More Is Faster: Why Population Size Matters in Biological Search.

Many biological scenarios have multiple cooperating searchers, and the timing of the initial first contact between any one of those searchers and its target is critically important. However, we are unaware of biological models that predict how long it takes for the first of many searchers to discover a target. We present a novel mathematical model that predicts initial first contact times between searchers and targets distributed at random in a volume. We compare this model with the extreme first passage time approach in physics that assumes an infinite number of searchers all initially positioned at the same location. We explore how the number of searchers, the distribution of searchers and targets, and the initial distances between searchers and targets affect initial first contact times. Given a constant density of uniformly distributed searchers and targets, the initial first contact time decreases linearly with both search volume and the number of searchers. However, given only a single target and searchers placed at the same starting location, the relationship between the initial first contact time and the number of searchers shifts from a linear decrease to a logarithmic decrease as the number of searchers grows very large. More generally, we show that initial first contact times can be dramatically faster than the average first contact times and that the initial first contact times decrease with the number of searchers, while the average search times are independent of the number of searchers. We suggest that this is an underappreciated phenomenon in biology and other collective search problems.

Quantitative analyses of T cell motion in tissue reveals factors driving T cell search in tissues.

T cells are required to clear infection, and T cell motion plays a role in how quickly a T cell finds its target, from initial naive T cell activation by a dendritic cell to interaction with target cells in infected tissue. To better understand how different tissue environments affect T cell motility, we compared multiple features of T cell motion including speed, persistence, turning angle, directionality, and confinement of T cells moving in multiple murine tissues using microscopy. We quantitatively analyzed naive T cell motility within the lymph node and compared motility parameters with activated CD8 T cells moving within the villi of small intestine and lung under different activation conditions. Our motility analysis found that while the speeds and the overall displacement of T cells vary within all tissues analyzed, T cells in all tissues tended to persist at the same speed. Interestingly, we found that T cells in the lung show a marked population of T cells turning at close to 180o, while T cells in lymph nodes and villi do not exhibit this "reversing" movement. T cells in the lung also showed significantly decreased meandering ratios and increased confinement compared to T cells in lymph nodes and villi. These differences in motility patterns led to a decrease in the total volume scanned by T cells in lung compared to T cells in lymph node and villi. These results suggest that the tissue environment in which T cells move can impact the type of motility and ultimately, the efficiency of T cell search for target cells within specialized tissues such as the lung.

Challenges in cybersecurity: Lessons from biological defense systems.

Defending against novel, repeated, or unpredictable attacks, while avoiding attacks on the 'self', are the central problems of both mammalian immune systems and computer systems. Both systems have been studied in great detail, but with little exchange of information across the different disciplines. Here, we present a conceptual framework for structured comparisons across the fields of biological immunity and cybersecurity, by framing the context of defense, considering different (combinations of) defensive strategies, and evaluating defensive performance. Throughout this paper, we pose open questions for further exploration. We hope to spark the interdisciplinary discovery of general principles of optimal defense, which can be understood and applied in biological immunity, cybersecurity, and other defensive realms.

Agent-based modeling predicts RAC1 is critical for ovarian cancer metastasis.

Experimental and computational studies pinpoint rate-limiting step(s) in metastasis governed by Rac1. Using ovarian cancer cell and animal models, Rac1 expression was manipulated, and quantitative measurements of cell-cell and cell-substrate adhesion, cell invasion, mesothelial clearance, and peritoneal tumor growth discriminated the tumor behaviors most highly influenced by Rac1. The experimental data were used to parameterize an agent-based computational model simulating peritoneal niche colonization, intravasation, and hematogenous metastasis to distant organs. Increased ovarian cancer cell survival afforded by the more rapid adhesion and intravasation upon Rac1 overexpression is predicted to increase the numbers of and the rates at which tumor cells are disseminated to distant sites. Surprisingly, crowding of cancer cells along the blood vessel was found to decrease the numbers of cells reaching a distant niche irrespective of Rac1 overexpression or knockdown, suggesting that sites for tumor cell intravasation are rate limiting and become accessible if cells intravasate rapidly or are displaced due to diminished viability. Modeling predictions were confirmed through animal studies of Rac1-dependent metastasis to the lung. Collectively, the experimental and modeling approaches identify cell adhesion, rapid intravasation, and survival in the blood as parameters in the ovarian metastatic cascade that are most critically dependent on Rac1.

