Modelling Degradation and Replication Kinetics of the Zika Virus In Vitro Infection

Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus–host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.

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Analysis of Ribonucleotide 5′-Triphosphate Analogs as Potential Inhibitors of Zika Virus RNA-Dependent RNA Polymerase by Using Nonradioactive Polymerase Assays

Antimicrobial Agents and Chemotherapy ◽

10.1128/aac.01967-16 ◽

2016 ◽

Vol 61 (3) ◽

Cited By ~ 24

Author(s):

Gaofei Lu ◽

Gregory R. Bluemling ◽

Paul Collop ◽

Michael Hager ◽

Damien Kuiper ◽

...

Keyword(s):

Rna Polymerase ◽

Zika Virus ◽

Nonstructural Protein ◽

Rna Dependent Rna Polymerase ◽

Antiviral Compounds ◽

Double Stranded Dna ◽

Virus Rna ◽

Potential Inhibitors

ABSTRACT Zika virus (ZIKV) is an emerging human pathogen that is spreading rapidly through the Americas and has been linked to the development of microcephaly and to a dramatically increased number of Guillain-Barré syndrome cases. Currently, no vaccine or therapeutic options for the prevention or treatment of ZIKV infections exist. In the study described in this report, we expressed, purified, and characterized full-length nonstructural protein 5 (NS5) and the NS5 polymerase domain (NS5pol) of ZIKV RNA-dependent RNA polymerase. Using purified NS5, we developed an in vitro nonradioactive primer extension assay employing a fluorescently labeled primer-template pair. Both purified NS5 and NS5pol can carry out in vitro RNA-dependent RNA synthesis in this assay. Our results show that Mn2+ is required for enzymatic activity, while Mg2+ is not. We found that ZIKV NS5 can utilize single-stranded DNA but not double-stranded DNA as a template or a primer to synthesize RNA. The assay was used to compare the efficiency of incorporation of analog 5′-triphosphates by the ZIKV polymerase and to calculate their discrimination versus that of natural ribonucleotide triphosphates (rNTPs). The 50% inhibitory concentrations for analog rNTPs were determined in an alternative nonradioactive coupled-enzyme assay. We determined that, in general, 2′-C-methyl- and 2′-C-ethynyl-substituted analog 5′-triphosphates were efficiently incorporated by the ZIKV polymerase and were also efficient chain terminators. Derivatives of these molecules may serve as potential antiviral compounds to be developed to combat ZIKV infection. This report provides the first characterization of ZIKV polymerase and demonstrates the utility of in vitro polymerase assays in the identification of potential ZIKV inhibitors.

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Spectral characterization of ciliary beating: variations of frequency with time

AJP Cell Physiology ◽

10.1152/ajpcell.1985.249.1.c160 ◽

1985 ◽

Vol 249 (1) ◽

pp. C160-C165 ◽

Cited By ~ 57

Author(s):

D. Eshel ◽

Y. Grossman ◽

Z. Priel

Keyword(s):

Mathematical Model ◽

Power Spectra ◽

Ciliary Beating ◽

Isolated Lung ◽

Ciliary Cell ◽

The Mathematical Model ◽

Beating Frequency ◽

Over Time ◽

Dominant Frequencies

Ciliary beating frequency in tissue culture from frog palate and isolated lung was optically examined using instrumentation that was adjusted to measure a fraction of the surface area of a single ciliary cell. Consecutive 1-s segments of the analogue signal were fast Fourier transformed (FFT) to obtain a power spectrum. At room temperature, these power spectra changed over time from 1 s to the next. Each spectrum contained several dominant frequencies of similar intensities. Cooling the preparation resulted in a single-peak spectrum that was constant over time. A mathematical model is proposed to simulate these findings. The results and the mathematical model support the hypothesis that ciliary beating frequency fluctuates over short periods of time.

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In vitro and in vivo characterization of erythrosin B and derivatives against Zika virus

Acta Pharmaceutica Sinica B ◽

10.1016/j.apsb.2021.10.017 ◽

2021 ◽

Author(s):

Zhong Li ◽

Jimin Xu ◽

Yuekun Lang ◽

Xiangmeng Wu ◽

Saiyang Hu ◽

...

