Spatiotemporal Hierarchy Research Articles

Forecasting to support EMS tactical planning: what is important and what is not.

Forecasting emergency medical service (EMS) call volumes is critical for resource allocation and planning. The development of many commercial and free software packages has made a variety of forecasting methods accessible. Practitioners, however, are left with little guidance on selecting the most appropriate method for their needs. Using 5 years of data from 3 cities in Alberta, we compute exponential smoothing and benchmark forecasts for 8-hour periods for each ambulance station catchment area and with a forecast horizon of two weeks-a spatio-temporal resolution appropriate for tactical planning. The methods that we consider differ on three spectra: the number and type of time-series components, whether forecasts are computed individually or jointly, and the way in which forecasts at a specific resolution are converted to forecasts at the resolution of interest. We find that it is important to include a weekly seasonal component when forecasting EMS demand. Multiplicative seasonality, however, shows no benefit over additive seasonality. Adding other time-series components (e.g., trend, ARMA errors, Box-Cox transformation) does not improve performance. Spatial resolutions of station catchment area and lower, and temporal resolution of 4-24 hours perform similarly. We adapt an existing hierarchical forecasting framework to a two-dimensional spatio-temporal hierarchy, but find that hierarchical reconciliation of forecasts does not improve performance at the forecast resolution of interest for tactical planning. Neither does jointly forecasting time series. We show that added complexity does not materially improve forecasting performance. The simple methods that we find perform well are easy to implement and interpret, making implementation in practice more likely. In a simulation study we alter the empirical weekly patterns and demonstrate how extreme differences between the weekly seasonality patterns of different regions cause hierarchically-reconciled bottom-up approaches to outperform top-down approaches.

Dynamic mode decomposition and short-time prediction of PM2.5 using the graph Neural Koopman network

Analyzing and accurately predicting the spatiotemporal dynamics of PM2.5 remain challenging. The existing spatiotemporal prediction approaches are associated with high model complexity and limited interpretability. Conventional methods combining Koopman theory and deep learning often neglect spatial correlations in spatiotemporal data. This study used the hourly PM2.5 dataset of the Beijing-Tianjin-Hebei region to reveal its spatiotemporal hierarchy using Koopman mode decomposition to identify the key dynamic modes. Furthermore, a Spatial Physics Constrained Learning (SPCL) model utilizing a graph representation learning method was proposed to combine the graph topological information of the PM2.5 spatial features with the Koopman feature function. The results showed that PM2.5 has growth, decay, and oscillation modes as well as daily, weekly, monthly, and yearly periods. SPCL achieved mean absolute error, root mean square error (RMSE), correlation r, and index of agreement values of 9.678, 13.922, 0.864, and 0.921, respectively. The average RMSE at 12 h improved by 16.1%, 12.7%, 0.9%, and 3.5% compared with using Long short-term Memory, Graph Convolutional Networks and Long Short-Term Memory Networks, Spatio-Temporal Graph Convolutional Networks, and Dynamic Spatiotemporal Graph Convolution Network, respectively. By discretizing the neural network hidden layers, the explanatory key of PM2.5 modes was elucidated, which demonstrated enhanced stability.

Unsupervised Characterization of Prediction Error Markers in Unisensory and Multisensory Streams Reveal the Spatiotemporal Hierarchy of Cortical Information Processing.

Elicited upon violation of regularity in stimulus presentation, mismatch negativity (MMN) reflects the brain's ability to perform automatic comparisons between consecutive stimuli and provides an electrophysiological index of sensory error detection whereas P300 is associated with cognitive processes such as updating of the working memory. To date, there has been extensive research on the roles of MMN and P300 individually, because of their potential to be used as clinical markers of consciousness and attention, respectively. Here, we intend to explore with an unsupervised and rigorous source estimation approach, the underlying cortical generators of MMN and P300, in the context of prediction error propagation along the hierarchies of brain information processing in healthy human participants. The existing methods of characterizing the two ERPs involve only approximate estimations of their amplitudes and latencies based on specific sensors of interest. Our objective is twofold: first, we introduce a novel data-driven unsupervised approach to compute latencies and amplitude of ERP components accurately on an individual-subject basis and reconfirm earlier findings. Second, we demonstrate that in multisensory environments, MMN generators seem to reflect a significant overlap of "modality-specific" and "modality-independent" information processing while P300 generators mark a shift toward completely "modality-independent" processing. Advancing earlier understanding that multisensory contexts speed up early sensory processing, our study reveals that temporal facilitation extends to even the later components of prediction error processing, using EEG experiments. Such knowledge can be of value to clinical research for characterizing the key developmental stages of lifespan aging, schizophrenia, and depression.

