A mechanistic analysis of spontaneous cancer remission phenomenon: identification of genomic basis and effector biomolecules for therapeutic applicability

Abstract

Based on the well-documented studies, numerous tumors episodically regress permanently without treatment. Knowing the host tissue-initiated causative factors would offer considerable translational applicability, as a permanent regression process may be therapeutically replicated on patients. For this, we developed a systems biological formulation of the regression process with experimental verification and identified the relevant candidate biomolecules for therapeutic utility. We devised a cellular kinetics-based quantitative model of tumor extinction in terms of the temporal behavior of three main tumor-lysis entities: DNA blockade factor, cytotoxic T-lymphocyte and interleukin-2. As a case study, we analyzed the time-wise biopsy and microarrays of spontaneously regressing melanoma and fibrosarcoma tumors in mammalian/human hosts. We analyzed the differentially expressed genes (DEGs), signaling pathways, and bioinformatics framework of regression. Additionally, prospective biomolecules that could cause complete tumor regression were investigated. The tumor regression process follows a first-order cellular dynamics with a small negative bias, as verified by experimental fibrosarcoma regression; the bias is necessary to eliminate the residual tumor. We identified 176 upregulated and 116 downregulated DEGs, and enrichment analysis showed that the most significant were downregulated cell-division genes: TOP2A–KIF20A–KIF23–CDK1–CCNB1. Moreover, Topoisomerase-IIA inhibition might actuate spontaneous regression, with collateral confirmation provided from survival and genomic analysis of melanoma patients. Candidate molecules such as Dexrazoxane/Mitoxantrone, with interleukin-2 and antitumor lymphocytes, may potentially replicate permanent tumor regression process of melanoma. To conclude, episodic permanent tumor regression is a unique biological reversal process of malignant progression, and signaling pathway understanding, with candidate biomolecules, may plausibly therapeutically replicate the regression process on tumors clinically.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13205-023-03515-0.

Introduction

Combination therapy or multimodal treatment is an incisive approach used to treat different types of cancer (Bayat Mokhtari et al. 2017). It is a combination of at least two of these three modalities: chemotherapy, radiotherapy, and immunotherapy (Combination Treatments | SEER Training 2022). Radiation therapy or surgery is typically local therapy for cancer that has spread locally, while chemotherapy and immunotherapy are systemic therapies that address the fundamental problem of cancer spread in the metastatic phase (Tannock 1989). Regarding systemic therapy, chemotherapy is often used as a first modality, it is inexpensive, and generally eliminates the majority of the tumor cells. Typically, chemotherapy drugs work by impeding DNA replication capacity, so that the cells cannot replicate. Since malignant cells reproduce faster than normal cells (which are usually in stable non-dividing conditions), the drugs preferentially damage malignant cells considerably more than normal cells. Nevertheless, chemotherapy and radiotherapy also somewhat adversely affect the other normal surrounding tissue, particularly by impeding the protective leucocyte system, for example by damaging the haematopoietic cells in the marrow (Hubenak et al. 2014; MacDonald 2009). Hence as a remedial course of action, the modality of immunotherapy or biological therapy has been introduced, which helps the immunological agent to seek out the malignant cells and eliminate them, while also avoiding action on normal cells. Immunotherapy is indeed an antitumor therapy that can enhance the immune system to counter various types of cancer (Kirkwood et al. 2012). Furthermore, there are a few categories of immunotherapy that use checkpoint inhibitors, cytokines, or immunomodulators (Treating Cancer with Immunotherapy | Types of Immunotherapy 2022). In immunotherapy, both immune cells (innate and adaptive cells) impair the tumor cell population. Innate immune cells include monocytes, dendritic cells, and natural killer cells, whereas adaptive cells include T cells and B cells (Borghaei et al. 2009).

Though the outcome of malignancy is often lethal, some malignant focus can undergo extinction naturally by the biochemical and immunological environment of the host tissue. This elimination is a well-documented process, termed spontaneous regression or remission of cancer, where there is no further recurrence of malignancy. Here, the host tissue may establish internally produced chemotherapy-like and immunotherapy-like milieu, i.e., DNA alkylation is enabled or replication is impaired, while the leucocytes and interleukin-2 is activated to attack the malignant cells. Though the leucocytes damage the tumor cells, they do not assail normal tissue cells. According to a study of numerous clinical cases of spontaneous cancer remission by Everson and Cole, the immune process is one of the main factors in the spontaneous regression of tumors (Cole 1981). Indeed, spontaneous regression is an internally generated “endogenous” process, while tumor remission by treatment is externally or “exogenously” produced intervention. The phenomenon of spontaneous cancer regression is a well-recorded phenomenon (Salman 2016). However, the mechanism of spontaneous regression is poorly understood. Nevertheless, it would be more advantageous if the mechanism of spontaneous regression could be comprehended so that the physician could replicate the regression process on a patient’s tumor clinically so that the tumor becomes eliminated. Formulating the mechanistic analysis and insights into the tumor regression process is the main aim of our endeavor here.

However, the researcher generally encounters a malignant growth in its progression phase; the reversal process of complete spontaneous regression of tumors happens subclinically in human populations at a 22–46% rate, as per the Wisconsin and Scandinavian Cancer Screening Registries, which have long-term monitored the populations of 2.95 million and 0.34 million people, respectively (Fryback et al. 2006; Zahl et al. 2011). In fact, in post-mortem studies, it has been noticed that about half of subjects have malignant lesions in prostate and uterine cervix, with evidence of complete containment. Moreover, many malignant neuroblastoma patients have full regression from larger-sized tumors (Cole 1981). To underscore, a PubMed search shows over 14,000 titles of papers dealing with spontaneous cancer regression, encompassing virtually all types of malignancies, e.g., carcinomas, sarcomas, melanomas, lymphomas, etc. (Spontaneous regression of cancer or spontaneous remission of cancer—Search Results—PubMed 2022). Indeed, an incisive model has been developed to elucidate the energetics or biothermodynamic framework of spontaneous tumor regression (Dutta and Roy 2000; Roy et al. 2002).

For instance, melanoma cases can undergo fully effective spontaneous regression (PubMed has 585 cases studied in detail; Spontaneous cancer regression of melanoma—Search Results—PubMed 2022), and this melanoma regression occurs appreciably at 10–35% (Blessing and McLaren 1992). Indeed, analysis of 10,098 melanoma regression patients showed that these patients can have incisive clinical correlates (Ribero et al. 2015). Understanding melanoma regression is critically needed, as it is the malignancy whose incidence is accelerating maximally (Blessing and McLaren 1992). Actually, spontaneous cancer regression covers virtually all types of malignancy, grades and classes (Salman 2016). In our study, we have investigated the phenomenon of spontaneous regression of malignant melanoma tumor as a case study, so as to delineate the therapeutic application. Here, we endeavor to develop a general quantitative methodology of permanent tumor regression while protecting normal tissue, whether the extinction of malignant cells is induced endogenously (by host tissue) or exogenously (by chemotherapy and immunotherapy). An important aspect here is that we show a malignant lesion can undergo permanent regression by an optimized synchronization of (1) antitumor immunological and cytotoxic effectors based on the tumor load or tumor cell population, and (2) normal tissue protection as formalized by minimization of tissue toxicity. Furthermore, we established the signaling pathways that enable spontaneous cancer regression with the help of microarray gene expression data. In addition, we have performed network pharmacology and pathway enrichment analysis to find out the most significant genes and thereby identify therapeutic agents that can replicate the spontaneous regression process. Collateral corroboration of the projected efficacy of the candidate therapeutic molecules are provided from human survival analysis and tumor histopathological assessment.

This paper is organized in the following way. In the “Materials and methods” section, we have used the systems biology approach to develop the general quantitative methodology (first-order kinetics and negative bias approach) for the permanent tumor regression process (whether endogenous or exogenous regression), along with protection of normal tissue. Thereafter, with the help of network pharmacology techniques, we have analyzed microarray data of malignant melanoma regression as a case study. In the “Results” section, we have shown how the tumor regression process follows our theoretical model, whereby there should occur a general unitary pattern of time-wise orchestration of the three antitumor entities: DNA blockage, cytotoxic T-cell, and interleukin-2. Thence, pathway enrichment analysis shows that the most potent genes (e.g., TOP2A) are the downregulated ones mainly related to cell cycle regulation and DNA replication damage. Subsequently, our bioinformatics studies identified the drug derivatives that can replicate the tumor regression process. Finally, we corroborated our findings with both rodent and human systems. In the “Discussion” section, we have given an integrated perspective of our findings with a broader viewpoint, and indicated the preclinical and clinical significance of our results. In the “Conclusion” section, we have provided a synopsis of our findings and their implications.