Keyword(s):

Zika Virus ◽

Erythrosin B ◽

In Vivo Characterization

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Damping and Bandgap Characteristics of a Viscoelastic Tensegrity Damper

Journal of Vibration and Acoustics ◽

10.1115/1.4051091 ◽

2021 ◽

pp. 1-47

Author(s):

Mohamed Raafat ◽

Amr Baz

Keyword(s):

Mathematical Model ◽

Material Characterization ◽

Structural Vibrations ◽

New Class ◽

Structural Applications ◽

Theoretical Predictions ◽

Specific Frequency ◽

The Mathematical Model ◽

Theory And Experiments

Abstract A theoretical and experimental investigation of a new class of a tensegrity-based structural damper is presented. The damper is not only capable of attenuating undesirable structural vibrations, as all conventional dampers, but also capable of completely blocking the transmission of vibration over specific frequency bands by virtue of its periodicity. Such dual functionality distinguishes the tensegrity damper over its counterparts of existing structural dampers. Particular emphasis is placed here in presenting the concept and developing the mathematical model of the dynamics of a unit cell the damper. The model is then coupled with a Floquet-Bloch analysis in order to identify the bandgap characteristics of the damper. The predictions of the mathematical model are validated experimentally using a prototype of the damper which is built using 3D printing. A comprehensive material characterization of the damper is performed followed by a detailed extraction of the static and dynamic behavior of the damper in order to validate the theoretical predictions. Close agreement is observed between theory and experiments. The developed theoretical and experimental techniques provide invaluable means for the design of this new class of dampers particularly for critical structural applications.

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A Musculoskeletal Model of the Equine Forelimb for Determining Surface Stresses and Strains in the Humerus—Part II. Experimental Testing and Model Validation

Journal of Biomechanical Engineering ◽

10.1115/1.2898729 ◽

2008 ◽

Vol 130 (4) ◽

Cited By ~ 2

Author(s):

Sarah Pollock ◽

Susan M. Stover ◽

M. L. Hull ◽

Larry D. Galuppo

Keyword(s):

Mathematical Model ◽

Stress Fracture ◽

Biceps Brachii ◽

Experimental Testing ◽

Longitudinal Axis ◽

Principal Strain ◽

Longitudinal Strains ◽

The Mathematical Model ◽

Experimental Strains

The first objective of this study was to experimentally determine surface bone strain magnitudes and directions at the donor site for bone grafts, the site predisposed to stress fracture, the medial and cranial aspects of the transverse cross section corresponding to the stress fracture site, and the middle of the diaphysis of the humerus of a simplified in vitro laboratory preparation. The second objective was to determine whether computing strains solely in the direction of the longitudinal axis of the humerus in the mathematical model was inherently limited by comparing the strains measured along the longitudinal axis of the bone to the principal strain magnitudes and directions. The final objective was to determine whether the mathematical model formulated in Part I [Pollock et al., 2008, ASME J. Biomech. Eng., 130, p. 041006] is valid for determining the bone surface strains at the various locations on the humerus where experimentally measured longitudinal strains are comparable to principal strains. Triple rosette strain gauges were applied at four locations circumferentially on each of two cross sections of interest using a simplified in vitro laboratory preparation. The muscles included the biceps brachii muscle in addition to loaded shoulder muscles that were predicted active by the mathematical model. Strains from the middle grid of each rosette, aligned along the longitudinal axis of the humerus, were compared with calculated principal strain magnitudes and directions. The results indicated that calculating strains solely in the direction of the longitudinal axis is appropriate at six of eight locations. At the cranial and medial aspects of the middle of the diaphysis, the average minimum principal strain was not comparable to the average experimental longitudinal strain. Further analysis at the remaining six locations indicated that the mathematical model formulated in Part I predicts strains within ±2 standard deviations of experimental strains at four of these locations and predicts negligible strains at the remaining two locations, which is consistent with experimental strains. Experimentally determined longitudinal strains at the middle of the diaphysis of the humerus indicate that tensile strains occur at the cranial aspect and compressive strains occur at the caudal aspect while the horse is standing, which is useful for fracture fixation.

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Gas-Tight Oxides - Reality or Just a Hope

Materials Science Forum ◽

10.4028/www.scientific.net/msf.522-523.93 ◽

2006 ◽

Vol 522-523 ◽

pp. 93-102 ◽

Cited By ~ 10

Author(s):

C. Anghel ◽

Gunnar Hultquist ◽

Qian Dong ◽

J. Rundgren ◽

Isao Saeki ◽

...

