Lastly, we studied the reduction of

Lastly, we studied the reduction of the solution space after secondary optimization. For the E. coli iAF1260 model with splitting, secondary optimization reduced the solution space to only one or a few vertices (Table 2). In case of [P.sub.L]-minimization, only vertices can be optimal solutions, since convex combinations increase the number of active reactions. Compared to minimization of [P.sub.J] and [P.sub.C], the solution space after minimization of [P.sub.L] contained more vertices in all of the tested growth conditions. This was expected because [P.sub.L] is solely based on the number of active reactions, specific flux values are not of interest. Taking these flux values into account typically results in more diverse outcomes. Hence, it is less likely to find as many vertices with a minimal [P.sub.J]. Similarly, adding different protein costs to each reactions further diversifies these outcomes. As a result, the optimal solution space for [P.sub.C]-minimization resulted in a unique flux distribution for all tested growth conditions.

Discussion

The recently developed computational method, CoPE-FBA (Comprehensive Polyhedra Enumeration Flux Balance Analysis) [16], offers the premise of a simplified biological understanding of the optimal solution space of metabolic network models; a kind of understanding which is not possible with other popular methods such as Flux Variability Analysis [14] and Flux Coupling Analysis [25]. We further developed this method: Rather than enumerating the minimal generating set, we used reversible-reaction splitting [31, 32] to enumerate all non-decomposable flux pathways in the optimum. This allows us to focus solely on the vertices for the analysis of optimal flux pathways.

Enumerating all non-decomposable flux pathways in the optimum is a very demanding task compared to enumerating only a (small) subset of these flux pathways; especially for CoPE-FBA as presented by Kelk et al [16]. Therefore, we also developed an efficient computational method, CoPE-FBA 2.0, for the (unique) characterization of the optimal solution space. We can now characterize the optimal solution space in the order of minutes for most (bacterial) genome-scale models on just an ordinary computer. CoPE-FBA 2.0 is efficient because it first determines the subnetworks and subsequently enumerates the vertices for each subnetwork (see Methods for more details). To illustrate this, the 120 x [10.sup.6] vertices enumerated for E. coli under aerobic growth conditions originate from eight subnetworks with respectively 6, 3, 5184, 3,2, 54,2, 2 vertices. This means that while we determined in total only 5256 vertices (the sum), we actually enumerated 120.932.352 vertices (the multiplication) within 15 minutes on an ordinary computer.

Hasil (Bahasa Indonesia) 1:

Terakhir, kita mempelajari pengurangan ruang solusi setelah optimasi sekunder. Untuk iAF1260 E. coli model dengan membelah, optimasi sekunder dikurangi ruang solusi hanya satu atau beberapa simpul (Tabel 2). Dalam kasus [P.sub.L]-minimalisasi, simpul hanya dapat menjadi solusi yang optimal, karena kombinasi cembung meningkatkan jumlah reaksi aktif. Dibandingkan minimasi [P.sub.J] dan [P.sub.C], Ruang solusi setelah minimasi [P.sub.L] terdapat simpul lain dalam semua kondisi pertumbuhan yang diuji. Ini diharapkan karena [P.sub.L] semata-mata didasarkan pada jumlah reaksi aktif, spesifik fluks nilai tidak menarik. Mempertimbangkan nilai-nilai fluks ini biasanya menghasilkan hasil yang lebih beragam. Oleh karena itu, sangat kecil kemungkinannya untuk menemukan sebanyak simpul dengan minimal [P.sub.J]. Demikian pula, menambahkan biaya protein yang berbeda untuk setiap reaksi lebih lanjut diversifikasi hasil tersebut. Sebagai akibatnya, solusi optimal ruang bagi [P.sub.C]-minimalisasi mengakibatkan distribusi fluks unik untuk semua kondisi pertumbuhan yang diuji.DiskusiThe recently developed computational method, CoPE-FBA (Comprehensive Polyhedra Enumeration Flux Balance Analysis) [16], offers the premise of a simplified biological understanding of the optimal solution space of metabolic network models; a kind of understanding which is not possible with other popular methods such as Flux Variability Analysis [14] and Flux Coupling Analysis [25]. We further developed this method: Rather than enumerating the minimal generating set, we used reversible-reaction splitting [31, 32] to enumerate all non-decomposable flux pathways in the optimum. This allows us to focus solely on the vertices for the analysis of optimal flux pathways.Enumerasi semua jalur bebas-decomposable fluks yang optimal adalah tugas yang sangat menuntut dibandingkan enumerasi hanya subset (kecil) dari jalur fluks ini; terutama untuk mengatasi-FBA yang disajikan oleh Kelk et al [16]. Oleh karena itu, kami juga mengembangkan efisien komputasi metode, mengatasi-FBA 2.0, untuk karakterisasi (unik) ruang solusi optimal. Kita sekarang dapat ciri ruang solusi optimal dalam menit untuk kebanyakan model skala genom (bakteri) pada komputer yang biasa. Mengatasi-FBA 2.0 efisien karena pertama menentukan Subnetwork dan kemudian membilang Vertex untuk setiap subnet mask (Lihat metode untuk rincian lebih lanjut). Untuk menggambarkan hal ini, 120 x [10.sup.6] simpul disebutkan untuk E. coli kondisi pertumbuhan aerobik berasal dari delapan Subnetwork dengan masing-masing 6, 3, 5184, 3,2, 54,2, 2 simpul. Ini berarti bahwa sementara kita menentukan di simpul hanya 5256 total (jumlah), kita benar-benar dihitung 120.932.352 simpul (perkalian) dalam waktu 15 menit pada komputer biasa.