Materials and methods

The entire workflow is divided into two steps: Part 1: Formulation of quantitative systems analysis, and Part 2: Formulation of genomic and pharmacological analysis.

Part 1: Formulation of quantitative systems analysis

Constructing the systems biology approach

Tumor remission can occur either endogenously (as spontaneous regression, actuated by host tissue) or exogenously (therapy-induced regression). The reaction dynamics of elimination of tumor cell population M (during exogenous tumor regression by therapeutic agents as chemotherapy drugs that induces DNA damage) tend to follow first-order chemical reaction rate kinetics (Perry et al. 2012); hence, the tumor cell population M decreases asymptotically with time (Dutta and Roy 2000). Likewise, in endogenous or spontaneous regression of the tissue lesion or malignancy, the tumor cell population exponentially decreases with time (Biktimirov et al. 2005; Vladimirova 2019). Thus, the exponential decreasing trajectory M = M₀ exp (− εt) is the intensity of the tumor regression effect (Fig. 1a), with M₀ being the initial tumor population and ε, the rate parameter, i.e., the intensity of the tumor regression effect.

Fig. 1.

Permanent tumor elimination process by first-order kinetics. a In customary therapy, the elimination of the tumor cell population M(t) follows the exponentially decreasing curve, with the vast majority of tumor cells are eliminated, however, there is the persistence of residual tumor cells asymptotically under the graph, which might produce tumor recurrence after the end of therapy duration. b A negative bias shift process added to the exponentially decreasing trajectory enables the residual tumor cell population to become zero at a definitive finite time t_F. This curve M(t) also decreases exponentially by the first-order kinetics process and approaches the negative bias value (− M*). Hence, at point F the tumor cell population undergoes extinction, and there are no more tumor cells to reproduce, i.e., complete regression of tumor occurs, eliminating the malignant growth

As the tumor follows an asymptotic decreasing trajectory, there always remains a residual tumor cell population under the asymptotic tail of the graph as the curve never reaches exact zero population, which means there remains some finite population of tumor cells because of which the tumor can recur. Hence, we need an alternative technique to make this exponentially decreasing graph become exactly zero population in a definitive time point t_F. This can be done using the process of negative biasing, whereby the exponentially decreasing curve asymptotically reaches a negative value − M* (negative bias), so that the curve has zero value at that time point t_F (Fig. 1b). With this biasing, the first-order exponential equation becomes:

$$M=\left(M_0+M^{\ast }\right)exp\left(-\epsilon t\right)-M^{\ast }$$ 1

Thus, the negative bias is:

$$M^{\ast }=-M_{0}exp\left(-\epsilon t_{\text{F}}\right)/\left(1-exp\left(-\epsilon t_{\text{F}}\right)\right).$$ 2

Formulation of computational biology model of extinction of tumor cell population

We formulated the process of tumor regression by analyzing interaction of tumor cells with immune cells. We represented the interaction of different cellular populations in terms of the schema in Fig. 2. To develop the quantitative mathematical model of the tumor regression phenomenon, we consider the interaction between different cells, namely the tumor populations of cells, circulating lymphocytes, and natural killer cells, respectively, denoted by M, B, and K, respectively. Here, we represent different cell dynamics in the schema, as shown in Fig. 2. Let A, D, and C denote the intensity levels, respectively, of antitumor lymphocyte (e.g., cytotoxic T-lymphocyte population), interleukin-2 (concentration), and DNA chemomodulation, namely DNA interference in cells, e.g., concentration level of DNA-damaging entities in tumor tissue. We can represent the interaction between the different cellular populations and can formulate the quantitative temporal dynamics as described in Supplementary file-1.

Fig. 2.

Schema of the interaction among the malignant tumor and the antitumor factors in its environment during both endogenous regression and exogenous regression of the tumor (i.e., host tissue-induced regression or treatment-induced regression)

Model corroboration by collateral experimental findings: complete elimination of malignant cell population by first-order kinetics

Now, we furnish the observations of permanent spontaneous regression of malignant fibrosarcoma tumors in mammalian systems (rodents). Here, the tumor is induced by injecting rats with a malignant cell culture of AK-5 fibrosarcoma tumor. After injection, some of the animals (36%, group-A) have massive malignant growth that rapidly turns fatal, while the other animals (64%, group-B) show decline and permanent disappearance of the tumor (Hicks et al. 2006). In the latter group of tumor-regressed animals (group-B), one observes that by 8–10 h of tumor cells inoculation, a high activation of infiltrating leucocyte cell occurs, of which lymphocytes form a major portion (such as T cells, natural killer cells, etc.) (Hicks et al. 2006). Therein, in another experiment, fibrosarcoma cells were injected at the dorsal back of wild-type rats (type-WT); the cells grew to become significant lesions of 300–800 mg by day-6. Then, leucocyte transfer from Type-B rats to these tumor-bearing wild-type host rats (type-WT) was done. Thereby, the tumor lesion in wild-type rats gradually underwent complete regression and extinction, without any sign of recurrence even at and after 300 days.

Part 2: Formulation of genomic and pharmacological analysis

Our system biology model provides a route for complete tumor elimination with normal host tissue being protected. Here, we validate our theoretical model using experimental immunohistochemical findings of the melanoma tumor regression process.

Microarray investigation of preclinical study

We obtained the microarray information of the process of spontaneous tumor regression of melanoma from ArrayExpress database (https://www.ebi.ac.uk/arrayexpress): Experiment (E-MEXP-1152 (https://www.ebi.ac.uk/arrayexpress/experiments/E-MEXP-1152/) (Rambow et al. 2008). In this study, Libechov minipigs (MeLiM) that were bearing malignant cutaneous melanoblastoma tumor (Rambow et al. 2008) were used. Here, in a majority of the pigs, the tumor progresses and becomes fatal, but in a minority of the animals, the tumor grows up to a certain time and then spontaneously regresses and heals, and these minority animals stay healthy. In this investigation, time-dependent gene expression profiling of 6 such minority pigs, whose tumor initially grew and then regressed permanently, was assessed at five different time points, t₀–t₄ (at 3-weekly intervals) during the full course of regression (3 months). We accessed the raw data information (E-MEXP-1152.raw.1.zip) to validate our theoretical mathematical model of spontaneous cancer regression using this experiment.

Identification of differentially expressed genes (DEGs) of tumor regression

Subsequently, we utilized R-platform and its Bioconductor packages statistical facility (http://www.bioconductor.org/) (Jacob, BITS wiki 2017), to analyze the time-dependent gene profiling of the microarray information of the aforesaid spontaneously regressing melanoma tumor at the 5 different time points. We used the GCRAM algorithm for background correction and normalization. The differentially expressed genes (DEGs) were filtered by applying two cut-off criteria: − 2 > FC >  + 2 and p value < 0.05 after the unpaired t-test.

Biological signaling pathway analysis

We analyzed the aforesaid filtered DEGs, namely 70 genes at time point t₁, 322 genes at time point t₂, 1147 genes at time point t₃, and 1349 genes at t₄, using the Ingenuity Pathway Analysis platform (IPA). Of these, 61, 292, 1049, and 1227 genes for time points t₁, t₂, t₃, and t₄, were mapped by IPA. We undertook IPA core analysis on the identified genes for each time point and performed a comparison analysis to find out the signaling pathways and biological functional pathway analysis over the four time points (t₁–t₄) for the melanoma regression process.

Gene ontology and pathway enrichment analysis

Subsequently, we performed gene ontology (GO) analysis of identified differentially expressed genes (DEGs) using ClueGo, DAVID and FunRich platforms. We also examined pathway enrichment analysis with significant cellular component (CC), biological process (BP), and molecular function (MF), utilizing the ClueGo platform from Cytoscape (Shannon et al. 2003). The functionally related GO term analysis was adjusted with a kappa score greater than 0.4 and a p value < 0.05 (Pathan et al. 2015).

Protein–protein interaction network construction and hub-gene identification

We then built the protein–protein interaction (PPI) networks by string database on the Cytoscape platform (Szklarczyk et al. 2019). The Molecular Complex Detection (MCODE), a technique from Cytoscape, was used to screen modules of the PPI network with degree cut-off = 2, node score cut-off = 0.2, k-score = 2, and maximum depth = 100. The top 10 hub genes were identified by the CytoNCA method in the Cytoscape scheme (Tang et al. 2015).

