Various one and two-dimensional (1D and 2D) nanomaterials and their combinations are emerging as next-generation sensors because of their unique opto-electro-mechanical properties accompanied by large surface-to-volume ratio and high quality factor. Though numerous studies have demonstrated an unparalleled sensitivity of these materials as resonant nanomechanical sensors under vacuum isolation, an assessment of their performance in the presence of an interacting medium like fluid environment is scarce. Here, we report the mechanical damping behavior of a 1D single-walled carbon nanotube (SWCNT) resonator operating in the fundamental flexural mode and interacting with a fluid environment, where the fluid is placed either inside or outside of the SWCNT. A scaling study of dissipation shows an anomalous behavior in case of interior fluid where the dissipation is found to be extremely low and scaling inversely with the fluid density. Analyzing the sources of dissipation reveals that (i) the phonon dissipation remains unaltered with fluid density and (ii) the anomalous dissipation scaling in the fluid interior case is solely a characteristic of the fluid response under confinement. Using linear response theory, we construct a fluid damping kernel which characterizes the hydrodynamic force response due to the resonant motion. The damping kernel-based analysis shows that the unexpected behavior stems from time dependence of the hydrodynamic response under nanoconfinement. Our systematic dissipation analysis helps us to infer the origin of the intrinsic dissipation. We also emphasize on the difference in dissipative response of the fluid under nanoconfinement when compared to a fluid exterior case. Our finding highlights a unique feature of confined fluid–structure interaction and evaluates its effect on the performance of high-frequency nanoresonators. Understanding the response of carbon nanotube-based nanomechanical resonators when in contact with a fluid could broaden their applications range. Low-dimensional materials are attractive for nanoscale sensing because they have a very high resonant frequency, enabling high quality factors. Carbon nanotubes are one such material, but their resonant behavior has rarely been studied when in contact with a fluid. Now, Subhadeep De and Narayana Aluru from University of Illinois at Urbana-Champaign study the nanomechanical resonance of single-walled carbon nanotubes under two conditions: with fluid passing through, and with fluid surrounding. They analyze dissipation losses in these systems, with a view to widening the applications range of carbon nanotube resonators used in chemical and biological environments. One motivation towards miniaturization is making high-precision resonant mechanical sensors which can detect extremely small foreign mass, charge, force, etc.6. The unique optical8 and electronic properties11 of these low-dimensional materials can be coupled with their mechanical degrees of freedom to make the next generation sensors. During any such sensing process, ultra-high sensitivity can be attained when the resonator has low mass, large surface area, and very high resonant frequency13, all of which are inherently offered by 1D and 2D materials of nanometer dimension. However, different dissipative processes can interfere with the mechanical response of the resonators and limit their performance. The dissipation takes place due to the coupling of the resonant motion of interest, either with other internal degrees of freedom in the resonator, classified as an intrinsic source or with the external environment, classified as an extrinsic source. Typically, the ultimate performance of a resonator is evaluated under near-vacuum condition15, in which case only the intrinsic dissipation mechanisms are operative. But, such characterization may prove insufficient to assess their quality for applications involving biological17 and chemical20 sensing where an external gas or liquid environment is inevitably present. In such scenarios of a resonator in a fluid environment, estimating the net energy loss is not straightforward. Firstly, because the sources of dissipation can couple with each other and the coupling effect can manifest in each dissipation mechanism. Secondly, the response of the interacting media, fluid, in the parameter space of the resonant motion, which are gigahertz frequency and nanometer dimension is poorly understood and consequently, the resulting extrinsic dissipation, i.e., fluid dissipation, is difficult to estimate. In this regard, 1D or 2D high-frequency nanoresonators in a fluid environment is a platform not only to understand the individual dissipative processes and their coupling but also to probe the nature of fluid–structure interaction at the lower extremes of length and time scale.In the pursuit of miniaturization of devices, low-dimensional nanomaterials like carbon nanotubes22 and mediated by its phonons or thermal degrees of freedom. For smaller resonators of nanometer lengths operating at gigahertz frequencies, phonon-mediated dissipation due to Akhiezer mechanism24, anharmonic phonon scattering26, becomes more pronounced. For flexural vibration of 1D and 2D microresonators, nonlinear mode coupling, mode hybridization, and coupling to phonon bath are the dominant dissipation mechanisms29. Other forms of intrinsic dissipation could be mediated by the surface31 and structural defects32 and by the two-level states35 at low temperatures. Of all, phonon-mediated dissipation mechanisms are of major concern because it is ubiquitous to any resonator at room temperature. Viscous damping starts playing a significant role when the resonator is coupled with the fluid environment. The fluid can be placed, either outside the volume of the resonator or encapsulated in a channel inside the resonator. In the case of exterior fluid, the fluid damping is generally orders of magnitude higher than intrinsic damping and becomes a more important concern. This motivated the characterization of fluid damping interacting with vibrating micro-nano structures36 and nanoparticles37. It has been established that even “viscous” fluid can exhibit “viscoelastic” nature if the time scale for measurement becomes comparable to molecular timescales in the fluid. To account for the frequency dependent fluid response, a fluid relaxation parameter is incorporated in the constitutive relationship between shear stress and strain rate, and the classical Navier–Stokes (NS) equations are modified accordingly39. The effect of the fluid relaxation was observed in the case of gases through vibrating micro-nano resonators at kilohertz to megahertz frequencies40 and in case of liquids through vibrating nanoparticles at