A physical mechanism of heterogeneity in stem cell, cancer and cancer stem cell
aa r X i v : . [ q - b i o . M N ] F e b A physical mechanism of heterogeneity in stem cell, cancer andcancer stem cell
Chong Yu, , Qiong Liu, Cong Chen, and Jin Wang , , , ∗ State Key Laboratory of Electroanalytical ChemistryChangchun Institute of Applied Chemistry, Chinese Academy of SciencesChangchun, Jilin 130022, China University of Science and Technology of China College of PhysicsJilin University, Changchun, Jilin 130012, China Department of Chemistry, Physics & Applied MathematicsState University of New York at Stony BrookStony Brook, NY 11794-3400, USA ∗ Corresponding Authors: [email protected]
Abstract
Heterogeneity is ubiquitous in stem cells (SC), cancer cells (CS), and cancer stem cells (CSC). SC and CSC het-erogeneity is manifested as diverse sub-populations with self-renewing and unique regeneration capacity. Moreover, theCSC progeny possesses multiple plasticity and cancerous characteristics. Many studies have demonstrated that cancerheterogeneity is one of the greatest obstacle for therapy. This leads to the incomplete anti-cancer therapies and transitoryefficacy. Furthermore, numerous micro-metastasis leads to the wide spread of the tumor cells across the body which is thebeginning of metastasis. The epigenetic processes (DNA methylation or histone remodification etc.) can provide a sourcefor certain heterogeneity. In this study, we develop a mathematical model to quantify the heterogeneity of SC, CSC andcancer taking both genetic and epigenetic effects into consideration. We uncovered the roles and physical mechanismsof heterogeneity from the three aspects (SC, CSC and cancer). In the adiabatic regime (relatively fast regulatory bindingand effective coupling among genes), seven native states (SC, CSC, Cancer, Premalignant, Normal, Lesion and Hyper-plasia) emerge. In non-adiabatic regime (relatively slow regulatory binding and effective weak coupling among genes),multiple meta-stable SC, CS, CSC and differentiated states emerged which can explain the origin of heterogeneity. Inother words, the slow regulatory binding mimicking the epigenetics can give rise to heterogeneity. Elucidating the originof heterogeneity and dynamical interrelationship between intra-tumoral cells has clear clinical significance in helping tounderstand the cellular basis of treatment response, therapeutic resistance, and tumor relapse.
Keywords: SC, CSC, cancer, epigenetic, heterogeneity, metastasis Introduction
Cells are the basis for life. Cells can replicate [1] or differentiate [2]. Cells can switch phenotypes from the stem cellsto the differentiated cells. In the process of differentiation and development, mutations and genetic changes are oftennot significant[3]. The underlying gene regulatory networks are believed to provide the driving force for differentiation[4–6]. In stem cells, heterogeneity is often found [7, 8]. The heterogeneity here obviously does not come from geneticchanges such as mutations but must be from other roots. Epigenetics and micro-environments may provide sources forthe heterogeneity in stem cells[9, 10].Cancer is a systemic level disease which involves not only a mixture of tumor cells, but also the microenvironment,signal transduction, extracellular components etc.. In the early studies, genetic mutation was believed to be the maindriving force for the cancer initiation and progression[11–13]. Recent studies revealed that cancer is not just a geneticdisease, but should be considered as an ecosystem which is under environmental selection[14, 15]. The mutations aremore likely to appear when the cell lesions are developed. The mutant cells are subject to epigenetic influences andmicro-environmental pressures. They prefer to spread out to other organs. These can lead the mutant cells to acquiredifferent hallmarks of cancer[16]. As cancer involves epigenetic and micro-environmental influences, the studies on theunderlying cancer gene regulatory networks and how the networks change with respect to the epigenetics and environmenthave received recent attentions [4, 17–19].CSC is a type of tumor cells which occupy a very small proportion at about 1%-4%[20]. Recently, a growing numberof evidences revealed that CSC is the main driving force for cancer recurrence, drug resistance and migrate[21, 22]. If thecancerous mutations acquire a specific capacity, the stemness, the progeny may turn out to be the CSCs. If the somaticstem cells acquire disorder characteristics of cancer cells, the progeny maintains the stem cell-like self-renewal capabilityand possesses the cancerous characteristics. Therefore, the CSC progeny can have various tumor cell phenotypes and theself-renewal ability.Heterogeneity is one of the most significant contributors to various tumor