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.

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.

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'.

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.

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.

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.

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.

Fast and flexible: argentine ants recruit from nearby trails.

Argentine ants (Linepithema humile) live in groups of nests connected by trails to each other and to stable food sources. In a field study, we investigated whether some ants recruit directly from established, persistent trails to food sources, thus accelerating food collection. Our results indicate that Argentine ants recruit nestmates to food directly from persistent trails, and that the exponential increase in the arrival rate of ants at baits is faster than would be possible if recruited ants traveled from distant nests. Once ants find a new food source, they walk back and forth between the bait and sometimes share food by trophallaxis with nestmates on the trail. Recruiting ants from nearby persistent trails creates a dynamic circuit, like those found in other distributed systems, which facilitates a quick response to changes in available resources.

Quantifying the effect of colony size and food distribution on harvester ant foraging.

Desert seed-harvester ants, genus Pogonomyrmex, are central place foragers that search for resources collectively. We quantify how seed harvesters exploit the spatial distribution of seeds to improve their rate of seed collection. We find that foraging rates are significantly influenced by the clumpiness of experimental seed baits. Colonies collected seeds from larger piles faster than randomly distributed seeds. We developed a method to compare foraging rates on clumped versus random seeds across three Pogonomyrmex species that differ substantially in forager population size. The increase in foraging rate when food was clumped in larger piles was indistinguishable across the three species, suggesting that species with larger colonies are no better than species with smaller colonies at collecting clumped seeds. These findings contradict the theoretical expectation that larger groups are more efficient at exploiting clumped resources, thus contributing to our understanding of the importance of the spatial distribution of food sources and colony size for communication and organization in social insects.

A general model for effects of temperature on ectotherm ontogenetic growth and development.

The temperature size rule (TSR) is the tendency for ectotherms to develop faster but mature at smaller body sizes at higher temperatures. It can be explained by a simple model in which the rate of growth or biomass accumulation and the rate of development have different temperature dependence. The model accounts for both TSR and the less frequently observed reverse-TSR, predicts the fraction of energy allocated to maintenance and synthesis over the course of development, and also predicts that less total energy is expended when developing at warmer temperatures for TSR and vice versa for reverse-TSR. It has important implications for effects of climate change on ectothermic animals.

A general basis for quarter-power scaling in animals.

It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarter-power scaling can arise even when there is no underlying fractality. The canonical "fourth dimension" in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal "service volume" where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.

Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions of life.

The diversification of life involved enormous increases in size and complexity. The evolutionary transitions from prokaryotes to unicellular eukaryotes to metazoans were accompanied by major innovations in metabolic design. Here we show that the scalings of metabolic rate, population growth rate, and production efficiency with body size have changed across the evolutionary transitions. Metabolic rate scales with body mass superlinearly in prokaryotes, linearly in protists, and sublinearly in metazoans, so Kleiber's 3/4 power scaling law does not apply universally across organisms. The scaling of maximum population growth rate shifts from positive in prokaryotes to negative in protists and metazoans, and the efficiency of production declines across these groups. Major changes in metabolic processes during the early evolution of life overcame existing constraints, exploited new opportunities, and imposed new constraints.

Population stability, cooperation, and the invasibility of the human species.

The biogeographic expansion of modern humans out of Africa began approximately 50,000 years ago. This expansion resulted in the colonization of most of the land area and habitats throughout the globe and in the replacement of preexisting hominid species. However, such rapid population growth and geographic spread is somewhat unexpected for a large primate with a slow, density-dependent life history. Here, we suggest a mechanism for these outcomes by modifying a simple density-dependent population model to allow varying levels of intraspecific competition for finite resources. Reducing intraspecific competition increases carrying capacities, growth rates, and stability, including persistence times and speed of recovery from perturbations. Our model suggests that the energetic benefits of cooperation in modern humans may have outweighed the slow rate of human population growth, effectively ensuring that once modern humans colonized a region long-term population persistence was near inevitable. Our model also provides insight into the interplay of structural complexity and stability in social species.

Energy uptake and allocation during ontogeny.

All organisms face the problem of how to fuel ontogenetic growth. We present a model, empirically grounded in data from birds and mammals, that correctly predicts how growing animals allocate food energy between synthesis of new biomass and maintenance of existing biomass. Previous energy budget models have typically had their bases in rates of either food consumption or metabolic energy expenditure. Our model provides a framework that reconciles these two approaches and highlights the fundamental principles that determine rates of food assimilation and rates of energy allocation to maintenance, biosynthesis, activity, and storage. The model predicts that growth and assimilation rates for all animals should cluster closely around two universal curves. Data for mammals and birds of diverse body sizes and taxa support these predictions.

Scaling theory for information networks.

Networks distribute energy, materials and information to the components of a variety of natural and human-engineered systems, including organisms, brains, the Internet and microprocessors. Distribution networks enable the integrated and coordinated functioning of these systems, and they also constrain their design. The similar hierarchical branching networks observed in organisms and microprocessors are striking, given that the structure of organisms has evolved via natural selection, while microprocessors are designed by engineers. Metabolic scaling theory (MST) shows that the rate at which networks deliver energy to an organism is proportional to its mass raised to the 3/4 power. We show that computational systems are also characterized by nonlinear network scaling and use MST principles to characterize how information networks scale, focusing on how MST predicts properties of clock distribution networks in microprocessors. The MST equations are modified to account for variation in the size and density of transistors and terminal wires in microprocessors. Based on the scaling of the clock distribution network, we predict a set of trade-offs and performance properties that scale with chip size and the number of transistors. However, there are systematic deviations between power requirements on microprocessors and predictions derived directly from MST. These deviations are addressed by augmenting the model to account for decentralized flow in some microprocessor networks (e.g. in logic networks). More generally, we hypothesize a set of constraints between the size, power and performance of networked information systems including transistors on chips, hosts on the Internet and neurons in the brain.