Disentangling the growth curve of microbial culture

Many researchers have studied the population dynamics of microbe of microbes as a typical example of population dynamics. The Monod equation, which mainly focuses on the growth and stationary phases, is used when plotting a growth curve. However, the growth potential in the late stage of culture has been overlooked. Previous studies considered the direct degradation of products to the limiting substrate. In this study, we considered microbial growth during the stationary phase, which enables us to describe the dynamics precisely. The microbes were divided into two populations: one grew by consuming the limiting substrate and the other degraded the products by metabolism. According to the numerical analysis of our model, microbes may choose one of two strategies: one consumes substrates and expands quickly, and the other grows slowly while cleaning up the environment in which they thrive. Furthermore, we found three types of microbial growth depending on their ability to detect metabolite accumulation. Using experimentally measured data, this model can estimate the dynamics of cell density, the substrates, and the metabolites used. The model's disentangling of growth curves offers novel interpretive possibilities for culture system dynamics.

Attention guided neural ODE network for breast tumor segmentation in medical images

Breast cancer is the most common cancer in women. Ultrasound is a widely used screening tool for its portability and easy operation, and DCE-MRI can highlight the lesions more clearly and reveal the characteristics of tumors. They are both noninvasive and nonradiative for assessment of breast cancer. Doctors make diagnoses and further instructions through the sizes, shapes and textures of the breast masses showed on medical images, so automatic tumor segmentation via deep neural networks can to some extent assist doctors. Compared to some challenges which the popular deep neural networks have faced, such as large amounts of parameters, lack of interpretability, overfitting problem, etc., we propose a segmentation network named Att-U-Node which uses attention modules to guide a neural ODE-based framework, trying to alleviate the problems mentioned above. Specifically, the network uses ODE blocks to make up an encoder-decoder structure, feature modeling by neural ODE is completed at each level. Besides, we propose to use an attention module to calculate the coefficient and generate a much refined attention feature for skip connection. Three public available breast ultrasound image datasets (i.e. BUSI, BUS and OASBUD) and a private breast DCE-MRI dataset are used to assess the efficiency of the proposed model, besides, we upgrade the model to 3D for tumor segmentation with the data selected from Public QIN Breast DCE-MRI. The experiments show that the proposed model achieves competitive results compared with the related methods while mitigates the common problems of deep neural networks.

Ultrasound detected increase in optic disk height to identify elevated intracranial pressure: a systematic review

BACKGROUND

Elevated intracranial pressure (eICP) is a serious medical emergency that requires prompt identification and monitoring. The current gold standards of eICP detection require patient transportation, radiation, and can be invasive. Ocular ultrasound has emerged as a rapid, non-invasive, bedside tool to measure correlates of eICP. This systematic review seeks to explore the utility of ultrasound detected optic disc elevation (ODE) as an ultrasonographic finding of eICP and to study its sensitivity and specificity as a marker of eICP.

METHODS

This systematic review followed the preferred reporting items for systematic reviews and meta-analyses guidelines. We systematically searched PubMed, EMBASE, and Cochrane Central for English articles published before April 2023; yielding 1,919 total citations. After eliminating duplicates, and screening the records, we identified 29 articles that addressed ultrasonographically detected ODE.

RESULTS

The 29 articles included a total of 1249 adult and pediatric participants. In patients with papilledema, the mean ODE ranged between 0.6 mm and 1.2 mm. Proposed cutoff values for ODE ranged between 0.3 mm and 1 mm. The majority of studies reported a sensitivity between 70 and 90%, and specificity ranged from 69 to 100%, with a majority of studies reporting a specificity of 100%.

CONCLUSIONS

ODE and ultrasonographic characteristics of the optic disc may aid in differentiating papilledema from other conditions. Further research on ODE elevation and its correlation with other ultrasonographic signs is warranted as a means to increase the diagnostic accuracy of ultrasound in the setting of eICP.

Using compartmental models and Particle Swarm Optimization to assess Dengue basic reproduction number R 0 for the Republic of Panama in the 1999-2022 period

Nowadays, the ability to make data-driven decisions in public health is of utmost importance. To achieve this, it is necessary for modelers to comprehend the impact of models on the future state of healthcare systems. Compartmental models are a valuable tool for making informed epidemiological decisions, and the proper parameterization of these models is crucial for analyzing epidemiological events. This work evaluated the use of compartmental models in conjunction with Particle Swarm Optimization (PSO) to determine optimal solutions and understand the dynamics of Dengue epidemics. The focus was on calculating and evaluating the rate of case reproduction, R 0 , for the Republic of Panama. Three compartmental models were compared: Susceptible-Infected-Recovered (SIR), Susceptible-Exposed-Infected-Recovered (SEIR), and Susceptible-Infected-Recovered Human-Susceptible-Infected Vector (SIR Human-SI Vector, SIR-SI). The models were informed by demographic data and Dengue incidence in the Republic of Panama between 1999 and 2022, and the susceptible population was analyzed. The SIR, SEIR, and SIR-SI models successfully provided R 0 estimates ranging from 1.09 to 1.74. This study provides, to the best of our understanding, the first calculation of R 0 for Dengue outbreaks in the Republic of Panama.

McSNAC: A software to approximate first-order signaling networks from mass cytometry data

Background

Mass cytometry (CyTOF) gives unprecedented opportunity to simultaneously measure up to 40 proteins in single cells, with a theoretical potential to reach 100 proteins. This high-dimensional single-cell information can be very useful in dissecting mechanisms of cellular activity. In particular, measuring abundances of signaling proteins like phospho-proteins can provide detailed information on the dynamics of single-cell signaling processes. However, computational analysis is required to reconstruct such networks with a mechanistic model.