cell phenotypes. The heterogeneity canbe related to epigentics. Without basing the DNA sequence changes, diversity cell phenotypes can still be generatedthrough the epigenetic mechanisms, such as DNA methylation and histone modifications[23]. These will result the geneexpression change and the change of the cell phenotypes[24]. Epigenetic changes are heritable and can influence genefunction directly. The variations can be accumulated. They can then contribute to clonal selection and provide a sourcefor tumor cell heterogeneity.In this study, we start from a gene regulatory motif involving SC, CS, CSC, and differentiation with two oncogene ofcancer (P53 and MDM2), one marker gene of stem cell (OCT4), one marker gene of metastasis (ZEB) and two micro-RNAs (miR-145 and miR-200) which are crucial in the regulations. We develop a landscape framework to quantify theheterogeneity of SC, CSC and cancer. To explore the epigenetic aspects we vary the time scales of the regulatory processof protein binding/unbinding with respect to protein synthesis/degradation rate.In our previous work, we have explored the fast adiabatic binding/unbinding gene regulation regime in details [25].In adiabatic regime, seven steady states are emerged, Normal, Premalignant, Cancer, SC, CSC, Lesion and Hyperplasiastate. In this work, we mainly study slow fast non-adiabatic binding/unbinding gene regulation regime in details. Innon-adiabatic regime, diverse intermediate meta-stable states are emerged in the results of our model. This was onlyobserved previously in the experiments. These results can help us to understand what controls the epigenetic process indifferent cell states and also provide physical mechanism for the heterogeneity. This work presents a new way to quantify2he cancer heterogeneity from epigenetic perspective. This can provide insights into heterogeneity involved in cancer, SC,and CSC, and may ultimately lead to new approaches to cancer therapy.
We start with a gene regulatory network motif to illustrate the relationship among SC, CS, CSC involving vital regulatorygenes and microRNAs. In the motif, there are 6 nodes. P53 and MDM2 are the oncogenes of cancer. OCT4 is a markergene for stem cell, ZEB is a crucial regulator of EMT during cancer development and two microRNAs (miR145 andmiR200) which are vital to the regulations.In the motif (Fig.1) , gene OCT4, P53 and ZEB self activate themselves[26]. OCT4 promotes the transcription ofmiR-200[27] and miR-200 represses the translation of ZEB[28]. In the meantime, OCT4 inhibits the transcription of miR-145[29] and miR-145 inhibits the translation of ZEB[30], OCT4[29] and MDM2[31]. The two micro-RNAs (miR-200and miR-145) inhibit the expression of ZEB[26, 32] and ZEB also represses the translation of the two micro-RNAs[30].P53 promotes the expression of MDM2[33, 34] and miR-200 represses the translation of OCT4[35]. MDM2 inhibits theexpression of P53[34] and is inhibited by miR-145[31].The underlying dynamics of the gene regulatory motif is stochastic. One can apply Gillespie algorithm[36] to quantifythe stochastic dynamics and statistical distribution of gene expressions. To describe the biological process precisely, a setof time scale parameters of each process can be defined. The model’s chemical reactions can be expressed as follow: G αβ A + ( n + ) B h A GGGGGGGBF GGGGGGG f A G αβ A + ( n ) B (1) G α β A + ( n + ) C h A GGGGGGGBF GGGGGGG f A G α β A + ( n ) C (2) G αβ A + ( n + ) D h A GGGGGGGBF GGGGGGG f A G αβ A + ( n ) D (3) ( n ) G A g GGGGBF GGGG k ( n + ) G A (4)The parameters g denotes the protein synthesis rate and k denotes the protein degradation rate, h denotes the bindingrate and f denotes the unbinding rate of regulatory proteins to the target genes. The protein synthesis rate is influencedby the regulated gene number and regulated type. G denotes a gene. The gene A has three operator sites. Upper cornermark α , β of gene A denote a binding state of a binding site. ‘0’ and ‘1’ denote the unbinding and binding state. ProteinB,C and D are monomer, dimer and tetramer respectively.In Fig.1, we described the regulations of P53 and MDM2. Gene P53 has two operator sites. One is activation bindingsite, the other is repression binding site. Gene MDM2 has one activation binding site. The gene P53 and MDM2 translatedto related proteins with the synthesis rate of g and g . The protein production of P53 binding to the self-activation bindingsite with the binding rate of h a which can increase P53 synthesis rate. Protein P53 binding to the promoter of MDM2with the binding rate of h a . The protein production of MDM2 binding to the repression binding site with the bindingrate of h r which can decease MDM2 synthesis rate. The superscript of a and r represent “activation” and “repression”3espectively. The protein P53 