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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA


Alan Aguirre-Soto


Class of 2016


Alan Aguirre-Soto is a postdoctoral research associate at MIT, focusing on light-activated polymerization reactions in the presence of proteins for low-cost medical diagnostics devices. Alan was born in Mexico. His first programming language, learned while he was completing the International Baccalaureate (IB) program, was Pascal. He then graduated with a BS in chemical engineering with a minor in industrial engineering and polymers from the Instituto Tecnológico y de Estudios Superiores de Monterrey (ITESM) in Mexico. He also obtained a BS in applied chemistry from Reutlingen University in Germany as a Deutsche Akademische Austauchdienst (DAAD) scholar. As an undergrad, he won first place at the 2007 AIChE poster session in materials science, and founded the first Latin American AIChE student chapter. Later, Alan completed his MS and PhD degrees in chemical engineering at the University of Colorado Boulder. His doctoral thesis focused on the elucidation of the mechanisms of photocatalysis reactions to make polymer materials. To study these reactions, he designed and built software and hardware for the in situ monitoring of these chemical reactions, where handling huge quantities of spectroscopic data was a formidable challenge. During his PhD, Alan worked with undergraduate and high-school students promoting science, engineering and mathematics. Alan has been excited about Mathematica and the Wolfram Language since he heard about it during graduate school. He is thrilled about being part of the Wolfram Summer School. and particularly interested in using the Wolfram Language to guide the engineering of molecules that address urgent societal needs.

Project: 3D Polymer Growth around Proteins by Varying Binding Probability

The growth of a three-dimensional polymer network grafted to proteins bound to a surface serves as a signal amplification method to detect biomarkers of infectious diseases in devices analogous to pregnancy tests. The polymer networks formed are swollen by an aqueous dye solution to allow detection with the unaided eye for faster, accurate, highly sensitive medical diagnostics to deploy in resource-limited settings. The state-of-the-art system works because the polymer network grows faster around the target biomarker, i.e. only in positive diagnoses. However, the mechanism behind this bottom-up growth of the polymer network remains unknown. We hypothesized that the capture of the target protein on the surface alters the affinity of the polymer seeds to the surface. This results in a bottom-up concentration gradient of the polymer seeds. As a result, polymer growth and polymer seeds merging is fastest in the proximity of the capture biomarker. To test this hypothesis, we propose using Mathematica to model polymer growth as a three-dimensional lattice where randomly active sites represent the growing polymer seeds. By changing the probability, number and distribution of these active sites on the three-dimensional lattice, we simulate the effect that a higher-affinity surface would have on the origin and direction of the polymer growth. This is important because we want to avoid homogeneous polymer growth, as this leads to false positives in the medical diagnostics. Hence elucidating the mechanism and understanding how to enhance bottom-up polymer growth can enable the design of better systems for sensitive, high-accuracy bio sensors.

Our current design of this model involves a Mathematica program in which we use Graphics to visualize the three-dimensional lattice where the polymer will grow. We then plan to use an iterative algorithm that will create and update several lists and nested lists containing coordinates for the vertices and edges formed by the points in the lattice. One of the lists will contain the x,y,z coordinates for the randomly positioned active sites. In one simulation, a higher probability can be set for the creation of active at t=0 closer to the surface (y->0). In the control, we can run the simulation by setting the probability of creating active sites equal throughout the 3D grid. There is the possibility, as well as testing the effect, of modifying the probability of each active site growing in every step as functions of their positions on the lattice. This way we can evaluate the structures formed after n iterations. In this approach, we will start by assigning fixed positions to each active site, under the assumption that the speed of the translation of the polymer seeds in the water is much slower than the rate at which the polymer seeds grow and merge. If our hypothesis is correct, we expect to see a random growth from the origin of the 3D lattice in the case where we have a higher probability of active sites as y-> 0. In contrast, when the probabilities are equal throughout the space, we should see that the polymer grows homogeneously in the bulk of the space. The time at which the entire lattice is fully interconnected is referred to as the percolation threshold. This is threshold is typically associated with the gelation of the polymer network. It will be interesting to further analyze what the probabilities are analogous to, most likely in this case the binding energy of the hydrophobic polymer seeds to the hydrophobic moieties on the captured proteins.

The aim is to model the dynamics of the merging of polymer seeds into polymer networks under Brownian motion as a function of the affinity of the polymer seeds to proteins grafted to the bottom surface. We represent the affinity to the proteins using a normal distribution of the polymer seeds. Then we vary the values of the covariance matrix to analyze the trends in the number of particles, mean radii, maximum and minimum radius and Euclidean distance from the center as a function of time steps. This process is modeled as a stochastic process in which particle collisions are sought by solving the intersection of a cylinder and the surrounding resting spheres during asynchronous movements. The initial number of particles was 100, and their radius was initially defined as equal to 0.1 units in a 6-unit cubic lattice. The diffusion length was approximately scaled based on the known diffusion coefficient assuming Langevin dynamics. Each sphere is a cluster of linear polymer chains.

Favorite 3-Color 2D Totalistic Cellular Automaton

Rule 1012344820

I like this rule because it creates an irregular octahedron that has convex structures on all four sides, seen here as transitions from magenta to cyan. Furthermore, this rule seems particular even when compared to others I located with similar structures, in that the corners change color. In other cases, the magenta/yellow structures extend out into the corners as if they never end. In this case, however, they suddenly stop as cyan and magenta lines are formed perpendicular to the growth direction. Also, as I ran this rule for more steps, the color of the outer triangles changed from yellow to cyan exactly from 375 to 376 steps, which is also interesting. The growth of this cellular automaton appears to have a random character, but there is a recognizable structure pattern that emanates from the seemingly random growth. I browsed the universe between rules 1000000000 and 1128702085 at different step sizes. The rules around rule 1012344820 show either no growth whatsoever or they show some of the features of rule 1012344820, but not all. There's no growth in the next rule, 1012344821. The rule before seems to have a pattern that resembles the formation of some of the underlying features for rule 1012344820. It is as if the structure in rule 1012344820 was the pinnacle of a certain pattern that starts appearing in the rules before it, and that evolves in the rules after it.

In conclusion, I can say that this pattern caught my attention because it appears to be the transition between structures that die in all directions before reaching the edges, and structures that do not die out in any direction before reaching the edges.