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Wolfram Language

For Chemistry and Bioscience Computation
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Outline

Motivation

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  • Necessity of computation in modern research and teaching

    • Introductory Examples

    
  • Bio-Sequence Computation
    • 
  • Optimized Clustering of Noble Gas Atoms
    • 
  • Built-in Molecular Data Objects

    • Intermediate Examples

    
  • Spectral Lines
    • 
  • Counting Rings in a Molecule
    • 
  • Genomic Analysis
    • 
  • Functional Groups at a Glance

    • Advanced Examples

    
  • Segmentation and Classification of Cells
    • 
  • A Family Tree of Drugs
    • 
  • A Solubility Model in a Few Lines
    • ​
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    Motivation

    What Is Computation?

    Computation ⊃ {Chemical Formulae, Chemical Visualisation, Machine Learning, Optimisation, Probability, ODE & PDE Modelling, Molecular Dynamics, Calculus, Chemical & Drug Data, Signal Processing, Graphs & Networks, Mathematics, Agent-Based Simulation, Random Processes, Geo-Computation, Combinatorics, Control Theory, Functional Analysis…

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    Introductory Examples

    Bio-Sequence Computation

    Represent a DNA sequence:
    seq=BioSequence["DNA","CTTTTCGAGATCTCGGCGTCA"]
    Translate the sequence to a peptide:
    pep=BioSequenceTranslate[seq]
    Find out what the corresponding molecule is:
    Molecule[pep]
    Visualize it in 3D:
    MoleculePlot3D[Molecule[pep]]
    Look at a longer sequence and compare:
    gene=BioSequence
    coagulation factor V (proaccelerin, labile factor)
    GENE
    
    LongestCommonSubsequence[seq,gene]["SequenceString"]
    ​
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    Introductory Examples

    Optimized Clustering of Noble Gas Atoms

    The Lennard-Jones potential is an intermolecular potential that describes the potential energy of pairs of interacting atoms.
    Create a function to model the potential:
    ClearAll[ljPotential];​​ljPotential[r_,ϵ_:1.0,σ_:1.0]:=4ϵ
    12
    σ
    r
    -
    6
    σ
    r
    ;
    Plot the potential energy
    V
    LJ
    as a function of
    r
    (the distance between a pair of atoms):
    Plot[ljPotential[r],{r,0.7,2.5},Frame->True,FrameLabel->{"r","
    V
    LJ
    "},ImageSize->500]
    Create a function to calculate the total potential energy of a cluster of atoms:
    ClearAll[clusterEnergy];​​clusterEnergy[coords_List,potential_:ljPotential]:=Total[​​Map[​​potential,​​MapApply[​​EuclideanDistance,​​Subsets[coords,{2}]​​]​​]​​]
    Set up a random cluster and calculate its potential energy:
    Create a function to find a configuration that minimizes the potential energy of a cluster:
    Plot the random cluster in a minimal configuration:
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    Introductory Examples

    Built-in Molecular Data Objects

    Wolfram Language has a variety of data objects to represent chemical objects.

    ChemicalFormula

    Sometimes all you have is a chemical formula, which allows a considerable amount to be computed:

    “Chemical” Entities

    An entity in our knowledgebase with a host of curated data behind it:

    Molecule

    The number of chemical entities is large but finite, but the number of possible molecular structures is not. Molecule allows you to create any structure you want:
    Often you have a chemical name or SMILES string, both of which can be interpreted by Molecule:
    Or you have an image snipped from a paper:
    We can look a little more closely at that SMILES string:
    You don’t have to start with a name or any other information—you can just draw the molecule from scratch:
    And then you can generate 3D coordinates and plot it:

    MoleculePattern

    Wolfram Language allows searching for and highlighting arbitrarily defined substructures within a Molecule object:
    Use MoleculePattern to represent complex patterns like a carboxylic ester, using a combination of atoms and bonds:
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    Intermediate Examples

    Spectral Lines

    Use built-in spectral line data to get the properties of an atomic line for carbon near 600 nm:
    Get the state transitions for tungsten within the visible spectrum:
    Extract the wavelengths (and convert the magnitudes from angstroms to nanometers):
    Plot the results:
    Compare with the results for hydrogen:
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    Intermediate Examples