gigahertz frequencies41, respectively. The difference in the frequency range of observation is due to the difference in molecular timescales between gases and liquids. In all the cases of exterior fluid, the damping was consistently found to be directly proportional to the density or viscosity of the fluid. The case of fluid encapsulation exhibited some distinctive features like reduced fluid damping43 and nonmonotonic scaling with the fluid density or viscosity44. Those features, however, were shown to stem from the dynamics of the fluid under confinement. Because of the lower frequency in kilohertz and larger dimension of the fluid channel in micrometer, the oscillatory flow dynamics could be explained using classical NS equations without the fluid relaxation parameter. In this regard, the flexural phonon damping of nanotube resonators with confined fluid combines interesting and unexplored features of both phonon-mediated intrinsic damping and fluid damping. The confined fluid damping being low and comparable to the intrinsic dissipation, both become equally important. Each dissipation channel can exhibit some effect due to the presence of other entity. A large surface-to-volume ratio of these low-dimensional structures provides a scope to capture the effect. The flexural phonons interacting with the fluid can attain gigahertz frequencies, a range where the fluid response behavior is unknown. Additionally, the fluid interaction at the nanoscale structural interface bears the effect of slip46, density inhomogeneity47, and reorganization due to confinement48, all of which can effect the dissipation.The dominant mechanism behind dissipation varies significantly with the critical length of the resonator, the time scale of operation, and the mode of actuation. The intrinsic dissipation, for instance, in the case of beam resonators with micrometer cross-section and megahertz resonant frequency is dominated by thermoelastic dampingWe consider a 1D single-walled carbon nanotube (SWCNT) interacting with an argon environment at room temperature and study the damping of the fundamental flexural phonon with gigahertz resonant frequency. We set-up two different arrangements of the resonator–fluid system; in one, the fluid is solely confined inside the SWCNT . For the pressure range considered (~10–104 bars), argon in the reservoir exists either in the vapor or the supercritical state50. For any higher pressure, argon turns solid and will prevent the filling of the SWCNT. To compare the dissipation in the interior and the exterior cases, a correspondence is established between the reservoir or bulk density By varying reservoir pressure, argon can be confined inside the SWCNT with reduced densities ranging from ~0.01 to 0.57 (16.87–961.87 kg/m3) in the case of interior fluid, and 3) in the case of exterior fluid. A snapshot of the deformed SWCNT during the ringdown process is shown in Fig. 51ω1 and ν1 are the resonant frequency and the damping coefficient in fluid, m0 is the resonator mass, and Δm is the added mass due to the fluid during the fundamental flexural motion. The derivation is shown in Supplementary Section ω1 for different cases of argon coupled CNT system is shown in Fig. ω1 is majorly due to the added fluid mass, ν1 becomes significant and can contribute to the change for the highest densities.Ringdown is carried out for fluid densities ranging from m0, ν1 in Eq.  interacts with other phonons  of the SWCNT and the fluid atoms. For the fluid-coupled resonator system (sys), the total dissipation, (Q−1)sys (≡Q−1) is accounted by the intrinsic (int) dissipation governed by the phonons and extrinsic dissipation due to the fluid (flu). In the case of an empty SWCNT operating in vacuum (v), net dissipation, 26. However, the presence of fluid (f) in the fluid-coupled resonator can change the nature of the interaction of the fundamental flexural phonon (k = 1) with other phonons at the fluid–structure interface. If that is true, the intrinsic dissipation in the fluid-coupled resonator can be different from 53  or thermal motion54 (th) of the atoms in the SWCNT. We denote the fluid dissipation by During the resonant motion, the fundamental flexural phonon (Q−1)sys. In our case of SWCNT resonator in fluid, (Q−1)sys is obtained using nonequilibrium MD. The main challenge is the computation of the individual contributions namely 56 by the fluid on the fundamental flexural mode (k = 1) obtained from nonequilibrium MD during the ringdown. The modal hydrodynamic force, Fi,α)flu on each resonator atom  from time to frequency domain and evaluated at ω1. The formulation and subsequent derivation of the quality factor is shown in Supplementary Section ξ1 is a fraction that depends on the mode shape. Q−1)sysQ−1)sys with Q−1 obtained directly from nonequilibrium MD simulation is shown in Fig. k = 1) with the rest of the phonons  is not influenced by the presence of the fluid at the fluid–structure interface. Also, the inverse scaling of the damping of the fundamental flexural phonon can be ascribed to the scaling of the fluid dissipation.During experiments or simulations on ringdown, the dissipation measured from the amplitude decay of the structure is . Here, cf(t) parameterizes the dissipative part of the hydrodynamic force of the fluid on the SWCNT resonator in response to the fundamental flexural motion (k = 1). From the nonequilibrium MD of the ringdown, we can only compute ω = ω1 but not the time-dependent damping kernel cf(t). So, we compute cf(t) from equilibrium MD using a formulation based on linear response theory (LRT). In the next subsection, we verify the formulation by carrying out nonequilibrium MD and equilibrium MD simulations on a fluid-coupled resonator system with the resonator atoms frozen, i.e., no phonons . This acts as an external perturbation. During this process, the hydrodynamic force response on the mode, 57, where λ(t) = A1 sin(ω1t), and β = (kBT)−1. This is worked out in details in Supplementary Section cf(t) as LRTcf(t) for the resonator with no phonons as P1(t) as 1. We denote p I Fig.  at equilentclass1pt{minimacf(t) for the actual system and how another simulation setup, setup II .The simulation setup I with the resonator atoms frozen is used to verify the formulation of the damping kernel. However, the computed fluid damping kernel, k = 1) and all other phonons  are also present in the system due to the thermal motion of the atoms. The thermal motion of the SWCNT atoms can influence the hydrodynamic force response by the fluid, and consequently cf(t). However, in this case, we cannot directly apply the LRT and calculate cf(t) from equilibrium fluctuations of λ(t), defined previously, lies in the phase-space of the Hamiltonian of