Keyword(s):

Mathematical Model ◽

High Vacuum ◽

Ultra High Vacuum ◽

Gas Content ◽

Molar Ratio ◽

Protection Measure ◽

Straightforward Method ◽

Gas Tight ◽

The Mathematical Model

A better understanding of the transport properties of gases in oxides is certainly very important in many applications. In the case of metals, a general protection measure against corrosion implies formation of a dense metal oxide scale. The scale should act as a barrier against gas transport and consequently it needs to be gas-tight. This is often assumed but rarely, if ever, confirmed. Hence there is a need for characterization of micro- and/or meso- pores formed especially during the early oxidation stage of metallic materials. This paper presents a novel and relatively straightforward method for characterization of gas release from an oxide previously equilibrated in a controlled atmosphere. The geometry of the sample is approximated to be a plate. The plate can be self-supporting or constitute a scale on a substrate. A mathematical model for calculation of diffusivity and gas content is given for this geometry. A desorption experiment, involving a mass spectrometer placed in ultra high vacuum, can be used to determine diffusivity and amount of gas released with aid of the mathematical model. The method is validated in measurements of diffusivity and solubility of He in quartz and applied in characterization of two Zroxides and one Fe oxide. From the outgassed amounts of water and nitrogen the H2O/N2 molar ratio can be used to estimate an effective pore size in oxides.

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The mathematical model of temperature dependent growth of Scuticociliate Miamiensis avidus in vitro and in vivo conditions

Journal of fish pathology ◽

10.7847/jfp.2013.26.2.065 ◽

2013 ◽

Vol 26 (2) ◽

pp. 65-75

Author(s):

Chun-Young Oh

Keyword(s):

Mathematical Model ◽

Temperature Dependent ◽

Miamiensis Avidus ◽

Dependent Growth ◽

The Mathematical Model

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Advances in Zika Virus–Host Cell Interaction: Current Knowledge and Future Perspectives

International Journal of Molecular Sciences ◽

10.3390/ijms20051101 ◽

2019 ◽

Vol 20 (5) ◽

pp. 1101 ◽

Cited By ~ 14

Author(s):

Jae Lee ◽

Ok Shin

Keyword(s):

Host Cell ◽

Zika Virus ◽

Current Knowledge ◽

Cell Interaction ◽

Human Pathogens ◽

Zikv Infection ◽

In Vivo Models ◽

Host Cell Interaction

Emerging mosquito-transmitted RNA viruses, such as Zika virus (ZIKV) and Chikungunya represent human pathogens of an immense global health problem. In particular, ZIKV has emerged explosively since 2007 to cause a series of epidemics in the South Pacific and most recently in the Americas. Although typical ZIKV infections are asymptomatic, ZIKV infection during pregnancy is increasingly associated with microcephaly and other fetal developmental abnormalities. In the last few years, genomic and molecular investigations have established a remarkable progress on the pathogenic mechanisms of ZIKV infection using in vitro and in vivo models. Here, we highlight recent advances in ZIKV-host cell interaction studies, including cellular targets of ZIKV, ZIKV-mediated cell death mechanisms, host cell restriction factors that limit ZIKV replication, and immune evasion mechanisms utilized by ZIKV. Understanding of the mechanisms of ZIKV–host interaction at the cellular level will contribute crucial insights into the development of ZIKV therapeutics and vaccines.

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Correlation between Animal and Mathematical Models for Prostate Cancer Progression

Computational and Mathematical Methods in Medicine ◽

10.1080/17486700802517518 ◽

2009 ◽

Vol 10 (4) ◽

pp. 241-252 ◽

Cited By ~ 11

Author(s):

Z. Jackiewicz ◽

C. L. Jorcyk ◽

M. Kolev ◽

B. Zubik-Kowal

Keyword(s):

Mathematical Model ◽

Cancer Progression ◽

Growth Rates ◽

Numerical Solutions ◽

Initial Conditions ◽

Tumour Progression ◽

Prostate Cancer Progression ◽

The Mathematical Model

This work demonstrates that prostate tumour progressionin vivocan be analysed by using solutions of a mathematical model supplemented by initial conditions chosen according to growth rates of cell linesin vitro. The mathematical model is investigated and solved numerically. Its numerical solutions are compared with experimental data from animal models. The numerical results confirm the experimental results with the growth ratesin vivo.

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