetime distributions, modeled as transition rates in a renewal process. Applications are provided for the SVIS (Susceptible-Vaccinated-Infected-Susceptible) disease epidemic model to investigate the impacts of hazard rate functions (HRFs) on disease control. The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. Key statistical properties and the basic reproduction number ([Formula: see text]) are derived, and conditions for the system's asymptotic autonomy are established for specific lifetime distributions. Four HRF behaviors-monotonic, bathtub, reverse bathtub, and constant-are analyzed to determine conditions for disease eradication and the asymptotic population under these scenarios. Sensitivity analysis examines how HRF behaviors shape system trajectories. Numerical simulations illustrate the influence of diverse lifetime models on vaccine efficacy and immunity, offering insights for effective disease management.

Optimal control of agent-based models via surrogate modeling

This paper describes and validates an algorithm to solve optimal control problems for agent-based models (ABMs). For a given ABM and a given optimal control problem, the algorithm derives a surrogate model, typically lower-dimensional, in the form of a system of ordinary differential equations (ODEs), solves the control problem for the surrogate model, and then transfers the solution back to the original ABM. It applies to quite general ABMs and offers several options for the ODE structure, depending on what information about the ABM is to be used. There is a broad range of applications for such an algorithm, since ABMs are used widely in the life sciences, such as ecology, epidemiology, and biomedicine and healthcare, areas where optimal control is an important purpose for modeling, such as for medical digital twin technology.

Surrogate modeling and control of medical digital twins

The vision of personalized medicine is to identify interventions that maintain or restore a person's health based on their individual biology. Medical digital twins, computational models that integrate a wide range of health-related data about a person and can be dynamically updated, are a key technology that can help guide medical decisions. Such medical digital twin models can be high-dimensional, multi-scale, and stochastic. To be practical for healthcare applications, they often need to be simplified into low-dimensional surrogate models that can be used for optimal design of interventions. This paper introduces surrogate modeling algorithms for the purpose of optimal control applications. As a use case, we focus on agent-based models (ABMs), a common model type in biomedicine for which there are no readily available optimal control algorithms. By deriving surrogate models that are based on systems of ordinary differential equations, we show how optimal control methods can be employed to compute effective interventions, which can then be lifted back to a given ABM. The relevance of the methods introduced here extends beyond medical digital twins to other complex dynamical systems.

Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton's equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton's equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton's and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton's, variational, and Schrödinger equations are described. Employing the Hénon-Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton's equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes.

A review of mathematical modeling of bone remodeling from a systems biology perspective

Bone remodeling is an essential, delicately balanced physiological process of coordinated activity of bone cells that remove and deposit new bone tissue in the adult skeleton. Due to the complex nature of this process, many mathematical models of bone remodeling have been developed. Each of these models has unique features, but they have underlying patterns. In this review, the authors highlight the important aspects frequently found in mathematical models for bone remodeling and discuss how and why these aspects are included when considering the physiology of the bone basic multicellular unit, which is the term used for the collection of cells responsible for bone remodeling. The review also emphasizes the view of bone remodeling from a systems biology perspective. Understanding the systemic mechanisms involved in remodeling will help provide information on bone pathology associated with aging, endocrine disorders, cancers, and inflammatory conditions and enhance systems pharmacology. Furthermore, some features of the bone remodeling cycle and interactions with other organ systems that have not yet been modeled mathematically are discussed as promising future directions in the field.

From Average Transient Transporter Currents to Microscopic Mechanism─A Bayesian Analysis

Electrophysiology studies of secondary active transporters have revealed quantitative mechanistic insights over many decades of research. However, the emergence of new experimental and analytical approaches calls for investigation of the capabilities and limitations of the newer methods. We examine the ability of solid-supported membrane electrophysiology (SSME) to characterize discrete-state kinetic models with >10 rate constants. We use a Bayesian framework applied to synthetic data for three tasks: to quantify and check (i) the precision of parameter estimates under different assumptions, (ii) the ability of computation to guide the selection of experimental conditions, and (iii) the ability of our approach to distinguish among mechanisms based on SSME data. When the general mechanism, i.e., event order, is known in advance, we show that a subset of kinetic parameters can be "practically identified" within ∼1 order of magnitude, based on SSME current traces that visually appear to exhibit simple exponential behavior. This remains true even when accounting for systematic measurement bias and realistic uncertainties in experimental inputs (concentrations) are incorporated into the analysis. When experimental conditions are optimized or different experiments are combined, the number of practically identifiable parameters can be increased substantially. Some parameters remain intrinsically difficult to estimate through SSME data alone, suggesting that additional experiments are required to fully characterize parameters. We also demonstrate the ability to perform model selection and determine the order of events when that is not known in advance, comparing Bayesian and maximum-likelihood approaches. Finally, our studies elucidate good practices for the increasingly popular but subtly challenging Bayesian calculations for structural and systems biology.

Systems Biology Approaches to Understanding COVID-19 Spread in the Population

In essence, the COVID-19 pandemic can be regarded as a systems biology problem, with the entire world as the system, and the human population as the element transitioning from one state to another with certain transition rates. While capturing all the relevant features of such a complex system is hardly possible, compartmental epidemiological models can be used as an appropriate simplification to model the system's dynamics and infer its important characteristics, such as basic and effective reproductive numbers of the virus. These measures can later be used as response variables in feature selection methods to uncover the main factors contributing to disease transmissibility. We here demonstrate that a combination of dynamic modeling and machine learning approaches can represent a powerful tool in understanding the spread, not only of COVID-19, but of any infectious disease of epidemiological proportions.