the SWCNT resonator with phonons, at thermal equilibrium57. More precisely, λ(t) coincides with q1(t). Considering this, a workaround would be to suppress the fundamental flexural phonon and allow other phonons in the SWCNT during the equilibrium simulation. This is achieved by attaching a stiff spring (kstiff → ∞) at the mid-section along the length of the SWCNT . In this scenario, LRT can be used to calculate cf(t) for the SWCNT resonator, corresponding to a perturbation along ϕ1. Although the aforementioned fix affects the nature of few other phonons, the calculated cf(t) can effectively capture the influence of the thermal motion of the SWCNT atoms at the fluid–structure interface. For the resonator with phonon case, we denote cf(t) as In the actual case, the SWCNT resonator is vibrating in the fundamental flexural mode (cf(t) between the resonator with phonon case and the resonator with no-phonon case at different interior argon densities. The initial values, cf(0) of both the cases are approximately equal. In terms of the time dependence of cf(t), the two cases differ increasingly as we go towards higher densities. Especially for the highest density (cf(t) at longer times sys at lower densities can be approximated as Figure ω1 of the fundamental flexural mode at all interior argon densities. The comparison is shown in Fig. ω1 of the actual system. The frequencies may correspond to SWCNT resonator of much larger length (>20 nm) with the same radius. The scaling is shown in Fig. Having computed 44 with confinement length (lc) in ~1–10 μm and resonant frequency (f1) in ~100–500 of KHz. A formulation using classical NS equation with no-slip boundary condition by Sader et al.58 could quantify the fluid dissipation and nonmonotonic scaling. The nonmonotonicity was also observed in the case of nanochannel resonators with lc ~ 100–700 nm and f1 ~ 0.5–25 MHz43. However, in these nanochannel resonators the fluid dissipation could not be quantitatively explained using the formulation by Sader et al. This could be due to slip-effects at the fluid–structure interface and frequency dependence of slip length and viscosity46 which can be expected in our argon filled SWCNT system with lc ~ 1.3 nm and f1 ~ 107 GHz. Though Sader et al. model can be corrected by incorporating these effects under a multiscale approach47, it is not pursued in this study. Instead, a more direct method is employed where the dissipative behavior of the fluid is parameterized in terms of a damping kernel. Indeed, the fluid dissipation estimated using the damping kernel reveals a frequency dependent scaling behavior in the case of SWCNT with confined fluid.In this section, we discuss our findings in the light of previous studies on fluid damping in fluid channel-based resonators and intrinsic damping of flexural phonons in 1D and 2D resonators. The nonmonotonicity in fluid dissipation with density or viscosity of the fluid was first observed in microchannel resonators37. This prompted in comparing the fluid damping kernel The scaling for the confined fluid case is considerably different from the fluid exterior case which displays a conventional increase in fluid dissipation with densitymentclass2pt{minim28, mode hybridization29, and Akhiezer mechanism59. The nonlinear mode coupling is the coupling of the fundamental mode (k = 1) with the rest of the phonon ensemble due to the anharmonic terms in the resonator potential. Under this mode coupling, one way the fundamental mode can dissipate is by directly thermalizing with the rest of the phonons at some decay rate. In another way, the fundamental mode first transfers energy to a group of modes it is nonlinearly coupled with, and the mode group then thermalizes with their respective baths at particular rates. Here, a mode’s bath comprises the rest of the phonon modes and the fluid if fluid is present. Thus, the energy of the fundamental mode decays at a rate which is an average over the direct and the indirect thermalization rates and this phenomenon is called mode hybridization29. If the flexural motion associates a strain field in the structure, dissipation due to Akhiezer mechanism can play a role. Under Akhiezer mechanism, the strain coupling due to finite Grüneisen constants perturb the energy of all the phonons and they relax at some microscopic timescales by exchanging energy with their respective baths. Both the decay channels due to mode hybridization and Akhiezer mechanism would be affected by the presence of fluid60. Since, we found that 59.The fact that In conclusion, we report the mechanical energy dissipation during the fundamental flexural resonance of an SWCNT resonator coupled with interior and exterior argon. Our dissipation calculations involve ringdown simulations using molecular dynamics (MD). In the fluid-coupled resonator, we identify the two sources of dissipation as phonon-mediated intrinsic dissipation and extrinsic dissipation due to the fluid. The intrinsic dissipation results from the anharmonic coupling and direct thermalization of the fundamental flexural phonon with the rest of the phonon ensemble. The intrinsic dissipation under this mechanism remains unaffected by fluid interactions. The fluid dissipation component contributes to the unexpected scaling of the net dissipation with density in the fluid interior case. To understand the mechanism underlying the unexpected behavior, a fluid damping kernel is formulated using the LRT. The fluid damping kernel captures the dissipative response of the fluid to the flexural motion. The magnitude of fluid dissipation is shown to be accurately quantifiable using the fluid damping kernel. The kernel is used to examine the effect of thermal motion of the resonator atoms (or phonons) on the fluid dissipation. It is found that the thermal motion does not affect till moderately high fluid densities lz) 20 nm is constructed which forms the resonating structure. The structure is made of 3280 carbon atoms and resembles a tube  of 0.68 nm. Argon is considered as the fluid medium. The interaction between the resonating structure and the fluid is studied in two different cases: (i) SWCNT with interior fluid and (ii) SWCNT with exterior fluid. In the case of SWCNT with interior fluid  is defined to surround the fluid outside SWCNT in the radial direction and a periodic boundary condition is applied in all the three directions. The bonded interaction between the carbon atoms in the SWCNT is described by the modified Tersoff potential61. Two-body Lennard–Jones (LJ) potential62 is used to model the non-bonded interaction between the argon atoms of the fluid and between the argon atoms of the fluid and the carbon atoms of the SWCNT.A  SWCNT of length  SWCNT atoms. Then, the argon