Methods

We propose our Mass cytometry Signaling Network Analysis Code (McSNAC), a new software capable of reconstructing signaling networks and estimating their kinetic parameters from CyTOF data. McSNAC approximates signaling networks as a network of first-order reactions between proteins. This assumption often breaks down as signaling reactions can involve binding and unbinding, enzymatic reactions, and other nonlinear constructions. Furthermore, McSNAC may be limited to approximating indirect interactions between protein species, as cytometry experiments are only able to assay a small fraction of protein species involved in signaling.

Results

We carry out a series of in silico experiments here to show (1) McSNAC is capable of accurately estimating the ground-truth model in a scalable manner when given data originating from a first-order system; (2) McSNAC is capable of qualitatively predicting outcomes to perturbations of species abundances in simple second-order reaction models and in a complex in silico nonlinear signaling network in which some proteins are unmeasured.

Conclusions

These findings demonstrate that McSNAC can be a valuable screening tool for generating models of signaling networks from time-stamped CyTOF data.

Decoding the double trouble: A mathematical modelling of co-infection dynamics of SARS-CoV-2 and influenza-like illness

After the detection of coronavirus disease 2019 (Covid-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, Hubei Province, China in late December, the cases of Covid-19 have spiralled out around the globe. Due to the clinical similarity of Covid-19 with other flulike syndromes, patients are assayed for other pathogens of influenza like illness. There have been reported cases of co-infection amongst patients with Covid-19. Bacteria for example Streptococcus pneumoniae, Staphylococcus aureus, Klebsiella pneumoniae, Mycoplasma pneumoniae, Chlamydia pneumonia, Legionella pneumophila etc and viruses such as influenza, coronavirus, rhinovirus/enterovirus, parainfluenza, metapneumovirus, influenza B virus etc are identified as co-pathogens. In our current effort, we develop and analysed a compartmental based Ordinary Differential Equation (ODE) type mathematical model to understand the co-infection dynamics of Covid-19 and other influenza type illness. In this work we have incorporated the saturated treatment rate to take account of the impact of limited treatment resources to control the possible Covid-19 cases. As results, we formulate the basic reproduction number of the model system. Finally, we have performed numerical simulations of the co-infection model to examine the solutions in different zones of parameter space.

Modeling and Global Sensitivity Analysis of Strategies to Mitigate Covid-19 Transmission on a Structured College Campus

In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to "normal" in-person operations, but it is not clear if-or for how long-campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced's student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals.

A mathematical model captures the role of adenyl cyclase Cyr1 and guanidine exchange factor Ira2 in creating a growth-to-hyphal bistable switch in Candida albicans

Recent biochemical experiments have indicated that in Candida albicans, a commensal fungal pathogen, the Ras signaling pathway plays a significant role in the yeast-to-hyphal transition; specifically, two enzymes in this pathway, Adenyl Cyclase Cyr1 and GTPase activating protein Ira2, facilitate this transition, in the presence of energy sensor ATP. However, the precise mechanism by which protein interactions between Ira2 and Cyr1 and the energy sensor ATP result in the yeast-to-hyphal transition and create a switch-like process are unknown. We propose a new set of biochemical reaction steps that captures all the essential interactions between Ira2, Cyr1, and ATP in the Ras pathway. With the help of chemical reaction network theory, we demonstrate that this set of biochemical reaction steps results in bistability. Further, bifurcation analysis of the differential equations based on this set of reaction steps supports the existence of a bistable switch, and this switch may act as a checkpoint mechanism for the promotion of growth-to-hyphal transition in C. albicans.

Ticks on the Run: A Mathematical Model of Crimean-Congo Haemorrhagic Fever (CCHF)-Key Factors for Transmission

Crimean-Congo haemorrhagic fever (CCHF) is a zoonotic disease caused by the Crimean-Congo hemorrhagic fever virus (CCHFV). Ticks of the genus Hyalomma are the main vectors and represent a reservoir for the virus. CCHF is maintained in nature in an endemic vertebrate-tick-vertebrate cycle. The disease is prevalent in wide geographical areas including Asia, Africa, South-Eastern Europe and the Middle East. It is of great importance for the public health given its occasionally high case/fatality ratio of CCHFV in humans. Climate change and the detection of possible CCHFV vectors in Central Europe suggest that the establishment of the transmission in Central Europe may be possible in future. We have developed a compartment-based nonlinear Ordinary Differential Equation (ODE) system to model the disease transmission cycle including blood sucking ticks, livestock and human. Sensitivity analysis of the basic reproduction number R0 shows that decreasing the tick survival time is an efficient method to control the disease. The model supports us in understanding the influence of different model parameters on the spread of CCHFV. Tick-to-tick transmission through co-feeding and the CCHFV circulation through transstadial and transovarial transmission are important factors to sustain the disease cycle. The proposed model dynamics are calibrated through an empirical multi-country analysis and multidimensional plot reveals that the disease-parameter sets of different countries burdened with CCHF are different. This information may help decision makers to select efficient control strategies.

Prediction of anti-CD25 and 5-FU treatments efficacy for pancreatic cancer using a mathematical model

BACKGROUND

Pancreatic ductal adenocarcinoma (PDAC) is a highly lethal disease with rising incidence and with 5-years overall survival of less than 8%. PDAC creates an immune-suppressive tumor microenvironment to escape immune-mediated eradication. Regulatory T (Treg) cells and myeloid-derived suppressor cells (MDSC) are critical components of the immune-suppressive tumor microenvironment. Shifting from tumor escape or tolerance to elimination is the major challenge in the treatment of PDAC.

