Escherichia coli chemotaxis to competing stimuli in a microfluidic device with a constant gradient

In natural systems bacteria are exposed to many chemical stimulants; some attract chemotactic bacteria as they promote survival, while others repel bacteria because they inhibit survival. When faced with a mixture of chemoeffectors, it is not obvious which direction the population will migrate. Predicting this direction requires an understanding of how bacteria process information about their surroundings. We used a multiscale mathematical model to relate molecular level details of their two-component signaling system to the probability that an individual cell changes its swimming direction to the chemotactic velocity of a bacterial population. We used a microfluidic device designed to maintain a constant chemical gradient to compare model predictions to experimental observations. We obtained parameter values for the multiscale model of Escherichia coli chemotaxis to individual stimuli, α-methylaspartate and nickel ion, separately. Then without any additional fitting parameters, we predicted the response to chemoeffector mixtures. Migration of E. coli toward α-methylaspartate was modulated by adding increasing concentrations of nickel ion. Thus, the migration direction was controlled by the relative concentrations of competing chemoeffectors in a predictable way. This study demonstrated the utility of a multiscale model to predict the migration direction of bacteria in the presence of competing chemoeffectors.

Multiscale Modelling of De Novo Anaerobic Granulation

A multiscale mathematical model is presented to describe de novo granulation, and the evolution of multispecies granular biofilms, in a continuously fed bioreactor. The granule is modelled as a spherical free boundary domain with radial symmetry. The equation governing the free boundary is derived from global mass balance considerations and takes into account the growth of sessile biomass as well as exchange fluxes with the bulk liquid. Starting from a vanishing initial value, the expansion of the free boundary is initiated by the attachment process, which depends on the microbial species concentrations within the bulk liquid and their specific attachment velocity. Nonlinear hyperbolic PDEs model the growth of the sessile microbial species, while quasi-linear parabolic PDEs govern the dynamics of substrates and invading species within the granular biofilm. Nonlinear ODEs govern the evolution of soluble substrates and planktonic biomass within the bulk liquid. The model is applied to an anaerobic, granular-based bioreactor system, and solved numerically to test its qualitative behaviour and explore the main aspects of de novo anaerobic granulation: ecology, biomass distribution, relative abundance, dimensional evolution of the granules and soluble substrates, and planktonic biomass dynamics within the bioreactor. The numerical results confirm that the model accurately describes the ecology and the concentrically layered structure of anaerobic granules observed experimentally, and that it can predict the effects on the process of significant factors, such as influent wastewater composition; granulation properties of planktonic biomass; biomass density; detachment intensity; and number of granules.

A multiscale spatiotemporal model explains succession in the early infant gut microbiota as a switch from aerobic to anaerobic metabolism

The human intestinal microbiome starts to form immediately after birth, and can greatly influence the health of the infant. During the first days facultative anaerobic species generally dominate, followed by a dominance of strictly anaerobic species, particularly Bifidobacterium species. An early transition to Bifidobacterium is associated with health benefits. To study the mechanisms of this transition and its hypothesised relation to oxygen, we introduce a multiscale mathematical model that considers metabolism, spatial bacterial population dynamics and resource sharing. Based on publicly available metabolic network data, the model predicts that differences in oxygen availability explain some of the observed individual variation in succession to anaerobic species. The model also predicts that anaerobic Bifidobacterium species become dominant through metabolizing lactose with a suboptimal yield, but a higher anaerobic growth rate than its competitors. The current work is the first step towards a more comprehensive understanding of the formation of a steady state adult colonic microbiota.

HIV Propagation in a Population Group Considering Infection in the Immune System Of Each Infected Individual

A multiscale mathematical model is proposed seeking to study the propagation dynamics of the Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through sexual contact without protection, considering the use of antiretroviral therapy (ART) and therapeutic failure. The model consists in a scale-free complex network that follows a power law, coupled with the immunological dynamics of each individual, that is, it considers the infection by the virus in the immune system of each HIV carrier, through a system of non-linear differential equations that govern the infection’s behavior in the immune system. Propagation of the virus in the network is modelled by taking into account information from the immunological status of each person. The study found that for a population to have high HIV prevalence, it is not necessary at the beginning of the simulation time for the virus to propagate rapidly. In addition, the study proves that with a higher number of sexual partners, there will be greater prevalence of HIV in the population and that the use of ART helps to control the propagation of the infection in the population. As an interesting result, it was also found that there is a higher number of HIV carriers who abandon ART than those who have access to it.