A Review of Computational Approach for S-system-based Modeling of Gene Regulatory Network

Inference of gene regulatory network (GRN) from time series microarray data remains as a fascinating task for computer science researchers to understand the complex biological process that occurred inside a cell. Among the different popular models to infer GRN, S-system is considered as one of the promising non-linear mathematical tools to model the dynamics of gene expressions, as well as to infer the GRN. S-system is based on biochemical system theory and power law formalism. By observing the value of kinetic parameters of S-system model, it is possible to extract the regulatory relationships among genes. In this review, several existing intelligent methods that were already proposed for inference of S-system-based GRN are explained. It is observed that finding out the most suitable and efficient optimization technique for the accurate inference of all kinds of networks, i.e., in-silico, in-vivo, etc., with less computational complexity is still an open research problem to all. This paper may help the beginners or researchers who want to continue their research in the field of computational biology and bioinformatics.

Beyond classical theories: An integrative mathematical model of mating dynamics and parental care

Classical theories, such as Bateman's principle and Trivers' parental investment theory, attempted to explain the coevolution of sexual selection and parental care through simple verbal arguments. Since then, quantitative models have demonstrated that it is rarely that simple because many non-intuitive structures and non-linear relationships are actually at play. In this study, we propose a new standard for models of mating dynamics and parental care, emphasizing the clarity and use of mathematical and probabilistic arguments, the meaning of consistency conditions, and the key role of spatial densities and the law of mass action. We used adaptive dynamics to calculate the evolutionary trajectory of the total care duration. Our results clearly show how the outcomes of parental care evolution can be diverse, depending on the quantitative balance between a set of dynamical forces arising from relevant differences and conditions in the male and female populations. The intensity of sexual selection, synergy of care, care quality, and relative mortality rates during mating interactions and caring activities act as forces driving evolutionary transitions between uniparental and biparental care. Sexual selection reduces the care duration of the selected sex, uniparental care evolves in the sex that offers the higher care quality, higher mortality during mating interactions of one sex leads to more care by that sex, and higher mortality during caring activities of one sex favours the evolution of uniparental care in the other sex. Both synergy and higher overall mortality during mating interactions can stabilize biparental care when sexual selection reduces the care duration of the selected sex. We discuss how the interaction between these forces influences the evolution of care patterns, and how sex ratios can vary and be interpreted in these contexts. We also propose new directions for future developments of our integrative model, creating new comparable analyses that share the same underlying assumptions and dynamical frameworks.

Dominance analysis of competing protein assembly pathways

Most proteins form complexes consisting of two or more subunits, where complex assembly can proceed via two competing pathways: co-translational assembly of a mature and a nascent subunit, and post-translational assembly by two mature protein subunits. Assembly pathway dominance, i.e., which of the two pathways is predominant under which conditions, is poorly understood. Here, we introduce a reaction-diffusion system that describes protein complex formation via post- and co-translational assembly and use it to analyze the dominance of both pathways. Special features of this new system are (i) spatially inhomogeneous sources of reacting species, (ii) a combination of diffusing and immobile species, and (iii) an asymmetric binding competition between the species. We study assembly pathway dominance for the spatially homogeneous system and find that the ratio of production rates of the two protein subunits determines the long-term pathway dominance. This result is independent of the binding rate constants for post- and co-translational assembly and implies that a system with an initial post-translational assembly dominance can eventually exhibit co-translational assembly dominance and vice versa. For exactly balanced production of both subunits, the assembly pathway dominance is determined by the steady state concentration of the subunit that can bind both nascent and mature partners. The introduced system of equations can be applied to describe general dynamics of assembly processes involving both diffusing and immobile components.

GraphLncLoc: long non-coding RNA subcellular localization prediction using graph convolutional networks based on sequence to graph transformation

The subcellular localization of long non-coding RNAs (lncRNAs) is crucial for understanding lncRNA functions. Most of existing lncRNA subcellular localization prediction methods use k-mer frequency features to encode lncRNA sequences. However, k-mer frequency features lose sequence order information and fail to capture sequence patterns and motifs of different lengths. In this paper, we proposed GraphLncLoc, a graph convolutional network-based deep learning model, for predicting lncRNA subcellular localization. Unlike previous studies encoding lncRNA sequences by using k-mer frequency features, GraphLncLoc transforms lncRNA sequences into de Bruijn graphs, which transforms the sequence classification problem into a graph classification problem. To extract the high-level features from the de Bruijn graph, GraphLncLoc employs graph convolutional networks to learn latent representations. Then, the high-level feature vectors derived from de Bruijn graph are fed into a fully connected layer to perform the prediction task. Extensive experiments show that GraphLncLoc achieves better performance than traditional machine learning models and existing predictors. In addition, our analyses show that transforming sequences into graphs has more distinguishable features and is more robust than k-mer frequency features. The case study shows that GraphLncLoc can uncover important motifs for nucleus subcellular localization. GraphLncLoc web server is available at http://csuligroup.com:8000/GraphLncLoc/.

