Mathematical Model Of Network Research Articles

Prevalence of and gene regulatory constraints on transcriptional adaptation in single cells

BackgroundCells and tissues have a remarkable ability to adapt to genetic perturbations via a variety of molecular mechanisms. Nonsense-induced transcriptional compensation, a form of transcriptional adaptation, has recently emerged as one such mechanism, in which nonsense mutations in a gene trigger upregulation of related genes, possibly conferring robustness at cellular and organismal levels. However, beyond a handful of developmental contexts and curated sets of genes, no comprehensive genome-wide investigation of this behavior has been undertaken for mammalian cell types and conditions. How the regulatory-level effects of inherently stochastic compensatory gene networks contribute to phenotypic penetrance in single cells remains unclear.ResultsWe analyze existing bulk and single-cell transcriptomic datasets to uncover the prevalence of transcriptional adaptation in mammalian systems across diverse contexts and cell types. We perform regulon gene expression analyses of transcription factor target sets in both bulk and pooled single-cell genetic perturbation datasets. Our results reveal greater robustness in expression of regulons of transcription factors exhibiting transcriptional adaptation compared to those of transcription factors that do not. Stochastic mathematical modeling of minimal compensatory gene networks qualitatively recapitulates several aspects of transcriptional adaptation, including paralog upregulation and robustness to mutation. Combined with machine learning analysis of network features of interest, our framework offers potential explanations for which regulatory steps are most important for transcriptional adaptation.ConclusionsOur integrative approach identifies several putative hits—genes demonstrating possible transcriptional adaptation—to follow-up on experimentally and provides a formal quantitative framework to test and refine models of transcriptional adaptation.

Mathematical and artificial neural network modeling to predict the heat transfer of mixed convective electroosmotic nanofluid flow with Helmholtz-Smoluchowski velocity and multiple slip effects: An application of soft computing

The growing popularity of artificial neural networks (ANNs) is due to their exceptional capability in handling complex and highly nonlinear mathematical problems. ANNs provide a flexible computational framework that is extremely useful in complex fields such as biological computation, fluid dynamics, and biotechnology. Consequently, this study utilizes machine learning techniques to examine the heat transfer in mixed convective Electroosmotic Nanofluid flow, considering Helmholtz-Smoluchowski velocity and multiple slip effects on an exponentially stretching surface. Different influential factors, including, thermal radiation, viscous dissipation, joule heating, linear thermal heat source/sink and exponential thermal heat source/sink are considered in this investigation. In the current study, graphene oxide and magnesium oxide are used as nanomaterials, with ethylene glycol serving as the base fluid. The bvp4c solver in Matlab is employed to solve nonlinear versions of established mathematical problems, including those related to the skin friction coefficient, heat transfer rates, velocity, and temperature. The artificial neural network model is structured to handle several tasks: data selection, network construction, network training, and evaluating performance employing the mean square error metric. The significance of parameter on subjective profiles is demonstrated though tables and graphical representation. The Numerical results and artificial neural network results have been compared. The results showed that there is excellent validation between numerical results and artificial neural network results.

Reviewing mathematical models of sperm signaling networks.

Dave Garbers' work significantly contributed to our understanding of sperm's regulated motility, capacitation, and the acrosome reaction. These key sperm functions involve complex multistep signaling pathways engaging numerous finely orchestrated elements. Despite significant progress, many parameters and interactions among these elements remain elusive. Mathematical modeling emerges as a potent tool to study sperm physiology, providing a framework to integrate experimental results and capture functional dynamics considering biochemical, biophysical, and cellular elements. Depending on research objectives, different modeling strategies, broadly categorized into continuous and discrete approaches, reveal valuable insights into cell function. These models allow the exploration of hypotheses regarding molecules, conditions, and pathways, whenever they become challenging to evaluate experimentally. This review presents an overview of current theoretical and experimental efforts to understand sperm motility regulation, capacitation, and the acrosome reaction. We discuss the strengths and weaknesses of different modeling strategies and highlight key findings and unresolved questions. Notable discoveries include the importance of specific ion channels, the role of intracellular molecular heterogeneity in capacitation and the acrosome reaction, and the impact of pH changes on acrosomal exocytosis. Ultimately, this review underscores the crucial importance of mathematical frameworks in advancing our understanding of sperm physiology and guiding future experimental investigations.