    Counting Rings in a Molecule

    In chemistry and cheminformatics, counting rings in a molecule helps describe its structure, stability and reactivity. Ring counts are used in predicting properties like aromaticity, classifying compounds and generating molecular descriptors for drug design and materials science. Chemists use the smallest set of smallest rings (SSSR) as a consistent measure for the number of rings in a molecule.
    Start with biphenyl, a small molecule with two benzene rings joined by a single bond:
    Naphthalene has two rings that are fused together by a shared bond:
    Note that the SSSR does not include the outer envelope ring containing all 10 carbon atoms, because mathematically it can be formed by combining the smaller rings. To count all cycles, convert the molecule to a Graph and then call FindCycle:
    Why do chemists use the SSSR instead of enumerating all cycles in the graph? There is both a chemical and a practical answer. Consider a larger structure like this cycloamylose:
    The SSSR for this molecule has eight rings with six atoms and 24 rings with 40 atoms:
    Enumerating all possible cycles increases the number of 40-atom rings to 256:
    By looking at only the SSSR, a greater emphasis is placed on the smaller rings, which are much more relevant to the overall chemistry of this molecule. This alone makes the SSSR count a more useful topological descriptor for property prediction models. Another reason to prefer the SSSR is practical: namely, that it can be computed much more efficiently. For example, finding the SSSR for buckminsterfullerene is done very quickly:
    All of the five- and six-membered rings are contained in the SSSR:
    By contrast, the number of total cycles in buckminsterfullerene is exponentially large and not countable in a reasonable time:
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    Intermediate Examples

    Genomic Analysis

    We can use a resource function to perform a sequence similarity search for a nucleotide sequence, targeting the human genome:
    Compare the original with the aligned sequence:
    Get information on the identified gene including location, associated biological activities, molecular functions, SNPs and biological pathways:
    Find the protein structure associated with the gene:
    Visualize the protein structure:
    Find the biological pathway associated with the gene:
    Get information on pathways:
    Visualize one of the pathways:
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    Intermediate Examples

    Functional Groups at a Glance

    Fingerprint a handful of familiar drugs:
    Everything the fingerprint found in lidocaine, the local anesthetic. Its secondary amide and tertiary amine are both there, along with the six aromatic atoms of its benzene ring and six rotatable bonds:
    Which contain a tertiary aliphatic amine, the basic nitrogen found in many drugs?
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    Advanced Examples

    Segmentation and Classification of Cells

    Look at an image of stained cells from a rat brain, some of which have fluorescent marker uptake:
    Stained rat brain cells are visible in the blue image channel:
    Extract a background mask with automatic pixel intensity thresholding:
    Find a seed point for every cell by looking for maxima at a given scale:
    Obtain a cell segmentation via a watershed algorithm:
    The fluorescent marker is visible in the green channel. Measure the amount of fluorescence in each cell segment:
    Estimate the distribution:
    Visualize all the cells with more than a certain fluorescent uptake:
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    Advanced Examples

    A Family Tree of Drugs

    Molecules with similar fingerprints have similar structures. Here we fingerprint 15 drugs from five therapeutic classes and cluster them by the Jaccard (Tanimoto) distance between their fingerprints. The clustering is never told the classes; we only use them to color the labels afterward:
    Color each drug's label by its class:
    The opioids, benzodiazepines, beta blockers and NSAIDs each form their own branch. Simvastatin doesn't join the other statins: it's derived from a fungal natural product and looks nothing like the fully synthetic atorvastatin and rosuvastatin. The fingerprint sees structure, not pharmacology.
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    Advanced Examples

    A Solubility Model in a Few Lines

    Machine learning functions like Predict need every example to be the same kind of object, usually a fixed-length vector. A fingerprint turns any molecule, whatever its size, into exactly that.
    We encode each molecule with MACCS keys. This is a classic fingerprint of 166 yes-or-no questions about a molecule's structure, such as whether it contains a ring or an OH group. Those are the kinds of features that affect solubility, so this small fingerprint works well here.
    We train on 900 randomly chosen molecules and hold out the rest for testing:
    How does the model do on the 228 molecules it hasn't seen? In the comparison plot, a perfect model would put every point on the dashed diagonal. The R² score is typically around 0.6 and varies a little with the random split:
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    Summary

    
  • Unified solution for chemistry and bioscience students, researchers and professionals
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  • State-of-the-art symbolic and numerical computation
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  • Access to real-world data
    • 
  • Powerful and immediate visualization tools
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    Next Steps

    Become a Wolfram Language User

    
  • Start a free 15-day trial
    • 
  • Check if you have access through your organization here
    • 
  • Explore interactive courses on Wolfram U

    • References

    
  • See our Public Resources here
    • 
  • Chemistry Core Areas page
    • 
  • Wolfram Solution for Biosciences
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