RESULTS

In a mathematical model, we combine distinct treatment modalities for PDAC, including 5-FU chemotherapy and anti- CD25 immunotherapy to improve clinical outcome and therapeutic efficacy. To address and optimize 5-FU and anti- CD25 treatment (to suppress MDSCs and Tregs, respectively) schedule in-silico and simultaneously unravel the processes driving therapeutic responses, we designed an in vivo calibrated mathematical model of tumor-immune system (TIS) interactions. We designed a user-friendly graphical user interface (GUI) unit which is configurable for treatment timings to implement an in-silico clinical trial to test different timings of both 5-FU and anti- CD25 therapies. By optimizing combination regimens, we improved treatment efficacy. In-silico assessment of 5-FU and anti- CD25 combination therapy for PDAC significantly showed better treatment outcomes when compared to 5-FU and anti- CD25 therapies separately. Due to imprecise, missing, or incomplete experimental data, the kinetic parameters of the TIS model are uncertain that this can be captured by the fuzzy theorem. We have predicted the uncertainty band of cell/cytokines dynamics based on the parametric uncertainty, and we have shown the effect of the treatments on the displacement of the uncertainty band of the cells/cytokines. We performed global sensitivity analysis methods to identify the most influential kinetic parameters and simulate the effect of the perturbation on kinetic parameters on the dynamics of cells/cytokines.

CONCLUSION

Our findings outline a rational approach to therapy optimization with meaningful consequences for how we effectively design treatment schedules (timing) to maximize their success, and how we treat PDAC with combined 5-FU and anti- CD25 therapies. Our data revealed that a synergistic combinatorial regimen targeting the Tregs and MDSCs in both crisp and fuzzy settings of model parameters can lead to tumor eradication.

Modeling HIV-1 Within-Host Dynamics After Passive Infusion of the Broadly Neutralizing Antibody VRC01

VRC01 is a broadly neutralizing antibody that targets the CD4 binding site of HIV-1 gp120. Passive administration of VRC01 in humans has assessed the safety and the effect on plasma viremia of this monoclonal antibody (mAb) in a phase 1 clinical trial. After VRC01 infusion, the plasma viral load in most of the participants was reduced but had particular dynamics not observed during antiretroviral therapy. In this paper, we introduce different mathematical models to explain the observed dynamics and fit them to the plasma viral load data. Based on the fitting results we argue that a model containing reversible Ab binding to virions and clearance of virus-VRC01 complexes by a two-step process that includes (1) saturable capture followed by (2) internalization/degradation by phagocytes, best explains the data. This model predicts that VRC01 may enhance the clearance of Ab-virus complexes, explaining the initial viral decay observed immediately after antibody infusion in some participants. Because Ab-virus complexes are assumed to be unable to infect cells, i.e., contain neutralized virus, the model predicts a longer-term viral decay consistent with that observed in the VRC01 treated participants. By assuming a homogeneous viral population sensitive to VRC01, the model provides good fits to all of the participant data. However, the fits are improved by assuming that there were two populations of virus, one more susceptible to antibody-mediated neutralization than the other.

Coexistence of Hopf-born rotation and heteroclinic cycling in a time-delayed three-gene auto-regulated and mutually-repressed core genetic regulation network

In this work, we study the behavior of a time-delayed mutually repressive auto-activating three-gene system. Delays are introduced to account for the location difference between DNA transcription that leads to production of messenger RNA and its translation that result in protein synthesis. We study the dynamics of the system using numerical simulations, computational bifurcation analysis and mathematical analysis. We find Hopf bifurcations leading to stable and unstable rotation in the system, and we study the rotational behavior as a function of cyclic mutual repression parameter asymmetry between each gene pair in the network. We focus on how rotation co-exists with a stable heteroclinic flow linking the three saddles in the system. We find that this coexistence allows for a transition between two markedly different types of rotation leading to strikingly different phenotypes. One type of rotation belongs to Hopf-induced rotation while the other type, belongs to heteroclinic cycling between three saddle nodes in the system. We discuss the evolutionary and biological implications of our findings.

Constructing and analysing dynamic models with modelbase v1.2.3: a software update

BACKGROUND

Computational mathematical models of biological and biomedical systems have been successfully applied to advance our understanding of various regulatory processes, metabolic fluxes, effects of drug therapies, and disease evolution and transmission. Unfortunately, despite community efforts leading to the development of SBML and the BioModels database, many published models have not been fully exploited, largely due to a lack of proper documentation or the dependence on proprietary software. To facilitate the reuse and further development of systems biology and systems medicine models, an open-source toolbox that makes the overall process of model construction more consistent, understandable, transparent, and reproducible is desired.

RESULTS AND DISCUSSION

We provide an update on the development of modelbase, a free, expandable Python package for constructing and analysing ordinary differential equation-based mathematical models of dynamic systems. It provides intuitive and unified methods to construct and solve these systems. Significantly expanded visualisation methods allow for convenient analysis of the structural and dynamic properties of models. After specifying reaction stoichiometries and rate equations modelbase can automatically assemble the associated system of differential equations. A newly provided library of common kinetic rate laws reduces the repetitiveness of the computer programming code. modelbase is also fully compatible with SBML. Previous versions provided functions for the automatic construction of networks for isotope labelling studies. Now, using user-provided label maps, modelbase v1.2.3 streamlines the expansion of classic models to their isotope-specific versions. Finally, the library of previously published models implemented in modelbase is growing continuously. Ranging from photosynthesis to tumour cell growth to viral infection evolution, all these models are now available in a transparent, reusable and unified format through modelbase.

CONCLUSION

With this new Python software package, which is written in currently one of the most popular programming languages, the user can develop new models and actively profit from the work of others. modelbase enables reproducing and replicating models in a consistent, tractable and expandable manner. Moreover, the expansion of models to their isotopic label-specific versions enables simulating label propagation, thus providing quantitative information regarding network topology and metabolic fluxes.

On multistep tumor growth models of fractional variable-order

Fractional mathematical oncology is a research topic that applies non-integer order calculus to tackle cancer problems such as tumor growth analysis or its optimal treatment. This work proposes a multistep exponential model with a fractional variable-order representing the evolution history of a tumor. Model parameters are tuned according to variable fractional order profiles while assessing their capability of fitting a clinical time series. The results point to the superiority of the proposed model in describing the experimental data, thus providing new perspectives for modeling tumor growth.

