Modelling spatio-temporal interactions between second messengers Ca 2 + and cAMP in a pancreatic β -cell

Calcium serves as a widespread second messenger in almost every human and animal cell. The regulation of various cellular processes, such as transcriptional control and the kinetics of membrane channels, is significantly influenced by intracellular calcium ions (Ca2 + ), and linkages between Ca2 + and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca2 + levels in pancreatic β -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca2 + in β -cells and its interactions with the intracellular dynamics of cyclic adenosine monophosphate (cAMP) is poorly understood. Therefore, the current investigation proposes a mathematical model to illustrate the spatiotemporal dynamical interaction between Ca2 + and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the β -cell are incorporated. The numerical results were obtained by MATLAB simulations using the finite element method and the Crank-Nicolson method. The current study aims to offer an update on regulation between Ca2 + and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the β -cell. The model gives the individual effect of each parameter on the regulation of Ca2 + and cAMP profiles in a β -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.

Memory impacts in hepatitis C: A global analysis of a fractional-order model with an effective treatment

BACKGROUND AND OBJECTIVE

Hepatitis virus infections are affecting millions of people worldwide, causing death, disability, and considerable expenditure. Chronic infection with hepatitis C virus (HCV) can cause severe public health problems because of their high prevalence and poor long-term clinical outcomes. Thus a fractional-order epidemic model of the hepatitis C virus involving partial immunity under the influence of memory effect to know the transmission patterns and prevalence of HCV infection is studied. Investigating the transmission dynamics of HCV makes the issue more interesting. The HCV epidemic model and worldwide dynamics are examined in this study. Calculate the basic reproduction number for the HCV model using the next-generation matrix technique. We determine the model's global dynamics using reproduction numbers, the Lyapunov functional approach, and the Routh-Hurwitz criterion. The model's reproduction number shows how the disease progresses.

METHODS

A fractional differential equation model of HCV infection has been created. Maximum relevant parameters, such as fractional power, HCV transmission rate, reproduction number, etc., influencing the dynamic process, have been incorporated. The model's numerical solutions are obtained using the fractional Adams method. Finally, numerical simulations support the theoretical conclusions, showing the great agreement between the two.

RESULTS

In the fractional-order HCV infection model, the memory effect, which is not seen in the classical model, was shown on graphs so that disease dynamics and vector compartments could be seen. We found that the fractional-order HCV infection model has more stages of freedom than regular derivatives. Fractional-order derivations, which may be the best and most reliable, explained bodily approaches better than classical order.

CONCLUSION

The current study modeled and analyzed a fractional-order HCV infection model. The current approach results in a much better understanding of HCV transmission in a population, which leads to important insights into its spread and control, such as better treatment dosage for different age groups, identifying the best control measure, improving health, prolonging life, reducing the risk of HCV transmission, and effectively increasing the quality of life of HCV patients. The creation of a fractional-order HCV infection model, which provides a better understanding of HCV transmission dynamics and leads to significant insights for better treatment dosages, identification of optimal control measures, and ultimately improvement of the quality of life for HCV patients, is the study's major outcome.

A Model for the Coexistence of Competing Mechanisms for Ca 2 + Oscillations in T-lymphocytes

Ca 2 + is a ubiquitous signaling mechanism across different cell types. In T-cells, it is associated with cytokine production and immune function. Benson et al. have shown the coexistence of competing Ca 2 + oscillations during antigen stimulation of T-cell receptors, depending on the presence of extracellular Ca 2 + influx through the Ca 2 + release-activated Ca 2 + channel (Benson in J Biol Chem 29:105310, 2023). In this paper, we construct a mathematical model consisting of five ordinary differential equations and analyze the relationship between the competing oscillatory mechanisms.. We perform bifurcation analysis on two versions of our model, corresponding to the two oscillatory types, to find the defining characteristics of these two families.

