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Pregnancy Timeline by SemestersDevelopmental TimelineFertilizationFirst TrimesterSecond TrimesterThird TrimesterFirst Thin Layer of Skin AppearsEnd of Embryonic PeriodEnd of Embryonic PeriodFemale Reproductive SystemBeginning Cerebral HemispheresA Four Chambered HeartFirst Detectable Brain WavesThe Appearance of SomitesBasic Brain Structure in PlaceHeartbeat can be detectedHeartbeat can be detectedFinger and toe prints appearFinger and toe prints appearFetal sexual organs visibleBrown fat surrounds lymphatic systemBone marrow starts making blood cellsBone marrow starts making blood cellsInner Ear Bones HardenSensory brain waves begin to activateSensory brain waves begin to activateFetal liver is producing blood cellsBrain convolutions beginBrain convolutions beginImmune system beginningWhite fat begins to be madeHead may position into pelvisWhite fat begins to be madePeriod of rapid brain growthFull TermHead may position into pelvisImmune system beginningLungs begin to produce surfactant
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Can math predict our growth and diseases?

A biologist and mathematician are studying mathematics in biology. Their goal is to recreate the mathematics behind the "emergence of function" within a cell. They want to give biologists algorithms for cell division in development, and possibly, how to predict when it will go wrong in cancers.

How do our genes give rise to proteins, proteins to cells, and cells to tissues and organs? What makes a cluster of cells become a liver, or a muscle? The incredible complexity of how these biological systems interact boggles the mind — and drives the work of biomedical scientists around the world. Now a mathematician and biologist are formalizing a way of thinking about these concepts that may help us understand our bodies successes and failures, and those incidents in other living things.

Writing in the Proceedings of the National Academy of Sciences PNAS, the pair from the University of Michigan (U-M) Medical School and University of California, Berkeley introduce a framework for using math to understand how genetic information along with the interactions between cells, can give rise to a particular type of tissue.

They note it's a highly idealized plan — and cannot that takes into account every detail of this process, called 'emergence of function'. But, by making a simplified mathematical model, they hope to create a tool scientists find useful in understanding what is expected to happen over time in living tissue.

Indika Rajapakse PhD, U-M Medical School assistant professor of computational medicine, and Stephen Smale PhD, Berkeley professor emeritus, have worked independently on these concepts for several years. They draw on the work of Alan Turing, the pioneering British mathematician. Turing is famous for creating a predefined set of rules to determine a result — the result being breaking secret coded war plans — from a set of variables Nazi code writers were changing daily. The "Turing machine" is the computer algorithm which helped end WWII.

Toward the end of his life, Turing began looking at the mathematics underpinning natural patterns of stripes, spots and spirals in living things. The reaction–diffusion theory of morphogenesis attemps to explain the biological process causing an organism to develop its shape.  Alan Turing predicted a mechanism for morphogenesis based on two different chemical signals — one activating growth and one deactivating growth — which would set up patterns for an organism's development. His theory came decades before scientists actually observed and verified that such signalling patterns exist.

"Our approach adapts Turing's technique, combining genome dynamics within a cell and the diffusion dynamics between cells."

Indika Rajapakse PhD, Assistant Professor, Computational Medicine and Bioinformatics, University of Michigan Medical School, Ann Arbor, Michigan, USA.

Rajapakse's team of biologists and engineers capture human genome dynamics in three dimensions using biochemistry together with high resolution imaging. Stephen Smale PhD, is considered a pioneer of modeling dynamical systems that change over time and in space. He won the Fields Medal in 1966 — the highest prize in mathematics.

An organism's genes remain the same throughout life, however, how a cell uses that information does not remain the same.

Genes may be "hardwired" into a cell, but how they are expressed/function depends on factors such as the epigenetic tags added by environmental factors.

The Defense Advanced Research Projects Agency, or DARPA now funds Rajapakse's research exploring the emergence of function. Rajapakse will focuse on cancer and cell reprogramming, collaborating with fellow members of the U-M Translational Oncology Program and Thomas Ried MD, at the National Cancer Institute. Their goal is to use mathematics to explain the latest results of basic cancer research.

The 19th International Conference on Mathematical and Computational Biology is being held October 30 - 31, 2017 in Barcelona, Spain.

A basic problem in biology is understanding how information from a single genome gives rise to function in a mature multicellular tissue. Genome dynamics stabilize to give rise to a protein distribution in a given cell type, which in turn gives rise to the identity of a cell. We build a highly idealized mathematical foundation that combines the genome (within cell) and the diffusion (between cell) dynamical forces. The trade-off between these forces gives rise to the emergence of function. We define emergence as the coordinated effect of individual components that establishes an objective not possible for an individual component. Our setting of emergence may further our understanding of normal tissue function and dysfunctional states such as cancer.

This work presents a mathematical study of tissue dynamics. We combine within-cell genome dynamics and diffusion between cells, so that the synthesis of the two gives rise to the emergence of function, akin to establishing “tissue homeostasis.” We introduce two concepts, monotonicity and a weak version of hardwiring. These together are sufficient for global convergence of the tissue dynamics.

Key words: diffusion emergence genome dynamics monotonicity tissue dynamics

Reference: PNAS, February 14, 2017 doi: 10.1073/pnas.1621145114
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Using advanced mathematics, researchers hope to create models of biological systems
that help our understanding of normal development as well as diseases.
Image Credit: University of Michigan

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