Endogenous BAX and BAK form mosaic rings of variable size and composition on apoptotic mitochondria

One hallmark of apoptosis is the oligomerization of BAX and BAK to form a pore in the mitochondrial outer membrane, which mediates the release of pro-apoptotic intermembrane space proteins into the cytosol. Cells overexpressing BAX or BAK fusion proteins are a powerful model system to study the dynamics and localization of these proteins in cells. However, it is unclear whether overexpressed BAX and BAK form the same ultrastructural assemblies following the same spatiotemporal hierarchy as endogenously expressed proteins. Combining live- and fixed-cell STED super-resolution microscopy, we show that overexpression of BAK results in novel BAK structures, which are virtually absent in non-overexpressing apoptotic cells. We further demonstrate that in wild type cells, BAK is recruited to apoptotic pores before BAX. Both proteins together form unordered, mosaic rings on apoptotic mitochondria in immortalized cell culture models as well as in human primary cells. In BAX- or BAK- single-knockout cells, the remaining protein is able to form rings independently. The heterogeneous nature of these rings in both wild type as well as single-knockout cells corroborates the toroidal apoptotic pore model.

Insighting Drivers of Population Exposure to Ambient Ozone (O3) Concentrations across China Using a Spatiotemporal Causal Inference Method

Ground-level ozone (O3) is a well-known atmospheric pollutant aside from particulate matter. China as a global populous country is facing serious surface O3 pollution. To detect the complex spatiotemporal transformation of the population exposure to ambient O3 pollution in China from 2005 to 2019, the Bayesian multi-stage spatiotemporal evolution hierarchy model was employed. To insight the drivers of the population exposure to ambient O3 pollution in China, a Bayesian spatiotemporal LASSO regression model (BST-LASSO-RM) and a spatiotemporal propensity score matching (STPSM) were firstly applied; then, a spatiotemporal causal inference method integrating the BST-LASSO-RM and STPSM was presented. The results show that the spatial pattern of the annual population-weighted ground-level O3 (PWGLO3) concentrations, representing population exposure to ambient O3, in China has transformed since 2014. Most regions (72.2%) experienced a decreasing trend in PWGLO3 pollution in the early stage, but in the late stage, most areas (79.3%) underwent an increasing trend. Some drivers on PWGLO3 concentrations have partial spatial spillover effects. The PWGLO3 concentrations in a region can be driven by this region’s surrounding areas’ economic factors, wind speed, and PWGLO3 concentrations. The major drivers with six local factors in 2005–2014 changed to five local factors and one spatial adjacent factor in 2015–2019. The driving of the traffic and green factors have no spatial spillover effects. Three traffic factors showed a negative driving effect in the early stage, but only one, bus ridership per capita (BRPC), retains the negative driving effect in the late stage. The factor with the maximum driving contribution is BRPC in the early stage, but PM2.5 pollution in the late stage, and the corresponding driving contribution is 17.57%. Green area per capita and urban green coverage rates have positive driving effects. The driving effects of the climate factors intensified from the early to the later stage.

