Predicting protein-ligand binding affinity is a fundamental challenge in drug discovery. Recent advances in deep learning have led to the development of numerous models, many of which rely on three-dimensional protein-ligand complex structures and focus primarily on affinity prediction. In this study, we introduce an Algebraic Graph Neural Network (AGNN) model designed to encode molecular structures into a low-dimensional graph representation while preserving critical biochemical interactions. While algebraic graph theory has been widely used in physical modeling and molecular studies, traditional methods often struggle to accurately capture the complexity of biomolecular interactions. To address this limitation, our proposed AGNN model leverages multiscale weighted colored subgraphs to describe molecular interactions through a graph neural network. These representations allow the model to effectively learn the geometric and topological features of protein-ligand complexes. The AGNN model integrates graph convolution layers and attention mechanisms to refine feature extraction and improve the interpretability of learned embeddings. Furthermore, we incorporate gradient boosting decision trees (GBDTs) to enhance the prediction of binding affinities by capturing nonlinear relationships between molecular features. Our approach is extensively validated using benchmark datasets, including PDBBind and CASF-2016, demonstrating superior performance in binding affinity prediction compared to state-of-the-art scoring functions.
This study focusses on one-dimensional (1D) modeling of transient transdermal drug delivery across the epidermis via stratum corneum. In order to mimic in this manuscript how drugs pass through the skin, Fick’s second law has been incorporated as a flow governing equation in microneedles and is solved using a Lattice Boltzmann model. In this study we have assumed that the contact region between skin and drug as a point. To depict this phenomenon, the effect of parameters such as time duration, diffusion coefficient, length of the microneedle, initial drug concentration, cumulative flux and fraction of the drug delivered has been investigated. To validate the present model, the obtained results are compared with an existing analytical results.
Blood is a multifaceted colloidal suspension of plasma as an aqueous electrolyte-protein fluid and cellular components, mainly red blood cells, the rheology of which is influenced by mutually reinforcing hydrodynamic and chemical interactions, such as protein-mediated aggregation, plasma composition, and solute transport. These physicochemical interactions are magnified in stenosed micro vessels resulting in great changes in effective viscosity and haematocrit distribution. The present study develops a theoretical two-layer model in order to explain the synergistic action of stenosis and microcirculation on Jeffrey fluid dynamics. The middle region is modelled as a viscoelastic Jeffrey fluid, which considers the red blood cell elasticity and shear-thinning effect, and the outer layer as a Newtonian plasma. The governing equations are analytically solved with slip boundary conditions and mild stenosis with analytic expressions of velocity profiles, flow flux, effective viscosity, core haematocrit, and mean haematocrit. The findings indicate that an effective viscosity is positively proportional to stenosis height, channel half-width and slip parameter and negatively related to the Jeffrey parameter, and thus, the interplay between the viscous recovery of red blood cells and the breakup of plasma-protein networks induced by shear is demonstrated. Moreover, core and mean haematocrit drop off with a growing degree of stenosis and slip, as predicted by the Fahraeus-Lindqvist effect and the law of colloidal segregation. The suggested framework combines rheological modelling and chemical understanding connecting the flow changes caused by stenosis with the transport of solutes, reaction-diffusion dynamics, and drug and nanoparticle delivery efficacy, which provides a chemically informed view of hemorheology with potential biomedical chemistry, pharmaceutical formulation, and clinical diagnostics applications.
Three-phase fluid-structure interaction (FSI) problems couple the motion of solid structures and two different fluids, often exhibiting complex dynamics and posing challenges for computational investigation. The main objective of this paper is to present a new computational framework for the modeling, simulation, and application of such problems. To that end, we propose an integrated numerical algorithm that utilizes the volume of fluid method for the two-fluid flow and the immersed boundary method for the fluid-solid interaction, with a special emphasis on three-phase FSI computation in micro-scale settings. To demonstrate our methodology, we conduct a pilot FSI study on cellulose microfibrils in plant cell walls by simulating the interaction between microfibrils and two fluids, pectin and water. We investigate the evolution of the flow fields, the speed and spatial organization of the microfibrils, and the impact of different initial settings on microfibril dynamics. We find that the microfibril-pectin-water interaction leads to transversely oriented microfibrils with respect to the elongation axis of the plant cell. The simulation results indicate that our methodology may provide a novel approach to investigate the complex behavior of microfibrils and gain insights into the intrinsic dynamical properties of such microstructures.