Spatially distributed infection increases viral load in a computational model of SARS-CoV-2 lung infection.

A key question in SARS-CoV-2 infection is why viral loads and patient outcomes vary dramatically across individuals. Because spatial-temporal dynamics of viral spread and immune response are challenging to study in vivo, we developed Spatial Immune Model of Coronavirus (SIMCoV), a scalable computational model that simulates hundreds of millions of lung cells, including respiratory epithelial cells and T cells. SIMCoV replicates viral growth dynamics observed in patients and shows how spatially dispersed infections can lead to increased viral loads. The model also shows how the timing and strength of the T cell response can affect viral persistence, oscillations, and control. By incorporating spatial interactions, SIMCoV provides a parsimonious explanation for the dramatically different viral load trajectories among patients by varying only the number of initial sites of infection and the magnitude and timing of the T cell immune response. When the branching airway structure of the lung is explicitly represented, we find that virus spreads faster than in a 2D layer of epithelial cells, but much more slowly than in an undifferentiated 3D grid or in a well-mixed differential equation model. These results illustrate how realistic, spatially explicit computational models can improve understanding of within-host dynamics of SARS-CoV-2 infection.

CT Colonography: Improving Interpretive Skill by Avoiding Pitfalls.

An earlier incorrect version of this article appeared online. This article was corrected on December 20, 2019.

Distributed Adaptive Search in T Cells: Lessons From Ants.

There are striking similarities between the strategies ant colonies use to forage for food and immune systems use to search for pathogens. Searchers (ants and cells) use the appropriate combination of random and directed motion, direct and indirect agent-agent interactions, and traversal of physical structures to solve search problems in a variety of environments. An effective immune response requires immune cells to search efficiently and effectively for diverse types of pathogens in different tissues and organs, just as different species of ants have evolved diverse search strategies to forage effectively for a variety of resources in a variety of habitats. Successful T cell search is required to initiate the adaptive immune response in lymph nodes and to eradicate pathogens at sites of infection in peripheral tissue. Ant search strategies suggest novel predictions about T cell search. In both systems, the distribution of targets in time and space determines the most effective search strategy. We hypothesize that the ability of searchers to sense and adapt to dynamic targets and environmental conditions enhances search effectiveness through adjustments to movement and communication patterns. We also suggest that random motion is a more important component of search strategies than is generally recognized. The behavior we observe in ants reveals general design principles and constraints that govern distributed adaptive search in a wide variety of complex systems, particularly the immune system.

How does mobility help distributed systems compute?

Brains are composed of connected neurons that compute by transmitting signals. The neurons are generally fixed in space, but the communication patterns that enable information processing change rapidly. By contrast, other biological systems, such as ant colonies, bacterial colonies, slime moulds and immune systems, process information using agents that communicate locally while moving through physical space. We refer to systems in which agents are strongly connected and immobile as solid, and to systems in which agents are not hardwired to each other and can move freely as liquid. We ask how collective computation depends on agent movement. A liquid cellular automaton (LCA) demonstrates the effect of movement and communication locality on consensus problems. A simple mathematical model predicts how these properties of the LCA affect how quickly information propagates through the system. While solid brains allow complex network structures to move information over long distances, mobility provides an alternative way for agents to transport information when long-range connectivity is expensive or infeasible. Our results show how simple mobile agents solve global information processing tasks more effectively than similar systems that are stationary. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Liquid brains, solid brains.

Cognitive networks have evolved a broad range of solutions to the problem of gathering, storing and responding to information. Some of these networks are describable as static sets of neurons linked in an adaptive web of connections. These are 'solid' networks, with a well-defined and physically persistent architecture. Other systems are formed by sets of agents that exchange, store and process information but without persistent connections or move relative to each other in physical space. We refer to these networks that lack stable connections and static elements as 'liquid' brains, a category that includes ant and termite colonies, immune systems and some microbiomes and slime moulds. What are the key differences between solid and liquid brains, particularly in their cognitive potential, ability to solve particular problems and environments, and information-processing strategies? To answer this question requires a new, integrative framework. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Quantitative Measurement of Naïve T Cell Association With Dendritic Cells, FRCs, and Blood Vessels in Lymph Nodes.

