Dynamics Of Biological Systems Research Articles

Advancing a biomechanical framework for cellular interaction and mechanotransduction analysis using data mining techniques

As biomechanics advances, understanding the structural and functional dynamics of biological systems at molecular and cellular levels becomes increasingly critical. This study investigates a biomechanical framework for analyzing cellular interaction forces and information flow in mechanotransduction processes. Leveraging Data Mining (DM) technology, we evaluate cellular system efficiency and adaptation mechanisms under varying biomechanical stimuli, simulating stress conditions akin to high parallel processing loads. The proposed algorithm achieves an accuracy of 95.27% in predicting cellular response behaviors, with system stability maintained above 90% under simulated mechanical stress. These findings highlight the potential of computational methods to enhance our understanding of cellular resilience and adaptation in biomechanical contexts. Ultimately, this work contributes to the development of robust, adaptive models for studying the mechanobiology of cells and tissues, advancing diagnostic and therapeutic approaches in molecular and cellular biomechanics.

Population and within-host dynamics of biological systems

Population and within-host dynamics of biological systems

Element-wise and recursive solutions for the power spectral density of biological stochastic dynamical systems at fixed points

Stochasticity plays a central role in nearly every biological process, and the noise power spectral density (PSD) is a critical tool for understanding variability and information processing in living systems. In steady state, many such processes can be described by stochastic linear time-invariant (LTI) systems driven by Gaussian white noise, whose PSD is a complex rational function of the frequency that can be concisely expressed in terms of their Jacobian, dispersion, and diffusion matrices, fully defining the statistical properties of the system's dynamics at steady state. Here, we arrive at compact, element-wise solutions of the rational function coefficients for the auto- and cross-spectrum that enable the explicit analytical computation of the PSD in dimensions n=2,3,4. We further present a recursive Leverrier-Faddeev-type algorithm for the exact computation of the rational function coefficients. Crucially, both solutions are free of matrix inverses. We illustrate our element-wise and recursive solutions by considering the stochastic dynamics of neural systems models, namely, FitzHugh-Nagumo (n=2), Hindmarsh-Rose (n=3), Wilson-Cowan (n=4), and the stabilized supralinear network (n=22), as well as an evolutionary game-theoretic model with mutations (n=5,31). We extend our approach to derive a recursive method for calculating the coefficients in the power-series expansion of the integrated covariance matrix for interacting spiking neurons modeled as Hawkes processes on arbitrary directed graphs. Published by the American Physical Society 2024

DynProfiler: a Python package for comprehensive analysis and interpretation of signaling dynamics leveraged by deep learning techniques.

Signaling dynamics encode important features and regulatory mechanisms of biological systems, and recent studies have reported the use of simulated signaling dynamics with mechanistic modeling as biomarkers for human diseases. Given the success of deep learning techniques, it is expected that they can extract informative patterns from simulation results more effectively than traditional approaches involving manual feature selection, which can be used for subsequent analyses, such as patient stratification and survival prediction. Here, we propose DynProfiler, which utilizes the entire signaling dynamics, including intermediate variables, as input and leverages deep learning techniques to extract informative features without requiring any labels. Furthermore, DynProfiler incorporates a modern explainable AI solution to provide quantitative time-dependent importance scores for each dynamics. Using simulated dynamics of patients with breast cancer as an example, we demonstrate DynProfiler's ability to extract high-quality features that can predict mortality risk and identify important dynamics, highlighting upregulated phosphorylated GSK3β as a biomarker for poor prognosis. Overall, this tool can be useful for clinical application, as well as for elucidating biological system dynamics. The DynProfiler Python library is available in GitHub at https://github.com/okadalabipr/DynProfiler.

Utilising an in silico model to predict outcomes in senescence-driven acute liver injury

Currently liver transplantation is the only treatment option for liver disease, but organ availability cannot meet patient demand. Alternative regenerative therapies, including cell transplantation, aim to modulate the injured microenvironment from inflammation and scarring towards regeneration. The complexity of the liver injury response makes it challenging to identify suitable therapeutic targets when relying on experimental approaches alone. Therefore, we adopted a combined in vivo-in silico approach and developed an ordinary differential equation model of acute liver disease able to predict the host response to injury and potential interventions. The Mdm2fl/fl mouse model of senescence-driven liver injury was used to generate a quantitative dynamic characterisation of the key cellular players (macrophages, endothelial cells, myofibroblasts) and extra cellular matrix involved in liver injury. This was qualitatively captured by the mathematical model. The mathematical model was then used to predict injury outcomes in response to milder and more severe levels of senescence-induced liver injury and validated with experimental in vivo data. In silico experiments using the validated model were then performed to interrogate potential approaches to enhance regeneration. These predicted that increasing the rate of macrophage phenotypic switch or increasing the number of pro-regenerative macrophages in the system will accelerate the rate of senescent cell clearance and resolution. These results showcase the potential benefits of mechanistic mathematical modelling for capturing the dynamics of complex biological systems and identifying therapeutic interventions that may enhance our understanding of injury-repair mechanisms and reduce translational bottlenecks.

