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Presented by, Pradeepa K N

Reverse Engineering Time Discrete Finite Dynamical Systems : A Feasible Undertaking ? Delgado-Eckert E (2009). Presented by, Pradeepa K N. Introduction:. R everse engineering of biochemical and gene regulatory networks is the important problem.

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Presented by, Pradeepa K N

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  1. Reverse Engineering Time Discrete Finite Dynamical Systems: A Feasible Undertaking?Delgado-Eckert E (2009) Presented by, Pradeepa K N

  2. Introduction: • Reverseengineering of biochemical and gene regulatory networks is the important problem. • Reverse engineering approach – top-down method • Different Top-down algorithms  Different models  Different Mathematical Framework. • For each model type – suitable mathematical framework to study the performance & limitations.

  3. Objective: • Identify minimal requirement on data sets. • Identify the optimal data sets – quality & quantity.

  4. Gene Regulatory Networks Collection of DNA segments in a cell. Interact with each other indirectly with other substances in the cell. Governing the expression levels of mRNA and proteins.

  5. Gene Regulation:

  6. Laubenbacher Stigler Algorithm: • A top-down reverse engineering algorithm. • Modeling of time discrete finite dynamical systems. • Considers the biochemical networks • Discretize the concentration levels of interacting chemicals to elements of the finite system.

  7. Key Steps: • Identifying Term Order • Generalizing the Boolean approach to asynchronous updating of the state variables.

  8. Minimal requirements on a data set based on how many terms the functions to be reverse engineered display • Optimal data sets were characterized using a geometric property called “general position”. • A constructive method to generate optimal data sets, provided a co-dimensional condition.

  9. TERM-ORDER-FREE REVERSE ENGINEERING METHOD: • Generalization of LS algorithm that does not depend on Term order. • Formula for the probability of finding the correct model, provided the data set satisfies an optimality criterion. • Asymptotic behavior of the probability formula for a growing number of variables n (i.e. interacting chemicals) was analyzed. • Formula converges to zero .

  10. Even if, • optimal data set + the restrictions imposed by the use of term orders • are overcome, the reverse engineering problem remains unfeasible. • Experimentally impracticable amounts of data are available. • This result discouraged the elaborating on the algorithmic aspects of the term-order-free reverse engineering method.

  11. The LS algorithm first takes, • input : the discretized time series and generates functions. • LS algorithm takes, • input : monomial order and • generates the normal form of function with respect to polynomial functions • This functions vanishes on data inputs.

  12. RESULTS AND DISCUSSION: • If the data set = X and only term orders, the LS-algorithm is used with X as input data. • Probability of finding f = 0. • Using the term-order-free reverse engineering method with X, the LS-algorithm(fed with X) could not find the correct function.

  13. The minimal requirements on a set: The LS-algorithm reverse engineers f based on the knowledge of the values that it takes on every point in the set X: If the LS-algorithm is used to reverse engineer a nonzero function The data set X used must contain points were the function does not vanish. Requiresat leastt different data points to completely reverse engineer f.

  14. Advantages: This method do not impose constraints on the set of candidate terms that can be used to construct a solution. Even though such sets can be constructed, further research is required to prove their existence in general terms. If no optimal sets can be determined, it is still advantageous to work with pseudo-optimal data sets.

  15. The Optimal Data Sets: • The identified optimal data sets are sets  of discretized vectors. • In a real application, the optimal data set X has to be transformed back (or “undiscretized”) to a corresponding set  of real vectors. • This transformation can be performed using an “inverse” function of the discretization mapping.

  16. Difficulty: • To provide an exact formula for the probability that the LS-algorithm will find the correct model under the assumption that an optimal data set is used as input. • The use of term orders inherent to the LS-algorithm. • No such formula for deriving the probability of LS – algorithm.

  17. Overcoming this problem by considering a generalization of the LS-algorithm, the term-order-free reverse engineering method. • Advantages: It allows for the calculation of the success probability . • It also eliminates the issues and arbitrariness linked to the use of term orders.

  18. Conclusion: Open problem – formula for the success probability of LS algorithm (random term order). The mathematical algorithmic method based on, discretization, some type of convergence as the discretization gets finer and finer is highly desirable. After a certain degree of resolution, the method is capable of catching essential properties which will not vary significantly if the resolution is further increased.

  19. To be investigated: • Gröbnerbases approaches by dropping the requirement for term orders. • To what extent the LS-algorithm could advantageously be adapted to the use of these approaches. • The feasibility of such an adaption as well as its computational aspects remain to be investigated.

  20. Thank you

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