Spatiotemporal Feature Hierarchy-Based Blind Prediction of Natural Video Quality via Transfer Learning

In this paper, we propose a pyramidal spatiotemporal feature hierarchy (PSFH)-based no-reference (NR) video quality assessment (VQA) method using transfer learning. First, we generate simulated videos by a generative adversarial network (GAN)-based image restoration model. The residual maps between the distorted frames and simulated frames, which can capture rich information, are utilized as one input of the quality regression network. Second, we use 3D convolution operations to construct a PSFH network with five stages. The spatiotemporal features incorporating the shared features transferred from the pretrained image restoration model are fused stage by stage. Third, with the guidance of the transferred knowledge, each stage generates multiple feature mapping layers that encode different semantics and degradation information using 3D convolution layers and gated recurrent units (GRUs). Finally, five approximate perceptual quality scores and a precise prediction score are obtained by fully connected (FC) networks. The whole model is trained under a finely designed loss function that combines pseudo-Huber loss and Pearson linear correlation coefficient (PLCC) loss to improve the robustness and prediction accuracy. According to the extensive experiments, outstanding results can be obtained compared with other state-of-the-art methods. Both the source code and models are available online. <xref ref-type="fn" rid="fn1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</xref>

Modularity in Nervous Systems—a Key to Efficient Adaptivity for Deep Reinforcement Learning

Modularity as observed in biological systems has proven valuable for guiding classical motor theories towards good answers about action selection and execution. New challenges arise when we turn to learning: Trying to scale current computational models, such as deep reinforcement learning (DRL), to action spaces, input dimensions, and time horizons seen in biological systems still faces severe obstacles unless vast amounts of training data are available. This leads to the question: does biological modularity also hold an important key for better answers to obtain efficient adaptivity for deep reinforcement learning? We review biological experimental work on modularity in biological motor control and link this with current examples of (deep) RL approaches. Analyzing outcomes of simulation studies, we show that these approaches benefit from forms of modularization as found in biological systems. We identify three different strands of modularity exhibited in biological control systems. Two of them—modularity in state (i) and in action (ii) spaces—appear as a consequence of local interconnectivity (as in reflexes) and are often modulated by higher levels in a control hierarchy. A third strand arises from chunking of action elements along a (iii) temporal dimension. Usually interacting in an overarching spatio-temporal hierarchy of the overall system, the three strands offer major “factors” decomposing the entire modularity structure. We conclude that modularity with its above strands can provide an effective prior for DRL approaches to speed up learning considerably and making learned controllers more robust and adaptive.

Spatiotemporal characteristics and drivers of Chinese urban total noise pollution from 2007 to 2019.

Noise pollution as a result of urbanization and socioeconomic development threatens human health and has become a major environmental problem worldwide, particularly for urban residents. Based on observed equivalent noise data of 113 major Chinese cities, a Bayesian spatiotemporal hierarchy model (BSTHM) was employed to investigate the spatiotemporal characteristics of urban noise pollution in China from 2007 to 2019. Meanwhile, the BART model was adopted to explore the drivers of urban noise pollution. The mean and medium of the equivalent noise of the 113 major cities decreased from 2007 to 2011 but increased from 2011 to 2019; the corresponding annual growth is 0.0793 dB and 0.0947 dB per year. The overall spatial pattern has a certain geographical feature. The cities located in the eastern and north-eastern coastal regions generally have a higher level of noise pollution, and the western and southwestern cities have a lower level. One hundred cities not only have greater noise pollution but also an increasing trend. Although the 52 cities located in Western China have less noise pollution, they have increasing local trends. The results indicate that economic and social factors are the main drivers of noise pollution of China; the explanatory power is 46.2%. Traffic factors are also relatively important drivers, of which bus ridership is the leading one. In terms of the natural environment, climatic factors, including temperature and relative humidity, and presence of green areas containing parkland and general green land are the main determinants.

No Outside: A Continuum Model of the Cosmos

Over the last sixty years computational modeling of dynamical systems has increasingly come to rival theory and experiment as a legitimate contributor to the ever growing body of scientific knowledge. In particular, the ability to model systems’ future and past states—to speed up or slowdown their inter/intra-relationships—has revealed once hidden spatial and temporal patterns that complicate taxonomic conventions, e.g., those separating living from non-living levels of organization. The fixed position of the viewing subject is, itself, destabilized in this modeling process as temporal frames become relativized. What follows are some thoughts on what it might mean were the human to be willing to untether itself from its imagined privileged position within a spatiotemporal hierarchy and explore instead the proposition of an open-ended spatiotemporal continuum.