Identification of candidate drugs from hub-gene interaction

Thence, we utilized the CyTargetLinker technique from Cytoscape (Kutmon et al. 2019), to identify the candidate pharmacological molecules that can target the dysregulated genes that we identified from the analysis of our spontaneous melanoma tumor regression process. We constructed Homo sapiens drug–target interactions link set from the pharmacological library DrugBank (Wishart et al. 2018) and from the DGIdb system (https://www.dgidb.org/search_interactions).

Molecular processes study and drug–ligand interaction

We conducted a molecular interaction study using our proteins of interest (e.g., protein TOP2A (PDB ID- 4FM9; Chain A) with different ligands. For this, we used the method of (Wendorff et al. 2012). We used the autodock 1.5.7 tool for investigating the molecular inhibiting interaction using the Lamarckian genetic algorithm. Before docking, all the heteroatoms and water molecules were removed from the protein crystal structure. Then, 2D SDF files of different ligands were accessed from the PubChem system, and Prix platform did feather energy minimization. Ligand and macromolecule preparation were conducted by adding polar hydrogen bond atoms, Kollman charges, solvation parameters, and grid box formation. The grid point spacing was 0.500 Angstroms, and the coordinates of the central Grid point were 44.552, 35.073, and 9.781 Å with grid box size 39, 50, and 29Å in the x, y, and z directions. Finally, both protein and ligand structures were saved as. pdbqt format for docking analysis.

Corroboration on human subjects: normal controls and melanoma tumor patients

We then used the Human Protein Atlas (THPA), an open-access bank and platform that maps all the human proteins in cells, tissues, and organs by integrating various omics technologies, which helps us to probe the human proteome (The Human Protein Atlas 2022). We used this THPA platform to investigate the overall survival rate of melanoma patients having high-versus-low hub-gene expression with a significant p value. Next, we used the Gene Expression Profiling Interactive Analysis (GEPIA; http://gepia.cancer-pku.cn/index.html), an interactive analysis and visualization tool, for further verification of the functionalities of hub genes and for finding the difference in gene expression level in the melanoma tissue (cutaneous skin melanoma, SKCM) vis-à-vis the normal skin tissue(GEPIA (Gene Expression Profiling Interactive Analysis) 2022). The resultant data were then mapped in the TCGA database and GTEx database using the GEPIA facility for Box Plots.

Results

With the help of the system biology approach, we first computed the temporal variation of different cell dynamics in (i) the usual treatment scenario where there is often tumor recurrence, and (ii) permanent exogenous or exogenous tumor regression. Then, we corroborated the experimental findings from the preclinical and clinical study of tumor regression with our theoretical model and explored the signaling pathways related to spontaneous tumor regression. Lastly, we provided the network pharmacology analysis corresponding to spontaneous melanoma regression.

Part 1: Formulation of quantitative systems analysis

Tumor regression under conventional therapy (without negative bias): tumor relapse

We considered a tumor with an initial malignant cell population (M₀): 2 × 10⁷, natural killer cell population: 10⁵, cytotoxic T-cell population: 5 × 10⁴, and circulating lymphocytes: 10⁹. These realistic values are adapted from an earlier analysis of tumor dynamics (de Pillis et al. 2006). The initial number of malignant cells corresponds to an actual tumor that can just be radiologically detected, such as a metastatic melanoma deposit in the liver [radiological detection threshold ≈ 1 cc. tumor, having 2 × 10⁷ cancer cells (Del Monte 2009)]. All the other constants utilized in our model are from (de Pillis et al. 2006), including the tumor cell growth rate a = 0.301/day. It may be noted that in the last citation, the deceleration rate of logistic tumor growth b = 1.01 × 10^–9, whereby the maximum population of tumor cells tolerated by the body (carrying capacity of an adult) is 1/b, i.e., 9.8 × 10⁸ malignant cells. In the simulation, we consider both an adult and a 10-year child. For a 10-year child, the body weight is half an adult (Hall and Guyton 2011), so we take the carrying capacity at half the adult volume, i.e., 4.8 × 10⁸ malignant cells (= 1/b), so that now b = 2.04 × 10^–9.

Our formulation here is the case of conventional chemotherapy and immunotherapy protocol of melanoma, using (i) chemotherapy: standard nine chemotherapy pulses, once every 10 days (dacarbazine 5 mg/kg/day pulse), (ii) interleukin-2 cytokine: 6 pulses of 500,000 i.u/kg/day, from day-8 through day-11, with (iii) cytotoxic T-cells: total 10⁹ cells on day-7 and day-8. We now apply these values to the basic eqns. (A)–(G) (Supplementary file-1) that are solved to provide tumor cell population M while time elapses. Figure 3 shows that the tumor cell population first decreases to about 300,000 malignant cells but later increases to high values (≈ a billion malignant cells) indicating cancer relapse. The cell population corresponds to a substantial tumor of size ≈ 5 cm., and this growth will produce widespread invasion and fatality. While Fig. 3 shows the simulation for a child, for an adult the simulation graphs are similar, indicating lethality.

Fig. 3.

Conventional protocol of treatment using chemotherapy with immunotherapy. This utilizes the DNA-blocking alkylator agent dacarbazine, with immunotherapy (interleukin-2 with cytotoxic T-lymphocyte). The treatment fails to eliminate the malignant melanoma tumor cells, and following the treatment duration there is a recurrence of the tumor

First-order kinetics: path for complete tumor regression

Now, we come to the modeling of the spontaneous tumor regression process as per the methodology mentioned in Sect. S.3 (Supplementary file-1). For the tumor and cellular parameters, we take the same values as the adult case in the earlier "Tumor regression under conventional therapy (without negative bias): tumor relapse", section having an initial tumor population of 10⁷ malignant cells. As per Sect. S.3 (Supplementary file-1), we select the desired time of tumor extinction of 48 days, and from Fig. 1b, we found that bias M* = 1.8986 × 10⁵ cells (this is a relatively small amount with respect to the initial malignant cell population of 2 × 10⁷ cells, i.e., Negative bias ≈ 1% of initial tumor load). Hence, using a simulation step of 0.01 s, we solved the separate set of the aforesaid equations (A)–(F) as shown in Fig. 2 to obtain the time-wise variation of the level of three antitumor entities (concentrations of DNA damage factor and of interleukin-2, and cytotoxic T-cell population). We put the latter three values in Equation (G) (Fig. S1.2, Supplementary file-1), solving which shows that the tumor cell population become zero at 48 days. We have used customized MATLAB codes for numerical simulation of the above tumor elimination process. We showed the simulation results in Fig. 4. The tumor population trajectory definitively meets the time-axis at 48 days and the tumor cell population becomes zero from that time onwards (Fig. 4).

Fig. 4.

Permanent elimination of malignant melanoma tumor under first-order kinetics. a Tumor cell population shows consistent decline with time, with complete elimination of the malignant tumor at 46 days by following first-order kinetics with a small negative biasing. b Time-wise bimodal profile of cytotoxic T-cell needed for eliminating tumor cells. c Time-wise unimodal profile of DNA damage level needed for extinction of tumor cells (damage of DNA is estimated in terms of the equivalent amount of alkylator substance (as dacarbazine) which produces a similar amount of DNA damage, please see text). d Time-wise stationary concentration profile of Interleukin-2 needed for tumor extinction (the curve maintains a uniform level)

General characteristics of permanent tumor regression process

By performing multiple simulations, we noted that there is a general common pattern, which indicates that to induce complete tumor regression, the three antitumor entities should have three distinct temporal profiles:

1. Monophasic intensity for the activation of DNA damage (e.g., chemical alkylation), showing one peak temporally (Fig. 5a).

2. Biphasic intensity for lymphocyte activation, displaying two temporal peaks (Fig. 5b)

3. Uniform intensity for interleukin-2 activation, where constancy in level is observed (Fig. 5c).

Fig. 5.

