DOI: 10.5061/dryad.5x69p8df1
title: Bigger is faster in the scalable adaptive immune response

description: Zoonotic pathogens represent a growing global risk, yet the speed of
 adaptive immune activation across mammalian species remains poorly
 understood. Despite orders-of-magnitude differences in size and metabolic
 rate, we show that the time to initiate adaptive immunity is remarkably
 consistent across species. To understand this invariance, we analyse
 empirical data showing how the numbers and sizes of lymph nodes scale with
 body mass, finding that larger animals have both more and larger lymph
 nodes. Using scaling theory and our mathematical model, we show that
 larger lymph nodes enable faster search times, conferring an advantage to
 larger animals that otherwise face slower biological times. This enables
 mammals to maintain, or even accelerate, the time to initiate the adaptive
 immune response as body size increases. We validate our analysis in
 simulations and compare it to empirical data.
description: To validate our mathematical model, we implement an agent-based
 model (ABM), termed the Initial First Contact Time (IFCT) model, using the
 MASON libraries [1] in Java. The model simulates two types of agents - T
 cells (searchers) and Dendritic Cells (DCs) (targets). Both are uniformly
 distributed within a cubic representation of a Lymph Node (LN). LN space
 is modeled as a continuous Cartesian grid in three dimensions with fixed
 reflective boundaries. The IFCT model is run as a
 discrete-time simulation, with each time step representing one second. At
 the beginning of each simulation run, a predefined number of T cells and
 DCs are initialized (see \Cref{tab:inputDataTable}). The positions of DC
 are static throughout the simulation. T cells, on the other hand, move in
 each time step with either Brownian motion or a persistent random walk,
 which was modeled from empirical data in Fricke et al.[2]. We model T cell
 motion without considering collisions so that T cells pass through each
 other. We run the IFCT model for the two bounding
 cases, one in which N<sub>DC</sub> is proportional to
 M<sup>0</sup>, i.e., a constant, and another where
 N<sub>DC</sub>  is proportional to
 M<sup>0.5</sup>. Each case is simulated for five different
 animal mass (M) values. For each M, we run 100 experimental replicas for
 each combination of factors, where the initial distribution of the T cells
 and DC is stochastic. We assume that there is a contact between a T cell
 and DC when their centers are within 10 microns. The simulation result
 from the IFCT model confirms that the distribution of contact times is
 exponential, an assumption that underpins the theoretical
 derivation. Mass (M) 10 g 10^2 ^g 10^3 ^g 10^4 ^g 10^5 ^g 
 V<sub>LN</sub> ∝
 M<sup>0.5</sup>ln(cM)  (mm<sup>3</sup>)
 7.3 46 220 920 3600 N<sub>TC</sub> ∝
 M<sup>0.5</sup> 20 63 200 630 2000 N<sub>DC</sub> ∝
 M<sup>0.5</sup> 80 250 800 2500 8000 N<sub>DC</sub> ∝
 M<sup>0</sup> 200 200 200 200 200 
 [1] S. Luke, G. C. Balan, L. Panait, C.
 Cioffi-Revilla, S. Paus, MASON: A Java multi-agent simulation library, in
 Proceedings of Agent 2003 Conference on Challenges in Social Simulation,
 vol. 9 (2003). [2] G. M. Fricke, K. A. Letendre, M. E.
 Moses, J. L. Cannon, Persistence and adaptation in immunity: T cells
 balance the extent and thoroughness of search. PLoS Computational Biology
 12 (3), e1004818 (2016).
description: # Bigger is faster in the scalable adaptive immune response ## Description
 of the data and file structure Main folder: IFCT.zip This repository
 contains simulated T cell–dendritic cell (DC) initial first-contact time
 (IFCT) and mean first-contact time (MFCT) data under two different lymph
 node (LN) volume–mass scaling hypotheses and two different T cell
 migration modes. All simulations represent a population of naïve T cells
 searching for a cognate DC inside a 3-D lymph node. Data are organized by:
 LN scaling: 1\. V_M^0.5 — LN volume ∝ M^0.5 2\. V_M^0.67 — LN volume ∝
 M^0.67 Migration mode: 1\. BM — Brownian Motion (random walk) 2\. CRW —
 Correlated Random Walk DC scaling: 1\. DCConstant — number of DCs does not
 scale with M 2\. DCHalf — number of DCs scales as M^0.5 Each simulation
 produces distributions of first-contact times for multiple LN volumes (5
 volumes per condition, corresponding to 5 LN sizes), and for 100
 stochastic simulations per volume, the V_M^0.67 folder, which only
 contains 20 IFCT data for BM (DCConstant, DCHalf). **Directory
 Structure:** ├── V_M^0.5/ │ ├── BM_V_M^0.5/ │ │ ├── BMDCConstant_RawData/
 │ │ │ ├── BM_DCConstant11.csv │ │ │ ├── BM_DCConstant12.csv            .  
          . │ │ │ └── BM_DCConstant5100.csv │ │ ├── BMDCHalf_RawData/ │ │ │
 ├── BM_DCHalf11.csv │ │ │ ├── BM_DCHalf12.csv            .            . │
 │ │ └── … BM_DCHalf5100.csv │ │ ├── BM_IFCT_DCConstant.csv │ │ ├──
 BM_IFCT_DCHalf.csv │ │ ├── BM_MFCT_DCConstant.csv │ │ └──
 BM_MFCT_DCHalf.csv │ │ │ ├── CRW_V_M^0.5/ │ │ ├── CRWDCConstant_RawData/ │
 │ │ ├── CRW_DCConstant11.csv │ │ │ ├── CRW_DCConstant12.csv            .  
          . │ │ │ └── CRW_DCConstant5100.csv │ │ ├── CRWDCHalf_RawData/ │ │
 │ ├── CRW_DCHalf11.csv │ │ │ ├── CRW_DCHalf12.csv            .          
  . │ │ │ └── CRW_DCHalf1100.csv │ │ ├── CRW_IFCT_DCConstant.csv │ │ ├──
 CRW_IFCT_DCHalf.csv │ │ ├── CRW_MFCT_DCConstant.csv │ │ └──
 CRW_MFCT_DCHalf.csv │ └── V_M^0.67/ │ ├── BM_IFCT_DCConstant.csv │ ├──
 BM_IFCT_DCHalf.csv **Code/Software:** After extracting the zip file user
 can use any text editor to see the data file. The data is originally
 generated from the JAVA code. ## Access information Other publicly
 accessible locations of the data: * NA Data was derived from the following
 sources: *
 [https://github.com/BCLab-UNM/BiggerIsBetter](https://github.com/BCLab-UNM/BiggerIsBetter) (may not yet be published)