Utility of Point-of-Care Ultrasound in the Diagnosis of Idiopathic Intracranial Hypertension in the Emergency Department

BACKGROUND

Emergency physicians are frequently required to identify and triage patients with increased intracranial pressure (ICP). Idiopathic intracranial hypertension (IIH) is a possible cause that must be considered. Its prognosis depends on prompt recognition and treatment, and progression of the disease can lead to permanent vision loss and considerable morbidity. Point-of-care ultrasound can rapidly identify elevated ICP. Measurements of the optic nerve sheath diameter (ONSD) and optic disc elevation (ODE) can act as surrogates for ICP.

CASE SERIES

We describe five cases in which ultrasound was used to identify increased ICP and aid clinical decision-making. In several of the cases, ultrasound was used to confirm a suspicion for IIH and initiate therapy while awaiting the results of a more time-consuming and technically challenging test, such as lumbar puncture or optical coherence tomography. One of the patients was pregnant, and sonographic evidence of elevated ICP helped avoid exposing the patient to unnecessary radiation. WHY SHOULD AN EMERGENCY PHYSICIAN BE AWARE OF THIS?: Ultrasound is a quick and versatile tool for screening patients with neurologic symptoms, and when integrated into the proper clinical context, can reduce the use of more invasive tests. It can be particularly useful in patients with pathology that may not show abnormalities on computed tomography scan or in whom lumbar puncture is technically difficult, making patients at risk for IIH well-suited to examination by ultrasound. We use a cutoff of 5 mm for ONSD and 0.6 mm for ODE, though there are no universally agreed on cutoff values.

Studying the spatial temporal spread of the citrus tristeza virus through ODEs and Bernoulli trials

The Citrus tristeza virus (CTV) is one of the most economically devastating citrus diseases worldwide. The spread of CTV in eastern Spain was studied by Gottwald et al. with the goal of determining the spatio-temporal mechanisms of spread. Since the subjects in this study are individual trees, it is natural to think of infections as Bernoulli trials. This approach is difficult however, due to the spatial and temporal dependence of the observations. Consequently, a system of ordinary differential equations (ODE) was used to model the probabilities of infection as well as the spatial and temporal dependence. Given the parameters in the ODE, the probabilities of infection are treated as conditionally independent. Using the conditional independence we then specify the joint likelihood function as a Poisson binomial distribution. For the purpose of model selection and hypothesis testing we, employed accumulated prediction error (APE) which has connections to both Bayesian and frequentist frameworks. We demonstrated the robustness of our method in accounting for spatio-temporal dependencies in the data by accurately predicting the spatial distribution of the disease through Join Counts.

Mechanistic modeling explains the dsRNA length-dependent activation of the RIG-I mediated immune response

In cell-intrinsic antiviral immunity, cytoplasmic receptors such as retinoic acid-inducible gene I (RIG-I) detect viral double-stranded RNA (dsRNA) and trigger a signaling cascade activating the interferon (IFN) system. This leads to the transcription of hundreds of interferon-stimulated genes (ISGs) with a wide range of antiviral effects. This recognition of dsRNA not only has to be very specific to discriminate foreign from self but also highly sensitive to detect even very low numbers of pathogenic dsRNA molecules. Previous work indicated an influence of the dsRNA length on the binding behavior of RIG-I and its potential to elicit antiviral signaling. However, the molecular mechanisms behind the binding process are still under debate. We compare two hypothesized RIG-I binding mechanisms by translating them into mathematical models and analyzing their potential to describe published experimental data. The models consider the length of the dsRNA as well as known RIG-I binding motifs and describe RIG-I pathway activation after stimulation with dsRNA. We show that internal RIG-I binding sites in addition to cooperative RIG-I oligomerization are essential to describe the experimentally observed RIG-I binding behavior and immune response activation for different dsRNA lengths and concentrations. The combination of RIG-I binding to internal sites on the dsRNA and cooperative oligomerization compensates for a lack of high-affinity binding motifs and triggers a strong antiviral response for long dsRNAs. Model analysis reveals dsRNA length-dependency as a potential mechanism to discriminate between different types of dsRNAs: It allows for sensitive detection of small numbers of long dsRNAs, a typical by-product of viral replication, while ensuring tolerance against non-harming small dsRNAs.

Locally temperature - driven mathematical model of West Nile virus spread in Germany

West Nile virus (WNV) is an arthropod-borne virus (arbovirus) transmitted by the bites of infected mosquitoes. WNV can also infect horses and humans, where it may cause serious illness and can be fatal. Birds are the natural reservoir, and humans, equines and probably other mammals are dead-end hosts. In 2018, WNV occurred for the first time in Germany, affecting birds and horses. Seroconversion of an exposed veterinarian has also been reported. It is therefore of importance to evaluate the circumstances, under which WNV may establish in Germany as a whole or in particular favourable regions. In our current work, we formulate a dynamic model to describe the spreading process of West Nile virus in the presence of migratory birds. To investigate the possible role of migratory birds in the dissemination of WNV in Germany, we include the recurring presence of migratory birds through a mechanistic ordinary differential equations (ODE) model system. We also perform a sensitivity analysis of the infection curves. Seasonal impacts are also taken into consideration. As result, we present an analytical expression for the basic reproduction number R₀. We find that after introducing WNV into Germany, R₀ will be above the critical value in many regions of the country. Furthermore, we observe that in the south of Germany, the disease reoccurs in the following season after the introduction. We include a potential distribution map associated with WNV cases in Germany to illustrate our findings in a spatial scale.