T cells play a vital role in eliminating pathogenic infections. To activate, naïve T cells search lymph nodes (LNs) for dendritic cells (DCs). Positioning and movement of T cells in LNs is influenced by chemokines including CCL21 as well as multiple cell types and structures in the LNs. Previous studies have suggested that T cell positioning facilitates DC colocalization leading to T:DC interaction. Despite the influence chemical signals, cells, and structures can have on naïve T cell positioning, relatively few studies have used quantitative measures to directly compare T cell interactions with key cell types. Here, we use Pearson correlation coefficient (PCC) and normalized mutual information (NMI) to quantify the extent to which naïve T cells spatially associate with DCs, fibroblastic reticular cells (FRCs), and blood vessels in LNs. We measure spatial associations in physiologically relevant regions. We find that T cells are more spatially associated with FRCs than with their ultimate targets, DCs. We also investigated the role of a key motility chemokine receptor, CCR7, on T cell colocalization with DCs. We find that CCR7 deficiency does not decrease naïve T cell association with DCs, in fact, CCR7-/- T cells show slightly higher DC association compared with wild type T cells. By revealing these associations, we gain insights into factors that drive T cell localization, potentially affecting the timing of productive T:DC interactions and T cell activation.

Modelling the effects of phylogeny and body size on within-host pathogen replication and immune response.

Understanding how quickly pathogens replicate and how quickly the immune system responds is important for predicting the epidemic spread of emerging pathogens. Host body size, through its correlation with metabolic rates, is theoretically predicted to impact pathogen replication rates and immune system response rates. Here, we use mathematical models of viral time courses from multiple species of birds infected by a generalist pathogen (West Nile Virus; WNV) to test more thoroughly how disease progression and immune response depend on mass and host phylogeny. We use hierarchical Bayesian models coupled with nonlinear dynamical models of disease dynamics to incorporate the hierarchical nature of host phylogeny. Our analysis suggests an important role for both host phylogeny and species mass in determining factors important for viral spread such as the basic reproductive number, WNV production rate, peak viraemia in blood and competency of a host to infect mosquitoes. Our model is based on a principled analysis and gives a quantitative prediction for key epidemiological determinants and how they vary with species mass and phylogeny. This leads to new hypotheses about the mechanisms that cause certain taxonomic groups to have higher viraemia. For example, our models suggest that higher viral burst sizes cause corvids to have higher levels of viraemia and that the cellular rate of virus production is lower in larger species. We derive a metric of competency of a host to infect disease vectors and thereby sustain the disease between hosts. This suggests that smaller passerine species are highly competent at spreading the disease compared with larger non-passerine species. Our models lend mechanistic insight into why some species (smaller passerine species) are pathogen reservoirs and some (larger non-passerine species) are potentially dead-end hosts for WNV. Our techniques give insights into the role of body mass and host phylogeny in the spread of WNV and potentially other zoonotic diseases. The major contribution of this work is a computational framework for infectious disease modelling at the within-host level that leverages data from multiple species. This is likely to be of interest to modellers of infectious diseases that jump species barriers and infect multiple species. Our method can be used to computationally determine the competency of a host to infect mosquitoes that will sustain WNV and other zoonotic diseases. We find that smaller passerine species are more competent in spreading the disease than larger non-passerine species. This suggests the role of host phylogeny as an important determinant of within-host pathogen replication. Ultimately, we view our work as an important step in linking within-host viral dynamics models to between-host models that determine spread of infectious disease between different hosts.

ROCK regulates the intermittent mode of interstitial T cell migration in inflamed lungs.

Effector T cell migration through tissues can enable control of infection or mediate inflammatory damage. Nevertheless, the molecular mechanisms that regulate migration of effector T cells within the interstitial space of inflamed lungs are incompletely understood. Here, we show T cell migration in a mouse model of acute lung injury with two-photon imaging of intact lung tissue. Computational analysis indicates that T cells migrate with an intermittent mode, switching between confined and almost straight migration, guided by lung-associated vasculature. Rho-associated protein kinase (ROCK) is required for both high-speed migration and straight motion. By contrast, inhibition of Gαi signaling with pertussis toxin affects speed but not the intermittent migration of lung-infiltrating T cells. Computational modeling shows that an intermittent migration pattern balances both search area and the duration of contacts between T cells and target cells. These data identify that ROCK-dependent intermittent T cell migration regulates tissue-sampling during acute lung injury.