Cross Talking Calcium, IP3 and Buffer Dynamics Alters ATP and NADH Level in Obese and Normal Hepatocyte Cell

The cross talk between calcium (Ca2+), IP3 and buffer dynamics regulate various mechanisms in hepatocyte cells. The study of independent systems of calcium, IP3, and buffer signaling provides limited information about cell dynamics. In the current study, coupled reaction-diffusion equations are used to design a cross-talk model for IP3, buffer, and calcium dynamics in a hepatocyte cell. The one-way feedback of calcium, buffer, and IP3 in ATP production, ATP degradation, and NADH production rate is incorporated into the model. Numerical simulation has been done using the Finite Element Method (FEM) along the spatial direction and the Crank-Nicolson (C-N) method along the temporal direction. The numerical results are analysed to determine the effects of alterations in processes of cross-talking dynamics of IP3, buffer, and calcium on ATP and NADH production and degradation rate of ATP in a hepatocyte cell under normal and obesity conditions. The comparative analysis of these findings unveils notable distinctions induced by obesity in calcium dynamics, ATP and NADH synthesis, and ATP degradation kinetics.

A Comprehensive Fuzzy Model for Understanding Neuronal Calcium Distribution in Presence of VGCC, Na+/Ca2+ Exchanger, Buffer, and ER Fluxes

Free Calcium ions in the cytosol are essential for many physiological and physical functions. The free calcium ions are commonly regarded as a second messenger, are an essential part of brain communication. Numerous physiological activities, such as calcium buffering and calcium ion channel flow, etc. influence the cytosolic calcium concentration. In light of the above, the primary goal of this study is to develop a model of calcium distribution in neuron cells when a Voltage-Gated Calcium Channel and Sodium Calcium Exchanger are present. As we know, decreased buffer levels and increased calcium activity in the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger lead to Alzheimer's disease. Due to these changes, the calcium diffusion in that location becomes disrupted and impacted by Alzheimer's disease. The model has been constructed by considering key factors like buffers and ER fluxes when Voltage-Gated Calcium Channels and Sodium Calcium Exchangers are present. Based on the physiological conditions of the parameters, appropriate boundary conditions have been constructed in the fuzzy environment. This model is considered a fuzzy boundary value problem with the source term and initial boundary conditions are modeled by triangular fuzzy functions. In this, paper we observed the approximate solution of the mathematical model which was investigated by the fuzzy undetermined coefficient method. The solution has been performed through MATLAB and numerical results have been computed using simulation. The observation made that the proper operation of the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger is critical for maintaining the delicate equilibrium of calcium ions, which regulates vital cellular activities. Dysregulation of Voltage-Gated Calcium Channel and Sodium Calcium Exchanger activity has been linked to neurodegenerative illnesses like Alzheimer's disease.

Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

The hepatocyte cells regulate the wide range of liver function by moderating cellular activities such as lipid, protein metabolism, carbohydrate, and interact with other cells for proliferation and maintenance. In hepatocyte cells, the concentration of calcium uptake is quite extensive from various agonists such as activeG α ${G_\alpha}$ subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum. The overproduction and degradation of calcium signals can cause homeostasis, liver inflammation, and liver diseases. The spatiotemporal behavior of calcium oscillation reveals the physiological role of these cellular entities in understanding the process of production and degradation. No computational attempt has been registered to date on the compound calcium regulation of these cellular entities including the memory of cells. Hence, the authors proposed a fractional order compartmental model that systematically simulates the exchange of calcium intake in cellular entities. The nonlinear equations of the rate of changes in the activeG α ${G_\alpha}$ subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum are coupled to form a nonlinear fractional order initial value problem. The existence and uniqueness, stability analysis of the model is performed that validate the theoretical results and explore the dynamic behaviour of calcium oscillation in each compartment.