On a Symmetry-Based Structural Deterministic Fractal Fractional Order Mathematical Model to Investigate Conjunctivitis Adenovirus Disease

In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional order derivatives. A complementary method involves analyzing the system of fractal fractional order equations by considering the set of symmetries of its solutions. By characterizing structures that relate to the fundamental dynamics of biological systems, symmetries offer a potent notion for the creation of mechanistic models. This study investigates a novel mathematical model for conjunctivitis adenovirus disease. Conjunctivitis is an infection in the eye that is caused by adenovirus, also known as pink eye disease. Adenovirus is a common virus that affects the eye’s mucosa. Infectious conjunctivitis is most common eye disease on the planet, impacting individuals across all age groups and demographics. We have formulated a model to investigate the transmission of the aforesaid disease and the impact of vaccination on its dynamics. Also, using mathematical analysis, the percentage of a population which needs vaccination to prevent the spreading of the mentioned disease can be investigated. Fractal fractional derivatives have been widely used in the last few years to study different infectious disease models. Hence, being inspired by the importance of fractal fractional theory to investigate the mentioned human eye-related disease, we derived some adequate results for the above model, including equilibrium points, reproductive number, and sensitivity analysis. Furthermore, by utilizing fixed point theory and numerical techniques, adequate requirements were established for the existence theory, Ulam–Hyers stability, and approximate solutions. We used nonlinear functional analysis and fixed point theory for the qualitative theory. We have graphically simulated the outcomes for several fractal fractional order levels using the numerical method.

A three-dimensional discrete fractional-order HIV-1 model related to cancer cells, dynamical analysis and chaos control

In this paper, we study a three-dimensional discrete-time model to describe the behavior of cancer cells in the presence of healthy cells and HIV-infected cells. Based on the Caputo-like difference operator, we construct the fractional-order biological system. This study's significance lies in developing a new approach to presenting a biological dynamical system. Since the qualitative analysis related to existence, uniqueness, and stability is almost the same as can be found in numerous existing papers, and comparing this study to other research, constructing a biological discrete system using the Caputo difference operator can be particularly important. Using powerful tools of nonlinear theory such as phase plots, bifurcation diagrams, Lyapunov exponent spectrum, and the 0-1 test, we establish that the proposed system can exhibit different biological states, including stable, periodic, and chaotic behaviors. Here, the route leading to chaos is period-doubling bifurcation. Furthermore, the level of chaos in the system is quantified using $C_{0}$ complexity and approximate entropy algorithms. The stabilization or suppression of chaotic motions in the fractional-order system is presented, where an efficient controller is designed based on the stability theory of the discrete-time fractional-order systems. Numerical simulations are provided to validate the theoretical results derived in this research paper.

Changes in ROS/RNS Levels in Endothelial Cells in Experimental Bacteremia.

A high-precision system was developed for the quantification of biological analytes in single cells (reactive oxygen species (ROS) and reactive nitrogen species (RNS)) based on the electrochemical amperometric method. The efficacy of this system was evaluated using an experimental bacteremia model. Endothelial cells exhibited increased ROS/RNS production when stimulated by Staphylococcus aureus. However, they remained inactive when exposed to either unprimed or primed neutrophils that had been pre-incubated with bacteria. It is noteworthy that the sequential stimulation of endothelial cells with bacteria followed by neutrophils resulted in a significant increase in the ROS/RNS level, which demonstrated a correlation with the number of neutrophils in contact with the endothelial cells. These results highlight the potential of our system to quantitatively assess ROS/RNS dynamics in complex biological systems. They also offer insights into the interplay between various cellular components in experimental bacteremia.