Optimisation of a multilevel logistics network for prepositioned warehouses under an omni-channel retail model

A new omni-channel retailing mode, prepositioned warehouses, which developed rapidly in China during the COVID-19 pandemic, was introduced, and a three-level logistics network optimisation model for agricultural products was presented. This study takes into account the characteristics of the omni-channel retail model, which combines the two delivery methods of vehicle delivery and consumer in-store purchase, adds the freshness penalty incurred by fresh agricultural products in the storage process of the prepositioned warehouse, and establishes a mathematical optimisation model of the three-stage logistics network of the prepositioned warehouse that meets the characteristics of omni-channel retailing on the basis of the classical EOQ inventory model. In this work, the shortest delivery time and the smallest total cost are set as the optimisation objectives, and the multi-objective problem is transformed into a single objective through normalisation and linear weighting methods to obtain a mixed-integer optimisation model. This paper solves the problems of site selection for prepositioned warehouses, merchandise replenishment strategies, and optimisation of delivery routes based on data from real cases. Additionally, through sensitivity analysis, the management inspiration of the enterprise is obtained.

Prediction of the pressure fluctuations in by-product gas pipeline networks in iron and steel enterprises using a spatiotemporal method

To overcome the problems of gas release, energy waste and pipeline leakage of dust erosion wear caused by the fluctuation of the by-product gas pressure in iron and steel enterprises, a 3D mathematical model of a by-product gas pipeline network was constructed in this study. Multi-condition numerical simulation analysis and spatiotemporal pressure fluctuation prediction modelling were also conducted. Firstly, the 3D mathematical model of a by-product gas pipeline network, with an error < 10%, was established by using computational fluid dynamics. Secondly, numerical simulations were conducted under multiple working conditions to study the pressure fluctuation law of the pipeline network and the erosion wear of the pipe wall. Finally, a rapid, accurate, adaptable prediction model was constructed using a spatiotemporal graph convolutional gated recurrent unit method with a combination of the numerical simulation data and pressure fluctuation law. The pressure fluctuation of the by-product gas pipeline network after a change in the blast furnace flow could be predicted in <2 s and the mean absolute percentage error of the prediction was < 2.6%.

Direct observation correlates NFκB cRel in B cells with activating and terminating their proliferative program

Antibody responses require the proliferative expansion of B cells controlled by affinity-dependent signals. Yet, proliferative bursts are heterogeneous, varying between 0 and 8 divisions in response to the same stimulus. NFκB cRel is activated in response to immune stimulation in B cells and is genetically required for proliferation. Here, we asked whether proliferative heterogeneity is controlled by natural variations in cRel abundance. We developed a fluorescent reporter mTFP1-cRel for the direct observation of cRel in live proliferating B cells. We found that cRel is heterogeneously distributed among naïve B cells, which are enriched for high expressors in a heavy-tailed distribution. We found that high cRel expressors show faster activation of the proliferative program, but do not sustain it well, with population expansion decaying earlier. With a mathematical model of the molecular network, we showed that cRel heterogeneity arises from balancing positive feedback by autoregulation and negative feedback by its inhibitor IκBε, confirmed by mouse knockouts. Using live-cell fluorescence microscopy, we showed that increased cRel primes B cells for early proliferation via higher basal expression of the cell cycle driver cMyc. However, peak cMyc induction amplitude is constrained by incoherent feedforward regulation, decoding the fold change of cRel activity to terminate the proliferative burst. This results in a complex nonlinear, nonmonotonic relationship between cRel expression and the extent of proliferation. These findings emphasize the importance of direct observational studies to complement gene knockout results and to learn about quantitative relationships between biological processes and their key regulators in the context of natural variations.

