Paper List

期刊: ArXiv Preprint
发布日期: 2026-03-10
BiophysicsMathematical Biology

Single-cell directional sensing at ultra-low chemoattractant concentrations from extreme first-passage events

University of Notre Dame | University of Utah

Vincent Fiorino, Sean D. Lawley, Alan E. Lindsay
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IN SHORT: This work addresses the core challenge of how a cell can rapidly and accurately determine the direction of a chemoattractant source when the signal is extremely weak (femto- to attomolar), and receptor binding events are discrete and rare.

核心创新

  • Methodology Derives the first analytic expressions for the joint asymptotic distribution of the earliest k hitting times and their angular locations on a 2D circular cell, revealing that θ_k,N ~ N(θ_0, σ²_k,N) where σ²_k,N ∝ ( (R-1)² / (R W) ) * (1 + (2 log k)/(1+W) ) and W ~ log N.
  • Theory Quantitatively demonstrates that early binding events (e.g., the first few arrivals) carry disproportionately more directional information than later arrivals, providing a theoretical basis for rapid cellular decision-making before a steady-state gradient is established.
  • Methodology Proposes and rigorously analyzes the performance of several source-direction estimators (from simple averaging of early impact locations to more complex MLEs), deriving explicit formulas for their expected error and variance (e.g., E[ρ_k^res] ≈ (D/R)(b_N + a_N(log k - 1))).

主要结论

  • The angular location θ_k of the k-th arriving molecule follows a normal distribution centered on the true source direction θ_0, with a variance that increases logarithmically with k (σ²_k,N ∝ log k), formally proving that earlier arrivals provide more precise directional cues.
  • A simple estimator averaging the first k impact locations (n_res) can achieve accurate directional sensing with small k; its error grows with k while its variance decreases (Var[ρ_k^res] ≈ 4D²/(R²k)*((a_N log k + b_N - a_N)² + a_N²)), highlighting a trade-off.
  • The theoretical framework successfully links key physical parameters (source distance R, initial molecule number N ~ 10³-10⁶, number of observed events k) to sensing performance, showing that accurate directional inference is possible even for R > 1 (source placed multiple cell radii away).
研究空白： Prior models of chemotaxis often relied on steady-state concentration gradients or receptor occupancy, which are not applicable in the ultra-low concentration regime where decisions must be made from a handful of discrete, stochastic binding events. This work fills the gap by providing a stochastic, non-equilibrium theoretical framework for directional sensing in this biologically relevant but mathematically challenging regime.

摘要: We investigate single-cell directional sensing from diffusing chemoattractant signals released by a localized source. We focus on the low-concentration regime in which receptor activity is discrete and cellular decisions are made on timescales far shorter than those required for steady-state concentration profiles or receptor occupancy to emerge. We derive analytic expressions for the joint distribution of receptor binding times and binding locations, conditional on the position of the source. We show that early binding events carry disproportionately more information about source directionality than later arrivals. Motivated by this observation, we propose and analyze several source-localization estimates that exploit early receptor binding statistics. Our results demonstrate that, even with a small number of binding events, cells possess sufficient information to rapidly and accurately infer the directionality of a diffusing chemoattractant source.