Automatically Selecting a Suitable Integration Scheme for Systems of Differential Equations in Neuron Models

On the level of the spiking activity, the integrate-and-fire neuron is one of the most commonly used descriptions of neural activity. A multitude of variants has been proposed to cope with the huge diversity of behaviors observed in biological nerve cells. The main appeal of this class of model is that it can be defined in terms of a hybrid model, where a set of mathematical equations describes the sub-threshold dynamics of the membrane potential and the generation of action potentials is often only added algorithmically without the shape of spikes being part of the equations. In contrast to more detailed biophysical models, this simple description of neuron models allows the routine simulation of large biological neuronal networks on standard hardware widely available in most laboratories these days. The time evolution of the relevant state variables is usually defined by a small set of ordinary differential equations (ODEs). A small number of evolution schemes for the corresponding systems of ODEs are commonly used for many neuron models, and form the basis of the neuron model implementations built into commonly used simulators like Brian, NEST and NEURON. However, an often neglected problem is that the implemented evolution schemes are only rarely selected through a structured process based on numerical criteria. This practice cannot guarantee accurate and stable solutions for the equations and the actual quality of the solution depends largely on the parametrization of the model. In this article, we give an overview of typical equations and state descriptions for the dynamics of the relevant variables in integrate-and-fire models. We then describe a formal mathematical process to automate the design or selection of a suitable evolution scheme for this large class of models. Finally, we present the reference implementation of our symbolic analysis toolbox for ODEs that can guide modelers during the implementation of custom neuron models.

Role of Cytokine Combinations on CD4+ T Cell Differentiation, Partial Polarization, and Plasticity: Continuous Network Modeling Approach

Purpose: We put forward a theoretical and dynamical approach for the semi-quantitative analysis of CD4+ T cell differentiation, the process by which cells with different functions are derived from activated CD4+ T naïve lymphocytes in the presence of particular cytokine microenvironments. We explore the system-level mechanisms that underlie CD4+ T plasticity-the conversion of polarized cells to phenotypes different from those originally induced. Methods: In this paper, we extend a previous study based on a Boolean network to a continuous framework. The network includes transcription factors, signaling pathways, as well as autocrine and exogenous cytokines, with interaction rules derived using fuzzy logic. Results: This approach allows us to assess the effect of relative differences in the concentrations and combinations of exogenous and endogenous cytokines, as well as of the expression levels of diverse transcription factors. We found either abrupt or gradual differentiation patterns between observed phenotypes depending on critical concentrations of single or multiple environmental cytokines. Plastic changes induced by environmental cytokines were observed in conditions of partial phenotype polarization in the T helper 1 to T helper 2 transition. On the other hand, the T helper 17 to induced regulatory T-cells transition was highly dependent on cytokine concentrations, with TGFβ playing a prime role. Conclusion: The present approach is useful to further understand the system-level mechanisms underlying observed patterns of CD4+ T differentiation and response to changing immunological challenges.

Competition or cooperation in transboundary fish stocks management: Insight from a dynamical model

An idealized system of a shared fish stock associated with different exclusive economic zones (EEZ) is modelled. Parameters were estimated for the case of the small pelagic fisheries shared between Southern Morocco, Mauritania and the Senegambia. Two models of fishing effort distribution were explored. The first one considers independent national fisheries in each EEZ, with a cost per unit of fishing effort that depends on local fishery policy. The second one considers the case of a fully cooperative fishery performed by an international fleet freely moving across the borders. Both models are based on a set of six ordinary differential equations describing the time evolution of the fish biomass and the fishing effort. We take advantage of the two time scales to obtain a reduced model governing the total fish biomass of the system and fishing efforts in each zone. At the fast equilibrium, the fish distribution follows the ideal free distribution according to the carrying capacity in each area. Different equilibria can be reached according to management choices. When fishing fleets are independent and national fishery policies are not harmonized, in the general case, competition leads after a few decades to a scenario where only one fishery remains sustainable. In the case of sub-regional agreement acting on the adjustment of cost per unit of fishing effort in each EEZ, we found that a large number of equilibria exists. In this last case the initial distribution of fishing effort strongly impact the optimal equilibrium that can be reached. Lastly, the country with the highest carrying capacity density may get less landings when collaborating with other countries than if it minimises its fishing costs. The second fully cooperative model shows that a single international fishing fleet moving freely in the fishing areas leads to a sustainable equilibrium. Such findings should foster regional fisheries organizations to get potential new ways for neighbouring fish stock management.

Derivation of Continuum Models from An Agent-based Cancer Model: Optimization and Sensitivity Analysis

BACKGROUND

Agent-based models provide a formidable tool for exploring complex and emergent behaviour of biological systems as well as accurate results but with the drawback of needing a lot of computational power and time for subsequent analysis. On the other hand, equation-based models can more easily be used for complex analysis in a much shorter timescale.

METHODS & OBJECTIVE

This paper formulates an ordinary differential equations and stochastic differential equations model to capture the behaviour of an existing agent-based model of tumour cell reprogramming and applies it to optimization of possible treatment as well as dosage sensitivity analysis.

RESULTS

For certain values of the parameter space a close match between the equation-based and agent-based models is achieved. The need for division of labour between the two approaches is explored.

Heterogeneous computing for epidemiological model fitting and simulation

Background

Over the last years, substantial effort has been put into enhancing our arsenal in fighting epidemics from both technological and theoretical perspectives with scientists from different fields teaming up for rapid assessment of potentially urgent situations. This paper focusses on the computational aspects of infectious disease models and applies commonly available graphics processing units (GPUs) for the simulation of these models. However, fully utilizing the resources of both CPUs and GPUs requires a carefully balanced heterogeneous approach.

Results

The contribution of this paper is twofold. First, an efficient GPU implementation for evaluating a small-scale ODE model; here, the basic S(usceptible)-I(nfected)-R(ecovered) model, is discussed. Second, an asynchronous particle swarm optimization (PSO) implementation is proposed where batches of particles are sent asynchronously from the host (CPU) to the GPU for evaluation. The ultimate goal is to infer model parameters that enable the model to correctly describe observed data. The particles of the PSO algorithm are candidate parameters of the model; finding the right one is a matter of optimizing the likelihood function which quantifies how well the model describes the observed data. By employing a heterogeneous approach, in which both CPU and GPU are kept busy with useful work, speedups of 10 to 12 times can be achieved on a moderate machine with a high-end consumer GPU as compared to a high-end system with 32 CPU cores.