atoms are placed at a pre-defined spacing in the cylindrical region inside the SWCNT in case of interior fluid and in the region between the cylindrical SWCNT and the cuboidal simulation box in case of exterior SWCNT. A different number of argon atoms are fitted inside those regions by altering the spacing, which results in different densities. The case with no argon atoms corresponds to an SWCNT resonator in the vacuum. A non-dimensional density can be calculated in each case as λ is i or b, corresponding to the interior and exterior fluid case respectively, M is the number of fluid atoms in the system, σ is its LJ diameter, and Vλ is the volume of space available for the fluid, which is Vi = πr2lz in case of interior fluid and Vb = (lxlylz − πr2lz) in case of exterior fluid, respectively. The fluid and the SWCNT atoms are, then, assigned some initial velocity drawn from a Gaussian distribution corresponding to a temperature, T (=300 K) and integrated under NVT64 ensemble for 5 ns to reach thermal equilibrium. The final structure of SWCNT with interior and exterior fluid is shown in Fig. We use the LAMMPS package65 ensemble, with the temperature set to 300 K. The simulation box of the reservoir adjusts its dimension to equilibrate at a particular fluid density for a given pressure. A relation of the bulk pressure with the bulk density To compare the interior and the exterior fluid cases, we reference the density of the interior fluid in terms of density and pressure of the bulk reservoir corresponding to the exterior fluid case. For this, we set up separate simulations of SWCNT inside a bulk argon reservoir  of the SWCNT. The mode shape, ϕ1 corresponds to one of the two degenerate fundamental flexural phonons of the doubly-clamped SWCNT resonator and is obtained using real space quasiharmonic (QHMR) method  ensemble as an isolated system. During this ringdown process, the extra energy of the fundamental flexural phonon is redistributed among all other phonon modes and fluid atoms. Consequently, the displacement, q1(t) and the velocity, q1(t) . Here, Esto is the maximum energy stored during the prescribed deformation. The simulation setup corresponding to setup II  to 160 carbon atoms at the mid-section of the resonator. The purpose is to restrict these atoms from moving in any of the three directions. Setup II is used to carry out equilibrium simulations only.For the purpose of dissipation analysis, we consider two more simulation setups of the fluid-coupled resonator system; setup I and setup II. In case of setup I (shown in Fig. Supplementary Information


Mounting evidence has demonstrated that angiogenesis plays an important role in tumour progression. However, the key regulators in tumour angiogenesis remain unclear. Recently, emerging reports have indicated that SIRT2 plays critical roles in proliferation, metastasis and tumourigenesis in diverse tumours. However, the function of SIRT2 in tumour angiogenesis and the mechanism underlying the regulation of angiogenesis by SIRT2 are still unknown. Here, we found that SIRT2 was upregulated in colorectal cancer tissues compared to that in normal samples and that the elevated SIRT2 was associated with poor prognosis in patients with colorectal cancer. In addition, a series of in vitro and in vivo experiments were performed to demonstrate the role of SIRT2 in tumour angiogenesis. We showed that silencing SIRT2 significantly suppressed tumour angiogenesis. Mechanistically, the knockdown of SIRT2 inhibited STAT3 phosphorylation, causing decreased secretion of VEGFA. Notably, we found that SIRT2 directly interacted with STAT3 and affected the phosphorylation of STAT3 and the translocation of phosphorylated STAT3 to the nucleus. Importantly, a series of rescue experiments suggested that the function of SIRT2 in tumour angiogenesis depends on the STAT3/VEGFA signalling pathway. Our findings provide insight into the important role of SIRT2 in colon tumour angiogenesis and suggest that SIRT2/STAT3/VEGFA might be a novel prognostic biomarker and a potential therapeutic target for patients with colorectal cancer. Although many therapeutic strategies, such as surgical resection, targeted molecular drug therapy and combined chemotherapy, have been performed for patients with CRC, the prognosis of CRC is still unfavourable4.Colorectal cancer (CRC) is one of the most common gastrointestinal tract cancers, and its incidence is increasing in most countries6. During cancer development, angiogenesis is believed to supply abundant nutrients and oxygen for cancer cell survival7. In addition, recent studies have shown that tumour cells strongly promote blood vessel formation by secreting a diversity of angiogenic factors, such as VEGFA, PDGFB, bFGF and EGF8. Currently, antiangiogenic therapy has been reported to effectively improve survival rates of patients with CRC, suggesting that inhibition of tumour angiogenesis is a potential way to treat CRC11. However, antiangiogenic therapy is controversial because patients may have intrinsic or secondary resistance to it12. Importantly, the underlying molecular mechanism of the regulation of angiogenesis remains poorly understood. Thus, it is urgent to further explore the mechanisms of tumour angiogenesis to obtain better therapeutic outcomes in patients with CRC.Accumulating evidence has revealed that angiogenesis, which is a complex process in which new blood vessels arise from pre-existing microvasculature, plays a critical role in tumour development13. Increasing evidence has demonstrated that SIRT2 plays important roles in tumourigenesis and tumour progression. For example, increased expression of SIRT2 is observed in breast cancer, and inhibition of SIRT2 significantly inhibits breast cancer growth14. Consistent with this report in breast cancer, a previous study has also shown that knockdown of SIRT2 decreases liver cancer invasion15. In colon cancer cell lines, pharmacological inhibition of SIRT2 strongly induces cell cycle arrest16. These findings suggest that SIRT2 might act as an oncogene in tumour progression and development. However, in contrast, a previous report has shown that SIRT2-deficient (SIRT2-KO) mice develop certain kinds of tumours through regulation of centrosome amplification17. Lower SIRT2 protein expression has been observed in both human head and neck squamous cell carcinoma and oesophageal adenocarcinoma19. These findings indicate that SIRT2 might function as a tumour suppressor. The above studies clearly show that SIRT2 plays vital roles in tumour progression, such as in the cell cycle and in tumour growth and metastasis, and its roles in tumour development may be dependent on the cellular and tissue context. However, the role of SIRT2 in tumour