The Slowest Shared Resonance: A Review of Electromagnetic Field Oscillations Between Central and Peripheral Nervous Systems.

Electromagnetic field oscillations produced by the brain are increasingly being viewed as causal drivers of consciousness. Recent research has highlighted the importance of the body’s various endogenous rhythms in organizing these brain-generated fields through various types of entrainment. We expand this approach by examining evidence of extracerebral shared oscillations between the brain and other parts of the body, in both humans and animals. We then examine the degree to which these data support one of General Resonance Theory’s (GRT) principles: the Slowest Shared Resonance (SSR) principle, which states that the combination of micro- to macro-consciousness in coupled field systems is a function of the slowest common denominator frequency or resonance. This principle may be utilized to develop a spatiotemporal hierarchy of brain-body shared resonance systems. It is predicted that a system’s SSR decreases with distance between the brain and various resonating structures in the body. The various resonance relationships examined, including between the brain and gastric neurons, brain and sensory organs, and brain and spinal cord, generally match the predicted SSR relationships, empirically supporting this principle of GRT.

Seeing the locust in the swarm: accounting for spatiotemporal hierarchy improves ecological models of insect populations

Ecological phenomena operate at different spatial scales and are not uniform across landscapes or through time. One ecological theory that attempts to account for scaling and spatiotemporal variances is hierarchical patch dynamics. It introduces a hierarchical patch network with smaller spatiotemporal scales being nested within larger scales. However, few studies have modeled its presence within animal population dynamics. Locusts are an excellent model for investigating the spatiotemporal hierarchy of animal population dynamics, due to their high migratory capacity, large geographic ranges that extend across widely differing environments, and available long‐term data on distributions. Here, we investigated the influence of preceding vegetation growth on desert locust Schistocerca gregaria and Australian plague locust Chortoicetes terminifera outbreaks on three spatial levels (species range &gt; geographic region &gt; land unit) and between seasons. Both species are dryland herbivores with population dynamics linked to habitat productivity pulses after rain. We used NDVI data (MODIS imagery) as a measure of vegetation growth in hierarchical generalized additive models at different scales. Locust outbreaks were either preceded by vegetation growth between 78 and 32 days (Australian plague locusts) or 32 and 20 days before (desert locust) the observation. Although prior vegetation growth characterized outbreaks of both species, the temporal pattern of NDVI differed between spatiotemporal levels. All model selection criteria selected for a similar spatial hierarchy for both species: geographic region &gt; land unit which supports the hierarchical patch dynamics paradigm. Further, it illuminates important timing differences between geographic regions and land units for preceding vegetation growth and locust outbreaks which can help locust managers identify when and where outbreaks occur. By acknowledging the spatiotemporal patterning of locust abundance, we account for heterogeneity of population dynamics throughout species ranges. Our findings demonstrate the importance of incorporating spatiotemporal variation in population models of insects and other animals.

China's ecosystem service value in 1992–2018: Pattern and anthropogenic driving factors detection using Bayesian spatiotemporal hierarchy model

Maintaining ecosystem services (ESs) and reducing ecosystem degradation are important goals for achieving sustainable development. However, under the influence of various anthropogenic factors, the total ecosystem service value (ESV) of China continues to decline, and the detailed processes involved in this decline are unclear. In this paper, a new long-term annual land cover dataset (the Climate Change Initiative Land Cover or CCI-LC dataset) with a spatial resolution of 300 m was employed to estimate the ESV of China, and Bayesian spatiotemporal hierarchy models were built to examine the detailed patterns and anthropogenic driving factors. From 1992 to 2018, the total ESV of China fluctuated and decreased from 3265.3 to 3253.29 billion US$ at an average rate of 0.55 billion US$ per year. Furthermore, the model revealed the spatiotemporal variations in the ESV pattern, and simultaneously detected the influences of 9 variables related to economic factors, population, infrastructure, energy, agriculture and ecological restoration, providing a convenient and effective method for ESV spatiotemporal analysis. The results enrich our understanding of the detailed spatiotemporal variation and anthropogenic driving factors underlying the declining ESV in China. These findings have substantial guiding implications for adjusting ecological regulation policies.

