A Model of Tumor Development

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Tumors develop in two distinct stages: (1) Initiation to Last-Common-Ancestor(LCA) where 6-8 “driver-mutations” occur sequentially over 10-50 years and (2) LCA to Metastasis where mutations occur more rapidly in parallel. In the first phase, mutations occur slowly and pierce 6-8 barriers to unrestrained growth by “hot-wiring” pro-growth pathways and then “shorting-out” pro-death pathways . In the second phase, genomic instability creates a large-heterogeneous-population that is well-equipped to compete against bigger-picture-limitations such as oxygen-availability, tissue-size, attacking immune cells and chemotherapies.

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Intense-Exercise Recovery Timeline (~1 week)

Immune-SC-muscle-v12

We’ve made several timelines on the adaptive-response that follows intense exercise ranging from: 2-3 months it takes to “get in shape” to the the 12 hours it takes to cement muscle-memory in the brain. One topic we have not discussed is the 1-week it takes to recover-and-rebuild from an intense bout of exercise.

Interesting, it is the immune-system (not stem cells) that manage the whole repair and rebuilding process. To use a building analogy, the immune system: (1) demolishes the old building (damaged muscle) and (2) erects the steel-sub-structure (extracellular matrix). Only then do the stem-cells install plumbing, electricity and internet (new muscle). On other words, the immune-cellsbuild the building” while the stem-cellsmake it functional.”

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A ‘Canonical’ Cancer-Network Map

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Cancer is a complex disease that is defined by at least 10 different “Hallmarks” that reflect mutation or epigenetically-driven reprogramming of normal cellular circuits. Over the past year, I have compiled a document that attempts to combine what’s known about the intra-cellular network that underlie these “Cancer Hallmarks.” This project started out as a single-page infographic but has since expanded into the 2 foot x 3 foot poster pictured above.

My goal was (and is) to create a comprehensive network map that is conceptually accessible to help me (and now others) think about the “big picture” of cancer networks. Of course, this poster is a work in progress and I will continue to update it over time. Below, I give a brief conceptual description of each module I have used to organize this “Canonical” Cancer-Network Map.

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A Cancer-Therapy Timeline

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I recently finished two excellent books (The Biology of Cancer and The Death of Cancer) that really helped me start to understand the “big picture” of cancer research (in the lab AND the clinic). These books inspired us to piece together a timeline on the history of cancer therapy which ended up being a bit larger than we expected. Click on the image above for a PDF of our Cancer Therapy Poster (3′ x 1′). Below you can find a summary of all the abbreviations and references used for this project.

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A Math-History Timeline

math-timeline-v12

The history of mathematics can be divided into three periods:

  1. The Measurement and Shapes period (<77,000BC – 600AD): Mathematics first rose to preeminence with the agricultural revolution, around ~8,000BC, as a practical tool to organize economics and civilization(trade, accounting, taxes, etc.). Only with the Greeks (~600BC) did mathematics become a pure subject which was pursued for the purpose of “understanding”. Unfortunately, the Roman Empire did not share the Greek’s interest in “pure knowledge” and Europe forgot much what it had learned for the next 1000 years.

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How do you “Fractionate” a Cell?

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Different scientific questions focus on different parts of the cell and it is often necessary to break a cell up into those different pieces (figure above). While various “-omic” methods are well suited to answering global/systems-level questions for the four catagories listed above (e.g. microscopy, genomics, proteomics, metabolomics) they often lack the resolution of fractionation-methods to answer molecular level questions.

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Data-Inference vs Predictive-Modeling

Data Inference vs Predictive Models

Quantitative methods in science can be categorized via their typical place within the scientific method as (1) Inferential which is focused primarily on data analysis and (2) Predictive which is focused on formulating mechanistic hypotheses through modeling. In the figure above we summarize some of the most common methods that fall within each of these categories.

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Introduction to Bayesian Inference

Disease Probability from Symptoms

Baysian statistical inference is a very useful method to “back predict” the probability of a hypotheses from data frequency. In the example above, our “hypothesis” is a disease and our “data” is the an associated symptom.” Now, diseases are not measured directly, but rather, are diagnosed based on a combination of symptoms. Bayesian inference allows us to calculate the “Probability of Disease given Symptom 1 (p(D|S1)) with the following information:
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DNA Sequencing Methods

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While DNA-sequencing methods are diverse and complex they can be grouped into three categories which share several common features: 1. DNA Fragmentation, 2. Fragment Amplification, 3. Sequencing via Fluorescent-Synthesis. These categories are:
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PCR Mutagenesis: Overlap Extension

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Polymerase Chain-Reaction (PCR) has become the backbone of most Methods in Molecular Biology and site-specific mutagenesis no exception. The key to PCR-based mutation of DNA is careful design of primers. In the simplest case, a point-mutation can be inserted into all PCR products by adding a point mutation to all primers. Unfortunately, for linear DNA, this method only works for mutagenesis at the ends of the template (where the primers bind).

Overlap extension, is a powerful 2-step, multi-PCR technique that can insert mutations at any position and of any size (including whole deletions or insertions). It accomplished this using chimeric primers to (1) cut out pieces of DNA and (2) reassemble them at overlap points:
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Kinetics #6: Pulse-Chase Experiments

catalysis-kinetics-intuition-v6

In our sixth post on Understanding Kinetics, we consider pulse-chase experiments which are a common method to study bio-synthetic pathways. In pulse-chase experiments:

  1. A “pulse” of labeled metabolite (P) is added to culture media.
  2. The down-stream intermediates ((P1, P2, P3, etc.)) are measured (“chase“) with mass-spectrometry or radiation.

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Kinetics #5: Molecular Complexes (e.g. drug-target)

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In our fifth post on Understanding Kinetics, we consider the speed at which molecular complexes form. This is the fundamental mechanism underlying drug action (i.e. drugs inhibition their targets) and cellular signalling (i.e. ligands activate their receptors) and is probably the most important “kinetic effect” to consider in experimental design. Here again we use previously derived mathematical models1 to define some simple rules for the timescales/half-lives and magnitude of these reactions (figure above).

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Kinetics #4: Reversible On-Off States

kinetics-reverse-on-off-v02

In our fourth post in the Understanding Kinetics series we consider the speed at which proteins can turn off (A) or on (B). The dynamics of such processes are important to consider when designing experiments (i.e. How long should I wait to take a measurement?) and understanding Network Motifs in signalling cascades. Luckily we can use exact mathematical models (equations below1) for such processes to define some intuitive rules for the timescales/half-lives and magnitude of these reactions (figure above).

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Why Sleep is Important for Training

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It’s well known that physical rest is important for athletic training but mental rest/relaxation, is also a very important factor. An excellent article1 and primer2 on this topic was recently published and the major take away was: “muscle memory”/motor-control is set during rest through a “mental replaying” of the training-activity. In other words, if you want your final kick in a 5k or marathon to feel natural, make sure you get plenty of sleep after workouts!

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A History of Modern Science

science-timeline-v11

Science, as we now think of it, only really started about 400 years ago when Francis Bacon unified theory, observation, and experiment in his: “A New Method.” Before this “unified procedure,” science was a patchwork of “lucky guesses” which over-emphasized one tool or another (For example, Aristotle loved reason and hated mathematics whereas Pythagoras believed the world could only be described by pure mathematics).

In addition, quantitative experimentation and the idea of “testing a hypothesis,” only really became practically feasible with inventions of the early Renaissance. Below we give more detail on some these key milestones in the advancement of research, physics, chemistry and biology.

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