Model of Calcium Dynamics Regulating [Formula: see text], ATP and Insulin Production in a Pancreatic [Formula: see text]-Cell

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ([Formula: see text]) and adenosine triphosphate (ATP) in various cells including pancreatic [Formula: see text]-cells. The calcium signaling mechanisms regulating [Formula: see text], ATP and insulin responsible for various functions of [Formula: see text]-cells are still not well understood. Any disturbance in these mechanisms can alter the functions of [Formula: see text]-cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation for calcium dynamics and a system of first-order differential equations for [Formula: see text], ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of [Formula: see text]-production and degradation, ATP production and insulin secretion on calcium dynamics in a [Formula: see text]-cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of [Formula: see text], ATP and insulin levels in a [Formula: see text]-cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of [Formula: see text], ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in [Formula: see text], ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases.

2D dynamic analysis of the disturbances in the calcium neuronal model and its implications in neurodegenerative disease

Ca2+ signaling is an essential function of neurons to control synaptic activity, memory formation, fertilization, proliferation, etc. Protein and voltage-dependent calcium channels (VDCCs) maintain an adequate level of calcium concentration ([Ca2+]). An alteration in [Ca2+] leads to the death of the neurons that start the primary symptoms of the disease. The present study deals with cell memory-based mathematical modeling of Ca2+ that is characterized by the presence of protein and VDCC. We developed a two-dimensional Ca2+ neuronal model to study the spatiotemporal behavior of the Ca2+ profile. All principal parameters like buffer concentration, diffusion coefficient, VDCC fluxes, etc. are incorporated in this model. Apposite initial and boundary conditions are applied to the physiology of the problem. We obtained an approximate Ca2+ profile by the fractional integral transform method. The application of obtained results is performed to provide its implications to estimate the [Ca2+] in neurodegenerative disease. It is observed that the protein and VDCC provide a significant impact in the presence of cell memory. The memory of cells shrinks the Ca2+ flow from elevation and provides better results to estimated Ca2+ flow in the disease state.

A two-dimensional finite element model of intercellular cAMP signaling through gap junction channels

While cyclic adenosine monophosphate (cAMP) is typically considered an intracellular signal, it has been shown to spread between adjacent cells through connexin-based gap junction channels, promoting gap junctional intercellular communication (GJIC). Gap junction-mediated signaling is critical for the coordinated function of many tissues, and have been linked with cardiovascular disease, neurogenerative disease, and cancers. In particular, it plays a complex role in tumor suppression or promotion. This work introduces a two-dimensional finite element model that can describe intercellular cAMP signaling in the presence of gap junctions on membrane interfaces. The model was utilized to simulate cAMP transfer through one and two gap junction channels on the interface of a cluster of two pulmonary microvascular endothelial cells. The simulation results were found to generally agree with what has been observed in the literature in terms of GJIC. The research outcomes suggest that the proposed model can be employed to evaluate the permeability properties of a gap junction channel if its cAMP volumetric flow rate can be experimentally measured.

Effect of disturbances in neuronal calcium and IP3 dynamics on β-amyloid production and degradation

Overproduction and accumulation of β-amyloid and its improper clearance can cause neurotoxicity leading to Alzheimer's disease. The production and degradation of β-amyloid depend on the calcium ([Ca2+]) and IP3 dynamics in the nerve cells. Thus, there is a need to understand the impacts of disturbances in the processes of [Ca2+] and IP3 dynamics on β-amyloid production and its degradation. Here, a model is proposed to investigate the role of [Ca2+] and IP3 dynamics on β-amyloid production and degradation. The problem is formulated in terms of the initial boundary value problem involving the system of two reaction-diffusion equations respectively for [Ca2+] and IP3 in the nerve cell. The solution is obtained by employing the Finite element approach. The numerical results are used to analyze the impact of various mechanisms of calcium and IP3 dynamics on β-amyloid production and degradation in a neuron cell. The results indicate that disturbances in any of the constitutive processes of interdependent calcium and IP3 dynamics like source influx, buffering, serca pump, and IP3 dynamics, etc. can cause dynamic changes in β-amyloid production and degradation, which in turn can be the cause of neurotoxicity and neuronal disorders like Alzheimer's disease. Thus, the relationships obtained by the proposed model among various mechanisms can be useful in addressing the challenges of identifying specific constitutive processes causing neuronal disorders like Alzheimer's disease, etc., and developing the framework for their diagnosis and treatment.