The research on cancer cells has proposed many hypotheses as a basic conceptual framework for understanding how normal cells transform into cancer cells. Cancer cells are assumed to undergo a multilevel mutation process from normal cells to cancer cells. A kinetics model of the multistep transformation of normal cells into cancer cells was developed to provide insight into the fundamental aspects of cancer cell evolution. The kinetic model is composed of coupled ordinary differential equations to describe the mutation process. This combination of equations can describe how mutational processes, such as angiogenesis, cell death rates, genetic instability, and replication rates. The main predictions of the multistep mutation model are based on the fastest-growing cancer cells. The new estimation method was used in this study to estimate the parameters in the kinetics model. Parameters were estimated using the particle swarm optimization algorithm. A new technique in this study, parameters are estimated to obtain the possible contribution of each parameter to the fastest-growing cancer cells. The results of this study present a new estimate of the multilevel mutation process based on parameters from breast cancer data.
We develop a crossbridge model in which an attached crossbridge behaves like a linear spring with a variable rest length. We assume in particular that the rest length has a linear force–velocity relation, and that the force and rest length are both zero at the moment of crossbridge attachment. Crossbridges that are not attached in our model have a fixed probability per unit time of attachment, and attached crossbridges have a probability per unit time of detachment that is a function of the crossbridge force. This detachment rate is uniquely determined by the requirement that a limiting form of the model should reproduce the force-velocity curve and heat of shortening discovered by A.V. Hill (A. V. Hill, The heat of shortening and the dynamic constants of muscle, Proc. Roy. Soc. Lond. B – Biol. Sci. 126 (1938), 136–195), and the detachment rate turns out to be a linearly decreasing function of the crossbridge force. The parameters of the model are determined by a fit to steady-state experimental data; and then an event-driven stochastic simulation methodology is introduced in order to study the behavior of the model in a simulated quick-release experiment. The model explains how the crossbridge can act like a linear spring on a fast time scale but have very different properties on a slower time scale.
To examine the dynamics of a predator’s interaction with two prey species, this study develops a comprehensive mathematical model that accounts for ecological complexities, including the Allee effect, prey switching behavior, and prey refuge. The presence of multiple prey in the natural environment allows predators to switch between two prey whenever conditions warrant, including the predilection for one prey over the other and, more realistically, the reality of competition in the wild. In this work, a specific type of functional response to switching was described, involving a refuge factor that is more abundant in the first prey species than in the others. Based on the proposed biological model, the first prey uses refuge to evade predators, while the second prey is in danger and has an Allee threshold that affects its breeding efficiency. However, as the number of conspecific prey decreases, prey switching occurs. A single predator–prey situation cannot be a stable state, but in the absence of a predator and the presence of two prey species, a stable state can coexist. The equilibrium points of the system are determined analytically, and their local and global stability is thoroughly investigated using Lyapunov functions and Jacobian analysis. The theoretical results are validated by numerical simulations, which also demonstrate how changes in key parameters affect system behavior. The results highlight how the interaction of ecological factors and switching behavior can either stabilize or destabilize population dynamics by revealing critical thresholds for predator survival and prey coexistence.
