Presentation_1_Modeling Active Cell Movement With the Potts Model.PDF

<p>In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time.</p

Video_1_Modeling Active Cell Movement With the Potts Model.MOV

<p>In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time.</p

Video_2_Modeling Active Cell Movement With the Potts Model.AVI

<p>In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time.</p

Velocity of calcium waves.

<p>Mean calcium wave velocity (<i>v_w</i>) <i>vs</i>. the intercluster distance <i>d</i> and the pump strength <i>p</i>. Blue bullets: estimations obtained from the simulation results. The light-blue plane corresponds to the root square of the fitting: </p><p></p><p></p><p><mi>v</mi><mi>w</mi><mn>2</mn></p><mo stretchy="false">(</mo><mi>d</mi><mo>,</mo><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><mn>107.43</mn><mo>−</mo><mn>10.99</mn><mi>d</mi><mo>−</mo><mn>12.19</mn><mi>p</mi><p></p><p></p>. The coefficient of determination of the data fitting proposed is <i>R</i>² = 0.83.<p></p

Ca_<i>T</i> for different release events.

<p>Total amount of calcium as a function of the pump strength <i>p</i> and the intercluster distance <i>d</i>. (A) Ca_<i>T</i> averaged over all events, (B) Ca_<i>T</i> averaged over puffs, (C) Ca_<i>T</i> averaged over propagating waves, and (D) Ca_<i>T</i> averaged over abortive waves. Vertical axes were scaled by a factor 10⁶. Note that the vertical scales are different.</p

Analysis of spatial-temporal profiles.

<p>A: Calcium density plot showing a typical outcome of the model simulation (horizontal axes: space, vertical axes: time). B: Thresholded image, black spots are regions where the Ca⁺² level exceeds 0.3 <i>μ</i>M. C: All spots shown in B are counted and characterized (intensity, size, duration and velocity, i.e., angle <i>α</i>).</p

Statistical analysis of Ca²⁺ waves.

<p>(A) Number of Ca²⁺ wave release events <i>vs</i>. intercluster distance for different values of pump strength <i>p</i>. (B) Value of intercluster distance corresponding to the maximum number of Ca²⁺ waves (<i>d</i>_<i>max</i>) as a function of <i>p</i>. (C) Mean wave duration <i>vs</i>. intercluster distance for different values of pump strength <i>p</i>. Waves are classified according to the spatial criteria (more details in the text).</p

Typical outcomes of the model simulation.

<p>Calcium density in fragments of space (horizontal) × time (vertical) for <i>d</i> = 2.5 <i>μ</i>m. Whereas for <i>p</i> = 1.8 <i>μ</i>M/s different kinds of release events coexist (A), for <i>p</i> = 1.6 <i>μ</i>M/s global release events are prevalent (B). Two fronts annihilate each other upon collision (white star in B).</p

Parameter values for the model.

<p>Other parameters are given in the figure captions.</p

Phase diagram in the <i>d</i>–<i>p</i> space.

<p>The plot shows a region dominated by propagating waves (<i>n_w</i> > <i>n_aw</i>) and a region where the abortive waves are more abundant (<i>n_aw</i> > <i>n<i>w</i></i>). Calcium release events are classified according to the spatial criterion (dashed line) and the calcium released criterion (solid line).</p