A dynamic compartment model for xylem loading and long-distance transport of iron explains the effect of kanamycin on metal uptake in Arabidopsis

Arabidopsis plants exposed to the antibiotic kanamycin (Kan) display altered metal homeostasis. Further, mutation of the WBC19 gene leads to increased sensitivity to kanamycin and changes in iron (Fe) and zinc (Zn) uptake. Here we propose a model that explain this surprising relationship between metal uptake and exposure to Kan. We first use knowledge about the metal uptake phenomenon to devise a transport and interaction diagram on which we base the construction of a dynamic compartment model. The model has three pathways for loading Fe and its chelators into the xylem. One pathway, involving an unknown transporter, loads Fe as a chelate with citrate (Ci) into the xylem. This transport step can be significantly inhibited by Kan. In parallel, FRD3 transports Ci into the xylem where it can chelate with free Fe. A third critical pathway involves WBC19, which transports metal-nicotianamine (NA), mainly as Fe-NA chelate, and possibly NA itself. To permit quantitative exploration and analysis, we use experimental time series data to parameterize this explanatory and predictive model. Its numerical analysis allows us to predict responses by a double mutant and explain the observed differences between data from wildtype, mutants and Kan inhibition experiments. Importantly, the model provides novel insights into metal homeostasis by permitting the reverse-engineering of mechanistic strategies with which the plant counteracts the effects of mutations and of the inhibition of iron transport by kanamycin.

Homeostasis and injectivity: a reaction network perspective

Homeostasis represents the idea that a feature may remain invariant despite changes in some external parameters. We establish a connection between homeostasis and injectivity for reaction network models. In particular, we show that a reaction network cannot exhibit homeostasis if a modified version of the network (which we call homeostasis-associated network) is injective. We provide examples of reaction networks which can or cannot exhibit homeostasis by analyzing the injectivity of their homeostasis-associated networks.

ANALYTICAL SINGULAR VALUE DECOMPOSITION FOR A CLASS OF STOICHIOMETRY MATRICES

We present the analytical singular value decomposition of the stoichiometry matrix for a spatially discrete reaction-diffusion system. The motivation for this work is to develop a matrix decomposition that can reveal hidden spatial flux patterns of chemical reactions. We consider a 1D domain with two subregions sharing a single common boundary. Each of the subregions is further partitioned into a finite number of compartments. Chemical reactions can occur within a compartment, whereas diffusion is represented as movement between adjacent compartments. Inspired by biology, we study both (1) the case where the reactions on each side of the boundary are different and only certain species diffuse across the boundary and (2) the case where reactions and diffusion are spatially homogeneous. We write the stoichiometry matrix for these two classes of systems using a Kronecker product formulation. For the first scenario, we apply linear perturbation theory to derive an approximate singular value decomposition in the limit as diffusion becomes much faster than reactions. For the second scenario, we derive an exact analytical singular value decomposition for all relative diffusion and reaction time scales. By writing the stoichiometry matrix using Kronecker products, we show that the singular vectors and values can also be written concisely using Kronecker products. Ultimately, we find that the singular value decomposition of the reaction-diffusion stoichiometry matrix depends on the singular value decompositions of smaller matrices. These smaller matrices represent modified versions of the reaction-only stoichiometry matrices and the analytically known diffusion-only stoichiometry matrix. Lastly, we present the singular value decomposition of the model for the Calvin cycle in cyanobacteria and demonstrate the accuracy of our formulation. The MATLAB code, available at www.github.com/MathBioCU/ReacDiffStoicSVD, provides routines for efficiently calculating the SVD for a given reaction network on a 1D spatial domain.

De-risking clinical trial failure through mechanistic simulation

Drug development typically comprises a combination of pre-clinical experimentation, clinical trials, and statistical data-driven analyses. Therapeutic failure in late-stage clinical development costs the pharmaceutical industry billions of USD per year. Clinical trial simulation represents a key derisking strategy and combining them with mechanistic models allows one to test hypotheses for mechanisms of failure and to improve trial designs. This is illustrated with a T-cell activation model, used to simulate the clinical trials of IMA901, a short-peptide cancer vaccine. Simulation results were consistent with observed outcomes and predicted that responses are limited by peptide off-rates, peptide competition for dendritic cell (DC) binding, and DC migration times. These insights were used to hypothesise alternate trial designs predicted to improve efficacy outcomes. This framework illustrates how mechanistic models can complement clinical, experimental, and data-driven studies to understand, test, and improve trial designs, and how results may differ between humans and mice.

Model-based translation of DNA damage signaling dynamics across cell types

Interindividual variability in DNA damage response (DDR) dynamics may evoke differences in susceptibility to cancer. However, pathway dynamics are often studied in cell lines as alternative to primary cells, disregarding variability. To compare DDR dynamics in the cell line HepG2 with primary human hepatocytes (PHHs), we developed a HepG2-based computational model that describes the dynamics of DDR regulator p53 and targets MDM2, p21 and BTG2. We used this model to generate simulations of virtual PHHs and compared the results to those for PHH donor samples. Correlations between baseline p53 and p21 or BTG2 mRNA expression in the absence and presence of DNA damage for HepG2-derived virtual samples matched the moderately positive correlations observed for 50 PHH donor samples, but not the negative correlations between p53 and its inhibitor MDM2. Model parameter manipulation that affected p53 or MDM2 dynamics was not sufficient to accurately explain the negative correlation between these genes. Thus, extrapolation from HepG2 to PHH can be done for some DDR elements, yet our analysis also reveals a knowledge gap within p53 pathway regulation, which makes such extrapolation inaccurate for the regulator MDM2. This illustrates the relevance of studying pathway dynamics in addition to gene expression comparisons to allow reliable translation of cellular responses from cell lines to primary cells. Overall, with our approach we show that dynamical modeling can be used to improve our understanding of the sources of interindividual variability of pathway dynamics.