Challenges in Understanding the Biological and Pharmacological Responses Based on Emergent Complexity in Biological Systems: From Bone Metabolism to General Physiology

Biological systems are complex, and although researchers strive to understand them, the accumulated knowledge often complicates integrative comprehension. Consolidating this knowledge can provide insights into the landscape of specific biological events. Our study on bone metabolism, focusing on the behavior of the receptor activator of nuclear factor kappa B (RANK) and its ligand (RANKL) highlighted the challenges in understanding its role across different cell types. At the same time, the study underscores the importance of exploring interactions between various players (cell types and genes/proteins) in complex systems, which is a core focus of systems biology. Analysis by mathematical models is a potentially powerful tool for describing the dynamic behavior of components in the interaction networks. However, such model-based analyses are limited by parameter availability and reliability. To address this, we proposed two approaches, i.e., sequential simulation and system-wide behavior constraints. Sequential simulation of small dynamic models offers potential in reproducing behavior in larger networks, as seen in toxicity analysis of sunitinib-related adverse effects. System-wide constraints derived from "homeostasis" help reduce the parameter search space in large-scale models, as demonstrated in model-based analysis of the effects of non-steroidal anti-inflammatory drugs (NSAIDs) on the arachidonic acid pathway. These analytical approaches offer insights into biological system dynamics and can enhance our understanding of pharmacological effects that result from perturbations in complexities of biological systems.

Molecular mechanisms of precise timing in cell lysis

Many biological systems exhibit precise timing of events, and one of the most known examples is cell lysis, which is a process of breaking bacterial host cells in the virus infection cycle. However, the underlying microscopic picture of precise timing remains not well understood. We present a novel theoretical approach to explain the molecular mechanisms of effectively deterministic dynamics in biological systems. Our hypothesis is based on the idea of stochastic coupling between relevant underlying biophysical and biochemical processes that lead to noise cancellation. To test this hypothesis, we introduced a minimal discrete-state stochastic model to investigate how holin proteins produced by bacteriophages break the inner membranes of gram-negative bacteria. By explicitly solving this model, the dynamic properties of cell lysis are fully evaluated, and theoretical predictions quantitatively agree with available experimental data for both wild-type and holin mutants. It is found that the observed threshold-like behavior is a result of the balance between holin proteins entering the membrane and leaving the membrane during the lysis. Theoretical analysis suggests that the cell lysis achieves precise timing for wild-type species by maximizing the number of holins in the membrane and narrowing their spatial distribution. In contrast, for mutated species, these conditions are not satisfied. Our theoretical approach presents a possible molecular picture of precise dynamic regulation in intrinsically random biological processes.

Quantifying superimposed protein flow dynamics in live cells using spatial filtering and spatiotemporal image correlation spectroscopy.

Flow or collective movement is a frequently observed phenomenon for many cellular components including the cytoskeletal proteins actin and myosin. To study protein flow in living cells, we and others have previously used spatiotemporal image correlation spectroscopy (STICS) analysis on fluorescence microscopy image time series. Yet, in cells, multiple protein flows often occur simultaneously on different scales resulting in superimposed fluorescence intensity fluctuations that are challenging to separate using STICS. Here, we exploited the characteristic that distinct protein flows often occur at different spatial scales present in the image series to disentangle superimposed protein flow dynamics. We employed a newly developed and an established spatial filtering algorithm to alternatively accentuate or attenuate local image intensity heterogeneity across different spatial scales. Subsequently, we analysed the spatially filtered time series with STICS, allowing the quantification of two distinct superimposed flows within the image time series. As a proof of principle of our analysis approach, we used simulated fluorescence intensity fluctuations as well as time series of nonmuscle myosin II in endothelial cells and actin-based podosomes in dendritic cells and revealed simultaneously occurring contiguous and noncontiguous flow dynamics in each of these systems. Altogether, this work extends the application of STICS for the quantification of multiple protein flow dynamics in complex biological systems including the actomyosin cytoskeleton.

Instabilities and self–organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID–19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread–anchored in physical considerations–lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing–type instabilities, and the concomitant emergence of steady–state patterns under the interplay between three critical model parameters–the saturation parameter, the noise intensity, and the transmission rate. Employing a second–order perturbation analysis to investigate stability, we uncover both diffusion–driven and noise–induced instabilities and corresponding self–organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

A versatile tissue-rolling technique for spatial-omics analyses of the entire murine gastrointestinal tract.