Conclusions

Utilizing GPUs for parameter inference can bring considerable increases in performance using average host systems with high-end consumer GPUs. Future studies should evaluate the benefit of using newer CPU and GPU architectures as well as applying this method to more complex epidemiological scenarios.

Predicting the impact of combined therapies on myeloma cell growth using a hybrid multi-scale agent-based model

Multiple myeloma is a malignant still incurable plasma cell disorder. This is due to refractory disease relapse, immune impairment, and development of multi-drug resistance. The growth of malignant plasma cells is dependent on the bone marrow (BM) microenvironment and evasion of the host's anti-tumor immune response. Hence, we hypothesized that targeting tumor-stromal cell interaction and endogenous immune system in BM will potentially improve the response of multiple myeloma (MM). Therefore, we proposed a computational simulation of the myeloma development in the complicated microenvironment which includes immune cell components and bone marrow stromal cells and predicted the effects of combined treatment with multi-drugs on myeloma cell growth. We constructed a hybrid multi-scale agent-based model (HABM) that combines an ODE system and Agent-based model (ABM). The ODEs was used for modeling the dynamic changes of intracellular signal transductions and ABM for modeling the cell-cell interactions between stromal cells, tumor, and immune components in the BM. This model simulated myeloma growth in the bone marrow microenvironment and revealed the important role of immune system in this process. The predicted outcomes were consistent with the experimental observations from previous studies. Moreover, we applied this model to predict the treatment effects of three key therapeutic drugs used for MM, and found that the combination of these three drugs potentially suppress the growth of myeloma cells and reactivate the immune response. In summary, the proposed model may serve as a novel computational platform for simulating the formation of MM and evaluating the treatment response of MM to multiple drugs.

Mathematical Modeling Approaches in Plant Metabolomics

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Qualitative Analysis of an ODE Model of a Class of Enzymatic Reactions : Some Results on Global Stability of Messenger RNA-MicroRNA Interaction

The present paper analyzes an ODE model of a certain class of (open) enzymatic reactions. This type of model is used, for instance, to describe the interactions between messenger RNAs and microRNAs. It is shown that solutions defined by positive initial conditions are well defined and bounded on [Formula: see text] and that the positive octant of [Formula: see text] is a positively invariant set. We prove further that in this positive octant there exists a unique equilibrium point, which is asymptotically stable and a global attractor for any initial state with positive components; a controllability property is emphasized. We also investigate the qualitative behavior of the QSSA system in the phase plane [Formula: see text]. For this planar system we obtain similar results regarding global stability by using Lyapunov theory, invariant regions and controllability.

Planning horizon affects prophylactic decision-making and epidemic dynamics

The spread of infectious diseases can be impacted by human behavior, and behavioral decisions often depend implicitly on a planning horizon—the time in the future over which options are weighed. We investigate the effects of planning horizons on epidemic dynamics. We developed an epidemiological agent-based model (along with an ODE analog) to explore the decision-making of self-interested individuals on adopting prophylactic behavior. The decision-making process incorporates prophylaxis efficacy and disease prevalence with the individuals’ payoffs and planning horizon. Our results show that for short and long planning horizons individuals do not consider engaging in prophylactic behavior. In contrast, individuals adopt prophylactic behavior when considering intermediate planning horizons. Such adoption, however, is not always monotonically associated with the prevalence of the disease, depending on the perceived protection efficacy and the disease parameters. Adoption of prophylactic behavior reduces the epidemic peak size while prolonging the epidemic and potentially generates secondary waves of infection. These effects can be made stronger by increasing the behavioral decision frequency or distorting an individual’s perceived risk of infection.

Spatially heterogeneous populations with mixed negative and positive local density dependence

Identifying the steady states of a population is a key issue in theoretical ecology, that includes the study of spatially heterogeneous populations. There are several examples of real ecosystems in patchy environments where the habitats are heterogeneous in their local density dependence. We investigate a multi-patch model of a single species with spatial dispersal, where the growth of the local population is logistic in some localities (negative density dependence) while other patches exhibit a strong Allee effect (positive density dependence). When the local dynamics is logistic in each patch and the habitats are interconnected by dispersal then the total population has only the extinction steady state and a componentwise positive equilibrium, corresponding to persistence in each patch. We show that animal populations in patchy environments can have a large number of steady states if local density dependence varies over the locations. It is demonstrated that, depending on the network topology of migration routes between the patches, the interaction of spatial dispersal and local density dependence can create a variety of coexisting stable positive equilibria. We give a detailed description of the multiple ways dispersal can rescue local populations from extinction.

Computational Methods to Model Persistence

Bacterial persister cells are dormant cells, tolerant to multiple antibiotics, that are involved in several chronic infections. Toxin-antitoxin modules play a significant role in the generation of such persister cells. Toxin-antitoxin modules are small genetic elements, omnipresent in the genomes of bacteria, which code for an intracellular toxin and its neutralizing antitoxin. In the past decade, mathematical modeling has become an important tool to study the regulation of toxin-antitoxin modules and their relation to the emergence of persister cells. Here, we provide an overview of several numerical methods to simulate toxin-antitoxin modules. We cover both deterministic modeling using ordinary differential equations and stochastic modeling using stochastic differential equations and the Gillespie method. Several characteristics of toxin-antitoxin modules such as protein production and degradation, negative autoregulation through DNA binding, toxin-antitoxin complex formation and conditional cooperativity are gradually integrated in these models. Finally, by including growth rate modulation, we link toxin-antitoxin module expression to the generation of persister cells.