Systems modeling of oncogenic G-protein and GPCR signaling reveals unexpected differences in downstream pathway activation

Mathematical models of biochemical reaction networks are an important and emerging tool for the study of cell signaling networks involved in disease processes. One promising potential application of such mathematical models is the study of how disease-causing mutations promote the signaling phenotype that contributes to the disease. It is commonly assumed that one must have a thorough characterization of the network readily available for mathematical modeling to be useful, but we hypothesized that mathematical modeling could be useful when there is incomplete knowledge and that it could be a tool for discovery that opens new areas for further exploration. In the present study, we first develop a mechanistic mathematical model of a G-protein coupled receptor signaling network that is mutated in almost all cases of uveal melanoma and use model-driven explorations to uncover and explore multiple new areas for investigating this disease. Modeling the two major, mutually-exclusive, oncogenic mutations (Gαq/11 and CysLT2R) revealed the potential for previously unknown qualitative differences between seemingly interchangeable disease-promoting mutations, and our experiments confirmed oncogenic CysLT2R was impaired at activating the FAK/YAP/TAZ pathway relative to Gαq/11. This led us to hypothesize that CYSLTR2 mutations in UM must co-occur with other mutations to activate FAK/YAP/TAZ signaling, and our bioinformatic analysis uncovers a role for co-occurring mutations involving the plexin/semaphorin pathway, which has been shown capable of activating this pathway. Overall, this work highlights the power of mechanism-based computational systems biology as a discovery tool that can leverage available information to open new research areas.

Identifying Bayesian optimal experiments for uncertain biochemical pathway models

Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.

Data-driven mathematical modeling of sleep consolidation in early childhood

Across early childhood development, sleep behavior transitions from a biphasic pattern (a daytime nap and nighttime sleep) to a monophasic pattern (only nighttime sleep). The transition to consolidated nighttime sleep, which occurs in most children between 2- and 5-years-old, is a major developmental milestone and reflects interactions between the developing homeostatic sleep drive and circadian system. Using a physiologically-based mathematical model of the sleep-wake regulatory network constrained by observational and experimental data from preschool-aged participants, we analyze how developmentally-mediated changes in the homeostatic sleep drive may contribute to the transition from napping to non-napping sleep patterns. We establish baseline behavior by identifying parameter sets that model typical 2-year-old napping behavior and 5-year-old non-napping behavior. Then we vary six model parameters associated with the dynamics of and sensitivity to the homeostatic sleep drive between the 2-year-old and 5-year-old parameter values to induce the transition from biphasic to monophasic sleep. We analyze the individual contributions of these parameters to sleep patterning by independently varying their age-dependent developmental trajectories. Parameters vary according to distinct evolution curves and produce bifurcation sequences representing various ages of transition onset, transition durations, and transitional sleep patterns. Finally, we consider the ability of napping and non-napping light schedules to reinforce napping or promote a transition to consolidated sleep, respectively. These modeling results provide insight into the role of the homeostatic sleep drive in promoting interindividual variability in developmentally-mediated transitions in sleep behavior and lay foundations for the identification of light- or behavior-based interventions that promote healthy sleep consolidation in early childhood.

Research on a Three-Stage Dynamic Reactive Power Optimization Decoupling Strategy for Active Distribution Networks with Carbon Emissions

The reactive power optimization of an active distribution network can effectively deal with the problem of voltage overflows at some nodes caused by the integration of a high proportion of distributed sources into the distribution network. Aiming to address the limitations in previous studies of dynamic reactive power optimization using the cluster partitioning method, a three-stage dynamic reactive power optimization decoupling strategy for active distribution networks considering carbon emissions is proposed in this paper. First, a carbon emission index is proposed based on the carbon emission intensity, and a dynamic reactive power optimization mathematical model of an active distribution network is established with the minimum active power network loss, voltage deviation, and carbon emissions as the satisfaction objective functions. Second, in order to satisfy the requirement for the all-day motion times of discrete devices, a three-stage dynamic reactive power optimization decoupling strategy based on the partitioning around a medoids clustering algorithm is proposed. Finally, taking the improved IEEE33 and PG&amp;E69-node distribution network systems as examples, the proposed linear decreasing mutation particle swarm optimization algorithm was used to solve the mathematical model. The results show that all the indicators of the proposed strategy and algorithm throughout the day are lower than those of other methods, which verifies the effectiveness of the proposed strategy and algorithm.