Tissues are dynamic and complex biological systems composed of specialized cell types that interact with each other for proper biological function. To comprehensively characterize and understand the cell circuitry underlying biological processes within tissues, it is crucial to preserve their spatial information. Here we report a simple mounting technique to maximize the area of the tissue to be analyzed, encompassing the whole length of the murine gastrointestinal (GI) tract, from mouth to rectum. Using this method, analysis of the whole murine GI tract can be performed in a single slide not only by means of histological staining, immunohistochemistry and in situ hybridization but also by multiplexed antibody staining and spatial transcriptomic approaches. We demonstrate the utility of our method in generating a comprehensive gene and protein expression profile of the whole GI tract by combining the versatile tissue-rolling technique with a cutting-edge transcriptomics method (Visium) and two cutting-edge proteomics methods (ChipCytometry and CODEX-PhenoCycler) in a systematic and easy-to-follow step-by-step procedure. The entire process, including tissue rolling, processing and sectioning, can be achieved within 2-3 d for all three methods. For Visium spatial transcriptomics, an additional 2 d are needed, whereas for spatial proteomics assays (ChipCytometry and CODEX-PhenoCycler), another 3-4 d might be considered. The whole process can be accomplished by researchers with skills in performing murine surgery, and standard histological and molecular biology methods.

A perspective on active glassy dynamics in biological systems

AbstractDynamics is central to living systems. Many experiments in the last two decades have revealed glassy dynamics in diverse biological systems, showing a transition between a solid-like and a fluid-like state. The biological systems have nontrivial characteristics: they are active with novel control parameters and immense complexity. Moreover, glassiness in these systems has many nontrivial features, such as the behavior of dynamical heterogeneity and readily found sub-Arrhenius relaxation dynamics. Theoretical treatments of these systems are generally challenging due to their nonequilibrium nature and large number of control parameters. We first discuss the primary characteristics of a glassy system and then review the experiments that started this field and simulations that have led to a deeper understanding. We also show that despite many challenges in these systems, it has been possible to develop theories that have played a significant role in unifying diverse phenomena and bringing insights. The field is at the interface of physics and biology, freely borrowing tools from both disciplines. We first discuss the known equilibrium scenario and then present the primary changes under activity.

Possible future evolutionary consequences to Homo as a result of the implementation of biotechnology

Biotechnology has become one of the most powerful forces on the planet, since it is capable of altering life processes at a molecular level. Since human bodies are dynamic biological systems, medicine requires to understand the evolutionary antecedents of Homo, especially in relation to neurohormonal regulation. Furthermore, increasing human dependence on biotechnology has led to relaxed natural selection in Homo, with subsequent increase of genetic load. In this paper, we speculate on the possible consequences of the application of parsimoniously derived biotechnologies onto the biological system of humans, with special attention to three areas: 1. human brain augmentation; 2. biotechnology and public health; 3. relaxed natural selection and genetic load. Human ability to manipulate and alter the structure and function of the body may not only make natural selection redundant but will be guided by a teleology whose purpose will seek to improve upon nature’s design.

A science-driven approach to optimize the design for a biological small-angle neutron scattering instrument

Biological small-angle neutron scattering (SANS) instruments facilitate critical analysis of the structure and dynamics of complex biological systems. However, with the growth of experimental demands and the advances in optical systems design, a new neutron optical concept is necessary to overcome the limitations of current instruments. This work presents an approach to include experimental objectives (i.e. the science to be supported by a specific neutron scattering instrument) in the optimization of the neutron optical concept. The approach for a proposed SANS instrument at the Second Target Station of the Spallation Neutron Source at Oak Ridge National Laboratory, USA, is presented here. The instrument is simulated with the McStas software package. The optimization process is driven by an evolutionary algorithm using McStas output data, which are processed to calculate an objective function designed to quantify the expected performance of the simulated neutron optical configuration for the intended purpose. Each McStas simulation covers the complete instrument, from source to detector, including realistic sample scattering functions. This approach effectively navigates a high-dimensional parameter space that is otherwise intractable; it allows the design of next-generation SANS instruments to address specific scientific cases and has the potential to increase instrument performance compared with traditional design approaches.

Quantifying Microsecond Solution-Phase Conformational Dynamics of a DNA Hairpin at the Single-Molecule Level.

