Gaussian and multimodal distributio

Gaussian and multimodal distributions of vertices after secondary optimization. We

studied the distributions of objective values of a secondary optimization over the vertices obtained in the first optimization. For each vertex, we determined the pathway length [P.sub.L], pathway sum of absolute fluxes [P.sub.J], and pathway cost [P.sub.C] (see Methods). Similar to work done by Shlomi et al. [10], our protein cost definition was solely based on enzyme-synthesis cost. For instance, we did not take the protein lifetimes into account. Ignoring protein lifetimes implies that [P.sub.J] and [P.sub.C] are closely related; [P.sub.C] is taking [P.sub.J] multiplied with a protein cost for each individual reaction. In Fig. 5, we thus only show the results for [P.sub.L] and [P.sub.C]. Initially, we intuitively expected many vertices with intermediate [P.sub.L], [P.sub.J], and [P.sub.C], and few with relatively low or high [P.sub.L], [P.sub.J], and [P.sub.C]. In other words, we expected a Gaussian-shaped distribution for both [P.sub.L], [P.sub.J], and [P.sub.C]. As expected, the [P.sub.L] was indeed Gaussian-shaped distributed for all tested growth conditions. This is illustrated by the dashed black lines in the top panel of Fig. 5 which correspond to a Gaussian distribution where we used the sample mean and standard deviation as input.

[FIGURE 5 OMITTED]

In contrast, [P.sub.C] was clustered into distinct groups, i.e. a multimodal distribution. An accurate determination of pathway cost is a challenge and we hypothesized that a different cost function could show a different distribution. Therefore, we investigated four different definitions of protein cost: minimum, maximum, average, and equal (i.e. sum of absolute fluxes; [P.sub.J]). When multiple proteins were associated to a particular reaction via an OR rule, the minimum, maximum or average was taken (for more details see Methods). In all cases, we found a multimodal distribution. Nonetheless, we did find an effect of the cost function; taking the "minimal" cost function typically resulted in the largest difference between both clusters, while taking the "equal" cost function typically resulted in the smallest difference between both clusters (S2 Table, S6 Fig.). These results show that for explaining the multimodal distribution of vertex cost, the effect of fluxes was much more important than the effect of protein costs.

Hasil (Bahasa Indonesia) 1:

Distribusi Gaussian dan multimodal dari simpul setelah optimasi sekunder. Kamibelajar distribusi nilai-nilai tujuan optimasi sekunder atas simpul yang diperoleh dalam optimasi pertama. Untuk setiap vertex, kita menentukan jalur panjang [P.sub.L], jalur jumlah mutlak fluks [P.sub.J], dan jalur biaya [P.sub.C] (Lihat metode). Mirip dengan pekerjaan yang dilakukan oleh Shlomi et al. [10], protein kami biaya definisi semata-mata berdasarkan biaya enzim-sintesis. Misalnya, kami tidak mengambil tahan protein ke account. Mengabaikan protein tahan menyiratkan bahwa [P.sub.J] dan [P.sub.C] berhubungan erat; [P.sub.C] adalah mengambil [P.sub.J] dikalikan dengan biaya protein untuk reaksi masing-masing individu. Dalam gambar 5, kami dengan demikian hanya menampilkan hasil untuk [P.sub.L] dan [P.sub.C]. Pada awalnya, kami secara intuitif diharapkan banyak simpul dengan menengah [P.sub.L], [P.sub.J], dan [P.sub.C], dan beberapa dengan relatif rendah atau tinggi [P.sub.L], [P.sub.J], dan [P.sub.C]. Dengan kata lain, kita diharapkan distribusi Gaussian berbentuk untuk kedua [P.sub.L], [P.sub.J], dan [P.sub.C]. Seperti yang diharapkan, [P.sub.L] adalah memang berbentuk Gaussian didistribusikan untuk semua kondisi pertumbuhan yang diuji. Ini diilustrasikan oleh garis hitam putus di panel atas 5 gambar yang sesuai dengan distribusi Gaussian dimana kami menggunakan sampel mean dan deviasi standar sebagai masukan.[GAMBAR 5 DIHILANGKAN]In contrast, [P.sub.C] was clustered into distinct groups, i.e. a multimodal distribution. An accurate determination of pathway cost is a challenge and we hypothesized that a different cost function could show a different distribution. Therefore, we investigated four different definitions of protein cost: minimum, maximum, average, and equal (i.e. sum of absolute fluxes; [P.sub.J]). When multiple proteins were associated to a particular reaction via an OR rule, the minimum, maximum or average was taken (for more details see Methods). In all cases, we found a multimodal distribution. Nonetheless, we did find an effect of the cost function; taking the "minimal" cost function typically resulted in the largest difference between both clusters, while taking the "equal" cost function typically resulted in the smallest difference between both clusters (S2 Table, S6 Fig.). These results show that for explaining the multimodal distribution of vertex cost, the effect of fluxes was much more important than the effect of protein costs.