СПРОЩЕНА ІМІТАЦІЙНА МОДЕЛЬ НАВАНТАЖЕННЯ В ЗАМКНЕНІЙ МЕРЕЖІ КОМУТАЦІЇ ПАКЕТІВ

An approach to simplified simulation modeling of packet switching network load has been developed. The simulated representation of network processes is based on a simplified mathematical model of the packet switching network, which is based on a dis-cretized description of the load states of the network nodes and corresponds to the repre-sentation of the current state of the network in the tasks of managing its load. Changes in the node's filling state are modeled as a process of reproduction and death, and in the full load model, two factors of change are taken into account: the node's exchange of load with network users and transit load flow passing through it. To study an artificially se-lected "part of the network functioning process" - an approach to transit load modeling in a load-locked network is proposed. The approach allows for significant simplifications and ensures the leveling of the negative impact of simplifications on "load closure" (en-sures the rule of constant amount of load in a closed network). The developed simulation model, firstly, creates the basis for the improvement of the complete model, and secondly, it is convenient for working out routing algorithms when analyzing them from the point of view of indicators of the ability to "influence" the load in the network. The obtained re-sults are generalized, but attention is focused on the example of satellite packet switching networks.

SIMPLIFIED SIMULATION MODEL OF LOAD IN A CLOSED PACKET SWITCHING NETWORK

An approach to simplified simulation modeling of packet switching network load has been developed. The simulated representation of network processes is based on a simplified mathematical model of the packet switching network, which is based on a discretized description of the load states of the network nodes and corresponds to the representation of the current state of the network in the tasks of managing its load. Changes in the node's filling state are modeled as a process of reproduction and death, and in the full load model, two factors of change are taken into account: the node's exchange of load with network users and transit load flow passing through it. To study an artificially selected "part of the network functioning process" - an approach to transit load modeling in a load-locked network is proposed. The approach allows for significant simplifications and ensures the leveling of the negative impact of simplifications on "load closure" (ensures the rule of constant amount of load in a closed network). The developed simulation model, firstly, creates the basis for the improvement of the complete model, and secondly, it is convenient for working out routing algorithms when analyzing them from the point of view of indicators of the ability to "influence" the load in the network. The obtained results are generalized, but attention is focused on the example of satellite packet switching networks.

Improving pressure monitoring and control in order to reduce water loss in water urban public systems

Water losses from distribution systems are present in all situations. Reducing them to zero is impossible. Modern technologies for operating water distribution networks are an effective means of reducing water losses. In this sense, the conducted research aimed at testing some solutions to improve the monitoring and control of pressure in a distribution network. The mathematical model of the water distribution network was developed and calibrated (Mike Urban application) and the hydraulic modeling of the network was carried out. The results were obtained through: periodic simulations with the help of the monitoring application; comparisons for flow and pressure values, data collected from field measurements, data obtained from SCADA application. These complex analyzes allow the identification, in the shortest possible time, of existing problems and areas with losses.

A Spatial Artificial Chemistry Implementation of a Gene Regulatory Network Aimed at Generating Protein Concentration Dynamics.

Gene regulatory networks are networks of interactions in organisms responsible for determining the production levels of proteins and peptides. Mathematical and computational models of gene regulatory networks have been proposed, some of them rather abstract and called artificial regulatory networks. In this contribution, a spatial model for gene regulatory networks is proposed that is biologically more realistic and incorporates an artificial chemistry to realize the interaction between regulatory proteins called the transcription factors and the regulatory sites of simulated genes. The result is a system that is quite robust while able to produce complex dynamics similar to what can be observed in nature. Here an analysis of the impact of the initial states of the system on the produced dynamics is performed, showing that such models are evolvable and can be directed toward producing desired protein dynamics.

Astrocyte control bursting mode of spiking neuron network with memristor-implemented plasticity

A mathematical model of a spiking neuron network accompanied by astrocytes is considered. The network is composed of excitatory and inhibitory neurons with synaptic connections supplied by a memristor-based model of plasticity. Another mechanism for changing the synaptic connections involves astrocytic regulations using the concept of tripartite synapses. In the absence of memristor-based plasticity, the connections between these neurons drive the network dynamics into a burst mode, as observed in many experimental neurobiological studies when investigating living networks in neuronal cultures. The memristive plasticity implementing synaptic plasticity in inhibitory synapses results in a shift in network dynamics toward an asynchronous mode. Next,it is found that accounting for astrocytic regulation in glutamatergic excitatory synapses enable the restoration of ‘normal’ burst dynamics. The conditions and parameters of such astrocytic regulation’s impact on burst dynamics established.