The antitumor entities are found to have the following common time-wise varying patterns to enable permanent regression of malignant tumor with different initial conditions: a Unimodal temporal intensity of DNA blockade factor, b Bimodal temporal intensity of Cytotoxic T-cell, c Uniform stationary temporal intensity of interleukin-2

Model corroboration by collateral experimental findings: complete tumor eradication by first-order kinetics

We now furnish experimental preclinical findings of complete permanent tumor regression that provide empirical corroboration of two kinetic conditions for regression: first-order kinetics and negative bias. We show that the experimental findings of permanent tumor regression follow the tumor extinction dynamics of Fig. 1b, that is:

$$M=\left(M_0+M^{\ast }\right)exp(-\epsilon t)-M^{\ast },$$

where the negative bias is $M$*$=-[M$₀ $\exp (-\epsilon t$_F$)]/(1-\exp (-\epsilon t$_F$)).$

We show in Fig. 6a the data points that represent the average value of 10 such regressing experimental cases, the findings being obtained from the above-cited investigation (Hicks et al. 2006), the first day of the time-axis in Fig. 6a starts from day-6 of tumor implantation, when the tumor actually starts to regress and decline. Actually, the microscopic appearance of the regressing tumor shows increasing decline and sparseness of tumor cells, together with the formation of fibrotic scar healing due to generation of fibroblasts, leaving the necrotic core of tumor to atrophy and degenerate. We will now infer the values of the bias shift M* and the first-order exponentially decrementing trajectory of tumor cell population, by utilizing the experimental findings. As mentioned, the baseline tumor lesions induced by the injection in the control animals are 300–800 mg (average 550 mg, i.e., 0.55 g, or 0.55 cc. of tissue). Details of the tumor growth and regression information are available (Hicks et al. 2006). After tumor implantation of the control animals, the immunomodulation by leucocyte transfer from group-B rats to a subset of the control animals were done on day 4 post-implantation. At day-6 post-implantation, the tumor size in the latter subset of animals peaked to 174% of the average baseline of 550 mg. tumor tissue (i.e., peaked to 957 mg), and then the tumor gradually underwent complete permanent regression. Since 1 cc. or 1 g. of tumor tissue is taken to have 10⁷ malignant cells (Del Monte 2009), their initial population in this lesion can be estimated as 9.5935 × 10⁶ malignant cells (this is thus the estimated value of M₀).

Fig. 6.

Model corroboration by collateral experimental findings: feasibility of complete elimination of malignant cell population by means of first-order kinetics and mild negative bias. a The data points are experimental values of the tumor cells population as mammalian malignant fibrosarcoma tumor undergoes permanent spontaneous regression, and tumor extinction occurs at day 19 in the rodent study. The first-order kinetics-based declining curve that fits the data is shown; note that there are appreciable tumor cells under the asymptotic tail of the graph, and this curve cannot account for zero tumor cell population at day 19. b Tumor recurrence after a month due to replication of the small residual cell population under the asymptotic tail of the mathematical exponential curve at day 19. c Tumor cell population extinction on 19th day accounted for by a first-order kinetic-based declining curve with a small negative bias. This new curve fits the experimental data, and definitively meets the time-axis (red horizontal line) around 18 days, whereby the tumor cell population becomes zero, this population becomes extinct as there are no tumor cells to replicate later. Here, the theoretically formulated mathematical curve is well validated by the experimental data points (blue circles) [goodness-of-fit criterion is satisfied using statistical χ² test]

The complete elimination of the tumor occurs at 21 days after leucocyte immunomodulation, i.e., at day-25 post-implantation [this corresponds to point P of tumor extinction in Fig. 6a]. Thus, the actual tumor elimination time duration t_F is the difference between the day-6 and day-25, i.e., t_F = 19 days. The experimental data points of Fig. 6a are shown in Table 1 (first and second columns). We now analyze the experimental data points with respect to the two situations of Fig. 1, that is (i) plain exponential decline case without negative bias (Fig. 1a), vis-a-vis (ii) exponential decline with negative bias (Fig. 1b), for both conditions the exponential decline occurs for 19 days.

Table 1.

Tumor cell population decline with time during the spontaneous regression process (Experimental findings compared with the two theoretical models of Fig. 1A and B)

Time duration since start of tumor regression process (Days)	Tumor load: Experimental data (No. of tumor cells)	Tumor load: First-order exponential model (No. of tumor cells)	Tumor load: First-order exponential model with small Negative Bias (No. of tumor cells)
0.0372/0	9,477,500	9,531,693	9,363,552
0.8748/1	8,663,800	7,815,517	7,763,503
2.1274/2	4,564,200	5,808,051	5,899,998
5.1057/5	2,185,100	2,867,349	3,025,948
6.0702/6	2,037,900	2,281,428	2,420,882
7.0768/7	2,890,300	1,797,213	1,907,887
8.0329/8	2,293,600	1,432,816	1,511,836
9.099/9	1,417,900	1,112,907	1,154,914
10.1058/10	945,200	876,660	884,118
11.0196/11	658,400	705,953	683,482
11.9925/12	379,400	560,580	508,389
13.0416/13	193,400	437,176	355,808
14.023/14	38,400	346,452	240,626
19.2087/19	0 (tumor fully eliminated)	101,365	0 (tumor fully eliminated)
30	0 (tumor fully eliminated)	≈28,600,000 (tumor increase and relapse)	0 (tumor fully eliminated)

Regarding the tumor elimination process, observe the close correspondence between column 2 (experimental data) and column 4 (theoretical computational model with first-order kinetics and mild negative bias). The goodness-of-fit criterion (statistical χ² test) is satisfied between these two columns

Exponential decline without negative bias

Using the experimental data points of Fig. 6a, we obtained the trajectory equation [M = M₀exp(− εt)] using the least squares method, and the trajectory is found to be:

$$M(\text{in million cells})=\left[9.59\times {10}^6\right]exp\left(-0.2367t\right),$$ 3

where time t is in days. At point P (t = 19 days) (Fig. 6a), Eq. 3 gives 101,365 malignant cells remaining, which is 0.94% of the initial tumor cell population, implying that the vast majority (over 99%) of tumor cells have been eliminated. Nevertheless, since the 19-day duration of the tumor regression process is over, this modest amount of residual malignant cells (101,365 cells) will start to increase again at the aforesaid tumor cell growth rate a =  + 0.301/day (Fig. 6b). Thus, from day 19 onwards, the tumor will grow as per the following equation, where τ denotes the number of days after the 19th day, so that there is malignant recurrence:

$$\text{Tumor relapse:}M=\left[0.1014\times {10}^6\right]exp\left(+0.301\tau \right).$$ 4

In a short time of a month (30th day, Fig. 6b), the tumor will have

$$M=28.6\text{million malignant cells}.$$

Table 1 (third column) shows the values of the tumor cell population as per the theoretical graph of Fig. 6b. We note the increasing divergence between the experimental data column (column 2) and the theoretical exponential model column (column 3) as time progresses; indeed, column 2 shows tumor extinction, while column 3 shows tumor increase and recurrence.

Exponential decline with negative bias

Here, we used the data points of Fig. 6a, and obtained the negative bias trajectory decline [M = (M₀ + M*)exp( − εt) − M*] by method of least squares, arriving at the equation:

$$M\left(\text{in million cells}\right)=\left[\left(9.39+0.262\right)e^{-0.21}\right]-0.262,$$ 5

which gives the bias value M* = 262,000 cells. Equation 5 is represented as the graph in Fig. 6c, showing that the curve definitively meets the time-axis at 19 days, showing that the tumor cell population becomes nil. As all tumor cells have become extinct, the tumor cell population remains zero for the rest of the time, whether 30 days or 300 days. Column 4 of Table 1 gives the values of the tumor cell population according to the graph of Fig. 6c. We observe the close agreement between the experimental data (column 2) and our theoretical negative bias model (column 4), especially notable is the concurrence in the later time points when the tumor undergoes complete extinction. Indeed, we find is a strong goodness-of-fit characteristic between columns 2 and 4, with the statistical χ² test being well satisfied.