A mathematical model is designed to investigate transmission dynamics of COVID-19 in a setting where both horizontal and vertical transmission of COVID-19 occur concurrently. The model incorporated two nonlinear vertical transmission routes of COVID-19, namely transmission of the COVID-19 to the fetus and also due to exposure at birth. Theoretical analysis revealed that nonlinear vertical transmission induces backward bifurcation phenomenon where COVID-19 exist even when basic reproduction number is below unity. Other bifurcation structure exhibited by the model is the atypical hysteresis effect. Time profiles disclosed that saturating constants associated with nonlinear vertical transmission rates cause a delay in the COVID-19 peak. The nonlinear autonomous model was transformed to a nonlinear non-autonomous model through incorporation of time-dependent controls. Numerical findings showed that optimal vaccination of susceptible individuals and optimal management of infectious cohort have the most beneficial impact, while monitoring of recovered individuals with the aim of preventing loss of infection-acquired immunity has the least benefit. Further, combination of optimal vaccination of susceptible and optimal management of infectious individuals was shown to have the highest efficiency index, demonstrating the capacity of the combined control measures to avert the most COVID-19 cases in the population.
We have developed a quadratic control policy describing permeability switching transients in a biological membrane and the mechanisms which govern nerve conduction regulation. The basis of our control policy is discussed in the context of solutions of the Hodgkin–Huxley equations of ionic hypothesis. The motivation behind identifying membrane switching transients lies in understanding the morphology of neural regulation during an action potential event. The novelty of identifying a formal membrane control policy lies in providing how a membrane effectively adapts to changes in permeability and through what governing mechanisms. Our control policy is developed using Lyapunov’s stability criteria. Our policy describes the inherent mechanisms of the membrane that act to drive its permeability from unstable firing to the resting potential state. We demonstrate that these permeability changes in state are governed by a switching function that depends on the membrane potential and a dominant ionic controlling parameter.
Aspirin, one of the most widely produced and consumed pharmaceuticals globally, presents an ideal case for exploring sustainable synthesis methods in pharmaceutical manufacturing. The conventional synthesis of aspirin, though widely practiced, often suffers from inefficiencies, excessive waste generation, and environmental concerns. This study presents a graph-theoretical framework for optimizing the aspirin synthesis pathway with a quantifiable alignment to green chemistry principles. A directed weighted graph was constructed, representing chemical species as nodes and reactions as edges, with weights derived from empirical reaction energy barriers and environmental impact metrics. Dynamic optimization algorithms, including an adaptation of the Bellman-Ford algorithm and cycle basis analysis, were employed to minimize total energy consumption and waste output. The proposed model achieved a 92% product yield, reduced waste generation by 63% (from 2.2 to 0.8 kg of waste per kg of aspirin), and lowered the energy requirement by 40% compared to the traditional synthesis process. The reaction efficiency index improved by 18.28%, while the average environmental impact factor decreased by 60.32%, validating the environmental and operational benefits of the approach. Although demonstrated using the aspirin pathway, the framework’s modular structure and reliance on quantifiable reaction parameters suggest its potential adaptability to other pharmaceutical syntheses, provided sufficient reaction data are available. This research not only offers a rigorous pathway optimization method but also bridges computational graph theory with industrial green chemistry applications.
This study aims to enhance coronavirus disease 2019 forecasting in Kenya by comparing the predictive performance of statistical, machine learning, and deep learning (DL) models for total cases, critical cases, severe cases, and total deaths, using data from April 2020 to August 2021. Six models – autoregressive integrated moving average (ARIMA), support vector regression, random forest (RF), recurrent neural network, long short-term memory, and gated recurrent unit – were evaluated with an 80–20 train-test split, employing root mean squared error, mean absolute error, mean absolute percentage error, and R2{R}^{2} metrics. The Diebold-Mariano (DM) test assessed statistical significance of error differences. Results reveal RF as the top performer, consistently achieving the lowest errors and highest R2{R}^{2} across all datasets, indicating superior accuracy in capturing nonlinear epidemic patterns. GRU outperformed other DL models, while ARIMA showed the weakest performance. The DM test confirmed significant differences in forecasting errors, with RF generally outperforming other models.