Comparison of mathematical frameworks for modeling erythropoiesis in the context of malaria infection

Malaria is an infectious disease present all around the globe and responsible for half a million deaths per year. A within-host model of this infection requires a framework capable of properly approximating not only the blood stage of the infection but also the erythropoietic process that is in charge of overcoming the malaria induced anemia. Within this context, we compare ordinary differential equations (ODEs) with and without age classes, delayed differential equations (DDEs), and discrete recursive equations (DREs) with age classes. Results show that ODEs without age classes are fair approximations that do not provide a crisp temporal representation of the processes involved, and inclusion of age classes only mitigates the problem to some degree. DDEs perform well with respect to generating the essentially fixed delay between cell production and cell removal due to age, but the inclusion of any other processes, such as sudden blood loss, becomes cumbersome. The framework that was found to perform best in representing the dynamics of red blood cells during malaria infection is a DRE with age classes. In this model structure, the amount of time a cell remains alive is easily controlled, and the addition of age dependent or independent processes is straightforward. All events that populations of cells face during their lifespan, like growth or adaptation in differentiation or maturation rate, are properly represented in this framework.

Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).

Skeletal muscle mitochondria of NDUFS4-/- mice display normal maximal pyruvate oxidation and ATP production

Mitochondrial ATP production is mediated by the oxidative phosphorylation (OXPHOS) system, which consists of four multi-subunit complexes (CI-CIV) and the FoF1-ATP synthase (CV). Mitochondrial disorders including Leigh Syndrome often involve CI dysfunction, the pathophysiological consequences of which still remain incompletely understood. Here we combined experimental and computational strategies to gain mechanistic insight into the energy metabolism of isolated skeletal muscle mitochondria from 5-week-old wild-type (WT) and CI-deficient NDUFS4-/- (KO) mice. Enzyme activity measurements in KO mitochondria revealed a reduction of 79% in maximal CI activity (Vmax), which was paralleled by 45-72% increase in Vmax of CII, CIII, CIV and citrate synthase. Mathematical modeling of mitochondrial metabolism predicted that these Vmax changes do not affect the maximal rates of pyruvate (PYR) oxidation and ATP production in KO mitochondria. This prediction was empirically confirmed by flux measurements. In silico analysis further predicted that CI deficiency altered the concentration of intermediate metabolites, modestly increased mitochondrial NADH/NAD+ ratio and stimulated the lower half of the TCA cycle, including CII. Several of the predicted changes were previously observed in experimental models of CI-deficiency. Interestingly, model predictions further suggested that CI deficiency only has major metabolic consequences when its activity decreases below 90% of normal levels, compatible with a biochemical threshold effect. Taken together, our results suggest that mouse skeletal muscle mitochondria possess a substantial CI overcapacity, which minimizes the effects of CI dysfunction on mitochondrial metabolism in this otherwise early fatal mouse model.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

Modeling the effects of systemic mediators on the inflammatory phase of wound healing

The normal wound healing response is characterized by a progression from clot formation, to an inflammatory phase, to a repair phase, and finally, to remodeling. In many chronic wounds there is an extended inflammatory phase that stops this progression. In order to understand the inflammatory phase in more detail, we developed an ordinary differential equation model that accounts for two systemic mediators that are known to modulate this phase, estrogen (a protective hormone during wound healing) and cortisol (a hormone elevated after trauma that slows healing). This model describes the interactions in the wound between wound debris, pathogens, neutrophils and macrophages and the modulation of these interactions by estrogen and cortisol. A collection of parameter sets, which qualitatively match published data on the dynamics of wound healing, was chosen using Latin Hypercube Sampling. This collection of parameter sets represents normal healing in the population as a whole better than one single parameter set. Including the effects of estrogen and cortisol is a necessary step to creating a patient specific model that accounts for gender and trauma. Utilization of math modeling techniques to better understand the wound healing inflammatory phase could lead to new therapeutic strategies for the treatment of chronic wounds. This inflammatory phase model will later become the inflammatory subsystem of our full wound healing model, which includes fibroblast activity, collagen accumulation and remodeling.

Integrated signaling pathway and gene expression regulatory model to dissect dynamics of Escherichia coli challenged mammary epithelial cells

Cells transform external stimuli, through the activation of signaling pathways, which in turn activate gene regulatory networks, in gene expression. As more omics data are generated from experiments, eliciting the integrated relationship between the external stimuli, the signaling process in the cell and the subsequent gene expression is a major challenge in systems biology. The complex system of non-linear dynamic protein interactions in signaling pathways and gene networks regulates gene expression. The complexity and non-linear aspects have resulted in the study of the signaling pathway or the gene network regulation in isolation. However, this limits the analysis of the interaction between the two components and the identification of the source of the mechanism differentiating the gene expression profiles. Here, we present a study of a model of the combined signaling pathway and gene network to highlight the importance of integrated modeling. Based on the experimental findings we developed a compartmental model and conducted several simulation experiments. The model simulates the mRNA expression of three different cytokines (RANTES, IL8 and TNFα) regulated by the transcription factor NFκB in mammary epithelial cells challenged with E. coli. The analysis of the gene network regulation identifies a lack of robustness and therefore sensitivity for the transcription factor regulation. However, analysis of the integrated signaling and gene network regulation model reveals distinctly different underlying mechanisms in the signaling pathway responsible for the variation between the three cytokine's mRNA expression levels. Our key findings reveal the importance of integrating the signaling pathway and gene expression dynamics in modeling. Modeling infers valid research questions which need to be verified experimentally and can assist in the design of future biological experiments.