angiogenesis has not yet been determined.SIRT2 is a histone deacetylase belonging to the sirtuin family of proteinsIn this study, we demonstrated that higher expression of SIRT2 occurs in CRC tissues compared with normal samples. Moreover, both in vitro and in vivo functional assays showed that knockdown of SIRT2 significantly decreased angiogenesis. We further showed that the function of SIRT2 in tumour angiogenesis was dependent on the STAT3/VEGFA signalling pathway in CRC cells. Our findings reveal the novel molecular mechanism by which SIRT2 plays a critical role in angiogenesis and provide a potential targeted therapeutic strategy for treating CRC.To examine the potential role of SIRT2 in CRC development, we first analysed the expression of SIRT2 in normal samples and CRC tissues with the Oncomine database. As shown in Fig. https://www.proteinatlas.org/), we also found that SIRT2 was upregulated in CRC tissues compared with normal samples and that patients with high-SIRT2 levels had a shorter overall survival time -expressing SW48 and SW480 cell lines using two lentivirus containing two different ShRNA sequences against SIRT2. Both western blot and qPCR assays showed that shRNA-SIRT2 effectively reduced the protein and mRNA expression levels of SIRT2 in SW480 and SW48 cells Fig. . InteresAlthough cell proliferation plays an important role in angiogenesis, previous studies have revealed that cell migration is also a vital step in angiogenesis. Thus, we further assessed the role of CM from ShSIRT2 cells in HUVEC migration. As shown in Fig. Mounting research has shown that many tumours secrete a diversity of angiogenic factors  to promote tumour angiogenesis. Thus, we asked if SIRT2 was involved in the secretion of these angiogenic factors. To test this hypothesis, we first examined the mRNA expression of various kinds of angiogenic factors in ShNC SW48 cells and ShSIRT2 SW48 cells. Interestingly, we found that knockdown of SIRT2 significantly inhibited VEGFA expression, but not the expression of other factors Fig. . MeanwhiTo investigate the potential role of VEGFA in SIRT2-mediated tumour angiogenesis, we evaluated the migratory ability of HUVECs incubated with CM from ShSIRT2 SW480 cells and stimulated with VEGFA. As shown in Fig. 21 and have demonstrated the important role of the well-known STAT3 pathway in tumour angiogenesis23, we hypothesized that SIRT2 regulates the secretion of VEGFA via the STAT3 signalling pathway. To test this hypothesis, we examined the phosphorylation and total levels of STAT3 in CRC cell lines. As shown in Fig. Given that previous reports have shown that a specific inhibitor of SIRT2 abolished the STAT3 signalling pathwayTo elucidate how SIRT2 regulates the STAT3 pathway, we analysed protein-protein interactions. We co-transfected HEK293T cells with Flag-STAT3 and HA-SIRT2 plasmids. The western blot data showed that Flag-STAT3 co-immunoprecipitated with HA-SIRT2; consistent with this finding, HA-SIRT2 also co-immunoprecipitated with Flag-STAT3 in HEK293T cell lysates Fig. . In agre24. Next, we transfected ShSIRT2 cells with STAT3C plasmids. Interestingly, we found that the decrease in VEGFA mRNA levels mediated by knockdown of SIRT2 was completely reversed by the overexpression of STAT3C  according to the methods in a previous reportT3C Fig. . More imT3C Fig. , suggestT3C Fig. . In addiT3C Fig. . Taken tTo further confirm the role of SIRT2 in tumour angiogenesis, we created a xenograft model in nude mice via the subcutaneous injection of ShNC SW480 cells or ShSIRT2#1 SW480 cells. Thirty-five days after injection, the mice were sacrificed for subsequent experiments. As shown in Fig. There is increasing evidence supporting an important role of SIRT2 in tumour development. However, the role of SIRT2 in tumour angiogenesis is still unclear. We hypothesized that a possible link exists between SIRT2 and tumour angiogenesis in CRC. In this study, we found that SIRT2 was upregulated in CRC tissues compared with that in matched normal samples. More importantly, we showed that high expression of SIRT2 was associated with a poor prognosis and a late tumour stage in CRC. The most striking finding of this study was that inhibition of SIRT2 inhibited proliferation, migration and tube formation in vitro. Several results suggested that the role of SIRT2 in tumour angiogenesis is dependent on the STAT3/VEGFA signalling pathway. In different CRC cell lines, we demonstrated that silencing SIRT2 markedly decreased the phosphorylation of STAT3 and suppressed the secretion of VEGFA. Furthermore, the suppression of VEGFA signals caused by knockdown of SIRT2 could be reversed by the overexpression of STAT3C. Our in vitro angiogenesis assay demonstrated that impaired tube formation mediated by knockdown of SIRT2 was abolished by the addition of VEGFA or the overexpression of STAT3C. In addition, our data showed that angiogenesis is significantly impaired in ShSIRT2 SW480 mice.25. McGlynn LM. et al. demonstrated that SIRT2 is involved in breast cancer and acts as a tumour suppressor or oncogene depending on the breast tumour grade26. Furthermore, it has been reported that SIRT2 directly deacetylates Slug to prevent Slug protein degradation and then promotes basal-like breast cancer development. In addition, there is a report showing that SIRT2 can promote liver cancer metastasis by regulating EMT progression. These findings clearly demonstrate that SIRT2 is involved in various aspects of tumour progression. However, its precise role in tumour progression is controversial. To date, there have been no studies investigating whether SIRT2 is involved in tumour angiogenesis. Mounting evidence has shown that tumour angiogenesis is critical for cancer proliferation and metastasis, and strategies based on antiangiogenic treatment have achieved definite success. This evidence prompted us to ask whether SIRT2 regulates tumour angiogenesis in CRC, which is one of the most common cancers worldwide. Interestingly, our results showed that SIRT2 was overexpressed in CRC and might be a prognosis marker. In addition, we reported that knockdown of SIRT2 significantly suppressed tube formation in CRC. These data imply that inactivation of SIRT2 in CRC has the potential to suppress CRC development through the regulation of tumour angiogenesis.Previous studies have demonstrated that the role of SIRT2 in tumour progression is dependent on the context of tissue type. In leukaemia cells, SIRT2 promotes cell proliferation via enhancing the production of NADPH27. Of note, many studies have shown that different kinds of cancer exhibit various responses to antiangiogenic treatment due to the abilities of different cancer cells to secrete various angiogenic