Remarks on the Mathematical Modeling of Gene and Neuronal Networks by Ordinary Differential Equations

In the theory of gene networks, the mathematical apparatus that uses dynamical systems is fruitfully used. The same is true for the theory of neural networks. In both cases, the purpose of the simulation is to study the properties of phase space, as well as the types and the properties of attractors. The paper compares both models, notes their similarities and considers a number of illustrative examples. A local analysis is carried out in the vicinity of critical points and the necessary formulas are derived.

A ‘Systemic’ Model of a Mind-Body Interaction

This paper shows that, by using a “systemic” mind theory and a formal model initially proposed by Neisser, it is possible to formally represent the mind-body communication processes as they are expressed within the psychoanalytic environment. In this paper, mathematical models of neural networks are used to demonstrate that Neisser’s hypothesis is reinforced if a temporal evolution appears. On the contrary, additional neurophysiological mechanisms must be postulated to show the differences between primary and secondary processes.

A new approach to mathematical modeling of chemical synapses

The purpose of this work is to study a new mathematical model of a ring neural network with unidirectional chemical connections, which is a singularly perturbed system of differential-difference equations with delay. Methods. A combination of analytical and numerical methods is used to study the existence and stability of special periodic solutions in this system, the so-called traveling waves. Results. The proposed methods make it possible to show that the ring system under study allows the number of stable traveling waves to increase with the number of oscillators in the network. Conclusion. In this article, we rethink and refine the previously proposed method of mathematical modeling of chemical synapses. On the one hand, it was possible to fully take into account the requirement of the Volterra structure of the corresponding equations and, on the other hand, the hypothesis of saturating conductivity. This makes it possible to observe the principle of uniformity: the new mathematical model is based on the same principles as the previously proposed model of electrical synapses.

Renewable energy based low-voltage distribution network for dynamic voltage regulation

With the continuous integration of renewable energy and the complexity of power system, dynamic voltage regulation of low-voltage distribution network has become an urgent problem to be solved. Through in-depth analysis and theoretical discussion, the mathematical model of low-voltage distribution network is established, and the control strategy based on renewable energy is designed for dynamic voltage regulation. Through simulation experiment and field verification, the superiority of the proposed method compared with the existing method is demonstrated. In addition, the sensitivity of the parameters and the stability of the control strategy are also comprehensively analyzed. Despite some limitations and challenges, the results of this study provide strong support for the sustainable, efficient and safe operation of low-voltage distribution networks, and further optimization and expansion in many aspects are needed in the future.

Determinants of financial well-being of the population of Tyumen oblast

The high differentiation of living standards within the boundaries of a complex subject of the Russian Federation actualizes the problems of studying the determinants of financial well-being of the population. The article analyzes four groups of data for Tyumen oblast with autonomous districts that are part of it for the period of 2013–2021, including: average per capita cash income of the population; structural indicators of the balance of monetary income and expenses of the population; volume of deposits and other funds of individuals (excluding escrow accounts); amount of debt on loans provided to resident individuals. We used methods of matching, plotting scattering diagrams, identifying trends. As a result, a number of the following determinants of financial well-being were identified. Among the population of autonomous districts prevails the desire to accumulate savings in the form of cash (by 2021 the amount reached 393 billion rubles). Persistent shortage of cash savings in the South of Tyumen oblast (– 164 billion rubles) is covered by a surplus formed in the districts. In all three RF subjects there is a significant decrease in the ratio of the volume of deposits of the population and the volume of debt on loans, which corresponds to the all-Russian trend. The well-being of the population of the South Tyumen oblast should be considered with the account of the effect of indicative consumption due to the inevitable differentiation in the income of visitors and local population, as well as differences in behavioral models, which consist in a higher degree of wastefulness among visitors. Additionally, the possibility of using the obtained results in the framework of mathematical and neural network modeling of the process of dynamics in the well-being of the Tyumen blast population is considered.