Part 2: Formulation of genomic and pharmacological analysis

Microarray investigation and analysis:

Raw data file (E-MEXP-1152.raw.1.zip) of melanoma microarray study of spontaneous cancer regression in pigs was obtained from the ArrayExpress database with experiment no. E-MEXP-1152 (E-MEXP-1152 (https://www.ebi.ac.uk/arrayexpress/experiments/E-MEXP-1152/) (Rambow et al. 2008). This zipped archive file contains 25 cel files having n = 6 tumors at t₀ and t₁ time points, n = 5 tumors at t₂ and t₃, and n = 3 tumors at t₄ (where n = no. of excised tumors). The tumor biopsies were taken at these five different time points (in days after birth: t₀ = 8 days, t₁ = 28 days (4 weeks); t₂ = 49 days (7 weeks), t₃ = 70 days (10 weeks), and t₄ = 91 days (13 weeks), i.e., each time point advancing by 3 weeks (Rambow et al. 2008). We analyzed this microarray data on the R-platform; for normalization and statistical analysis Bioconductor tools were used. An unpaired t-test was performed to find out the log₂—transform and the p value of the test was adjusted using the FDR algorithm. Differentially expressed genes were identified for all 4-time points (t₁–t₄) with respect to t₀, and the following two criteria were used, namely the fold-change (FC) should be greater than 2, and the p value should be less than 0.05. Thereby, we extracted 70, 322, 1147, and 1349 differentially expressed genes (DEGs) from the microarray data expressions at these four different time points: t₁, t₂, t₃, and t₄ (the expressions were calibrated with respect to the expression at the first time observation done at t₀ = 8 days after birth). Our findings are given below, where R denotes the ratio of the number of downregulated genes to upregulated genes (expressed as a percentage):

$$\begin{array}{cccc}(\text{i})\text{At}4\text{weeks:}& 54\text{genes upregulated},& 16\text{genes downregulated},& R=29.6\%.\\ (\text{ii})\text{At 7 weeks:}& \text{189 gene upregulated},& \text{133 genes downregulated},& R=70.4\%.\\ \left(\text{iii}\right)\text{At 10 weeks:}& \text{537 genes upregulated},& 610\text{genes downregulated,}& R=113.6\%.\\ \left(\text{iv}\right)\text{At 13 weeks:}& \text{569 genes upregulated},& 780\text{genes downregulated},& R=137.1\%.\end{array}$$

Note that the R value crosses the equipoised point of 100% in the third month, indicating that the number of downregulated genes > upregulated genes from that time onwards. We observe that as the tumor regression process proceeds, initially the number of upregulated genes exceeds that of downregulated genes, but as the process further advances, the reverse situation occurs, i.e., number of downregulated genes surpasses that of upregulated genes.

IPA signaling pathway analysis

After finding the aforesaid DEGs of the regressing melanoma tumor, we performed the Ingenuity Pathway Analysis (IPA core analysis) for each time point. IPA core analysis provided a graphical summary showing a ready perspective of the significant biological themes (Fig. 7). This feature enables us to highlight some of the powerful entities identified in the core analysis and shows how they are related to each other by creating a more comprehensive and understandable framework of what is being processed in the analysis. In Fig. 7, we show the graphical summary including the pertinent entities as canonical pathways, upstream regulators, diseases, and biological functions. Each entity selected for the network passes Fisher’s exact test (i.e., p value < 0.05). The biological process and regulators also pass an absolute z-score cut-off of 2 or greater. Nodes are colored by their activity predictor in the analysis, where orange nodes are predicted to be activated, and blue nodes are predicted to be inhibited (Fig. 7).

Fig. 7.

Graphical summary of comparison between two different time points: the first time point is when the tumor is progressing (left panel), the second time point is when it is regressing (right panel). The networks show a ready overview of the major biological entities such as canonical pathways, upstream regulators, diseases, and biological functions; here orange color nodes show the predicated activated entities, while blue color nodes show the predicated inhibited entities (the intensity of color is based on magnitude of z-score value in the analysis). In the regression phase (right panel), one can note that the inhibited region (blue) is in the upper right portion) and is mainly concerned with the first-order kinetics-based decline of malignant cell population, namely by DNA interference and inhibition of tumor cells replication. The lower red colored region (right panel) show activation of the other components producing tumor regression: Interleukin-2 and Lymphocyte activation (see "IPA signaling pathway analysis" section)

Now, we compare the aforesaid biological graphical network between time points t₁ and t₂, as the tumor regression process is underway across 3 weeks. At the t₁ time point (Fig. 7, first panel), the tumor has barely started to regress, it has been in the tumor progression stage just before that time. Hence in the first panel, we can observe that most activated biological functions are involved in carcinogenesis, such as adhesion of cancer cells, damage/degeneration of connective tissue (for cancer cells to invade), migration of skin cancer cell lines (due to the melanoma skin tumor activity), etc. In contrast, at time point t₂ (Fig. 7, second panel), the regression process is well proceeding; here we observe that the most highly activated entities are involved in cell cycle G2/M DNA damage checkpoint regulation (alteration of cell replication), immune response of phagocytes, leukocyte Extravasation signaling, differentiation of B lymphocytes, and increased response of leukocytes. From the second panel, we can observe the functionalities of all three antitumor components for tumor regression:

• (i) Retardation of cell replication as by DNA interference,
• (ii) Increased activation of interleukin-2,
• (iii) Enhanced activation of antitumor lymphocytes.

Regarding item (iii) above, we further noted the increased signaling activity of the extravasation of circulating leucocytes in the second panel. Indeed, one knows that during the immune response, the extravasation of circulating leucocyte through the vascular wall into the tumorous tissue, correlates with extravasation and actuation of lymphocytes (Ratner 1992). Furthermore, we can infer that the first phase of melanoma regression is shown by the situation time point t₂. Thus, the time point t₂ is the reversal in the path of melanoma progression: at time t₁ the malignant activity in the tumor was definitive, but at t₂ the melanoma progression has halted, and the inverse process, tumor regression, is now occurring.

Thereafter, we have used IPA’s interaction networks to provide a mechanistic understanding of how a group of data set molecules might work together, whether by physical interaction as a protein or by acting on each other via a less direct mechanism. These highly interconnected molecular networks are annotated with their likely biological function, which furnishes us with the framework of how they contribute to the biological process of tumor regression. We then ranked the networks in the order of their significance with respect to the probability of finding that the set of molecules in the given network occurs by random chance. We recapitulate that the regression phenomenon of this experiment has been activated from t₂ time point. Therefore, we have considered the most significant networks as cancer, cell cycle, and hematological condition/hematological disease; note that we have taken the hematological network as oncological phenomena involves hematological processes, as white blood cell activation, hypoxia, local bleeds, etc. Using the statistical significance scoring, we found the involvement of 30 focus genes (Fig. 8). We found that most of the downregulated genes at time point t₂ belong to cyclin-dependent kinases, cyclins and spindle formation/separation proteins, the names of the genes are given below. Downregulation of these genes enables retardation of cell division, so tumor progression is impeded, and tumor regression can occur.

Fig. 8.

The most significant gene network detected by IPA Pathway analysis at time point t₂ (tumor regression process has started and is underway): A total of 30 focus genes were identified and mapped to top IPA functional classes, such as cancer, cell cycle, and hematological disease (significance score = 45). The green nodes are the downregulated biological diseases and functions, while the red nodes are the upregulated molecules; and the intensity of the focus nodes is based on the data measurement value in our dataset

Downregulated genes at the initial phase of spontaneous tumor regression

Genes: CDC20, CDC27, CDC6, CCNB1, BUB1, BUB1B.

Identification of genes (DEGs) enabling first-order kinetics of tumor regression

To identify the genes responsible for the exponential decreasing curve of the tumor population, we have taken the common DEGs genes at time points t₂, t₃, and t₄, as the first sign of spontaneous regression is shown at time point t₂ (Fig. 7). Therefore, we have collected the genes expressed at all these 3-time points (regression phase) but have a negative or very low expression at time t₁ when tumor progression occurred. Using the Venn diagram, a total of 292 overlapping DEGs were identified; out of these, 176 are upregulated genes (Fig. 9a), and 116 are downregulated genes (Fig. 9b). These upregulated and downregulated genes are enumerated, respectively, in Supplementary file-2: Tables S1 and S2 with their fold-change values. The significance of these genes, both up- and downregulated, are elucidated later.

Fig. 9.

Venn diagram: identification of differentially expressed genes (DEGs) responsible for first-order decreasing curve of tumor extinction, while the tumor undergoes regression across the duration of regression, i.e., along the three time points t₂, t₃, t₃. The common intersection zones indicated the genes that were effective at all the time points, throughout the regression process. Thereby, a total of a 176 upregulated and b 116 downregulated genes are obtained for further analysis

Protein–protein networking analysis

We performed gene ontology (GO) and pathway enrichment analysis utilizing multiple databases, like KEGG pathway [(https://www.genome.jp/kegg/: release 102.0 (Kanehisa et al. 2016)], DAVID database (Dennis et al. 2003), FunRich (Pathan et al. 2015), and ClueGo (Bindea et al. 2009), with p < 0.05 as the cut-off criterion. The gene ontology (GO) of DEGs classified the differentially expressed genes in terms of three main aspects of the genes: cellular components (CC), the biological processes (BP) in which it participates, and its molecular function (MF). Our results follow:

Cellular component

The upregulated genes were enriched in the Plasma membrane (Fig. 10a) and maintained in the Tertiary granule, as shown in Fig. 10b. In contrast, the downregulated genes were involved in Nucleoplasm, Microtubila, Chromosome, Nucleus, and Microtubule cytoskeleton (Fig. 10c, d).

