By Raina Robeva, Terrell Hodge
Mathematical techniques and strategies in glossy Biology bargains a quantitative framework for reading, predicting, and modulating the habit of complicated organic structures. The ebook provides vital mathematical innovations, equipment and instruments within the context of crucial questions raised in sleek biology.
Designed round the ideas of project-based studying and problem-solving, the ebook considers organic issues comparable to neuronal networks, plant inhabitants development, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling instruments delivered to undergo on those subject matters contain Boolean and usual differential equations, projection matrices, agent-based modeling and a number of other algebraic techniques. Heavy computation in the various examples is eased by means of freely to be had open-source software.
- Features self-contained chapters with genuine organic learn examples utilizing freely on hand computational tools
- Spans a number of mathematical options at simple to complex levels
- Offers huge viewpoint at the makes use of of algebraic geometry/polynomial algebra in molecular platforms biology
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Extra info for Mathematical Concepts and Methods in Modern Biology. Using Modern Discrete Models
Sample text
S] is an increasing function of The right-hand side of this equation f ([S]) = KVmax m +[S] the substrate concentration with two properties: (i) lim f ([S]) = Vmax , and (ii) [S]→∞ Vmax f ([S] = K m ) = 2 . From a biological point of view, this reaction never occurs at a rate greater than Vmax . K m is the substrate concentration at which the reaction rate is equal to half of its maximum value Vmax . Furthermore, since Vmax = k3 E 0 > 0, the reaction rate is a linear increasing function of the initial enzyme concentration E 0 , which means that higher initial enzyme concentration makes the reaction go faster and this relationship between the rate and E 0 is linear.
The Lac repressor protein is a tetramer of identical subunits [11]. 4 Bistability arises in (L; A∗ ) space in the 3 variable lac operon model (y -axis is in logarithmic scale). For a range of L concentrations there are three coexisting steady states for the allolactose concentration. 055) mM of L concentration. 5 Time series simulation of the mRNA, β-galactosidase and allolactose concentrations. These plots were produced by numerically solving the 3 variable model when L = 50 × 10−3 mM. 4). The (∗)’s in these plots represent the location of the low and high stable steady states.
For those, “low” could truly mean “absent” and medium-level concentrations are biologically completely feasible. In the model from Eqs. 8), the authors take care to introduce designated Boolean variables for low lactose and allolactose to ensure that “low” means “some but not zero” [22]. , [26,27] and Chapter 2 of this volume) consider Boolean frameworks within which it is possible to distinguish between low, medium, and high lactose concentrations. Focusing on the medium range of lactose concentration is of particular interest since the lactose operon has been shown to exhibit bistability for medium levels of lactose.