factors31. We showed, in this study, that knockdown of SIRT2 inhibited VEGFA mRNA expression, but not PDGFB, bFGF or EGF expression. This finding suggested that the role of SIRT2 in tumour angiogenesis might involve VEGFA in CRC. Mechanistically, VEGFA is in fact the master mediator of tumour angiogenesis in different cancer types. Herein, we further demonstrated that the effect of SIRT2 knockdown on CRC angiogenesis was reversed by stimulation with VEGFA in vitro.There exists a common molecular mechanism for tumour angiogenesis. A diversity of angiogenic factors  secreted from tumour cells have been reported to play an important role in tumour angiogenesis34. It is worth noting that STAT3 has been reported to be sufficient to stimulate the secretion of VEGFA under normal culture conditions. However, HIF1A functions as a pro-angiogenic factor mainly under hypoxic conditions35. Similar to the findings for STAT3, we found in this work that inhibition of SIRT2 significantly attenuated tumour angiogenesis under normal culture conditions. Thus, we examined the changes in the STAT3 signalling pathway in CRC cells with inhibited SIRT2. Our results are consistent with previous results indicating that pharmacological inhibition of SIRT2 markedly decreases the phosphorylation of STAT3; in the present study, knockdown of SIRT2 strongly abolished the phosphorylation of STAT3 and delayed nuclear localization in CRC. In addition, we interestingly found that knockdown SIRT2 attenuated the combination of JAK2 and STAT3 to affect STAT3 signalling pathway. We were interested in exploring whether STAT3 was involved in tumour angiogenesis mediated by SIRT2 in CRC, so we conducted related experiments. The results presented herein clearly showed that continual activation of STAT3 could completely reverse the inhibitory effect of SIRT2 inhibition on tumour angiogenesis, suggesting that the role of SIRT2 in tumour angiogenesis is dependent on the STAT3 signalling pathway. Based on our data, we believe that the physiological or pathological inhibition of SIRT2 will be a novel therapeutic strategy for CRC treatment.Several upstream transcriptional factors, such as STAT3 and HIF1A, are known to activate VEGFA and promote the secretion of VEGFA in various cancer typesSW48, SW480 and HUVECs were all purchased from the American Type Culture Collection  and cultured in Dulbecco’s modified Eagle’s medium  supplemented with 10% foetal bovine serum (Gibco BRL) and 1% penicillin/streptomycin in a humidified incubator with 5% CO2 at 37 ℃. Antibodies against GAPDH (sc-137179), Flag (sc-166355) and HA (sc-7392) were purchased from Santa Cruz Biotechnology . Antibodies against SIRT2 (ab211033) and VEGFA (ab1316) were obtained from Abcam . Antibodies against Histone 3 (#4499), JAK2 (#3230), STAT3  and phospho-Stat3 (Tyr705) (#9145) were purchased from Cell Signaling Technology . Human VEGF factors were purchased from Multi Sciences. VEGFA was used to culture HUVEC cells in an amount of 100 ng/ml.Lentiviral vectors containing ShNC  and ShRNA-SIRT2  particles were bought from Shanghai Genechem Co., Ltd. The viral supernatant was used to transduce SW48 and SW480 cells according to the manufacturer’s protocol. STAT3C plasmids were generated using a Fast Mutagenesis System . The primers for STAT3C were 5’-AAGATCATGGATTGTACCTGCATCCTGGTGTCTCCA-3’ and 5’-GCAGGTACAATCCATGATCTTATAGCCCATGATGAT-3’. The full-length SIRT2 was cloned into a pCMV-HA vector. The primers for SIRT2 were 5’-ATGGCAGAGCCAGACCCCTCT-3’ and 5’-TCACTGGGGTTTCTCCCTCTC-3’.20. SIRT2 staining intensity was categorized: no staining as 0, weak as 1, moderate as 2 and strong as 3. The percentage of cells stained was categorized: no positive cells as 0, less than 25% positive cells as 1, 25%–50% positive cells as 2, 50%–75% positive cells as 3 and more than 75% positive cells as 4. We calculated the score of each sample by multiplying the SIRT2 staining intensity with the percentage scale. For statistical analysis, scores of 0 to 7 were considered low expression and scores of 8 to 12 considered high expression.CRC samples and matched adjacent normal tissues were obtained from patients with CRC. All patient tissues used in this study were approved by the Ethics Committee of Tongji Hospital, Wuhan, China, and were collected in agreement with the Declaration of Helsinki. Informed consent was obtained from each patient involved in this experiment before this study was carried out. Immunohistochemistry was performed as described in a previous study3/100 μl) were seeded into 96-well plates and treated with CM from ShNC SW480 cells or ShSIRT2 SW480 cells. At the indicated times , 10 μl of CCK was added to the medium. Following incubation for 2 h, the cell proliferation was assessed by measuring the absorbance of the medium.HUVECs (2 × 104/200 μl) were suspended using medium without serum. Next, cells were seeded into the upper chamber of a transwell chamber, and 500 μl of CM from ShNC cells or ShSIRT2 cells was added to the lower chamber. Then, cells were incubated for 16 h and stained with violet solution. Images were captured with a light microscope.HUVECs . After continuing to incubate for 8 h, the tube formation was observed under an inverted microscope , and the tube formation ability of the HUVECs was assessed by counting the number of branch points.Matrigel (50 μl) was placed into 96-well plates and solidified at 37 °C for 30 min. Then, 3 × 10SW480 cells were seeded on coverslips cultured in 24-well plates. When the cells were attached to the coverslips, they were fixed with 4% formaldehyde and then washed with cold PBS twice. Next, the cells were permeabilized with 0.1% Triton X-100 for 5 min, blocked with 1% bovine serum albumin for 1 h, and treated with the indicated primary antibodies overnight. After being incubated with secondary antibodies and DAPI, the cells were visualized under a confocal laser scanning microscope (Olympus FLUOVIEW FV1000).VEGFA levels were measured with ELISA kits according to the manufacturer’s instructions .For western blot assays, protein samples from tissues or cells were separated by SDS-PAGE and transferred onto PVDF membranes . The bands were incubated with their corresponding primary antibodies at 4 °C overnight and were then incubated with the corresponding HRP-conjugated secondary antibodies for 1 h at room temperature. The bands were visualized with ECL reagents . For immunoprecipitation assays, SW480 cells were cotransfected with Flag-STAT3 and HA-SIRT2 plasmids for 48 h. Then, the cells were harvested and lysed in NP40 lysis buffer for 30 min. The supernatants were precleared with 10 μl of protein A/G agarose beads for 2 h. The Flag or HA primary antibody was added into the supernatants and incubated at 