What is Entropy??

 
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Entropy (S) can be best understood as “the effect of probability on a physical or chemical processes”. This relationship is famously described by the Boltzmann entropy formula which relates the probability of a particular state (P1) to the chemical or mechanical work (ΔG) required to obtain that state.
Entropy changes(ΔS), are not probabilities per se but rather a conceptual bridge between probability and energy. In this equation, k is the Boltzmann constant, T is temperature, P is the probability of the considered state, ΔS is the entropy change and ΔG is the free energy change.

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Receptor # Threshold for Cell-Cell Adhesion

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How do two cells that can adhere, decide whether or not they should adhere? Typically, potentially adherent cells become adherent by increasing their adherence-receptor expression levels (R1/R2) past a certain “threshold” or “EC50” (see figure above). A classic 1984 paper defined this EC50 as a function of R1/R2‘s binding constant Ksoln as illustrated above for two average eukaryotic cells.1,2 This equilibrium model for cellular adhesion is described in more detail below.

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Model Organisms and DNA’s “Molecular Clock”

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“Model organisms” are the best-studied organisms in experimental biology. For a particular research questions a specific “model organism” is chosen for its balance of: (1) ease of use and (2) “generalizability” of results. For example

  • unicellular organisms(e.g. bacteria and yeast): are used to answer questions in basic biochemistry or molecular biology;
  • invertebrates (e.g. worms and flys): are used to answer questions in genetics or embryonic development
  • vertebrates (e.g. zebrafish to primates): are used in models of human disease (as they have requisite physiological and neurological complexity)

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The Maximal “Rate” of Evolution

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The timescales over which organisms “mutate” or “evolve” varies dramatically from months(viruses) to millions of years(animals). The figure above plots the average genome size in base-pairs (x-axis) versus the average mutation-rate(y-axis) for various organisms. In addition, a second y-axis (“minimum time to 1% mutation”) illustrate approximate timescales corresponding to each rate.

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Conditional Flow: “pit-stops” and “detours”

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Analogies are often the best tools to connect a program’s “functional logic” with the “abstract tools” of the programming language. Here, we outline the logical differences between common if-statement structures using a “Driving Analogy” drawn in parallel to a “Flow-Chart” and “Model Python Code.” We choose Python because it is one of the most intuitive and commonly used programming languages in biology.

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Understanding Binary with Poker Chips

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Computers store information with transistors or “switches” that have an on (“1”) or off (“0”) state. As a result, they must perform mathematical and logical operations using a binary (base-2) numbering system. For example, as can be see above, computers represent our the decimal/base-10 number “113” with the binary/base-2 number: “1110001”.

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Understanding Boolean Logic Gates

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Boolean algebra/digital logic is how computer hardware performs computations with a binary numbering system. In addition, Boolean operators (and, or, not, etc.) are critical components to all programming languages. The figure above conceptually summarizes the major Boolean Logic Gates using Venn Diagrams to represent the inputs (top) and outputs (bottom) that result.

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The “Spectrum” of Substitution vs. Elimination

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Substitution and elimination reactions (between Lewis-bases and alkyl-halides) are some of the first reactions taught in organic chemistry. The figure above, organizes the main factors that distinquish: SN1, SN2, E1 or E2 mechanisms into a single, 4-quadrant spectrum. We describe the heirarchy of these factors in more detail below.

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The Organic Chemistry of Baking Bread

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The chemistry that underlies the browning of bread. meats, etc. was first defined in 1912 by Louis-Camille Maillard and involves the polymerization of sugars and proteins. While this reaction is obviously messy (i.e. has many different pathways), the dominant chemical mechanisms were identified in a classic paper by John Hodge in 1953 and are outlined in the figure above. As you can see, bread-browning is mainly: amine(protein)-activated carbonyl(sugar) polymerization.

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A Timeline of the Universe, Life, and Civilization

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Historical reference points make understanding evolutionary time a lot easier by “calibrating” it. In the figure above we provide three parallel timelines depicting key events in the history of the universe (billions of years), animal evolution (millions of years) and human development (thousands of years). Major extinction events are marked by horizontal red lines. Additional details can be found below.

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Introduction to RT-PCR (gene/mRNA expression)

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Quantitiative Reverse-Transcriptase PCR (RT-PCR) is different from regular PCR in that it does not measure genes(i.e. DNA) per se but rather measures the EXPRESSION of those gene (i.e. mRNA). Given the fact gene expression (mRNA) can vary dramatically between cell-types, it is important to first isolate a single cell-type by:

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Introduction to PCR and Animal Genotyping

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In a follow up to our overview on DNA methods, we wanted to discuss PCR (polymerase chain reaction) which is one of the most sensitive and versatile techniques in molecular biology. PCR is a technique which selectively amplifies any targeted DNA from a complex mixture based on a set of framing primers. These primers are ~20 base oligonucleotides which we can (1) design based on a sequenced genome and (2) make/order based on solid-phase chemical synthesis. PCR has many applications (see partial list below) but is to test for a particular gene/mutation (i.e. “genotype”) in an animal (see figure above).

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Introduction to the “Family Tree” of DNA Methods

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Many methods in molecular biology are simply different combinations of a handful of techniques. These combinations can be represented as a “family tree” whose “trunk”/”backbone” is PCR (polymerase chain reaction) and whose “roots”/”foundation” is built upon: (1) chemical synthesis of short oligonucleotides, (2) fully sequenced genomes and (3) vectors derived from bacteria and viruses.

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Introduction to Super-resolution Microscopy

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While microscopic methods with protein and atom scale resolution – that don’t break the diffraction barrier! – exist (e.g. electron microscopy, atomic force microscopy, x-ray crystallography, etc.), they tend to be more practically difficult than fluorescence-based microscopy (see posts on Fluorescent Probes and Fluorescent Antibodies). Therefore, to give fluorescence microscopy nanometer resolution, several super resolution techniques have been developed that combine clever (1) optical/photophysical and (2) computational-processing tricks to “clean up” the “blurred data.”

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Understanding the Diffraction Limit in Microscopy

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Basic light microscopy can only resolve objects that are larger than 100 nm which means that while it can visualize animal cells (~10,000nm), organelles and bacteria (~1,000nm), it cannot visualize viruses (<100nm), proteins (<10nm) or small molecules(~1nm) (see post summarizing Biological Scales). This limitation is known as the “diffraction limit” and is caused by the fact light only interacts differently with objects separated by more than one wavelength (λ). Intuitively, its helpful to think of each of these wavelengths as “a minimum pixel size” for a computer image where: infrared light (λ ~ 10.0μm) has pixels 100 times larger than ultraviolet light (λ ~ 0.1μm).

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