Fig. 10.

Gene ontology (GO) analysis and significant enrichment of “cellular component” responsible for exponential decreasing curve in melanoma regression model; a, b GO analysis for upregulated differentially expressed genes (DEGs); c, d GO analysis for downregulated DEGs

Molecular functioning

The upregulated genes were mainly engaged in virus receptor activity and metallopeptidase activity (Fig. 11a, b). In contrast, the downregulated genes were related to kinase binding and also cyclin-dependent protein serine/threonine kinase activity (Fig. 11c, d).

Fig. 11.

Gene ontology analysis and significant enrichment of “molecular function” responsible for exponential decreasing curve in melanoma regression model; a, b GO analysis for upregulated DEGs; c, d GO analysis for downregulated DEGs

Biological processing

The upregulated genes were involved in cell growth or maintenance, and Leukocyte migration activity (Fig. 12a–c), whereas the downregulated genes were involved in regulation of mitotic cell cycle (Fig. 13a–c). The GO term analysis showed that most of the DEGs genes were enriched in immune cell activation, leukocyte migration, serine kinase activity, cell cycle, cell growth, and mitotic cell cycle regulation.

Fig. 12.

Gene ontology analysis and significant enrichment of “biological process” responsible for exponential decreasing curve in melanoma regression model; a, b GO analysis for upregulated DEGs; c pi-chart representation of GO analysis

Fig. 13.

Gene ontology analysis and significant enrichment of “biological process” responsible for exponential decreasing curve in melanoma regression model; a, b GO analysis for downregulated DEGs; c pi-chart representation of GO analysis

Functional enrichment analysis

We found from the enrichment data that two classes of genes are responsible for tumor regression. We also did find that the first class of genes activated the cellular immune system and leucocyte regulation, thus enabling these immune effector cells to damage and eliminate the tumor cells. On the other hand, the second class of genes were observed to be involved in blocking the cell cycle regulation or spindle formation, so the malignant cells would not be able to multiply. Thus these two classes of genes operate complimentarily for achieving full tumor regression, one class attacks the tumor cells, and the other class makes the tumor cells non-functional, without being able to multiply. Furthermore, enrichment analysis with different databases showed that the most significant GO terms for tumor regression belong to downregulated genes. Accordingly, biological pathway enrichment was performed which showed that the downregulated genes were enriched in the following entities (Fig. 14):

Cell cycle, mitotic phase, DNA replication, checkpoints of cell cycle, mitotic M-M/G1 phases, and G2/M DNA damage checkpoint.

Fig. 14.

Gene ontology analysis and significant enrichment of biological pathway responsible for exponential decreasing curve in the melanoma regression model for downregulated differentially expressed genes. The blue bars denote the percentage of genes, while the yellow line is the level of statistical significance of the genes [− log₁₀(p value)]. Note that there is very significant downregulation of the genes associated with tumor cell multiplication, such as Mitosis function, DNA replication, Cell cycle checkpoint functionality, Kinase signaling, etc. Such inhibition of malignant cell reproduction produces rapid decline in tumor cell population

To highlight, this finding signifies that one can control the tumor cell population and actuate the tumor regression process by intervening in the cell cycle regulation process and mitotic spindle formation process.

Protein–protein interaction analysis and sub-network analysis

We undertook the protein–protein interaction (PPI) analysis by utilizing STRING database facility in Cytoscape platform to retrieve the interacting genes. We mapped a total 176 upregulated genes (DEGs) into Cytoscape; out of these, 164 DEG genes of humans were recognized using Cytoscape, there being 428 edges (Supplementary file-2: Fig. S2. 1). Similarly, out of 116 downregulated DEGs, 115 genes were mapped into Cytoscape, having 1797 edges (Supplementary file-2: Fig. S2. 2). All the expressed DEGs and their edges are shown in Supplementary file-2: Fig. S2. 3. Thereafter, we selected the top three significant clusters within the protein–protein interaction network using the MCODE facility in the Cytoscape platform (Module 1, MCODE score = 54.4; Module 2, MCODE score = 8.444; Module 3, MCODE score = 6). Our MCODE analysis shows that Module 1 consists of 61 nodes and 1632 edges (Fig. 15a), Module 2 consists of 10 nodes and 38 edges (Fig. 15b), while Module 3 consist of 16 nodes and 45 edges (Fig. 15c). We have also performed the biological pathway enrichment analysis for the most significant item, Module 1, and these were mainly associated with the following entities (Fig. 15d):

Mitotic M-M/G1 phases, G2/M checkpoints, mitotic process, cell cycle, DNA replication, G2/M DNA damage checkpoints.

Fig. 15.

Sub-network of top 3 modules with seed node representation (in yellow color) from protein–protein Interaction (PPI) network: a Module 1, having KIF4A gene as a seed node; b Module 2 having RAC2 gene as a seed node; c Module13 having FCER1G gene as a seed node; (d) Biological pathway enrichment analysis of Module 1

Identification of hub genes

We demarcated the effect of gene functioning by utilizing the CytoNCA facility in the Cytoscape procedure, having different types of centrality analysis to identify the essential proteins in the biological network (Tang et al. 2015). Utilizing the CytoNCA method, we used the three centrality measures to assess the degree of influence of a gene’s function degree (Jeong et al. 2001), betweenness (Freeman et al. 1991) and closeness (Sabidussi 1966). Hence, from the PPI network with high degree of connectivity (Table 2), we identified the following configuration of genes that can be ranked using the effective centrality score, which is the product of the aforesaid three centrality measures:

Table 2.

Top 10 hub genes identification: CytoNCA analysis of PPI network

Display name	Degree	Betweenness	Closeness	Effective Score
TOP2A	69	1980.160771	0.016653687	2275.411484
KIF20A	66	1846.282413	0.016644713	2028.235524
KIF23	69	1227.289816	0.016646707	1409.693009
CDK1	72	1174.577395	0.016636744	1406.962366
CCNB1	68	1141.440679	0.01663774	1291.387552
RAD51AP1	66	994.5498801	0.016621824	1091.061357
BUB1B	66	422.550881	0.016622818	463.583088
CHEK1	67	393.7200322	0.016630773	438.7071859
CCNA2	69	335.982852	0.016632763	385.5942962
KIF11	67	212.022604	0.016623812	236.1497951

Top 10 hub genes

CDK1, CCNA2, KIF23, TOP2A, CCNB1, CHEK1, KIF11, BUB1B, RAD51AP1, KIF20A.

Using Cytoscape, we constructed the PPI network to show the interconnection between the top 10 hub genes (Fig. 16a), having 10 nodes and 45 edges. We utilized the STRING database to indicate the gene co-expression analysis of the ten hub genes, which shows that these genes may actively interact with each other (Fig. 16b). These findings suggest that the functioning of these ten hub genes might play a crucial role in the spontaneous regression of malignant melanoma tumors, manifesting in the first-order kinetics of the tumor decline. For example, considering the first hub gene above (CDK1), we noted that the overexpression of CDK1 indeed has a gross tumorigenic potential in melanoma (Ravindran Menon et al. 2018) and this CDK1 will interact with the other aforesaid hub genes (CCNB1, CHEK1, BUB1B and CCNA2) to activate the cell cycle, to make the tumor grow intensively and become invasive. In other words, under-expression of these genes (as CDK1) or pharmacological inhibition of the effect of these genes may induce melanoma regression.

Fig. 16.

a Construction of protein–protein interaction network of the top 10 hub genes, having 10 nodes and 45 edges; b The co-expression analysis of the 10 hub genes using the STRING platform, the color intensity of the triangle-matrix shows the level of confidence between two functionally connected proteins

Identification of candidate drugs

We have earlier identified the hub genes and their functionality which are responsible for the first-order decline of the malignant cells, enabling complete spontaneous tumor regression endogenously. The apparent question is that how can one induce a similarly efficient regression process exogenously, i.e., what could be candidate drug molecules that could function likewise to mimic the expression of the genes, so that if these candidate drugs are administered therapeutically to a progressing malignant melanoma tumor, then the tumor would undergo complete regression. Accordingly, we identified 34 drugs using the top 10 hub genes by further probing drug–gene interactions. Out of these 10 hub genes, we found that incisive targets of these drugs include genes: CDK1, CCNA2, TOP2A, and CHEK1 (Supplementary file-2: Table S3).