This study examines the impact of measurement errors on parameter estimates within hierarchical Bayesian semiparametric (HBS) models, with a focus on the Lotka–Volterra predator–prey model as a case study. By employing Gibbs sampling within the Markov Chain Monte Carlo framework, we simulate various levels of measurement errors to assess the robustness of these models. Results indicate that HBS models effectively account for measurement error, mitigating its adverse effects on the accuracy of parameter estimates, especially for complex, nonlinear systems like predator–prey dynamics. The study demonstrates that as sample sizes increase, the models’ ability to recover true population interaction parameters, such as prey birth rates and predator consumption rates, improves significantly. These findings underscore the importance of using advanced Bayesian methods to correct for measurement errors, ensuring reliable statistical inferences in fields like ecological modeling, environmental studies, and agricultural systems. The integration of HBS models enhances the reliability of complex data analyses, providing essential insights into nonlinear interactions in real-world systems.
Oncolytic virotherapy is one of the cancer treatments that kills cancer cells but leaves normal cells. Furthermore, mitogen-activated protein kinase (MEK) inhibitors boost chimeric antigen receptor expression and increase oncolytic virus entry into tumor cells, and TNF-α{\rm{\alpha }} inhibitors improve the effectiveness of oncolytic virotherapy. We propose a mathematical model of tumor involving oncolytic virotherapy, MEK inhibitors, and TNF-α{\rm{\alpha }} inhibitors. All model properties are performed. Three equilibrium points are computed, and their stabilities are analyzed. Additionally, optimal control is applied to the model to investigate the optimal strategy to reduce the load of tumor cells by using MEK inhibitors, TNF-α{\rm{\alpha }} inhibitors, and oncolytic virotherapy. Numerical results demonstrate that a combination of all three treatments leads to a significant increase in infected tumor cells and macrophages, resulting in more infections of tumor cells and stronger immune response. Both low and high levels of MEK inhibitors are applied in three-treatment combination to explore a role of MEK inhibitors, and a better result in high level of MEK inhibitors case is obtained. Hence, our results confirm that MEK inhibitors could lead to not only more oncolytic virus infection of tumor cells and more immune of macrophages but also limit the virus replication.
This study explores the dynamic characteristics of a fractional-order model for the hepatitis B virus (HBV) epidemic. We present the existence, uniqueness, and Ulam-Hyers stability of solutions for a fractional-order HBV model utilizing the Atangana-Baleanu-Caputo fractional operator with Mittag-Leffler kernels. For the fractional numerical simulations, we employ the Adams-Moulton numerical scheme. The results from the numerical solutions indicate that the parameter χ\chi (order of derivative) plays a crucial role, highlighting the importance of the two infection stages (acute and chronic) within the model. We observed the relationship between the basic reproduction number, the HBV transmission rate, the birth-rate, and the acutely infected individuals to the chronic stage.
In this article, we study a fractional-order prey-predator model incorporating prey refuge and predator harvesting, employing a Holling type III functional response. The model’s dynamics are explored using the consumption number C0{C}_{0}, providing a comprehensive understanding of its ecological implications. We establish the existence and uniqueness of the solution, ensuring the model’s mathematical robustness. Stability analysis is conducted to determine the conditions under which the system remains in equilibrium. Sensitivity analysis is performed to assess the importance of various parameters on the system’s behaviour with respect to the consumption number. Additionally, we investigate the occurrence of transcritical bifurcations, utilizing the prey refuge as a bifurcation parameter. Numerical simulations are carried out to illustrate the theoretical results and to provide deeper insights into the model’s dynamics. Our findings contribute to the understanding of fractional-order systems in ecological modelling and offer valuable perspectives on the management of predator-prey interactions in the presence of prey refuge and predator harvesting.
