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Today, The Visible Embryo is linked to over 600 educational institutions and is viewed by more than 1 million visitors each month. The field of early embryology has grown to include the identification of the stem cell as not only critical to organogenesis in the embryo, but equally critical to organ function and repair in the adult human. The identification and understanding of genetic malfunction, inflammatory responses, and the progression in chronic disease, begins with a grounding in primary cellular and systemic functions manifested in the study of the early embryo.

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Pregnancy Timeline by SemestersFetal liver is producing blood cellsHead may position into pelvisBrain convolutions beginFull TermWhite fat begins to be madeWhite fat begins to be madeHead may position into pelvisImmune system beginningImmune system beginningPeriod of rapid brain growthBrain convolutions beginLungs begin to produce surfactantSensory brain waves begin to activateSensory brain waves begin to activateInner Ear Bones HardenBone marrow starts making blood cellsBone marrow starts making blood cellsBrown fat surrounds lymphatic systemFetal sexual organs visibleFinger and toe prints appearFinger and toe prints appearHeartbeat can be detectedHeartbeat can be detectedBasic Brain Structure in PlaceThe Appearance of SomitesFirst Detectable Brain WavesA Four Chambered HeartBeginning Cerebral HemispheresFemale Reproductive SystemEnd of Embryonic PeriodEnd of Embryonic PeriodFirst Thin Layer of Skin AppearsThird TrimesterSecond TrimesterFirst TrimesterFertilizationDevelopmental Timeline
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Home | Pregnancy Timeline | News Alerts |News Archive Oct 7, 2013

 

Mathematics is the universal language behind physical science, according to USC chemist Chi Mak..






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Unlocking biology with math

Researchers develop a first-of-its-kind mathematical model for the biological process that keeps our immune system working.

Scientists at the University of Southern California (USC) have created a mathematical model that explains and predicts the biological process that creates antibody diversity – the phenomenon that keeps us healthy by generating robust immune systems through hypermutation.

The work is a collaboration between Myron Goodman, professor of biological sciences and chemistry at the USC Dornsife College of Letters, Arts and Sciences; and Chi Mak, professor of chemistry at USC Dornsife.


"To me, it was the holy grail. We can now predict the motion of a key enzyme that initiates hypermutations in immunoglobulin (Ig) genes."

Myron Goodman, professor, biological sciences and chemistry, USC Dornsife College of Letters, Arts and Sciences


Goodman first described the process that creates antibody diversity two years ago. In short, an enzyme called "activation-induced deoxycytidine deaminase" (or AID) moves up and down single-stranded DNA that encodes the pattern for antibodies and sporadically alters the strand by converting one nitrogen base to another, which is called "deamination."

The change creates DNA with a different pattern – a mutation.


These mutations, which AID creates a million-fold times more often than would otherwise occur, generate antibodies of all different sorts – giving you protection against germs that your body hasn't even seen yet.

"It's why when I sneeze, you don't die," Goodman said.


In studying the seemingly random motion of AID up and down DNA, Goodman wanted to understand why it moved how it did, and why it deaminated in some places much more than others.

"We looked at the raw data and asked what the enzyme was doing to create that," Goodman said. He and his team were able to develop statistical models whose probabilities roughly matched the data well, and were even able to trace individual enzymes visually and watch them work. But they were all just approximations, albeit reasonable ones.


Collaborating with Mak, however, offered something better: a rigorous mathematical model that describes the enzyme's motion and interaction with the DNA and an algorithm for directly reading out AID's dynamics from the mutation patterns.

At the time, Mak was working on the mathematics of quantum mechanics. Using similar techniques, Mak was able to help generate the model, which has been shown through testing to be accurate.


"Mathematics is the universal language behind physical science, but its central role in interpreting biology is just beginning to be recognized," Mak said. Goodman and Mak collaborated on the research with Phuong Pham, assistant research professor, and Samir Afif, a graduate student at USC Dornsife. An article on their work, which will appear in print in the Journal of Biological Chemistry on October 11, was selected by the journal as a "paper of the week."

Next, the team will generalize the mathematical model to study the "real life" action of AID as it initiates mutations during the transcription of Ig variable and constant regions, which is the process needed to generate immunodiversity in human B-cells.

Abstract
We formulate a master equation-based mathematical model to analyze random scanning and catalysis for enzymes that act on single-stranded (ss)DNA substrates. Catalytic efficiencies and intrinsic scanning distances are deduced from the distribution of positions and gap lengths between a series of catalytic events occurring over time, which are detected as point mutations in a lacZα-based reporter sequence containing enzyme target motifs. Mathematical analysis of the model shows how scanning motions become separable from the catalysis when the proper statistical properties of the mutation pattern are used to interpret the readouts. Two-point correlations between all catalytic events determine intrinsic scanning distances, while gap statistics between mutations determine their catalytic efficiencies. Applying this model to activation-induced deoxycytidine deaminase (AID), which catalyzes C→U deaminations processively on ssDNA, we have established that deaminations of AGC hot motifs occur at a low rate,~ 0.03 s-1, and low efficiency, ~3%. AID performs random bidirectional movements for an average distance of 6.2 motifs, at a rate of about 15 nt/s, ″dwells″ at a motif site for 2.7 s, while bound > 4 min to the same DNA molecule. These results provide new and important insights on how AID may be optimized for generating mutational diversity in Ig genes, and we discuss how the properties of AID acting freely on a ″naked″ ssDNA relate to the constrained action of AID during transcription-dependent somatic hypermutation and class-switch recombination.

This research was funded by National Institutes of Health (grants ES013192 and GM21422), and by the National Science Foundation (grant CHE-0713981).

Original press releas: http://news.usc.edu/#!/article/56001/usc-study-unlocks-biology-with-math/