After comparing three different databases (IPA, DGIdb, and Cytoscape), we found that only one gene, TOP2A is common in all databases among these four genes. Also, from the cBioPortal database, the alteration information of these four genes shows that most of the mutation (8%) was alone in the TOP2A gene (Fig. 17a). The increased expression of Topoisomerase II alpha (TOP2A) makes melanoma cancer cells resistant to chemotherapy (Song et al. 2013). According to an analysis, TOP2A inhibition induces cancer cell death by damaging DNA with a low toxicity effect to normal cells (Matias-Barrios et al. 2021). Thus, TOP2A functionality should be a potential biomarker for melanoma treatment. Hence, we focus more on the drugs related to the TOP2A gene. From three databases (IPA, DGIdb, and Cytoscape), we arrived at a total of 9 drugs that are common in all databases (Fig. 17b), and all these drugs modulate Topoisomerase II alpha, these candidate drugs can be categorized as per their functionalities as:

Fig. 17.

a An oncoprint summary across a set of melanoma tumors (skin cutaneous melanoma TCGA Pan-Cancer data) shows the genetic alteration connected with four main genes in total of 442 patients; b Common drugs from three databases (DGIdb, Cytoscape, and IPA)

Anthracycline derivatives:

Idarubicin, Epirubicin, Valrubicin, Daunorubicin, Doxorubicin.

Podophyllin derivatives:

Teniposide, Etoposide.

Adduction derivative:

Mitoxantrone.

Chelation derivative:

Dexrazoxane.

Some of these drugs are repurposed here, for instance, Dexrazoxane is a cardioprotective drug and anti-malarial agent, while Mitoxantrone is a drug also used in neuroinflammatory disease, such as multiple sclerosis.

Molecular docking for TOP2A

We have used a molecular in silico docking study to assess the affinity of the TOP2A gene with respect to the aforesaid nine drugs (Idarubicin, Epirubicin, Valrubicin, Teniposide, Dexrazoxane, Etoposide, Daunorubicin, Mitoxantrone, Doxorubicin), utilizing AutoDock analysis. Here we have taken a total of 12 amino-acid residues (GLY721, LYS723, GLN726, GLN773, ASN779, ASN851, GLY852, ARG929, LEU722, LEU771, ALA853, and TRP931) for TOP2A (Matias-Barrios et al. 2021). Those nine drugs were docked with TOP2A receptors, for acting as inhibitors. Four of these nine drugs are found to have excellent inhibitory action on the TOP2A receptor based on its binding energy. (Supplementary file-2: Table S4). The highest-ranking drug is the podophyllin derivative Tenoposide which uniquely has a sulfur-based thiophene-derived 5-membered ring. The docking study of these four ligands (two drugs from podophyllin derivative and two from anthracycline derivatives) with their receptors are shown in Fig. 18. Detailed information regarding the interacting amino-acid residues and the respective binding energies is in Table 3.

Fig. 18.

Computed structural comparison and binding features, respectively, of a Teniposide, b Etoposide, c Epirubicin, and d Doxorubicin against TOP2A receptor (PDB ID: 4FM9) (Visualization using UCSF Chimera and AutoDock)

Table 3.

The binding energy, inhibitory constant (Ki) and interacting amino-acid residues of the candidate drugs Teniposide, Etoposide, Epirubicin, and Doxorubicin against TOP2A receptor (PDB ID: 4FM9)

Drug	Total binding energy (kcal/mol)	VDW + H bond + dissolution energy (kcal/mol)	Calculated inhibitory constant (Ki-Nanomolar)	Interacting amino-acid residues
Teniposide	− 9.95	− 12.63	50.92	LYS723 GLN726 GLU854 TRP931 GLY796 LYS798
Etoposide	− 9.51	− 12.49	107.27	LYS723 ASN770 ASN851 PHE775 GLY777 LEU783
Epirubicin	− 8.77	− 12.05	372.72	ASN779 GLU854 LUE771 ARG929 GLY852 PHE775
Doxorubicin	− 8.64	− 11.92	461.78	ASN779 GLU854 GLY721 ALA853 GLY852 ASN851

Corroboration from human subjects and clinical patients

We have identified 34 drugs using the top 10 hub genes to explore the drug-gene interaction, which has the possible involvement in the exponential decreasing curve of spontaneous cancer regression (Supplementary file-2: Table S3). Regarding these 10 hub genes (Table 2), the promising targets of these drugs includes genes: CDK1, CCNA2, TOP2A, and CHEK1 (Supplementary file-2: Table S3). These four hub genes are now further investigated to narrow down our search. Here, we have used two techniques for garnering more information about the potential genes, these methods, respectively, utilize (i) GEPIA platform(“GEPIA (Gene Expression Profiling Interactive Analysis),” 2022), to find the difference in the gene expression levels between melanoma cancer tissue and normal tissue in human subjects, and (ii) THPA platform(“The Human Protein Atlas,” 2022), for the overall survival analysis of human melanoma patients with different levels of the gene expression. Our findings from these two procedures are, respectively, shown in Figs. 19 and 20. From Fig. 19 (based on analysis of 461 melanoma patients and 558 normal subjects are 461 and 558, respectively), we observed that all four genes are significantly expressed in melanoma tissue in humans, and among these genes, the TOP2A gene has the highest mean absolute value (near around 4.5). Furthermore, we note from Fig. 20 that human melanoma tumor patients with low expression levels of TOP2A gene have the lowest 3 years’ survival rate (at 53%), when compared to genes CDK1, CCNA2, and CHEK1(survival at 59%, 60%, and 60%, respectively). This analysis shows that (i) our approach of the focal significance of TOP2 gene is also applicable to the scenario of human melanoma patients (ii) among these four genes, investigating TOP2A gene may have high relevance to understanding the possible mechanism behind spontaneous cancer regression, as well as to development of novel therapeutic molecules in the human context.

Fig. 19.

Expression level of four hub genes in human subjects and clinical patients. The four panels of the heat maps show the expression levels of the four hub genes (a TOP2A, b CDK1, c CCNA2, and d CHEK1) in melanoma tissue (skin cutaneous melanoma) vis-à-vis normal skin tissue, based on TCGA data analyzed using GEPIA platform. The red and gray box plots in each panel represents melanoma tissues and normal skin tissues, respectively

Fig. 20.

Correspondence of hub genes with survival rates in clinical patients of malignant melanoma tumor. The Human Protein atlas was used to evaluate the overall survival rates of high and low expression of the genes: a TOP2A, b CDK1, c CCNA2, and d CHEK1 in patients with melanoma. Blue graphs: low expression of gene; Red graphs: high expression of gene

Discussion

The episodic natural phenomenon of spontaneous regression of malignant tumors occurs in many types of cancer, where the tumor is completely eliminated without any toxicity effects on the animal or patient. Making intensive endeavors to understand this unique natural phenomenon can provide much insight into the possibility of replicating such a regression process on a clinical tumor without appreciable side effects. One of the main concerns of oncological treatment is the toxic side effects of anticancer agents, which often limit the therapeutic intervention, leading to the deterioration of the patient. The non-toxic nature of spontaneous tumor regression is an added inducement to researchers on why the process should be investigated well.

In our present study, we have developed an integrative mathematical systems biology-based approach to the permanent spontaneous tumor regression process. We have shown that this tumor regression and extinction process is mainly due to first-order kinetics producing tumor cell decline, with a small negative bias necessary for the extinction of the residual tumor cells. We have also provided biological validation of our theoretical mathematical approach utilizing experimental findings of the malignant melanoma regression, as a case study model paradigm. Furthermore, our approach shows how three complementary entities (DNA blockage, antitumor lymphocyte, and cytokine activation) are orchestrated synergistically at different time segments to produce complete extinction of tumor cells. Thereby, we have elucidated a systems biology approach using the three aforesaid entities that could be used therapeutically to induce tumor elimination in the clinical situation. We now elaborate the different implications that our investigations have revealed.