Correlative nanophotonic approaches to enlighten the nanoscale dynamics of living cell membranes.

Dynamic compartmentalization is a prevailing principle regulating the spatiotemporal organization of the living cell membrane from the nano- up to the mesoscale. This non-arbitrary organization is intricately linked to cell function. On living cell membranes, dynamic domains or ‘membrane rafts' enriched with cholesterol, sphingolipids and other certain proteins exist at the nanoscale serving as signaling and sorting platforms. Moreover, it has been postulated that other local organizers of the cell membrane such as intrinsic protein interactions, the extracellular matrix and/or the actin cytoskeleton synergize with rafts to provide spatiotemporal hierarchy to the membrane. Elucidating the intricate coupling of multiple spatial and temporal scales requires the application of correlative techniques, with a particular need for simultaneous nanometer spatial precision and microsecond temporal resolution. Here, we review novel fluorescence-based techniques that readily allow to decode nanoscale membrane dynamics with unprecedented spatiotemporal resolution and single-molecule sensitivity. We particularly focus on correlative approaches from the field of nanophotonics. Notably, we introduce a versatile planar nanoantenna platform combined with fluorescence correlation spectroscopy to study spatiotemporal heterogeneities on living cell membranes at the nano- up to the mesoscale. Finally, we outline remaining future technological challenges and comment on potential directions to advance our understanding of cell membrane dynamics under the influence of the actin cytoskeleton and extracellular matrix in uttermost detail.

Spatiotemporal heterogeneity and its determinants of COVID-19 transmission in typical labor export provinces of China

BackgroundPrevious studies have indicated that the risk of infectious disease spread is greatest in locations where a population has massive and convenient access to the epicenter of an outbreak. However, the spatiotemporal variations and risk determinants of COVID-19 in typical labor export regions of China remain unclear. Understanding the geographical distribution of the disease and the socio-economic factors affecting its transmission is critical for disease prevention and control.MethodsA total of 2152 COVID-19 cases were reported from January 21 to February 24, 2020 across the 34 cities in Henan and Anhui. A Bayesian spatiotemporal hierarchy model was used to detect the spatiotemporal variations of the risk posed by COVID-19, and the GeoDetector q statistic was used to evaluate the determinant power of the potential influence factors.ResultsThe risk posed by COVID-19 showed geographical spatiotemporal heterogeneity. Temporally, there was an outbreak period and control period. Spatially, there were high-risk regions and low-risk regions. The high-risk regions were mainly in the southwest areas adjacent to Hubei and cities that served as economic and traffic hubs, while the low-risk regions were mainly in western Henan and eastern Anhui, far away from the epicenter. The accessibility, local economic conditions, and medical infrastructure of Wuhan in Hubei province all played an important role in the spatiotemporal heterogeneity of COVID-19 transmission. The results indicated that the q statistics of the per capita GDP and the proportion of primary industry GDP were 0.47 and 0.47, respectively. The q statistic of the population flow from Wuhan was 0.33. In particular, the results showed that the q statistics for the interaction effects between population density and urbanization, population flow from Wuhan, per capita GDP, and the number of doctors were all greater than 0.8.ConclusionsCOVID-19 showed significant spatiotemporal heterogeneity in the labor export regions of China. The high-risk regions were mainly located in areas adjacent to the epicenter as well as in big cities that served as traffic hubs. Population access to the epicenter, as well as local economic and medical conditions, played an important role in the interactive effects of the disease transmission.

Membrane targeting of core autophagy players during autophagosome biogenesis.