Severity of Placental Abruption in Restrained Pregnant Vehicle Drivers: Correct Seat Belt Use Confirmed by Finite Element Model Analysis

Despite wearing a seat belt, pregnant drivers often suffer from negative fetal outcomes in the event of motor accidents. In order to maintain the safety of pregnant drivers and their fetuses, we assessed the severity of placental abruption caused by motor vehicle collisions using computer simulations. We employed a validated pregnant finite element model to determine the area of placental abruption. We investigated frontal vehicle collisions with a speed of 40 km/h or less involving restrained pregnant drivers with a gestational age of 30 weeks. For a crash speed of 40 km/h, the placental abruption area was 7.0% with a correctly positioned lap belt across the lower abdomen; it was 36.3% with the belt positioned at the umbilicus. The area of placental abruption depended on collision speed, but we found that with a correctly positioned belt it likely would not lead to negative fetal outcomes. We examined the effects on placental abruptions of reconfiguring seat belt width and force limiter setting. A wider lap belt and lower force limiter setting reduced the area of placental abruption to 3.5% and 1.1%, respectively; however, they allowed more forward movement upon collision. A 2.5 kN force limiter setting may be appropriate with respect to both forward movement and reduced placental abruption area. This study confirmed the importance of correctly using seat belts for pregnant drivers. It provides valuable evidence about improving safety equipment settings.

Interactions of selected cardiovascular active natural compounds with CXCR4 and CXCR7 receptors: a molecular docking, molecular dynamics, and pharmacokinetic/toxicity prediction study

BACKGROUND

The chemokine CXCL12 and its two receptors (CXCR4 and CXCR7) are involved in inflammation and hematopoietic cell trafficking. This study was designed to investigate molecular docking interactions of four popular cardiovascular-active natural compounds; curcumin, resveratrol, quercetin, and eucalyptol; with these receptors and to predict their drug-like properties. We hypothesize that these compounds can modify CXCL12/CXCR4/CXCR7 pathway offering benefits for coronary artery disease patients.

METHODS

Docking analyses were carried and characterized by Molecular Environment (MOE) software. Protein Data Bank ( http://www.rcsb.org/ ) has been retrieved from protein structure generation and crystal structures of CXCR4 and CXCR7 receptors (PDB code = 3ODU and 6K3F). The active sites of these receptors were evaluated and extracted from full protein and molecular docking protocol was done for compounds against them. The presented parameters included docking scores, ligand binding efficiency, and hydrogen bonding. The pharmacokinetic/toxic properties (ADME/T) were calculated using SwissADME, ProTox-II, and Pred-hERG softwares to predict drug-like properties of the compounds. The thermochemical and molecular orbital analysis, and molecular dynamics simulations were also done.

RESULTS

All compounds showed efficient interactions with the CXCR4 and CXCR7 receptors. The docking scores toward proteins 3ODU of CXCR4 and 6K3F of CXCR7 were - 7.71 and - 7.17 for curcumin, - 5.97 and - 6.03 for quercetin, - 5.68 and - 5.49 for trans-resveratrol, and - 4.88 and - 4.70 for (1 s,4 s)-eucalyptol respectively indicating that all compounds, except quercetin, have more interactions with CXCR4 than with CXCR7. The structurally and functionally important residues in the interactive sites of docked CXCR4-complex and CXCR7-complex were identified. The ADME analysis showed that the compounds have drug-like properties. Only (1 s,4 s)-Eucalyptol has potential weak cardiotoxicity. The results of thermochemical and molecular orbital analysis and molecular dynamics simulation validated outcomes of molecular docking study.