Multiscale supercomputer modeling of gas purification processes by the adsorption method

Рассматривается проблема суперкомпьютерного моделирования процессов очистки воздушной среды от мелкодисперсных твердых загрязняющих примесей, кластеризованных в виде наночастиц. Моделируемый способ очистки предполагает применение нанофильтров и сорбентов. Оба способа очистки часто комбинируются в современных очистных системах. Способ очистки с помощью нанофильтров позволяет получить высокое качество, но является дорогостоящим вследствие необходимости частой замены фильтрующих элементов (мембран). Способ очистки с помощью сорбентов оказывается несколько хуже по качеству, однако позволяет проводить очистку многократно после промывки сорбента специальными жидкостями. Для оптимизации систем воздушной очистки, использующих нанофильтры и сорбенты, необходимо детальное исследование протекающих в системе очистки процессов. В предлагаемом исследовании рассматривается часть проблемы, связанная с прохождением воздушного потока, содержащего твердые наночастицы загрязнителя, через слой гранулированного сорбента. Для этого разработаны многомасштабная математическая модель, численный алгоритм и параллельная реализация модели на макроскопическом масштабе. Новизна подхода связана с использованием квазигазодинамической модели для описания течения в сорбирующем слое и нескольких вариантов граничных условий на гранулах сорбента. Предварительные расчеты показали возможность расчета течений подобного класса. This paper considers the problem of supercomputer modeling of processes for cleaning the air from fine-dispersed solid polluting impurities clustered in the form of nanoparticles. The simulated purification method involves the use of nanofilters and sorbents. Both the purification methods are often combined in modern treatment systems. The cleaning method using nanofilters allows one to obtain the high quality of purification, but is expensive due to the need for frequent replacement of filter elements (membranes). The cleaning method using sorbents is somewhat worse in quality, however, it allows cleaning many times after washing the sorbent with special liquids. To optimize air cleaning systems using nanofilters and sorbents, a detailed study of the processes occurring in the cleaning system is necessary. The proposed study considers part of the problem associated with the passage of an air stream containing solid pollutant nanoparticles through a layer of granular sorbent. To accomplish this, a multiscale mathematical model, a numerical algorithm and a parallel implementation of the model on a macroscopic scale have been developed. The novelty of the approach is associated with the use of a quasigasdynamic model to describe the flow in the sorbing layer and several variants of the boundary conditions on the sorbent granules. Preliminary calculations show the possibility of calculating flows of a similar class.

Advances on the Modelling of Blood Flows and Pressures in Humans through a New Multiscale Mathematical Model

Many biophysical factors affect human circulation, so that. [...]

Multiscale variation model and activity level estimation algorithm of the Earth's magnetic field based on wavelet packets

We suggest a wavelet-based multiscale mathematical model of geomagnetic field variations. The model is particularly capable of reflecting the characteristic variation and local perturbations in the geomagnetic field during the periods of increased geomagnetic activity. Based on the model, we have designed numerical algorithms to identify the characteristic variation component as well as other components that represent different geomagnetic field activity. The substantial advantage of the designed algorithms is their fully automatic performance without any manual control. The algorithms are also suited for estimating and monitoring the activity level of the geomagnetic field at different magnetic observatories without any specific adjustment to their particular locations. The suggested approach has high temporal resolution reaching 1 min. This allows us to study the dynamics and spatiotemporal distribution of geomagnetic perturbations using data from ground-based observatories. Moreover, the suggested approach is particularly capable of discovering weak perturbations in the geomagnetic field, likely linked to the nonstationary impact of the solar wind plasma on the magnetosphere. The algorithms have been validated using the experimental data collected at the IKIR FEB RAS observatory network. Keywords. Magnetospheric physics (storms and substorms)