and MDM2 dissociated from DNA with the unbinding rate of f a and f r respectively.The degradation rate of P53 and MDM2 are k and k respectively . Take P53 as an example, P53 is regulated by twogenes in the network motif. One is the self-activation , another is the repression of MDM2. The synthesis rate will beincreased or decreased by a factor of λ a or λ r , respectively. The synthesis rates of P53 are set as: g , g = g λ a , g = g λ r and g = g λ a λ r . The index number of g i j denotes the binding site number, and ‘1’ denotes the bindingstate and ‘0’ denotes the unbinding state. The protein synthesis rate at each time depends on the state of promoters at thattime. For simplicity of calculation, we set the unbinding rate as f for all binding sites and the protein degradation rateas k for all protein production. The binding rate depends on the polymeric form of the regulate protein. If the protein isa monomer, the binding rate of the protein A is h A = h A n B . If the protein is a dimer, the binding rate of the protein A is h A = h A n B ( n B − ) /
2. If the protein is tetramer, the binding rate of the protein A is h A = h A n B ( n B − )( n B − )( n B − ) / n B is the protein number of the regulate protein B. We only consider these three cases, because these three polymericforms are common in the biochemical reactions.We define the equilibrium constants: X eq = f / h and the adiabatic parameter: ω = f / k . ω is used to describe therelative time scale of the regulatory binding/unbinding to the synthesis/degradation. When the value of ω is large (termedas adiabatic regime), the regulation processes are relatively fast compared to the synthesis/degradation. This describesthe strong coupling regime where proteins once produced are immediately used for the regulations. In other words, theeffective gene regulatory interactions are strong. When the value of ω is small (termed as the non-adiabatic regime), thisdescribes the relatively slow regulation processes compared to the synthesis/degradation, where proteins once producedtake some time for the binding regulations. In other words, the effective gene regulatory interactions are weak [37–41]. After performing the stochastic simulations on the corresponding gene network with the specified reactions above usingGillespie algorithm [36], we can obtain the stochastic trajectories of the genes and associated mRNAs. We can thencollect the statistics and obtain the distributions of individual genes and joint distributions among these genes in the longtime limit. This provides the quantification of the landscape since probability representing the weight of the state isclosely linked to the potential landscape ( U = − lnP ). It is often difficult to visualize the landscape in multi-dimensions,we then choose the gene P53, ZEB and OCT4 to represent cancer, metastasis(EMT) and developmental(stem cell) char-acteristics. To display the landscape or the weight distribution of the states clearly, we show the comparisons of the3-dimensional landscapes as well as the 2-dimensional slices. Fig.2(a,b,c,d) show the 3-dimensional landscapes at pa-rameter ω = , , , OCT =
10 at parameter ω = , , , OCT =
40 at the parameter ω = , , , OCT =
80 atthe parameter ω = , , , ω is set as 1000 (fast binding/unbinding relative to syn-thesis/degradation) in the strong regulatory coupling adiabatic regime[42], seven states are emerged including Normal,Premalignant, Cancer and Lesion, CSC, Hyperplasia and SC states. This corresponds to our previous adiabatic results425]. When the adiabatic parameter ω becomes smaller, more steady states emerge in this non-adiabatic regime. Be-cause the gene regulation rate is slower than the protein synthesis and degradation, the gene regulations are more weaklycoupled. As a result, multiple metastable-states emerge as the regulatory proteins switch on and off the target gene lessfrequently. The slow regulation rate can reflect the non-adiabatic fluctuations and longer time scales of epigenetic effectssuch as DNA Methylation or histone remodifications[43]. Longer time of binding/unbinding regulations also indicate lesschance of coupling among genes at given time intervals. This reduces the effective interactions among genes. As a resultof less constraints in terms of the regulatory interactions, more states emerge. The multiple kinetic paths between eachtwo states also emerge and more transitions become available among states. The emergence of the multiple metastablebasin states can provide a physical mechanism for the origin of the heterogeneity [19, 38, 40].It is worthwhile to point out that mutations can lead to the heterogeneity by the changes of DNA sequences or thenodes for the gene networks. When mutation is less frequent such as in the cell differentiation and reprogramming process,the heterogeneity