Energy and time determine scaling in biological and computer designs.

Metabolic rate in animals and power consumption in computers are analogous quantities that scale similarly with size. We analyse vascular systems of mammals and on-chip networks of microprocessors, where natural selection and human engineering, respectively, have produced systems that minimize both energy dissipation and delivery times. Using a simple network model that simultaneously minimizes energy and time, our analysis explains empirically observed trends in the scaling of metabolic rate in mammals and power consumption and performance in microprocessors across several orders of magnitude in size. Just as the evolutionary transitions from unicellular to multicellular animals in biology are associated with shifts in metabolic scaling, our model suggests that the scaling of power and performance will change as computer designs transition to decentralized multi-core and distributed cyber-physical systems. More generally, a single energy-time minimization principle may govern the design of many complex systems that process energy, materials and information.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

Estimating biologically relevant parameters under uncertainty for experimental within-host murine West Nile virus infection.

West Nile virus (WNV) is an emerging pathogen that has decimated bird populations and caused severe outbreaks of viral encephalitis in humans. Currently, little is known about the within-host viral kinetics of WNV during infection. We developed mathematical models to describe viral replication, spread and host immune response in wild-type and immunocompromised mice. Our approach fits a target cell-limited model to viremia data from immunocompromised knockout mice and an adaptive immune response model to data from wild-type mice. Using this approach, we first estimate parameters governing viral production and viral spread in the host using simple models without immune responses. We then use these parameters in a more complex immune response model to characterize the dynamics of the humoral immune response. Despite substantial uncertainty in input parameters, our analysis generates relatively precise estimates of important viral characteristics that are composed of nonlinear combinations of model parameters: we estimate the mean within-host basic reproductive number,R0, to be 2.3 (95% of values in the range 1.7-2.9); the mean infectious virion burst size to be 2.9 plaque-forming units (95% of values in the range 1.7-4.7); and the average number of cells infected per infectious virion to be between 0.3 and 0.99. Our analysis gives mechanistic insights into the dynamics of WNV infection and produces estimates of viral characteristics that are difficult to measure experimentally. These models are a first step towards a quantitative understanding of the timing and effectiveness of the humoral immune response in reducing host viremia and consequently the epidemic spread of WNV.

Persistence and Adaptation in Immunity: T Cells Balance the Extent and Thoroughness of Search.

Effective search strategies have evolved in many biological systems, including the immune system. T cells are key effectors of the immune response, required for clearance of pathogenic infection. T cell activation requires that T cells encounter antigen-bearing dendritic cells within lymph nodes, thus, T cell search patterns within lymph nodes may be a crucial determinant of how quickly a T cell immune response can be initiated. Previous work suggests that T cell motion in the lymph node is similar to a Brownian random walk, however, no detailed analysis has definitively shown whether T cell movement is consistent with Brownian motion. Here, we provide a precise description of T cell motility in lymph nodes and a computational model that demonstrates how motility impacts T cell search efficiency. We find that both Brownian and Lévy walks fail to capture the complexity of T cell motion. Instead, T cell movement is better described as a correlated random walk with a heavy-tailed distribution of step lengths. Using computer simulations, we identify three distinct factors that contribute to increasing T cell search efficiency: 1) a lognormal distribution of step lengths, 2) motion that is directionally persistent over short time scales, and 3) heterogeneity in movement patterns. Furthermore, we show that T cells move differently in specific frequently visited locations that we call "hotspots" within lymph nodes, suggesting that T cells change their movement in response to the lymph node environment. Our results show that like foraging animals, T cells adapt to environmental cues, suggesting that adaption is a fundamental feature of biological search.

A spatial model of the efficiency of T cell search in the influenza-infected lung.

Emerging strains of influenza, such as avian H5N1 and 2009 pandemic H1N1, are more virulent than seasonal H1N1 influenza, yet the underlying mechanisms for these differences are not well understood. Subtle differences in how a given strain interacts with the immune system are likely a key factor in determining virulence. One aspect of the interaction is the ability of T cells to locate the foci of the infection in time to prevent uncontrolled expansion. Here, we develop an agent based spatial model to focus on T cell migration from lymph nodes through the vascular system to sites of infection. We use our model to investigate whether different strains of influenza modulate this process. We calibrate the model using viral and chemokine secretion rates we measure in vitro together with values taken from literature. The spatial nature of the model reveals unique challenges for T cell recruitment that are not apparent in standard differential equation models. In this model comparing three influenza viruses, plaque expansion is governed primarily by the replication rate of the virus strain, and the efficiency of the T cell search-and-kill is limited by the density of infected epithelial cells in each plaque. Thus for each virus there is a different threshold of T cell search time above which recruited T cells are unable to control further expansion. Future models could use this relationship to more accurately predict control of the infection.