This article explores how emotional feelings linked to stored memories of past experiences influence the present activity of the human brain. To analyse this, a mathematical model is considered describing the dynamics in a two-layered network in which the neurons in the first layer are involved in present activities and are influenced by cells in the second layer that carry the emotional feelings associated with memories of past experiences. Initially, this article establishes sufficient conditions for the stability of a unique equilibrium solution in the system for both constant and time-varying exogenous inputs. This indicates the situation where the present activities are not disturbed by emotions emanated from past memories. Furthermore, it is observed that certain variations in the exogenous inputs can induce oscillations within the system. To manage them, this study suggests the adjustment of specific parameters that could actually control certain fluctuations according to emotional responses to past and current memories. This control aims to stabilize the brain’s current activity, allowing it to reach a balanced state.
Recent studies have intensified the risk of post-COVID-19 cardiovascular diseases. In an effort to understand the intricate dynamics of COVID-19 infection, this article suggests a four-compartment model to portray the dynamic interplay between the susceptible population, the COVID-19-infected population detected without and with cardiovascular disease, and the recovered population. Basic properties such as nonnegativity and boundedness of solutions and the existence of disease-free and endemic equilibria are discussed. The model’s basic reproduction number is obtained. Sufficient conditions for local and global stability at the equilibrium point are established by restricting the functionals and parameters of the system. Numerical examples are illustrated to support the results. The relative significance of the model parameters to disease transmission is determined by performing a sensitivity analysis of the model. It is found that a rise in infection among the cardio population will drastically affect the overall infection rate compared to that of the noncardio population, supporting the real-time scenario. This model also emphasizes the importance of vaccination and treatment in controlling the spread of the virus.
Understanding the dynamics of infectious diseases using mathematical modeling is essential for developing prevention and control measures. Hepatitis B is still a major public health issue in many places, including Kenya, where the high incidence of illness presents serious difficulties. In this article, the existence and uniqueness of solutions for a fractional hepatitis B model in the Caputo sense were explored. Furthermore, using the Adams-type Predictor-Corrector method, numerical simulations of the fractional order model are carried out. The outcomes show how well the suggested control strategies work to stop the spread of hepatitis B virus.
This research presents a mathematical model of glioma growth dynamics with drug resistance, capturing interactions among five cell populations: glial cells, sensitive glioma cells, resistant glioma cells, endothelial cells, and neuron cells, along with two therapy agent populations: chemotherapy and anti-angiogenic therapy. Glioma is a malignant tumor originating from glial cells, undergoes chemotherapy-induced mutations, leading to drug-resistant glioma cells. This not only impacts glioma cells but also normal cells. Combining chemotherapy and anti-angiogenic therapy, the model employs a Holling type II response function, considering optimal dosages for treatment optimization. Through analysis, three equilibrium are identified: two stable and one unstable equilibrium points. Numerical simulations, employing phase portraits and trajectory diagrams, illustrate the combined therapies impact on glioma cells. In summary, this concise model explores glioma dynamics and drug resistance, offering insights into the efficacy of combined therapies, crucial for optimizing glioma treatment.
When planktonic bacteria adhere together to a surface, they begin to form biofilms, or communities of bacteria. Biofilm formation in a host can be extremely problematic if left untreated, especially since antibiotics can be ineffective in treating the bacteria. Certain lung diseases such as cystic fibrosis can cause the formation of biofilms in the lungs and can be fatal. With antibiotic-resistant bacteria, the use of phage therapy has been introduced as an alternative or an additive to the use of antibiotics in order to combat biofilm growth. Phage therapy utilizes phages, or viruses that attack bacteria, in order to penetrate and eradicate biofilms. In order to evaluate the effectiveness of phage therapy against biofilm bacteria, we adapt an ordinary differential equation model to describe the dynamics of phage-biofilm combat in the lungs. We then create our own phage-biofilm model with ordinary differential equations and stochastic modeling. Then, simulations of parameter alterations in both models are investigated to assess how they will affect the efficiency of phage therapy against bacteria. By increasing the phage mortality rate, the biofilm growth can be balanced and allow the biofilm to be more vulnerable to antibiotics. Thus, phage therapy is an effective aid in biofilm treatment.