CYP345E2, an antenna-specific cytochrome P450 from the mountain pine beetle, Dendroctonus ponderosae Hopkins, catalyses the oxidation of pine host monoterpene volatiles

The mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) is a significant pest of western North American pine forests. This beetle responds to pheromones and host volatiles in order to mass attack and thus overcome the terpenoid chemical defences of its host. The ability of MPB antennae to rapidly process odorants is necessary to avoid odorant receptor saturation and thus the enzymes responsible for odorant clearance are an important aspect of host colonization. An antenna-specific cytochrome P450, DponCYP345E2, is the most highly expressed transcript in adult MPB antenna. In in vitro assays with recombinant enzyme, DponCYP345E2 used several pine host monoterpenes as substrates, including (+)-(3)-carene, (+)-β-pinene, (-)-β-pinene, (+)-limonene, (-)-limonene, (-)-camphene, (+)-α-pinene, (-)-α-pinene, and terpinolene. The substrates were epoxidized or hydroxylated, depending upon the substrate. To complement DponCYP345E2, we also functionally characterized the NADPH-dependent cytochrome P450 reductase and the cytochrome b5 from MPB. DponCYP345E2 is the first cytochrome P450 to be functionally characterized in insect olfaction and in MPB.

Biological networks 101: computational modeling for molecular biologists

Computational modeling of biological networks permits the comprehensive analysis of cells and tissues to define molecular phenotypes and novel hypotheses. Although a large number of software tools have been developed, the versatility of these tools is limited by mathematical complexities that prevent their broad adoption and effective use by molecular biologists. This study clarifies the basic aspects of molecular modeling, how to convert data into useful input, as well as the number of time points and molecular parameters that should be considered for molecular regulatory models with both explanatory and predictive potential. We illustrate the necessary experimental preconditions for converting data into a computational model of network dynamics. This model requires neither a thorough background in mathematics nor precise data on intracellular concentrations, binding affinities or reaction kinetics. Finally, we show how an interactive model of crosstalk between signal transduction pathways in primary human articular chondrocytes allows insight into processes that regulate gene expression.

Stopped-flow fluorescence kinetic study of protein sliding and intersegment transfer in the target DNA search process

Kinetic characterizations of protein translocation on DNA are nontrivial because the simultaneous presence of multiple different mechanisms makes it difficult to extract the information specific to a particular translocation mechanism. In this study, we have developed new approaches for the kinetic investigations of proteins' sliding and intersegment transfer (also known as "direct transfer") in the target DNA search process. Based on the analytical expression of the mean search time for the discrete-state stochastic model, we derived analytical forms of the apparent rate constant kapp for protein-target association in systems involving competitor DNA and the intersegment transfer mechanism. Our analytical forms of kapp facilitate the experimental determination of the kinetic rate constants for intersegment transfer and sliding in the target association process. Using stopped-flow fluorescence data for the target association kinetics along with the analytical forms of kapp, we have studied the translocation of the Egr-1 zinc-finger protein in the target DNA association process. Sliding was analyzed using the DNA-length-dependent kapp data. Using the dependence of kapp on the concentration of competitor DNA, we determined the second-order rate constant for intersegment transfer. Our results indicate that a major pathway in the target association process for the Egr-1 zinc-finger protein is the one involving intersegment transfer to a nonspecific site and the subsequent sliding to the target.

In vivo, in vitro, and in silico studies suggest a conserved immune module that regulates malaria parasite transmission from mammals to mosquitoes

Human malaria can be caused by the parasite Plasmodium falciparum that is transmitted by female Anopheles mosquitoes. "Immunological crosstalk" between the mammalian and anopheline hosts for Plasmodium functions to control parasite numbers. Key to this process is the mammalian cytokine transforming growth factor-β1 (TGF-β1). In mammals, TGF-β1 regulates inducible nitric oxide (NO) synthase (iNOS) both positively and negatively. In some settings, high levels of NO activate latent TGF-β1, which in turn suppresses iNOS expression. In the mosquito, ingested TGF-β1 induces A. stephensi NOS (AsNOS), which limits parasite development and which in turn is suppressed by activation of the mosquito homolog of the mitogen-activated protein kinases MEK and ERK. Computational models linking TGF-β1, AsNOS, and MEK/ERK were developed to provide insights into this complex biology. An initial Boolean model suggested that, as occurs in mammalian cells, MEK/ERK and AsNOS would oscillate upon ingestion of TGF-β1. An ordinary differential equation (ODE) model further supported the hypothesis of TGF-β1-induced multiphasic behavior of MEK/ERK and AsNOS. To achieve this multiphasic behavior, the ODE model was predicated on the presence of constant levels of TGF-β1 in the mosquito midgut. Ingested TGF-β1, however, did not exhibit this behavior. Accordingly, we hypothesized and experimentally verified that ingested TGF-β1 induces the expression of the endogenous mosquito TGF-β superfamily ligand As60A. Computational simulation of these complex, cross-species interactions suggested that TGF-β1 and NO-mediated induction of As60A expression together may act to maintain multiphasic AsNOS expression via MEK/ERK-dependent signaling. We hypothesize that multiphasic behavior as represented in this model allows the mosquito to balance the conflicting demands of parasite killing and metabolic homeostasis in the face of damaging inflammation.

Mathematical modelling of cytokine-mediated inflammation in rheumatoid arthritis

Rheumatoid arthritis (RA) is a chronic inflammatory disease preferentially affecting the joints and leading, if untreated, to progressive joint damage and disability. Cytokines, a group of small inducible proteins, which act as intercellular messengers, are key regulators of the inflammation that characterizes RA. They can be classified into pro-inflammatory and anti-inflammatory groups. Numerous cytokines have been implicated in the regulation of RA with complex up and down regulatory interactions. This paper considers a two-variable model for the interactions between pro-inflammatory and anti-inflammatory cytokines, and demonstrates that mathematical modelling may be used to investigate the involvement of cytokines in the disease process. The model displays a range of possible behaviours, such as bistability and oscillations, which are strongly reminiscent of the behaviour of RA e.g. genetic susceptibility and remitting-relapsing disease. We also show that the dose regimen as well as the dose level are important factors in RA treatments.