Quantifying the rapid conformational dynamics of biological systems is fundamental to understanding the mechanism. However, biomolecules are complex, often containing static and dynamic heterogeneity, thus motivating the use of single-molecule methods, particularly those that can operate in solution. In this study, we measure microsecond conformational dynamics of solution-phase DNA hairpins at the single-molecule level using an anti-Brownian electrokinetic (ABEL) trap. Different conformational states were distinguished by their fluorescence lifetimes, and kinetic parameters describing transitions between these states were determined using two-dimensional fluorescence lifetime correlation (2DFLCS) analysis. Rather than combining fluorescence signals from the entire data set ensemble, long observation times of individual molecules allowed ABEL-2DFLCS to be performed on each molecule independently, yielding the underlying distribution of the system's kinetic parameters. ABEL-2DFLCS on the DNA hairpins resolved an underlying heterogeneity of fluorescence lifetimes and provided signatures of two-state exponential dynamics with rapid (<millisecond) transition times between states without observation of the substantially stretched exponential kinetics that had been observed in previous measurements on diffusing molecules. Numerical simulations were performed to validate the accuracy of this technique and the effects the underlying heterogeneity has on the analysis. Finally, ABEL-2DFLCS was performed on a mixture of hairpins and used to resolve their kinetic data.

A genetically encoded biosensor to monitor dynamic changes of c-di-GMP with high temporal resolution

Monitoring changes of signaling molecules and metabolites with high temporal resolution is key to understanding dynamic biological systems. Here, we use directed evolution to develop a genetically encoded ratiometric biosensor for c-di-GMP, a ubiquitous bacterial second messenger regulating important biological processes like motility, surface attachment, virulence and persistence. The resulting biosensor, cdGreen2, faithfully tracks c-di-GMP in single cells and with high temporal resolution over extended imaging times, making it possible to resolve regulatory networks driving bimodal developmental programs in different bacterial model organisms. We further adopt cdGreen2 as a simple tool for in vitro studies, facilitating high-throughput screens for compounds interfering with c-di-GMP signaling and biofilm formation. The sensitivity and versatility of cdGreen2 could help reveal c-di-GMP dynamics in a broad range of microorganisms with high temporal resolution. Its design principles could also serve as a blueprint for the development of similar, orthogonal biosensors for other signaling molecules, metabolites and antibiotics.

QM/MM Free Energy Calculations of Long-Range Biological Protonation Dynamics by Adaptive and Focused Sampling.

Water-mediated proton transfer reactions are central for catalytic processes in a wide range of biochemical systems, ranging from biological energy conversion to chemical transformations in the metabolism. Yet, the accurate computational treatment of such complex biochemical reactions is highly challenging and requires the application of multiscale methods, in particular hybrid quantum/classical (QM/MM) approaches combined with free energy simulations. Here, we combine the unique exploration power of new advanced sampling methods with density functional theory (DFT)-based QM/MM free energy methods for multiscale simulations of long-range protonation dynamics in biological systems. In this regard, we show that combining multiple walkers/well-tempered metadynamics with an extended system adaptive biasing force method (MWE) provides a powerful approach for exploration of water-mediated proton transfer reactions in complex biochemical systems. We compare and combine the MWE method also with QM/MM umbrella sampling and explore the sampling of the free energy landscape with both geometric (linear combination of proton transfer distances) and physical (center of excess charge) reaction coordinates and show how these affect the convergence of the potential of mean force (PMF) and the activation free energy. We find that the QM/MM-MWE method can efficiently explore both direct and water-mediated proton transfer pathways together with forward and reverse hole transfer mechanisms in the highly complex proton channel of respiratory Complex I, while the QM/MM-US approach shows a systematic convergence of selected long-range proton transfer pathways. In this regard, we show that the PMF along multiple proton transfer pathways is recovered by combining the strengths of both approaches in a QM/MM-MWE/focused US (FUS) scheme and reveals new mechanistic insight into the proton transfer principles of Complex I. Our findings provide a promising basis for the quantitative multiscale simulations of long-range proton transfer reactions in biological systems.

On Numerical Simulations of Variable-Order Fractional Cable Equation Arising in Neuronal Dynamics

In recent years, various complex systems and real-world phenomena have been shown to include memory and hereditary properties that change with respect to time, space, or other variables. Consequently, fractional partial differential equations containing variable-order fractional operators have been extensively resorted for modeling such phenomena accurately. In this paper, we consider the two-dimensional fractional cable equation with the Caputo variable-order fractional derivative in the time direction, which is preferable for describing neuronal dynamics in biological systems. A point-wise scheme, namely, the Crank–Nicolson finite difference method, along with a group-wise scheme referred to as the explicit decoupled group method are proposed to solve the problem under consideration. The stability and convergence analyses of the numerical schemes are provided with complete details. To demonstrate the validity of the proposed methods, numerical simulations with results represented in tabular and graphical forms are given. A quantitative analysis based on the CPU timing, iteration counting, and maximum absolute error indicates that the explicit decoupled group method is more efficient than the Crank–Nicolson finite difference scheme for solving the variable-order fractional equation.