Shape is data, and data is shape

.title[
# Shape is data, and data is shape
]
.subtitle[
## Mathematically phenotyping shapes and patterns<br>From molecules to organisms
]
.author[
### Erik Amézquita<br>—<br>Division of Plant Science & Technology<br>Department of Mathematics<br>University of Missouri<br>—
]
.date[
### 2025-04-07
]

---

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# About me: From MX to MI to MO at MU

## I work across multiple disciplines and countries

.right-column[
- 2013 - 2018 : Licenciatura (Bachelor): Mathematics @ Universidad de Guanajuato and CIMAT. Thesis focused on Topological Data Analysis applied to archaeology.

- 2018 - 2023 : PhD: Computational Mathematics, Science, and Engineering @ Michigan State University. Dissertation: Exploring the mathematical shape of plants. **Came for the math. Stayed for the plants.**

- 2023 - Present : PFFIE Postdoctoral Fellow @ Division of Plant Science & Technology (80%) / Department of Mathematics (20%) at MU.
]

---

# My work: Crossing and merging bridges

<div class="list" style="font-size: 14px; text-align: left;">
    <ul>
      <li>M Bentelspacher, <strong>EJA</strong>, S Adhikari, J Barros, SY Park (2024) "The early dodder gets the host: Decoding the coiling patterns of Cuscuta campestris with automated image processing". <em>Plant Cell Reports</em>.</li>
      <li><strong>EJA</strong>, MY Quigley, PJ Brown, E Munch, DH Chitwood (2024) "Allometry and volumes in a nutshell: Analyzing walnut morphology using three-dimensional X-ray computed tomography". <em>The Plant Phenome J</em>.</li>
      <li><strong>EJA</strong>, F Nasrin, KM Storey, M Yoshizawa (2023) "Genomics data analysis via spectral shape and topology." <em>PLOS One</em></li>
      <li>SA Cervantes-Pérez <em>et al.</em> (2024) "Tabula Glycine: The whole-soybean single-cell resolution transcriptome atlas." Submitted.</li>
      <li>Z Ji, <strong>EJA</strong>, L Newton, DH Chitwood, AM Thompson (2024) "From hand measurements to high throughput phenotyping: understanding maize canopy structure and predicting yield." Submitted.</li>
    </ul>
</div>

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# Roadmap for today

1. Introduction: Addressing the genotype-phenotype gap

1. The shape of spatial patterns of mRNA

1. The shape of the movement of a vampire plant

1. The shape of omics data analysis

1. The shape of things to come

1. Shaping the next generation of interdisciplinary scientists

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# 1. Introduction

## Shape is data, and data is shape

### Visual intuition &harr; Numbers

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# We use Topological Data Analysis (TDA)!

![](../figs/GLYMA_05G092200_TDA_c00541_transp.gif)

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# Phenotyping the shape of things to come

<div class="row" style="font-family: 'Yanone Kaffeesatz'; font-size:22px;">
  <div class="column" style="max-width:33%">
    <p style="line-height:0;text-align: center; font-size:28px">Phenotyping patterns</p>
    <img style="padding: 0 30px;" src="../figs/molecular_cartography_2x2.jpg"></img>
    <img style="padding: 0 30px;" src="../figs/persistence_images_1x1.svg"></img>
    <p style="text-align: center;">mRNA sub-cellular localization in soybean nodule cells.</p>
  </div>
  <div class="column" style="max-width:33%">
    <p style="line-height:0;font-size:28px;text-align: center;">Phenotyping movement</p>
    <img style="padding: 0 10px;" src="../../cuscuta/figs/qmlphv.gif"></img>
    <img style="padding: 35px 30px;" src="../../cuscuta/figs/avg_pl.svg"></img>
    <p style="text-align: center;">Tracking and describing <i>Cuscuta campestris</i> circumnutation</p>
  </div>
  <div class="column" style="max-width:33%">
    <p style="line-height:0;font-size:28px;text-align: center;">Phenotyping data</p>
    <img style="padding: 0 0px;" src="../../nasrin/figs/fpkm_raw_3.png"></img>
    <img style="padding: 30px 0px;" src="../../nasrin/figs/lung_fpkm_meancorr_eps1.0e+06_r40_g40.png"></img>
    <p style="text-align: center;">Reducing <strong>and</strong> clustering high-dimensional omics data</p>
  </div>
</div>

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# 2. Characterizing mRNA spatial patterns and distributions

## with Topological Data Analysis (TDA)

### In collaboration with Marc Libault

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# mRNA localization at a sub-cellular level

- Beyond gene expression counts: Spatial segregation and asymmetrical distribution of mRNA across the cytosol in the soybean nodule.

- Molecular Cartography&trade; data provided by the Libault Lab

.pull-left[
![](../figs/Infected_Cells_05G216000_red_05G092200_green.jpg)
Infected soybean nodule cells. Glyma.05G092200 in green. Glyma.05G216000 in red.
]

**Goals**: "How patterny is a pattern?"

- Quantify the spatial patterns followed by mRNA within individual cells.
- Mathematically model all observed mRNA sub-cellular distributions.
- *Use this mathematical model to differentiate cell types and genotypes.*

**Challenge**

- Develop a mathematical model that works for any cell size, orientation, shape, and dimension.

]

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# Traditional model: Density of transcripts

![](../figs/sublevel_both_bw3_S25_rho_cyto_GLYMA_05G092200.png)
![](../figs/sublevel_both_bw3_S25_rho_cyto_GLYMA_17G195900.png)

But this characterization discards sub-cellular information!

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# Same density, different patterns

![](../figs/molecular_cartography_2x4.png)

- 97 genes (including 10 bacterial ones) &rarr; 2 genes
- 2938 cells &rarr; 918 infected ones.

**Subcellular transcript patterns &harr; spatial location of the cell within the nodule**

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# Alternate model: Topological Data Analysis

![](../figs/GLYMA_05G092200_TDA_c00541_transp.gif)

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# TDA: Keep track of blobs and holes

![](../figs/GLYMA_05G092200_TDA_c02352_00.png)