CONCLUSIONS

Curcumin showed the top binding interaction against active sites of CXCR4 and CXCR7 receptors, with the best safety profile, followed by quercetin, resveratrol, and eucalyptol. All compounds demonstrated drug-like properties. Eucalyptol has promising potential because it can be used by inhalation or skin massage. To our knowledge, this is the first attempt to find binding interactions of these natural agents with CXCR4 and CXCR7 receptors and to predict their druggability.

Factors Affecting the Severity of Placental Abruption in Pregnant Vehicle Drivers: Analysis with a Novel Finite Element Model

We clarified factors affecting the severity of placental abruption in motor vehicle collisions by quantitively analyzing the area of placental abruption in a numerical simulation of an unrestrained pregnant vehicle driver at collision velocities of 3 and 6 m/s. For the simulation, we constructed a novel finite element model of a small 30-week pregnant woman, which was validated anthropometrically using computed tomography data and biomechanically using previous examinations of post-mortem human subjects. In the simulation, stress in the elements of the utero–placental interface was computed, and those elements exceeding a failure criterion were considered to be abrupted. It was found that a doubling of the collision velocity increased the area of placental abruption 10-fold, and the abruption area was approximately 20% for a collision velocity of 6 m/s, which is lower than the speed limit for general roads. This result implies that even low-speed vehicle collisions have negative maternal and fetal outcomes owing to placental abruption without a seatbelt restraint. Additionally, contact to the abdomen, 30 mm below the umbilicus, led to a larger placental abruption area than contact at the umbilicus level when the placenta was located at the uterus fundus. The results support that a reduction in the collision speed and seatbelt restraint at a suitable position are important to decrease the placental abruption area and therefore protect a pregnant woman and her fetus in a motor vehicle collision.

Computational studies by molecular docking of some antiviral drugs with COVID-19 receptors are an approach to medication for COVID-19

The COVID-19 outbreak is a matter of concern worldwide due to unavailability of promising treatment comprising medication or vaccination till date. The discovery of antiviral drug is of immense importance in the existing spread of novel coronavirus. The goal of the present study was to evolve an opposite antiviral drug against the novel COVID-19 virus. A directly succeeding perspective would be to use the prevailing influential drugs from several antimicrobial and chemotherapeutic agents. The encouraging approach is to identify promising drug molecules and compounds through virtual screening via molecular docking of FDA-approved drugs and some previously synthesized pyridone and coumarin derivatives for probable therapeutic outcome. In this conceptual milieu, an effort has been made to propose a computational in silico relationship among FDA-approved drugs and coronavirus-associated receptors and proteins. The study results were evaluated on the basis of a dock score by using molecular operating environment. Out of 15 compounds screened, the compounds with the best docking scores toward their targets was 3d. Therefore, compound 3d deserves further investigations and clinical trials as a possible therapeutic inhibitor of the COVID-19 caused by the novel SARS-CoV-2.

Molecular docking suggests repurposing of brincidofovir as a potential drug targeting SARS-CoV-2 ACE2 receptor and main protease

ABSTRACT

The current outbreak of the highly transmittable and life-threatening severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has evolved rapidly and posed a global health emergency. Many clinical trials are now being conducted to test possible therapies. To assist this, virtual screening via molecular docking was performed on several FDA-approved drugs, previously used in epidemics, and the top ten compounds were selected. These ten well-characterized drugs, previously used to treat malaria and Ebola infections, were screened based on their interactions with the SARS-CoV-2 ACE2 receptor and 3C-like protease. Compared to the other nine medicines, brincidofovir, an ether lipid ester analog of cidofovir with potent antiviral activity, showed the highest docking scores and binding interactions. Therefore, brincidofovir is worth further investigations and clinical trials as a possible therapeutic agent for the COVID-19 disease caused by the novel SARS-CoV-2.

GRAPHIC ABSTRACT