Autophagosomes are vital organelles required to facilitate the lysosomal degradation of cytoplasmic cargo, thereby playing an important role in maintaining cellular homeostasis. A number of autophagy-related (ATG) protein complexes are recruited to the site of autophagosome biogenesis where they act to facilitate membrane growth and maturation. Regulated recruitment of ATG complexes to autophagosomal membranes is essential for their autophagic activities and is required to ensure the efficient engulfment of cargo destined for lysosomal degradation. In this review, we discuss our current understanding of the spatiotemporal hierarchy between ATG proteins, examining the mechanisms underlying their recruitment to membranes. A particular focus is placed on the relevance of phosphatidylinositol 3-phosphate and the extent to which the core autophagy players are reliant on this lipid for their localisation to autophagic membranes. In addition, open questions and potential future research directions regarding the membrane recruitment and displacement of ATG proteins are discussed here.

Spatiotemporal Patterns of Ground Monitored PM2.5 Concentrations in China in Recent Years.

This paper firstly explores the space-time evolution of city-level concentrations showed a very significant seasonal cycle type fluctuation during the period between 13 May 2014 and 30 May 2017. The period from October to April following each year was a heavy pollution period, whereas the phase from April to October of the current year was part of a light pollution period. The average monthly concentrations in mainland China based on ground monitoring, employing a descriptive statistics method and a Bayesian spatiotemporal hierarchy model. Daily and weekly average concentrations in 338 cities in mainland China presented no significant spatial difference during the severe pollution period but a large spatial difference during light pollution periods. The severe pollution areas were mainly distributed in the Beijing-Tianjin-Hebei urban agglomeration in the North China Plain during the beginning of each autumn-winter season (September), spreading to the Northeast Plains after October, then later continuing to spread to other cities in mainland China, eventually covering most cities. pollution in China appeared to be a cyclic characteristic of first spreading and then centralizing in the space in two spring-summer seasons, and showed an obvious process of first diffusing then transferring to shrinkage alternation during the spring-summer season of 2015, but showed no obvious diffusion during the spring-summer season of 2016, maintaining a stable spatial structure after the shrinkage in June, as well as being more concentrated. The heavily polluted areas are continuously and steadily concentrated in East China, Central China and Xinjiang Province.

Controlling Spatiotemporal Mechanics of Supramolecular Hydrogel Networks with Highly Branched Cucurbit[8]uril Polyrotaxanes

AbstractAttempts to rationally tune the macroscopic mechanical performance of supramolecular hydrogel networks through noncovalent molecular interactions have led to a wide variety of supramolecular materials with desirable functions. While the viscoelastic properties are dominated by temporal hierarchy (crosslinking kinetics), direct mechanistic studies on spatiotemporal control of supramolecular hydrogel networks, based on host–guest chemistry, have not yet been established. Here, supramolecular hydrogel networks assembled from highly branched cucurbit[8]uril‐threaded polyrotaxanes (HBP‐CB[8]) and naphthyl‐functionalized hydroxyethyl cellulose (HECNp) are reported, exploiting the CB[8] host–guest complexation. Mechanically locking CB[8] host molecules onto a highly branched hydrophilic polymer backbone, through selective binary complexation with viologen derivatives, dramatically increases the solubility of CB[8]. Additionally, the branched architecture enables tuning of material dynamics of the supramolecular hydrogel networks via both topological (spatial hierarchy) and kinetic (temporal hierarchy) control. Relationship between macroscopic properties (time‐ and temperature‐dependent rheological properties, thermal stability, and reversibility), spatiotemporal hierarchy, and chain dynamics of the highly branched polyrotaxane hydrogel networks is investigated in detail. Such kind of tuning of material mechanics through spatiotemporal hierarchy improves our understanding of the challenging relationship between design of supramolecular polymeric materials and their complex viscoelasticity, and also highlights a facile strategy to engineer dynamic supramolecular materials.

Delineating antibody recognition against Zika virus during natural infection.