can still be significant. This could be due to the epigenetic changes such as histone remodification andDNA methylation which provide extra time scales effectively. This delays the regulation process and therefore weakensthe effective regulation strengths. Many states can emerge as a result of the weaker regulations, giving arise to theheterogeneity. The regulation strengths can also be changed directly through the kinetic regulation parameters in the genenetworks to explore the cell-cell variability in a population [44, 45]. The heterogeneity exists in cancer, CSC and SC which can be observed clearly from this model. In Fig.2, we can seethat when the parameter ω decreases (slower regulation and effectively weaker regulation strength), the heterogeneity ofCancer, CSC and SC states become more and more significant. As the SC heterogeneity is a common phenomenon inmammals[38], we mainly focus on the heterogeneity of cancer [40] and CSCs.The intercellular heterogeneity may result from clonal evolution driven by genetic instability[46]. This can lead tomany different phenotypes and functions. As seen here, the physical mechanism of the intracellular heterogeneity can bedue to the weakened regulatory interactions among the genes in the gene network motif [47, 48]. The epigenetic effectssuch as DNA methylation, CpG islands promoter hypermethylation, nucleosome remodelling and histone modificationcan elongate the kinetic process and therefore effectively weaken the gene interactions[49].In Fig.2(e), (f), (g) and (h), from left to right, the region of Cancer state basin is enlarged and finally connected tothe Lesion state when ω is decreased to 1. Experiments showed that accumulations of epigenetic modification such aspromoter methylation of the critical genes or DNA repair genes can induce lesions[50]. When the regulation rate slowsdown, the stochastic epigenetic modification in individual cancer cells has more choices of the adaptation and selection tofit the environments. Furthermore, such evolution may be different in time and space, and different fitness may appear indifferent environments and stages of the cancer for adaption. Some area may need hypoxia adaption, some area may needfast-growing adaption. When the cancer is developed, the adaption may evolve accordingly, even with the resistance ofthe drug.From Fig.2(i), (j), (k) and (l) we can see that, the boundary of CSC state basin gets enlarged which connects to SCand Cancer state hierarchically when ω is decreased. This hierarchy joins the normal tissues to stem cells and leads to arange of differentiated cancer cells. Importantly, the hierarchical structure which CSC supports is not realized through aone-path route. When the parameter ω is decreased, the paths became more widely spreaded. Moreover, the paths canbe plastic. So the terminally differentiated cancer cells can gain CSCs chracteristics under specific epigenetic conditions.5he SCs can gain cancer characteristics and become CSCs. Recently, some studies tracing of CD133+ cells provideddirect evidence that SCs were susceptible to cancerous transformation[51, 52]. Cancer is a complex and robust disease. The genetic and epigenetic alterations can lead to the cancer heterogeneity.In this study, we studied stochastic processes and associated slow non-adiabatic gene regulatory dynamics. We providea physical mechanism for heterogeneity from epigenetics. We quantitatively uncovered the heterogeneity of CSC, SCand cancer based on a key gene regulatory network. The heterogeneity has a close relation to the cancer therapy, as theheterogeneity may result various phenotypes in tumor. Understanding the mechanism of heterogeneity in CSC, SC andcancer can help us make progress in the cancer therapy.
This study was supported by NSFC grant no.91430217, ,MOST-China-Grant No.2016YFA0203200 and grant no.NSF-PHY-76066 and grant NSF-CHE-1808474.
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Nature Cell Biology , 15(4):338–344, 2013. igure 1: The regulatory network motif with 6 nodes and 16 regulations.(7 activations and 9 repressions. The arrows represent theactivating regulations and the short bars represent the repressing regulations)The hexagonal nodes represent the micro-RNAs, the oval nodes represent the genes. The parameter h , f , g and k represent the proteinbinding rate, the protein unbinding rate, the protein synthesis rate and the protein degradation rate. igure 2: The comparisons of the 3-dimensional landscape as well as the 2-dimensional slice when the parameter ω = , , , ω = , , , ω = OCT = , ,
80; (f),(j),(n) show the 2-dimensional slices when ω =
100 and
OCT = , ,
80; (g),(k),(o) show the 2-dimensional slice when ω =
10 and
OCT = , ,
80 and (h),(l),(p) show the 2-dimensional slicewhen ω = OCT = , ,
80 respectively80 respectively