Susceptibility to develop cancer varies among people, partially due to differences in genetic background. Ideally, healthy human-derived cells are used to investigate intracellular signaling pathways and their interindividual variability contributing to cancer susceptibility. Because cells from healthy human tissue are difficult to obtain and culture for periods longer than a few days, cell lines are often used as substitute. However, it is unclear to what extent signaling dynamics in cell lines represent dynamics in healthy human tissue. We asked whether we could reproduce interindividual variability in DNA damage response gene expression in a set of 50 human liver cell donors. Therefore, we built a mathematical model that simulates temporal expression dynamics of the DNA damage response in the HepG2 liver cell line upon chemical activation and used the simulations to create virtual donors. Our virtual donors displayed similar relations between genes as the samples from human donors, provided that we adjusted the strength of specific molecular interactions. Thus, our approach can be used to examine the applicability of widely used cell systems to healthy human tissue in terms of their dynamic responses.

Data-driven dynamical modelling of a pathogen-infected plant gene regulatory network: A comparative analysis

Recent advances in synthetic biology have enabled the design of genetic feedback control circuits that could be implemented to build resilient plants against pathogen attacks. To facilitate the proper design of these genetic feedback control circuits, an accurate model that is able to capture the vital dynamical behaviour of the pathogen-infected plant is required. In this study, using a data-driven modelling approach, we develop and compare four dynamical models (i.e. linear, Michaelis-Menten with Hill coefficient (Hill Function), standard S-System and extended S-System) of a pathogen-infected plant gene regulatory network (GRN). These models are then assessed across several criteria, i.e. ease of identifying the type of gene regulation, the predictive capability, Akaike Information Criterion (AIC) and the robustness to parameter uncertainty to determine its viability of balancing between biological complexity and accuracy when modelling the pathogen-infected plant GRN. Using our defined ranking score, we obtain the following insights to the modelling of GRN. Our analyses show that despite commonly used and provide biological relevance, the Hill Function model ranks the lowest while the extended S-System model ranks highest in the overall comparison. Interestingly, the performance of the linear model is more consistent throughout the comparison, making it the preferred model for this pathogen-infected plant GRN when considering data-driven modelling approach.

Discrete Biochemical Systems Theory

Almost every biomedical systems analysis requires early decisions regarding the choice of the most suitable representations to be used. De facto the most prevalent choice is a system of ordinary differential equations (ODEs). This framework is very popular because it is flexible and fairly easy to use. It is also supported by an enormous array of stand-alone programs for analysis, including many distinct numerical solvers that are implemented in the main programming languages. Having selected ODEs, the modeler must then choose a mathematical format for the equations. This selection is not trivial as nearly unlimited options exist and there is seldom objective guidance. The typical choices include ad hoc representations, default models like mass-action or Lotka-Volterra equations, and generic approximations. Within the realm of approximations, linear models are typically successful for analyses of engineered systems, but they are not as appropriate for biomedical phenomena, which often display nonlinear features such as saturation, threshold effects or limit cycle oscillations, and possibly even chaos. Power-law approximations are simple but overcome these limitations. They are the key ingredient of Biochemical Systems Theory (BST), which uses ODEs exclusively containing power-law representations for all processes within a model. BST models cover a vast repertoire of nonlinear responses and, at the same time, have structural properties that are advantageous for a wide range of analyses. Nonetheless, as all ODE models, the BST approach has limitations. In particular, it is not always straightforward to account for genuine discreteness, time delays, and stochastic processes. As a new option, we therefore propose here an alternative to BST in the form of discrete Biochemical Systems Theory (dBST). dBST models have the same generality and practicality as their BST-ODE counterparts, but they are readily implemented even in situations where ODEs struggle. As a case study, we illustrate dBST applied to the dynamics of the aryl hydrocarbon receptor (AhR), a signal transduction system that simultaneously involves time delays and stochasticity.

Rigorous Analysis of the Quasi-Steady-State Assumption in Enzyme Kinetics

We study, from a purely quantitative point of view, the quasi-steady-state assumption for the fundamental mathematical model of the general enzymatic reaction. In particular, (i) we introduce a simple, yet generic, algorithm for the proper scaling of the corresponding problem, (ii) we define the two essential parts (the standard and the reverse) of the quasi-steady-state assumption in a quantitative fashion, and (iii) we comment on the dispensable, although widely adopted, third part (the total) of it.

SMGen: A Generator of Synthetic Models of Biochemical Reaction Networks

Several software tools for the simulation and analysis of biochemical reaction networks have been developed in the last decades; however, assessing and comparing their computational performance in executing the typical tasks of computational systems biology can be limited by the lack of a standardized benchmarking approach. To overcome these limitations, we propose here a novel tool, named SMGen, designed to automatically generate synthetic models of reaction networks that, by construction, are characterized by relevant features (e.g., system connectivity and reaction discreteness) and non-trivial emergent dynamics of real biochemical networks. The generation of synthetic models in SMGen is based on the definition of an undirected graph consisting of a single connected component that, generally, results in a computationally demanding task; to speed up the overall process, SMGen exploits a main–worker paradigm. SMGen is also provided with a user-friendly graphical user interface, which allows the user to easily set up all the parameters required to generate a set of synthetic models with any number of reactions and species. We analysed the computational performance of SMGen by generating batches of symmetric and asymmetric reaction-based models (RBMs) of increasing size, showing how a different number of reactions and/or species affects the generation time. Our results show that when the number of reactions is higher than the number of species, SMGen has to identify and correct a large number of errors during the creation process of the RBMs, a circumstance that increases the running time. Still, SMGen can generate synthetic models with hundreds of species and reactions in less than 7 s.

Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods

Identifying the reactions that govern a dynamical biological system is a crucial but challenging task in systems biology. In this work, we present a data-driven method to infer the underlying biochemical reaction system governing a set of observed species concentrations over time. We formulate the problem as a regression over a large, but limited, mass-action constrained reaction space and utilize sparse Bayesian inference via the regularized horseshoe prior to produce robust, interpretable biochemical reaction networks, along with uncertainty estimates of parameters. The resulting systems of chemical reactions and posteriors inform the biologist of potentially several reaction systems that can be further investigated. We demonstrate the method on two examples of recovering the dynamics of an unknown reaction system, to illustrate the benefits of improved accuracy and information obtained.

Computational modeling of RNase, antisense ORF0 RNA, and intracellular compartmentation and their impact on the life cycle of the line retrotransposon

Nearly half of the human genome is occupied by repetitive sequences of ancient virus-like genetic elements. The largest class, comprising 17% of the genome, belong to the type 1 Long INterspersed Elements (LINE-1) and are the only class capable of autonomous propagation in the genome. When epigenetic silencing mechanisms of LINE-1 fail, the proteins encoded by LINE-1 engage in reverse transcription to make new copies of their own or other DNAs that are pasted back into the genome. To elucidate how LINE-1 is dysregulated as a result of carcinogen exposure, we developed a computational model of key elements in the LINE-1 lifecycle, namely, the role of cytosolic ribonuclease (RNase), RNA interference (RNAi) by the antisense ORF0 RNA, and sequestration of LINE-1 products into stress granules and multivesicular structures.

The model showed that when carcinogen exposure is represented as either a sudden increase in LINE-1 mRNA count, or as an increase in mRNA transcription rate, the retrotransposon copy number exhibits a distinct threshold behavior above which LINE-1 enters a positive feedback loop that allows the cDNA copy number to grow exponentially. We also found that most of the LINE-1 RNA was degraded via the RNAase pathway and that neither ORF0 RNAi, nor the sequestration of LINE-1 products into granules and multivesicular structures, played a significant role in regulating the retrotransposon’s life cycle. Several aspects of the prediction agree with experimental results and indicate that the model has significant potential to inform future experiments related to LINE-1 activation.

Low-Order Nonlinear Animal Model of Glucose Dynamics for a Bihormonal Intraperitoneal Artificial Pancreas

OBJECTIVE

The design of an Artificial Pancreas to regulate blood glucose levels requires reliable control methods. Model Predictive Control has emerged as a promising approach for glycemia control. However, model-based control methods require computationally simple and identifiable mathematical models that represent glucose dynamics accurately, which is challenging due to the complexity of glucose homeostasis.

METHODS

In this work, a simple model is deduced to estimate blood glucose concentration in subjects with Type 1 Diabetes Mellitus. Novel features in the model are power-law kinetics for intraperitoneal insulin absorption and a separate glucagon sensitivity state. Profile likelihood and a method based on singular value decomposition of the sensitivity matrix are carried out to assess parameter identifiability and guide a model reduction for improving the identification of parameters.

RESULTS

A reduced model with 10 parameters is obtained and calibrated, showing good fit to experimental data from pigs where insulin and glucagon boluses were delivered in the intraperitoneal cavity.

CONCLUSION

A simple model with power-law kinetics can accurately represent glucose dynamics submitted to intraperitoneal insulin and glucagon injections.

IMPORTANCE

The parameters of the reduced model were not found to lack of local practical or structural identifiability.

Uniqueness of weakly reversible and deficiency zero realizations of dynamical systems

A reaction network together with a choice of rate constants uniquely gives rise to a system of differential equations, according to the law of mass-action kinetics. On the other hand, different networks can generate the same dynamical system under mass-action kinetics. Therefore, the problem of identifying "the" underlying network of a dynamical system is not well-posed, in general. Here we show that the problem of identifying an underlying weakly reversible deficiency zero network is well-posed, in the sense that the solution is unique whenever it exists. This can be very useful in applications because from the perspective of both dynamics and network structure, a weakly reversible deficiency zero (WR₀) realization is the simplest possible one. Moreover, while mass-action systems can exhibit practically any dynamical behavior, including multistability, oscillations, and chaos, WR₀ systems are remarkably stable for any choice of rate constants: they have a unique positive steady state within each invariant polyhedron, and cannot give rise to oscillations or chaotic dynamics. We also prove that both of our hypotheses (i.e., weak reversibility and deficiency zero) are necessary for uniqueness.

DeepLncLoc: a deep learning framework for long non-coding RNA subcellular localization prediction based on subsequence embedding

Long non-coding RNAs (lncRNAs) are a class of RNA molecules with more than 200 nucleotides. A growing amount of evidence reveals that subcellular localization of lncRNAs can provide valuable insights into their biological functions. Existing computational methods for predicting lncRNA subcellular localization use k-mer features to encode lncRNA sequences. However, the sequence order information is lost by using only k-mer features. We proposed a deep learning framework, DeepLncLoc, to predict lncRNA subcellular localization. In DeepLncLoc, we introduced a new subsequence embedding method that keeps the order information of lncRNA sequences. The subsequence embedding method first divides a sequence into some consecutive subsequences and then extracts the patterns of each subsequence, last combines these patterns to obtain a complete representation of the lncRNA sequence. After that, a text convolutional neural network is employed to learn high-level features and perform the prediction task. Compared with traditional machine learning models, popular representation methods and existing predictors, DeepLncLoc achieved better performance, which shows that DeepLncLoc could effectively predict lncRNA subcellular localization. Our study not only presented a novel computational model for predicting lncRNA subcellular localization but also introduced a new subsequence embedding method which is expected to be applied in other sequence-based prediction tasks. The DeepLncLoc web server is freely accessible at http://bioinformatics.csu.edu.cn/DeepLncLoc/, and source code and datasets can be downloaded from https://github.com/CSUBioGroup/DeepLncLoc.

FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

Mathematical models of biochemical networks can largely facilitate the comprehension of the mechanisms at the basis of cellular processes, as well as the formulation of hypotheses that can be tested by means of targeted laboratory experiments. However, two issues might hamper the achievement of fruitful outcomes. On the one hand, detailed mechanistic models can involve hundreds or thousands of molecular species and their intermediate complexes, as well as hundreds or thousands of chemical reactions, a situation generally occurring in rule-based modeling. On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration, or to test the effect of perturbations. As a consequence, the computational capabilities of modern Central Processing Units can be easily overtaken, possibly making the modeling of biochemical networks a worthless or ineffective effort. To the aim of overcoming the limitations of the current state-of-the-art simulation approaches, we present in this paper FiCoS, a novel "black-box" deterministic simulator that effectively realizes both a fine-grained and a coarse-grained parallelization on Graphics Processing Units. In particular, FiCoS exploits two different integration methods, namely, the Dormand-Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations. We tested the performance of FiCoS against different deterministic simulators, by considering models of increasing size and by running analyses with increasing computational demands. FiCoS was able to dramatically speedup the computations up to 855×, showing to be a promising solution for the simulation and analysis of large-scale models of complex biological processes.

Data Driven Mathematical Model of FOLFIRI Treatment for Colon Cancer

Many colon cancer patients show resistance to their treatments. Therefore, it is important to consider unique characteristic of each tumor to find the best treatment options for each patient. In this study, we develop a data driven mathematical model for interaction between the tumor microenvironment and FOLFIRI drug agents in colon cancer. Patients are divided into five distinct clusters based on their estimated immune cell fractions obtained from their primary tumors' gene expression data. We then analyze the effects of drugs on cancer cells and immune cells in each group, and we observe different responses to the FOLFIRI drugs between patients in different immune groups. For instance, patients in cluster 3 with the highest T-reg/T-helper ratio respond better to the FOLFIRI treatment, while patients in cluster 2 with the lowest T-reg/T-helper ratio resist the treatment. Moreover, we use ROC curve to validate the model using the tumor status of the patients at their follow up, and the model predicts well for the earlier follow up days.

A systems biology approach to COVID-19 progression in population

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 of countries. Overall, we show that applications of uncommon strategies, such as methods and approaches from molecular systems biology research to mathematical epidemiology, may significantly advance our understanding of COVID-19 and other infectious diseases.

A model of dopamine and serotonin-kynurenine metabolism in cortisolemia: Implications for depression

A major factor contributing to the etiology of depression is a neurochemical imbalance of the dopaminergic and serotonergic systems, which is caused by persistently high levels of circulating stress hormones. Here, a computational model is proposed to investigate the interplay between dopaminergic and serotonergic-kynurenine metabolism under cortisolemia and its consequences for the onset of depression. The model was formulated as a set of nonlinear ordinary differential equations represented with power-law functions. Parameter values were obtained from experimental data reported in the literature, biological databases, and other general information, and subsequently fine-tuned through optimization. Model simulations predict that changes in the kynurenine pathway, caused by elevated levels of cortisol, can increase the risk of neurotoxicity and lead to increased levels of 3,4-dihydroxyphenylaceltahyde (DOPAL) and 5-hydroxyindoleacetaldehyde (5-HIAL). These aldehydes contribute to alpha-synuclein aggregation and may cause mitochondrial fragmentation. Further model analysis demonstrated that the inhibition of both serotonin transport and kynurenine-3-monooxygenase decreased the levels of DOPAL and 5-HIAL and the neurotoxic risk often associated with depression. The mathematical model was also able to predict a novel role of the dopamine and serotonin metabolites DOPAL and 5-HIAL in the ethiology of depression, which is facilitated through increased cortisol levels. Finally, the model analysis suggests treatment with a combination of inhibitors of serotonin transport and kynurenine-3-monooxygenase as a potentially effective pharmacological strategy to revert the slow-down in monoamine neurotransmission that is often triggered by inflammation.

Paradoxical relationships between active transport and global protein distributions in neurons

Neural function depends on continual synthesis and targeted trafficking of intracellular components, including ion channel proteins. Many kinds of ion channels are trafficked over long distances to specific cellular compartments. This raises the question of whether cargo is directed with high specificity during transit or whether cargo is distributed widely and sequestered at specific sites. We addressed this question by experimentally measuring transport and expression densities of Kv4.2, a voltage-gated transient potassium channel that exhibits a specific dendritic expression that increases with distance from the soma and little or no functional expression in axons. In over 500 h of quantitative live imaging, we found substantially higher densities of actively transported Kv4.2 subunits in axons as opposed to dendrites. This paradoxical relationship between functional expression and traffic density supports a model—commonly known as the sushi belt model—in which trafficking specificity is relatively low and active sequestration occurs in compartments where cargo is expressed. In further support of this model, we find that kinetics of active transport differs qualitatively between axons and dendrites, with axons exhibiting strong superdiffusivity, whereas dendritic transport resembles a weakly directed random walk, promoting mixing and opportunity for sequestration. Finally, we use our data to constrain a compartmental reaction-diffusion model that can recapitulate the known Kv4.2 density profile. Together, our results show how nontrivial expression patterns can be maintained over long distances with a relatively simple trafficking mechanism and how the hallmarks of a global trafficking mechanism can be revealed in the kinetics and density of cargo.

