A Systems Theoretic Approach to Systems and Synthetic by Vishwesh V. Kulkarni, Guy-Bart Stan, Karthik Raman

By Vishwesh V. Kulkarni, Guy-Bart Stan, Karthik Raman

The complexity of organic platforms has intrigued scientists from many disciplines and has given start to the hugely influential box of systems biology wherein a wide range of mathematical ideas, resembling flux stability research, and expertise structures, similar to subsequent iteration sequencing, is used to appreciate, elucidate, and are expecting the services of complicated organic structures. extra lately, the sector of synthetic biology, i.e., de novo engineering of organic platforms, has emerged. Scientists from quite a few fields are targeting easy methods to render this engineering procedure extra predictable, trustworthy, scalable, reasonable, and simple.

Systems and regulate idea is a department of engineering and technologies that conscientiously bargains with the complexities and uncertainties of interconnected structures with the target of characterising primary systemic houses resembling balance, robustness, conversation ability, and different functionality metrics. platforms and keep an eye on thought additionally strives to supply techniques and strategies that facilitate the layout of structures with rigorous promises on those houses. over the past a hundred years, it has made stellar theoretical and technological contributions in assorted fields resembling aerospace, telecommunication, garage, car, energy platforms, and others. Can it have, or evolve to have, the same impression in biology? The chapters during this ebook reveal that, certainly, structures and keep an eye on theoretic recommendations and methods may have an important effect in platforms and artificial biology.

Volume I presents a wide ranging view that illustrates the opportunity of such mathematical tools in structures and artificial biology. fresh advances in structures and artificial biology have basically verified the advantages of a rigorous and systematic procedure rooted within the ideas of platforms and keep watch over concept - not just does it result in interesting insights and discoveries however it additionally reduces the inordinately long trial-and-error technique of wet-lab experimentation, thereby facilitating major reductions in human and monetary assets. In quantity I, a few of the prime researchers within the box of structures and artificial biology display how platforms and keep watch over theoretic recommendations and strategies should be worthwhile, or should still evolve to be valuable, so one can know the way organic structures functionality.

As the eminent computing device scientist Donald Knuth positioned it, "biology simply has 500 years of fascinating difficulties to paintings on". This edited publication offers yet a small fraction of these for the good thing about (1) platforms and keep watch over theorists drawn to molecular and mobile biology and (2) biologists attracted to rigorous modelling, research and regulate of organic systems.

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Extra info for A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations

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8). 9). Case 2: There exists j0 ∈ {1, 2, . . , l} such that d j0 ,i0 ∈ R<0 . From the definition of i 0 , O(b j0 M j0 , t0 ) = i 0 ≤ m − 1. Therefore, for each i such that X i |M j0 , O( f i , t0 ) ≤ m − 1. From the definitions of C and m, this implies that for each i such that X i |M j0 , f i is RNN at t0 . Since b j0 ∈ R>0 , it follows that b j0 M j0 ◦ f is a product of RNN functions. 2, b j0 M j0 ◦ f is RNN at t0 and d j0 ,i0 ∈ R>0 , a contradiction. Hence, for i = 1, 2, . . , n, f i is RNN at t0 .

3. If c = ⇐c1 , c2 , . . , cn is a positive strong E -equilibrium point, then ˆ cˆ = ⇐cπ−1 (1) , cπ−1 (2) , . . , cπ−1 (n) ˆ is a positive strong E -equilibrium point. 4. For all e ∈ Eˆ , there exists t ∈ Ω such that e( fˆ(t)) = 0. 5. If Eˆ is natural, I ⊆ Ω ∩ R≥0 is connected, 0 ∈ I and f (0) is a non-negative point then for all t ∈ I ∩ R>0 , fˆ(t) is a positive point. 6. For i = 1, 2, . . , n, if π(i) ≤ nˆ then for all t ∈ Ω, f i (t) = fˆπ(i) (t). 7. For i = 1, 2, . . , n, if π(i) > nˆ then for all t1 , t2 ∈ Ω, f i (t1 ) = f i (t2 ).

E. ) In light of Theorem 10, Open Problem 1 is equivalent to the following statement. Open Problem 2 Let E be a finite, natural event-system of dimension n. Let x ∈ Rn>0 . Then there exists an open, simply-connected Ω ⊆ C, an E -process f on Ω and a positive strong E -equilibrium point c such that: 1. R≥0 ⊆ Ω. 2. f (0) = x. 3. f (t) → c as t → ∞ along the positive real line. e. 6 Finite Natural Atomic Event-Systems In this section, we settle Open 1 in the affirmative for the case of finite, natural, atomic event-systems.

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