Associated genes and pathways

Numerous studies have been performed to explore the mechanism behind the spontaneous cancer regression process during the past several decades. However, the studies need to be more comprehensive to systematically elucidate the exact factors behind this process. In contrast to prior studies that only focus on eliminating the cancer cells, our investigation is more focused on eradicating the malignant cells while protecting the normal tissue; these two aspects are implemented in the endogenous process of the spontaneous cancer remission phenomenon. As an exemplary case study, we have analyzed microarray data of spontaneous cancer regression in a well-documented mammalian melanoma system and formulated the involved genes and biological pathways that produce permanent tumor elimination from the experimental perspective. Finally, we identified the differentially expressed genes for five different time points (t₀–t₁–t₂–t₃–t₄) at three weeks apart (total 3 months’ duration), while the tumor changes from a progression phase to the regression phase and finally to the permanent eradication phase. We observed that the number of genes with altered levels of expression was maximum after midway, i.e., at time t₃, where the regression process was maximal. We found that the ratio of downregulated genes (with respect to the upregulated genes) increased while the regression process advanced in the following way: 29–71–113–137%. The downregulation of the genes enabled the inhibition of:

Cell cycle, mitotic phase, DNA replication, checkpoints of Cell cycle, mitotic M-M/G1 phases, and G2/M DNA damage checkpoint.

IPA analyses were performed to find the interactive pathway network, which shows that the first sign of spontaneous cancer regression is at time t₂; here the regression has started 1.5 months after the initial start of progression (time t₀). For the identification of differentially expressed genes (DEGs) for exponential decreasing tumor regression (i.e., first-order kinetic process), we have taken the common DEG genes at time points t₂, t₃, and t₄, since the first sign of spontaneous regression was shown at the time point t₂. Finally, we identified 292 DEG genes for this regression (176 upregulated and 116 downregulated). Furthermore, biological pathway enrichment showed that (i) Downregulated genes were mainly enriched in cell cycle, mitosis, DNA replication, cell cycle checkpoints, Mitotic M-M/G1 phases, and G2/M DNA damage checkpoint, while (ii) Upregulated genes were enriched in cell growth or maintenance, leukocyte migration activity, immune cell activity, and leucocyte regulation. We undertook protein–protein interaction analysis (PPI) and found the three significant clusters of genes using MCODE, and identified the most effective module consisting of 61 nodes and 1632 edges the module being again enriched in the following processes: cell cycle, mitosis, DNA replication, mitotic M-M/G1 phases, G2/M checkpoints, and G2/M DNA damage checkpoints (Fig. 19).

Nodal hubs and candidate molecules for inducing complete tumor regression

CytoNCA was used to find the 10 hub genes (CDK1, CCNA2, KIF23, TOP2A, CCNB1, CHEK1, KIF11, BUB1B, RAD51AP1, KIF20A) related to the exponential decreasing phenomenon of tumor regression process. From Table 2, the effective score of the TOP2A gene is the highest out of these 10 hub genes, which indicates that TOP2A may be a potential prognosis biomarker for grading the degree of invasiveness of melanoma cancer. Out of the 10 hub genes, we have identified four potential gene targets of the drugs i.e., the genes TOP2A, CDK1, CCNA2, and CHEK1. Targeting these identified candidate genes can serve as a potential source for gene therapy for permanent tumor regression in different types of cancer. For example, CHK1 gene activation may help to suppress tumor growth (Zhang and Hunter 2014). Similarly, CDK1 gene is a prognostic biomarker for the molecular pathology technique of Pan-cancer Analysis, and is also much significant in a broad gamut of oncology, and this gene can be used as a potential gene-targeted therapy (Yang et al. 2022). Likewise, from a gene targeting perspective, the chromosomal decatenation checkpoint is modulated by topoisomerases, and an important player in the process is the TOP2A gene which offers considerable prospects for gene therapy, aimed at personalized cancer treatment (Chen et al. 2015).

The Table S4 of Supplementary file-2 shows that most of the drugs were TOP2A inhibitors. Moreover, with the help of the GEPIA procedure and THPA platform, we validated the TOP2A functionality by showing that it has the highest expression rate and lowest survival rate compared to the other three genes in human melanoma patients. Subsequently, we performed molecular docking studies showing that two kinds of drug derivatives (podophyllin derivative and anthracycline derivatives) have high binding energy as TOP2A inhibitors. Indeed, Teniposide (podophyllotoxin derivative) has the highest binding energy (− 9.95 kilocal/mole, Table 3), which could be the potential drug to target melanoma cancer cells.

Clinical translation: permanent tumor elimination by first-order kinetics

Figure 4b–d panels show how the inputs of cytotoxic T-lymphocytes, DNA blockage, and interleukin-2 need to change time-wise for the melanoma tumor to undergo complete eradication, whether by the endogenous way (spontaneous regression) or by the exogenous way (therapy-induced regression). In the spontaneous regression mode, these inputs are themselves generated by the host tissue. The vertical axes of the three panels furnish the time-wise input produced by the host tissue. For instance, the DNA blockage axis (vertical axis in Fig. 4c) shows the amount of DNA blockage expressed equivalently in terms of DNA alkylation level, measured in terms of equivalent dacarbazine units. Regarding therapy-induced regression, these three inputs (T-lymphocytes, chemotherapy drug and interleukin-2) will be administered externally at the time-wise injection rate given in the vertical axes of the three panels (Fig. 4b–d). For instance, the DNA blockage axis shows the dacarbazine dose (in mg/day/kg body weight of the subject) required for melanoma tumor extinction. Since our present study delineates that the most efficient chemotherapy drug for regression would be Teniposide, one can give an equivalent Teniposide dose (chemotherapeutically, dacarbazine and Teniposide are, respectively, monovalent and divalent, while their molarities is 182 and 657, respectively), hence the Teniposide dose would be 1.81 times the dacarbazine level given in Fig. 4c.

Thus, one can note the benefits of investigating spontaneous tumor regression and its intensive implications for more efficacious therapeutic regression of a tumor. Molecular biology-based analysis of spontaneous regression of different types of tumors would give an insight into what pharmacological agent would be maximally helpful for regressing that type of tumor in the therapeutic setting. Our study shows that most tumor cells decline by first-order kinetics actuated by very few hub genes. A significant factor of this decline is DNA interference, as by small molecule candidate antineoplastic agents that modulate the effect of those hub genes. This is an encouraging sign since antineoplastic chemotherapy agents are generally smaller molecules and comparatively much more affordable than highly sophisticated newer antitumor interventions such as monoclonal antibodies, biosimilars or growth factor-modulating proteins. Of course, eliminating the small number of residual tumor cells may need interferon-2 and lymphocyte activation. However, the cost involved would not be prohibitive, as most of the tumor load has been eliminated. Hence, it would be desirable that microarray investigations of spontaneous regression cases of different tumors should be done in the future (we recollect there are already 30,000 studies on spontaneous cancer regression available in PubMed, as mentioned earlier). Thereby, for different tumor types, one could have the significant hub genes and the main chemotherapy agents for modulating the gene effects so that complete tumor regression could be induced from the clinical perspective.

Conclusion

Using a systems biology methodology, we have endeavored to analyze the mechanisms behind spontaneous cancer regression, and how normal tissue is protected during this tumor cell elimination. We also elucidated the treatment implications, so that the mechanistic knowledge could be utilized for therapeutically replicating the tumor regression process and normal tissue protection on clinical patients. Our approach was corroborated by experimental findings from rodent, pig and human studies. Indeed, a significant finding of our investigation is that this first-order kinetics-based tumor regression is enabled by three cytotoxic entities: DNA blockage, interleukin-2 and antitumor T-lymphocyte activation. Furthermore, another noteworthy finding is the malignant cell extinction process occurring at the last stage of tumor regression. Here, a small negative biasing (about 1%-2% of original tumor load) eliminates the small number of residual tumor cells under the asymptotic tail of the exponentially declining curve of tumor cell population, thereby the tumor becomes permanently extinct. Enrichment Analysis shows that the most significant genes are those whose downregulation produces arrest of tumor cell multiplication through DNA blockage, cell cycle retardation, and mitotic activity diminution. Among these genes, downregulation of TOP2A gene was found pivotal for melanoma regression, and this gene is highly upregulated in melanoma tissues in clinical patients. We also elucidated two classes of drugs (podophyllin derivative and anthracycline derivative) that block the TOP2A receptors, and could be possible therapeutic agents in melanoma patients, thereby having the potential to duplicate the process of tumor regression in the clinical context.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

BK: conceptualisation, methodology, validation, formal analysis, writing–original draft, writing—review and editing. CS, RL, PP, AB: methodology, formal analysis, validation. PKR: conceptualisation, methodology, validation, formal analysis, writing—original draft, writing—review and editing.

Data availability

All the data are included in this manuscript. For further clarifications, please communicate with the corresponding author PKR at Dept. of Life Sciences, Shiv Nadar University, Dadri 201314, India.

Declarations

Conflict of interest

The authors declare no conflict of interest, financial or otherwise.

Research involving human participants and/or animals.

The work performed in the manuscript does not involve any human participants or animal preparations.