Exact Maximal Reduction Of Stochastic Reaction Networks By Species Lumping

MOTIVATION

Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortunately, in all but simplest models the resulting discrete state-space representation hinders analytical tractability and makes numerical simulations expensive. Reduction methods can lower complexity by computing model projections that preserve dynamics of interest to the user.

RESULTS

We present an exact lumping method for stochastic reaction networks with mass-action kinetics. It hinges on an equivalence relation between the species, resulting in a reduced network where the dynamics of each macro-species is stochastically equivalent to the sum of the original species in each equivalence class, for any choice of the initial state of the system. Furthermore, by an appropriate encoding of kinetic parameters as additional species, the method can establish equivalences that do not depend on specific values of the parameters. The method is supported by an efficient algorithm to compute the largest species equivalence, thus the maximal lumping. The effectiveness and scalability of our lumping technique, as well as the physical interpretability of resulting reductions, is demonstrated in several models of signaling pathways and epidemic processes on complex networks.

AVAILABILITY

The algorithms for species equivalence have been implemented in the software tool ERODE, freely available for download from https://www.erode.eu.

Integration of biology, mathematics and computing in the classroom through the creation and repeated use of transdisciplinary modules

The integration of biology with mathematics and computer science mandates the training of students capable of comfortably navigating among these fields. We address this formidable pedagogical challenge with the creation of transdisciplinary modules that guide students toward solving realistic problems with methods from different disciplines. Knowledge is gradually integrated as the same topic is revisited in biology, mathematics, and computer science courses. We illustrate this process with a module on the homeostasis and dynamic regulation of red blood cell production, which was first implemented in an introductory biology course and will be revisited in the mathematics and computer science curricula.

BOUNDEDNESS OF A CLASS OF SPATIALLY DISCRETE REACTION-DIFFUSION SYSTEMS

Although the spatially discrete reaction-diffusion equation is often used to describe biological processes, the effect of diffusion in this framework is not fully understood. In the spatially continuous case, the incorporation of diffusion can cause blow-up with respect to the L ∞ norm, and criteria exist to determine whether the system is bounded for all time. However, no equivalent criteria exist for the discrete reaction-diffusion system. Due to the possible dynamical differences between these two system types and the advantage of using the spatially discrete representation to describe biological processes, it is worth examining the discrete system independently of the continuous system. Therefore, the focus of this paper is on determining sufficient conditions to guarantee that the discrete reaction-diffusion system is bounded for all time. We consider reaction-diffusion systems on a 1D domain with homogeneous Neumann boundary conditions and nonnegative initial data and solutions. We define a Lyapunov-like function and show that its existence guarantees that the discrete reaction-diffusion system is bounded. These results are considered in the context of four example systems for which Lyapunov-like functions can and cannot be found.

Recent advances in constraint and machine learning-based metabolic modeling by leveraging stoichiometric balances, thermodynamic feasibility and kinetic law formalisms

Understanding the governing principles behind organisms' metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.

Data Driven Mathematical Model of Colon Cancer Progression

Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated macrophages, a higher activation rate of macrophages leads to an increase in cancer cell density, demonstrating a negative effect of macrophages. Other tumors however, exhibit an opposite trend, showing a positive effect of macrophages in controlling tumor size. Although the results indicate that for all patients the size of the tumor is sensitive to the parameters related to macrophages, such as their activation and death rate, this research demonstrates that no single biomarker could predict the dynamics of tumors.

Receptor Models of Phagocytosis: The Effect of Target Shape

Phagocytosis is a remarkably complex process, requiring simultaneous organisation of the cell membrane, the cytoskeleton, receptors and various signalling molecules. As can often be the case, mathematical modelling is able to penetrate some of this complexity, identifying the key biophysical components and generating understanding that would take far longer with a purely experimental approach. This chapter will review a particularly important class of phagocytosis model, championed in recent years, that primarily focuses on the role of receptors during the engulfment process. These models are pertinent to a host of unsolved questions in the subject, including the rate of cup growth during uptake, the role of both intra- and extracellular noise, and the precise differences between phagocytosis and other forms of endocytosis. In particular, this chapter will focus on the effect of target shape and orientation, including how these influence the rate and final outcome of phagocytic engulfment.

