Rescaling of spatio-temporal sensing in eukaryotic chemotaxis

Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient - an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness, rather than the absolute concentration, of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels. However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts, each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients. Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies

社会性アメーバDictyostelium discoideumが示すcAMP応答のリスケーリング特性の一細胞解析

学位の種別:課程博士University of Tokyo(東京大学

Spatial FCD of the scale-invariant LEGI model upon static gradient stimuli.

<p>The input profile follows <i>S</i>(<i>x</i>,<i>y</i>) = <i>S</i>₀ + Δ<i>S x</i>, where the origin of the spatial coordinate <i>x</i> is located at the cell center. (a) Amplified response in the activator level <i>A</i>. The activator level <i>A</i> (red circle) and inhibitor level <i>B</i> (blue circle) are plotted against the input level <i>S</i> at each point on the cell periphery with both <i>A</i> and <i>B</i> normalized by the value at the center of the cell. The input stimulus used is <i>S</i>₀ = 0.1 and Δ<i>S</i> = 0.01. The black line indicates normalized <i>S</i>, which corresponds to an unamplified response. (b) The activator level <i>A</i> (red) and inhibitor level <i>B</i> (blue) at the cell front (solid line) and back (broken line) are plotted as a function of the mid-point input level <i>S</i>₀. The relative gradient is fixed as Δ<i>S</i> = 0.1<i>S</i>₀.</p

Schematic representation of the scale-invariant LEGI model.

<p>The model describes the dynamics of the levels of activator A and inhibitor B upon chemoattractant stimulus S. The arrows and the bar-ended arrow represent excitatory and inhibitory regulations between the signaling components, respectively.</p

Non-Genetic Diversity in Chemosensing and Chemotactic Behavior

Non-genetic phenotypic diversity plays a significant role in the chemotactic behavior of bacteria, influencing how populations sense and respond to chemical stimuli. First, we review the molecular mechanisms that generate phenotypic diversity in bacterial chemotaxis. Next, we discuss the functional consequences of phenotypic diversity for the chemosensing and chemotactic performance of single cells and populations. Finally, we discuss mechanisms that modulate the amount of phenotypic diversity in chemosensory parameters in response to changes in the environment

Two types of symmetry in the scale-invariant LEGI model.

<p>(a) Temporal FCD symmetry refers to the scale invariance of the equations excluding the coupling term. Spatial FCD symmetry means the scale invariance of the equations excluding the time derivative terms. (b) A trajectory of the activator level <i>A</i> of the model only with spatial FCD symmetry (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164674#pone.0164674.e002" target="_blank">Eq 2</a>; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164674#sec002" target="_blank">Models</a>) upon two-step inputs with identical fold change (<i>p</i> = 5) but different absolute levels. The inset shows the input variable <i>S</i>. (c) The activator level <i>A</i> (red) and inhibitor level <i>B</i> (blue) at the cell front (solid line) and back (broken line) are plotted as a function of the mid-point input level <i>S</i>₀ for the model only with temporal FCD symmetry. The relative gradient is fixed as Δ<i>S</i> = 0.1 <i>S</i>₀. (d, e) For the model only with spatial FCD symmetry (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164674#pone.0164674.e003" target="_blank">Eq 3</a>; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164674#sec002" target="_blank">Models</a>), the responses are plotted as in (b, c).</p

Responses of the scale-invariant LEGI model with a feedback network topology.

<p>(a) A schematic representation of the regulatory network of the model (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164674#pone.0164674.e004" target="_blank">Eq 4</a>; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164674#sec002" target="_blank">Models</a>). (b) A trajectory of the activator level <i>A</i> upon two-step inputs with identical fold change (<i>p</i> = 5) but different absolute levels. The inset shows the input variable <i>S</i>. (c) The activator <i>A</i> (red) and inhibitor <i>B</i> (blue) at the cell front (solid line) and back (broken line) under linear profiles of gradient, <i>S</i>(<i>x</i>,<i>y</i>) = <i>S</i>₀ + Δ<i>S x</i>, are plotted as a function of the mid-point input level <i>S</i>₀. The relative gradient is fixed as Δ<i>S</i> = 0.1 <i>S</i>₀. (d) Responses to wave stimuli are visualized as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164674#pone.0164674.g006" target="_blank">Fig 6e</a>. Specifically, spatio-temporal profiles of the activator level <i>A</i> along the cell periphery under wave stimuli <i>S</i>_slow (top left), <i>pS</i>_slow (top right), <i>S</i>_fast (bottom left) and <i>pS</i>_fast (bottom right), respectively.</p

Temporal fold-change detection (FCD) of the scale-invariant LEGI model in response to spatially uniform stimuli.

<p>The insets show the input variable <i>S</i> (green). (a) Trajectories of the activator level <i>A</i> (red) and the inhibitor level <i>B</i> (blue) upon single step input. (b) A trajectory of the activator level <i>A</i> upon two-step inputs with identical fold change (<i>p</i> = 5) but different absolute levels.</p

Responses of the scale-invariant LEGI model to complex stimuli.

<p>(a) The trajectories of the activator <i>A</i> at the cell front (solid line) and back (dotted line) are plotted upon a sudden reversal of a linear gradient (<i>S</i>(<i>x</i>, <i>y</i>) = <i>S</i>₀ + Δ<i>S x</i>, <i>S</i>₀ = 1 and Δ<i>S</i> = ± 0.1) at <i>t</i> = 20. The inset shows spatial profile of the activator level <i>A</i> at <i>t</i> = 0. (b) Responses to two point sources of input stimuli where the input profile is defined as <i>S</i>(<i>x</i>, <i>y</i>) = <i>C</i>₁ exp[−((<i>x</i> +<i>x</i>₀)² +<i>y</i>²)/2<i>V</i>] + <i>C</i>₂ exp[−((<i>x</i> − <i>x</i>₀)² + <i>y</i>²)/2<i>V</i>] (<i>x</i>₀ = 7.5 and <i>V</i> = 4). The positions of the point sources are indicated by the purple squares. (Top left) Spatial profile of the activator level <i>A</i> at the steady state in one point source stimulus, i.e., <i>C</i>₁ = 1 and <i>C</i>₂ = 0. (Bottom left) Spatial profile of the activator level <i>A</i> at the steady state in two point source stimuli, i.e., <i>C</i>₁ = <i>C</i>₂ = 1. (Right) Time series of the activator <i>A</i> at the cell front (solid line) and back (dashed line) upon application of another point source of <i>S</i> at t = 0 at the other side of the cell. The strength of the second signal <i>C</i>₂ is dynamically controlled as shown in the inset. (c) Responses of the model upon sequential changes of the input spatio-temporal profile, where a spatially graded stimulus (<i>S</i>(<i>x</i>, <i>y</i>) = <i>S</i>₀ + Δ<i>S x</i>, <i>S</i>₀ = 1 and Δ<i>S</i> = 0.15) (top left), then no stimulus (top middle) and then a spatially-homogeneous stimulus (<i>S</i>₀ = 0.3) (top right) are applied consecutively. Spatial profiles of the activator <i>A</i> at corresponding time points are shown at the bottom.</p