Zika virus (ZIKV) is an emerging mosquito-transmitted flavivirus that shares a considerable degree of homology with dengue virus (DENV). Here, we examined longitudinal antibody response against ZIKV during natural infection in 2 convalescent individuals. By decomposing the antibody recognition into DI/DII and DIII of the E glycoprotein, we showed their development in humans followed a spatiotemporal hierarchy. Plasma binding to DI/DII appeared to peak and wane during early infection with extensive cross-reactivity with DI/DII of DENV. Binding to DIII, however, peaked early but persisted months into the infection without detectable cross-reactivity with DIII of DENV. A clear trend of increase in DIII-specific neutralizing activity was observed over the course of infection. mAbs isolated during early infection are largely DI/DII specific, weakly neutralizing, and highly cross-reactive with DENV, while those from later infection are more diverse in recognition, potently neutralizing, and ZIKV specific. The most potent neutralizing mAb targeting the DIII provided 100% protection in mice from lethal ZIKV infection and could therefore serve as a promising candidate for antibody-based therapy and prevention. The dynamic features unveiled here will assist us to better understand the pathogenesis of ZIKV infection and inform rational design of vaccines.

Analytical Prediction of the Spatiotemporal Distribution of Chemoattractants around Their Source: Theory and Application to Complement-Mediated Chemotaxis.

The ability of motile immune cells to detect and follow gradients of chemoattractant is critical to numerous vital functions, including their recruitment to sites of infection and—in emerging immunotherapeutic applications—to malignant tumors. Facilitated by a multitude of chemotactic receptors, the cells navigate a maze of stimuli to home in on their target. Distinct chemotactic processes direct this navigation at particular times and cell-target distances. The expedient coordination of this spatiotemporal hierarchy of chemotactic stages is the central element of a key paradigm of immunotaxis. Understanding this hierarchy is an enormous interdisciplinary challenge that requires, among others, quantitative insight into the shape, range, and dynamics of the profiles of chemoattractants around their sources. We here present a closed-form solution to a diffusion–reaction problem that describes the evolution of the concentration gradient of chemoattractant under various conditions. Our ready-to-use mathematical prescription captures many biological situations reasonably well and can be explored with standard graphing software, making it a valuable resource for every researcher studying chemotaxis. We here apply this mathematical model to characterize the chemoattractant cloud of anaphylatoxins that forms around bacterial and fungal pathogens in the presence of host serum. We analyze the spatial reach, rate of formation, and rate of dispersal of this locator cloud under realistic physiological conditions. Our analysis predicts that simply being small is an effective protective strategy of pathogens against complement-mediated discovery by host immune cells over moderate-to-large distances. Leveraging our predictions against single-cell, pure-chemotaxis experiments that use human immune cells as biosensors, we are able to explain the limited distance over which the cells recognize microbes. We conclude that complement-mediated chemotaxis is a universal, but short-range, homing mechanism by which chemotaxing immune cells can implement a last-minute course correction toward pathogenic microbes. Thus, the integration of theory and experiments provides a sound mechanistic explanation of the primary role of complement-mediated chemotaxis within the hierarchy of immunotaxis, and why other chemotactic processes are required for the successful recruitment of immune cells over large distances.

Spatiotemporal hierarchy in antibody recognition against transmitted HIV-1 envelope glycoprotein during natural infection.

BackgroundMajority of HIV-1 infection is established by one transmitted/founder virus and understanding how the neutralizing antibodies develop against this virus is critical for our rational design an HIV-1 vaccine. ResultsWe report here antibody profiling of sequential plasma samples against transmitted/founder HIV-1 envelope glycoprotein in an epidemiologically linked transmission pair using our previously reported antigen library approach. We have decomposed the antibody recognition into three major subdomains on the envelope and showed their development in vivo followed a spatiotemporal hierarchy: starting with the ectodomain of gp41 at membrane proximal region, then the V3C3V4 and the V1V2 of gp120 at the membrane distal region. While antibodies to these subdomains appeared to undergo avidity maturation, the early anti-gp41 antibodies failed to translate into detectable autologous neutralization. Instead, it was the much delayed anti-V3C3V4 and anti-V1V2 antibodies constituted the major neutralizing activities.ConclusionsOur results indicate that the initial antibody response was severely misguided by the transmitted/founder virus and future vaccine design would need to avoid the ectodomain of gp41 and focus on the neutralizing targets in the V3C3V4 and V1V2 subdomains of gp120.Electronic supplementary materialThe online version of this article (doi:10.1186/s12977-016-0243-3) contains supplementary material, which is available to authorized users.