A simplified modelling framework facilitates more complex representations of plant circadian clocks

The circadian clock orchestrates biological processes so that they occur at specific times of the day, thereby facilitating adaptation to diurnal and seasonal environmental changes. In plants, mathematical modelling has been comprehensively integrated with experimental studies to gain a better mechanistic understanding of the complex genetic regulatory network comprising the clock. However, with an increasing number of circadian genes being discovered, there is a pressing need for methods facilitating the expansion of computational models to incorporate these newly-discovered components. Conventionally, plant clock models have comprised differential equation systems based on Michaelis-Menten kinetics. However, the difficulties associated with modifying interactions using this approach-and the concomitant problem of robustly identifying regulation types-has contributed to a complexity bottleneck, with quantitative fits to experimental data rapidly becoming computationally intractable for models possessing more than ≈50 parameters. Here, we address these issues by constructing the first plant clock models based on the S-System formalism originally developed by Savageau for analysing biochemical networks. We show that despite its relative simplicity, this approach yields clock models with comparable accuracy to the conventional Michaelis-Menten formalism. The S-System formulation also confers several key advantages in terms of model construction and expansion. In particular, it simplifies the inclusion of new interactions, whilst also facilitating the modification of regulation types, thereby making it well-suited to network inference. Furthermore, S-System models mitigate the issue of parameter identifiability. Finally, by applying linear systems theory to the models considered, we provide some justification for the increased use of aggregated protein equations in recent plant clock modelling, replacing the separate cytoplasmic/nuclear protein compartments that were characteristic of the earlier models. We conclude that as well as providing a simplified framework for model development, the S-System formalism also possesses significant potential as a robust modelling method for designing synthetic gene circuits.

The bioenergetics of integrin-based adhesion, from single molecule dynamics to stability of macromolecular complexes

The forces actively generated by motile cells must be transmitted to their environment in a spatiotemporally regulated manner, in order to produce directional cellular motion. This task is accomplished through integrin-based adhesions, large macromolecular complexes that link the actin-cytoskelton inside the cell to its external environment. Despite their relatively large size, adhesions exhibit rapid dynamics, switching between assembly and disassembly in response to chemical and mechanical cues exerted by cytoplasmic biochemical signals, and intracellular/extracellular forces, respectively. While in material science, force typically disrupts adhesive contact, in this biological system, force has a more nuanced effect, capable of causing assembly or disassembly. This initially puzzled experimentalists and theorists alike, but investigation into the mechanisms regulating adhesion dynamics have progressively elucidated the origin of these phenomena. This review provides an overview of recent studies focused on the theoretical understanding of adhesion assembly and disassembly as well as the experimental studies that motivated them. We first concentrate on the kinetics of integrin receptors, which exhibit a complex response to force, and then investigate how this response manifests itself in macromolecular adhesion complexes. We then turn our attention to studies of adhesion plaque dynamics that link integrins to the actin-cytoskeleton, and explain how force can influence the assembly/disassembly of these macromolecular structure. Subsequently, we analyze the effect of force on integrins populations across lengthscales larger than single adhesions. Finally, we cover some theoretical studies that have considered both integrins and the adhesion plaque and discuss some potential future avenues of research.

Global Positioning System: Understanding Long Noncoding RNAs through Subcellular Localization

The localization of long noncoding RNAs (lncRNAs) within the cell is the primary determinant of their molecular functions. LncRNAs are often thought of as chromatin-restricted regulators of gene transcription and chromatin structure. However, a rich population of cytoplasmic lncRNAs has come to light, with diverse roles including translational regulation, signaling, and respiration. RNA maps of increasing resolution and scope are revealing a subcellular world of highly specific localization patterns and hint at sequence-based address codes specifying lncRNA fates. We propose a new framework for analyzing sequencing-based data, which suggests that numbers of cytoplasmic lncRNA molecules rival those in the nucleus. New techniques promise to create high-resolution, transcriptome-wide maps associated with all organelles of the mammalian cell. Given its intimate link to molecular roles, subcellular localization provides a means of unlocking the mystery of lncRNA functions.

Modeling Long ncRNA-Mediated Regulation in the Mammalian Cell Cycle

Long noncoding RNAs (lncRNAs) are transcripts longer than 200 nucleotides that are not translated into proteins. They have recently gained widespread attention due to the finding that tens of thousands of lncRNAs reside in the human genome, and due to an increasing number of lncRNAs that are found to be associated with disease. Some lncRNAs, including disease-associated ones, play different roles in regulating the cell cycle. Mathematical models of the cell cycle have been useful in better understanding this biological system, such as how it could be robust to some perturbations and how the cell cycle checkpoints could act as a switch. Here, we discuss mathematical modeling techniques for studying lncRNA regulation of the mammalian cell cycle. We present examples on how modeling via network analysis and differential equations can provide novel predictions toward understanding cell cycle regulation in response to perturbations such as DNA damage.

Equilibrium, affinity, dissociation constants, IC5O: Facts and fantasies

The interaction between ligands and receptors is often described in terms of 50% inhibitory concentrations (IC50). However, IC50 values do not accurately reflect the dissociation constants (Kd), and the domain of application and precision of proposed approximations for Kd estimation are unclear. The effect of affinity and of experimental conditions on the differences between IC50 and Kd has been assessed from exact mass action law calculations and from computer simulations. Competitions between [¹¹¹ In]DTPA-indium and a few metal-DTPA complexes for binding to a specific antibody are discussed as a practical example. Exact calculations of competition assays have been implemented in Microsoft Excel and performed for a variety of concentrations of receptor, tracer, and competitor. The results are identical to those of software packages. IC50 is found larger than Kd by less than 20% only when tracer concentration is small compared with Kd and to the receptor concentration and when this receptor concentration is small compared with Kd. Otherwise, Kd and IC50 may be very different and approximations proposed in the literature to obtain Kd values from graphically derived IC50 are not acceptable as soon as the concentrations of tracer or of receptor approach Kd. Under most experimental conditions, IC50 values do not reflect Kd values. Using available software packages to determine and report Kd values would allow for more meaningful comparisons of results obtained under different experimental conditions.