Spatial Modeling of Drug Delivery Routes for Treatment of Disseminated Ovarian Cancer.

In ovarian cancer, metastasis is typically confined to the peritoneum. Surgical removal of the primary tumor and macroscopic secondary tumors is a common practice, but more effective strategies are needed to target microscopic spheroids persisting in the peritoneal fluid after debulking surgery. To treat this residual disease, therapeutic agents can be administered by either intravenous or intraperitoneal infusion. Here, we describe the use of a cellular Potts model to compare tumor penetration of two classes of drugs (cisplatin and pertuzumab) when delivered by these two alternative routes. The model considers the primary route when the drug is administered either intravenously or intraperitoneally, as well as the subsequent exchange into the other delivery volume as a secondary route. By accounting for these dynamics, the model revealed that intraperitoneal infusion is the markedly superior route for delivery of both small-molecule and antibody therapies into microscopic, avascular tumors typical of patients with ascites. Small tumors attached to peritoneal organs, with vascularity ranging from 2% to 10%, also show enhanced drug delivery via the intraperitoneal route, even though tumor vessels can act as sinks during the dissemination of small molecules. Furthermore, we assessed the ability of the antibody to enter the tumor by in silico and in vivo methods and suggest that optimization of antibody delivery is an important criterion underlying the efficacy of these and other biologics. The use of both delivery routes may provide the best total coverage of tumors, depending on their size and vascularity.

Bringing statistics up to speed with data in analysis of lymphocyte motility.

Two-photon (2P) microscopy provides immunologists with 3D video of the movement of lymphocytes in vivo. Motility parameters extracted from these videos allow detailed analysis of lymphocyte motility in lymph nodes and peripheral tissues. However, standard parametric statistical analyses such as the Student's t-test are often used incorrectly, and fail to take into account confounds introduced by the experimental methods, potentially leading to erroneous conclusions about T cell motility. Here, we compare the motility of WT T cell versus PKCθ-/-, CARMA1-/-, CCR7-/-, and PTX-treated T cells. We show that the fluorescent dyes used to label T cells have significant effects on T cell motility, and we demonstrate the use of factorial ANOVA as a statistical tool that can control for these effects. In addition, researchers often choose between the use of "cell-based" parameters by averaging multiple steps of a single cell over time (e.g. cell mean speed), or "step-based" parameters, in which all steps of a cell population (e.g. instantaneous speed) are grouped without regard for the cell track. Using mixed model ANOVA, we show that we can maintain cell-based analyses without losing the statistical power of step-based data. We find that as we use additional levels of statistical control, we can more accurately estimate the speed of T cells as they move in lymph nodes as well as measure the impact of individual signaling molecules on T cell motility. As there is increasing interest in using computational modeling to understand T cell behavior in in vivo, these quantitative measures not only give us a better determination of actual T cell movement, they may prove crucial for models to generate accurate predictions about T cell behavior.

PKCθ regulates T cell motility via ezrin-radixin-moesin localization to the uropod.

Cell motility is a fundamental process crucial for function in many cell types, including T cells. T cell motility is critical for T cell-mediated immune responses, including initiation, activation, and effector function. While many extracellular receptors and cytoskeletal regulators have been shown to control T cell migration, relatively few signaling mediators have been identified that can modulate T cell motility. In this study, we find a previously unknown role for PKCθ in regulating T cell migration to lymph nodes. PKCθ localizes to the migrating T cell uropod and regulates localization of the MTOC, CD43 and ERM proteins to the uropod. Furthermore, PKCθ-deficient T cells are less responsive to chemokine induced migration and are defective in migration to lymph nodes. Our results reveal a novel role for PKCθ in regulating T cell migration and demonstrate that PKCθ signals downstream of CCR7 to regulate protein localization and uropod formation.