- Our method not only identifies the critical state or tipping point at a single sample level, but also provides the sKLD-signaling markers for further practical application. - 2020 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0. - The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.. - As the limit of the normal state, the pre-disease state is a critical state just before the onset of deterioration.. - b Given a number of reference samples that are generally from normal cohort and represent the healthy or relatively healthy individuals, the sKLD score is capable to quantitatively evaluate the difference between two distributions of each gene, i.e., the background distribution that generated from a set of reference samples, and a perturbed distribution yielded from the single case sample. - c During the progression of a complex disease, the pre-disease state is indicated by the significant change of sKLD, i.e., the sKLD changes gradually when the system is in the normal state, while it increases abruptly when the system approaches the tipping point. - for identifying the pre-disease state of complex diseases.. - This DNB concept, directly from the critical slowing- down theory [15, 16], provides statistical method to se- lect relevant variables for the pre-disease state, that is, a small group of closely related variables (DNBs) convey early warning signals for the impending critical transi- tion by some drastic statistical indices [17, 18]. - Therefore, when there is only a single case sample available, it requires new computational method to explore the critical informa- tion, detect the early-warning signal and identify the pre-disease state.. - Here, we used a single-sample with high-throughput omics data, to identify the pre-disease state or early warning signals of the disease deterioration based on the sKLD score. - The successful identifica- tion of the pre-disease states in these diseases validated the effectiveness of sKLD method in quantifying the tip- ping point just before the critical transitions into severe disease states.. - In other word, the high level of sKLD in the vicinity of the critical parameter value s = 0 represents that the ref- erence distribution P is significantly different from the. - It is obvious that the sKLD would abruptly increase when the system is near the critical point, i.e., s = 0, which is in accordance with the bifurcation parameter value at s = 0 (see Eq. - It is seen that the median values of the box plots in Fig. - Identifying the critical transition for acute lung injury The sKLD has been applied to the microarray data of dataset GSE2565, which is obtained from a mouse ex- periment of phosgene-induced acute lung injury [34]. - Clearly, the significant change of sKLD successfully in- dicated the critical stages prior to the metastasis for all the five cancers (Fig. - The critical state of LUSC. - For the samples solely from the two stages around the critical transition point, i.e., stages IIA and IIB, the survival time of stage- IIA samples is longer than that of stage-IIB samples (p = 0.036. - Additional file 1:. - Some genes in the common “sKLD-signaling genes” have been re- ported to be associated with the process of LUSC (Table 1). - The critical state of LUAD. - For the samples solely from two stages IIB and IIIA around the critical transi- tion point, the survival time of stage-IIB samples is Table 1 The genes with high frequency in 13 “ sKLD-signaling genes ” groups in the critical stage (stage IIA) for LUSC. - Table 2 The functional enrichment of common “ sKLD-signaling genes ” in the critical stage samples for LUSC. - Additional file 1: Figure S5f) among the survival curves of samples from stages IIIA, IIIB, IV (the stages after the critical state), which show that stage IIB of LUAD is highly associated with the critical transition of survival time.. - Through literature searching, some genes in the common “sKLD-signaling genes” have been shown to be associated with the process of LUAD (Table 3). - The critical state of STAD. - Additional file 1: Figure S5 h) among survival curves of samples from the period prior to the critical transi- tion, i.e., stages IA-IIIA. - Table 3 The genes with high frequency in 59 “ sKLD-signaling genes ” groups in the critical stage (stage IIB) for LUAD Gene Frequency Location Family* Relation with cancer progression. - The critical state of THCA. - It is seen that the survival times of samples before the critical state were significantly longer than for samples after the critical state. - There was no significant dif- ference in survival curves among samples in stages III, IV Table 4 The functional enrichment of common “ sKLD-signaling genes ” in the critical stage samples for LUAD. - Table 5 The genes with high frequency in 20 “ sKLD-signaling genes ” groups in the critical stage (stage IIIB) for STAD Gene Frequency Location Family* Relation with cancer progression. - The critical state of COAD. - 4j, the survival time of samples before the critical state were obviously longer than that of samples after the critical state. - Specifically, the significant change of sKLD score indi- cates the pre-disease state of phosgene-induced acute lung injury before the deterioration into pulmonary edema, the critical stage of (stage IIA) of LUSC prior to the lymph nodes metastasis, the critical stage (stage IIB) of LUAD before lymph nodes were metastasized, the critical stage (stage IIIB) of STAD before distant metastasis, the critical stage (stage II) of THCA before lymph node metastasis, and the critical stage (stage II) of THCA before lymph node metastasis. - Third, it should be noted that sKLD is a model-free method, which implies that in the sKLD strategy there is neither feature selection nor model/parameter training Table 6 The functional enrichment of common “ sKLD-signaling genes ” in the critical stage samples for STAD. - From the above three properties, it is clear that the crit- ical transition of a system is actually indicated by “the. - transition of distribution”, that is, for some variables (DNB members), their distribution would significantly change when the system approaches the critical transition point.. - Algorithm to identify the tipping point based on sKLD Regarding a biological system as a time-dependent non- linear dynamical system with m genes/variables, then at each time point, the state of such system is expressed by a high-dimensional vector, i.e., the expressions of m genes/variables. - Specifically, for a gene g i , a Gaussian distribution D g i is fitted based on the k expressions of g i in the reference samples {S 1 , S 2. - [Step 5] Calculate the sKLD score based on Eq. - Thus, sKLD score can provide the early-warning signals of the critical transition. - The proposed method has been applied to six real data- sets, i.e., the time-course dataset GSE2565 from NCBI GEO database (http://www.ncbi.nlm.nih.gov/geo) and five stage-course datasets LUSC, LUAD, STAD, THCA and COAD from TCGA database (http://cancergenome.. - 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