4 °C overnight. After incubation with 50 μl of protein A/G agarose beads for 4 h at 4 °C, the beads were boiled with loading buffer. Then, the protein samples were used for the western blot assay.Total RNA was extracted with TRIzol . Then, cDNA was synthesized using PrimeScriptRT Mix . Then, the mRNA for the indicated genes was detected with an ABI 7300 Real-time PCR (RT-PCR) System using SYBR Green PCR Master Mix . The sequences of the gene-specific primer were as follows: SIRT2: forward: 5’-ATCCACCGGCCTCTATGACAA-3’, reverse: 5’-CGCATGAAGTAGTGACAGATGG-3’; GAPDH: forward: 5’-ATGGGGAAGGTGAAGGTCGG-3’, reverse: 5’-GACGGTGCCATGGAATTTGC-3’; PDGFB: forward: 5’-CTCGATCCGCTCCTTTGATGA-3’, reverse: 5’-CGTTGGTGCGGTCTATGAG-3’; VEGFA: forward: 5’-AGGGCAGAATCATCACGAAGT-3’, reverse: 5’-AGGGTCTCGATTGGATGGCA-3’; bFGF: forward: 5’-AGTGTGTGCTAACCGTTACCT-3’, reverse: 5’-ACTGCCCAGTTCGTTTCAGTG-3’, EGF, forward: 5’-TGTCCACGCAATGTGTCTGAA-3’, reverse: 5’-CATTATCGGGTGAGGAACAACC-3’. VEGFB: forward: 5’- GAGATGTCCCTGGAAGAACACA-3’, reverse: 5’-GAGTGGGATGGGTGATGTCAG-3’; VEGFC: forward: 5’-ATGTGTGTCCGTCTACAGATGT-3’, reverse: 5’-GGAAGTGTGATTGGCAAAACTGA-3’; VEGFD: forward: 5’-TCCCATCGGTCCACTAGGTTT-3’, reverse: 5’-AGGGCTGCACTGAGTTCTTTG-3’; VEGFE: forward: 5’-ATTCACAGCCCAAGGTTTCCT-3’, reverse: 5’-GGGTCTTCAAGCCCAAATCTT-3’ and PGF: forward: 5’-GAACGGCTCGTCAGAGGTG-3’, reverse: 5’-ACAGTGCAGATTCTCATCGCC-3’. GAPDH was used as an internal control.4 SW480 cells stably expressing ShNC or ShSIRT2#1. Beginning 7 days after injection, the tumour volume was examined every week. After 4 weeks, the mice were sacrificed for subsequent experiments. All animal experiments were conducted according to the NIH Guide for the Care and Use of Laboratory Animals and were approved by the Institutional Animal Care and Use Committee at Tongji Hospital.Four-week-old male BALB/c nude mice were purchased from Huafukang Bio-Technology . Sixteen mice were randomly divided into two groups. Then, the mice were subcutaneously injected with 50 × 10All data were analysed with GraphPad Prism 5.0 . Two-tailed Student’s t-tests and Kaplan-Meier analysis were used when appropriate. P < 0.05 was considered statistically significant.supplemental figure 1supplemental figure 2supplemental figure 3supplemental figure 4


Apart from offering insight into the biomechanisms involved in cancer, many recent mathematical modeling efforts aspire to the ultimate goal of clinical translation, wherein models are designed to be used in the future as clinical decision support systems in the patient-individualized context. Most significant challenges are the integration of multiscale biodata and the patient-specific model parameterization. A central aim of this study was the design of a clinically-relevant parameterization methodology for a patient-specific computational model of cervical cancer response to radiotherapy treatment with concomitant cisplatin, built around a tumour features-based search of the parameter space. Additionally, a methodological framework for the predictive use of the model was designed, including a scoring method to quantitatively reflect the similarity and bilateral predictive ability of any two tumours in terms of their regression profile. The methodology was applied to the datasets of eight patients. Tumour scenarios in accordance with the available longitudinal data have been determined. Predictive investigations identified three patient cases, anyone of which can be used to predict the volumetric evolution throughout therapy of the tumours of the other two with very good results. Our observations show that the presented approach is promising in quantifiably differentiating tumours with distinct regression profiles. The power of mathematical models lies in their ability to describe biological phenomena in the succinct language of mathematics, thereby helping to elucidate key mechanisms at play in cancer growth and response to treatment and ultimately develop predictive tools. The literature devoted to mathematical models of tumour response to therapy is vast.The contribution of mathematical modelling in cancer research has been ever-increasing6. The main incentive for all these studies has been the fact that the regression rate of cervical tumours during radiotherapy treatment has been suggested as an important predictor of local control and long-term survival. Importantly, there is a considerable variability among patients in the regression profile of their tumours6; in some cases tumour regression is exponential as a function of time throughout treatment. In others, tumours regress more slowly early in the treatment and the relative volume plots are characterized by an initial shoulder. Huang et al.6 developed a kinetic model incorporating the radiobiological parameters of radiosensitivity, tumour repopulation, and dead cell resolving, and used it to analyze the volume regression data of 80 cervical cancer patients as assessed by serial magnetic resonance imaging (MRI). The patients were treated with external beam radiation therapy (EBRT) followed by low-dose rate intracavitary brachytherapy. 26 patients received cisplatin-based chemotherapy, which was not explicitly modelled. The analysis permitted the estimation of tumour radiosensitivity and dead cell resolving time for individual patients. Moreover, since long-term follow-up data were available, these parameters were correlated with clinical outcome.Focusing on the specific case of cervical cancer response to treatment, important recent contributions includeet al.5 weekly MRI was used to measure tumour volume during EBRT treatment and oxymetry with the Eppendorf electrode to assess pre-treatment tumour hypoxic fractions. The radiobiological parameters included in the mathematical model were the in vivo surviving proportion of cells after 2 Gy (SP2), the cell clearance constant (TC), and the cell doubling time after the onset of accelerated repopulation (Tp). The model was fitted to the MRI-derived tumour volumes of 27 patients. The results indicate that SP2 and TC strongly influence the shape of the volume-response curves, while SP2 correlates with the pretreatment measurements of hypoxia.In the study of Lim et al.4 developed a model consisting in two ordinary differential equations to study the volume regression profiles of 15 cervical cancer patients, as assessed by computed tomography imaging, and performed their analyses both on a cohort- as well as on a patient-specific base. Lately, Arnesen et al.3, utilized a previously developed mathematical model of tumour shrinkage during fractionated radiotherapy7 to study the regression data of 25 cervical cancer patients. The model was based on similar biological parameters as the previous described ones: the doubling time of viable cells, the half time for clearance of doomed cells and the radiosensitivity parameter α of the well-known Linear Quadratic (LQ) model. The authors additionally studied three different fractionation patterns for dose escalation.Similarly, Belfatto 1. The incorporation of several biological phenomena in such complex models necessitates a large number of parameters with currently unidentified or very large value ranges. This implies the need to search very large parameter spaces in order to fit the model to clinical data. The experimental or clinical measurement of several parameters may be particularly laborious or currently impossible. An intuitive grasp of the implications of the values of such low-level parameters may even be practically infeasible in the clinical setting. Such issues have generally hindered the clinical application of multiscale mathematical oncological models.All these studies show the value of exploiting patient specific data through the use of mathematical models for studying the biological mechanisms regulating cervical cancer response to treatment, with numerous potential applications in the future. The applied mathematical models have been kept deliberately simple, and the considered radiobiological parameters were limited, in order to facilitate the integration of imaging-derived patient-specific data and the correlation analyses. It indeed remains a significant challenge to achieve a satisfactory compromise between the need to describe more realistically the involved biological mechanisms and the goal to develop clinically relevant and personalizable mathematical models that integrate multiscale biological data8 is a multiscale computational model of cervical cancer response to radiotherapy treatment in the patient-individualized context. The clinical orientation of the model has been a fundamental guiding principle throughout its development. CERONCO parameters are related to the explicit description of several important biological mechanisms. Central aims of this study were to clinically adapt CERONCO by exploiting sets of real multi-scale biodata, in a way that the previously described difficulties are minimized, and to demonstrate the potential of the model to offer qualitative and quantitative information on the regression profiles of cervical tumours, complementary to that of more simple radiobiological models.The CERvical cancer ONCOsimulator (CERONCO), developed within the context of the EU-funded DrTherapat projectFor this purpose, a clinically–enhanced model parameterization methodology has been designed. The central idea of the proposed methodology lies in a tumour features-based search of the parameter space. The proposed algorithm creates a one-to-many correspondence between a number of user-selected clinically meaningful tumour features and CERONCO’s model parameter values. These features do not constitute parameters of the mathematical model; instead, based on their values the system automatically assigns adequate values to the model parameters. In this way, an interface between the clinical and the mathematical reality of the studied tumours is devised, which is expected to significantly facilitate the usage of the model and the interpretation of its results in the clinical setting.Additionally, a methodological framework for the predictive use of the model was designed, which includes a scoring method to quantitatively reflect the similarity and bilateral predictive ability of any two tumours in terms of their regression profile. In the following sections, this framework is presented along with the results of predictive tests that have been performed at this stage of our research, by exploiting the datasets of eight cervical cancer patients.CERONCO is a predominantly discrete multiscale computational model of cervical cancer response to treatment  in the patient-individualized context. It makes use of the available multiscale  longitudinal data of the patient. CERONCO follows a cellular automaton approach.11 For basic concepts with regards to cisplatin chemotherapy modeling see11 and with regards to External Beam Radiation Therapy (EBRT) modeling see13, For related sensitivity analyses see11, A new simulation module has been developed for Pulsed Dose Rate Brachytherapy (PDR-BT) modeling. This module is presented below, along with a basic outline of the main simulation model, to facilitate the understanding of the current work.Core algorithms of the model can be found in our previous publications. These algorithms have been adapted and combined as necessary in order to address the particularities of the considered cervical cancer treatment. For the general features of the model see9 cells/cm3, unless more specific information for a particular tumour is available); each cell can belong in any of the following five classes: Stem cell; LIMP cell ; Terminally differentiated cell; Apoptotic cell; Necrotic cell. The cell cycle phases  and the dormant (G0) phase constitute subclasses in which stem or LIMP cells may reside.The region of interest  as derived from the imaging data is represented by a three-dimensional discretization mesh. The elementary volume of the mesh is called Geometrical Cell (GC). At initialization, each GC accommodates a number of biological cells  and β (beta) parameters are the linear and the quadratic radiosensitivity coefficients, respectively, of the irradiated cells.A new module simulating PDR-BT treatment has been developed, based on the modified LQ model with correction for incomplete repair21. It considers two cell-killing components: a linear component  and a quadratic component (beta component). The parameters alpha and beta determine the initial slope and the degree of downward curvature, respectively, of the survival curve. According to the most common mechanistic interpretation, the yield of lethal lesions is the sum of lethal lesions produced from single radiation tracks  and lethal lesions produced from two radiation tracks ; i.e. the latter quantifies the interaction of sublethal events. The dose at which these two components of cell killing are equal is the alpha/beta ratio. Since sublethal lesions can be repaired prior to resulting in a lethal event, the beta component is modified by the Lea-Catcheside time factor (GN) to take into account dependence on dose protraction or fractionation21. Protracting the exposure time potentially allows the first lesion to be repaired before the second is produced, and the LQ approach quantifies this effect21. In general, GN is determined by the rate of sublethal damage repair and the particular fractionation pattern with which the dose is delivered. It is a dimensionless quantity that can take values from 0 to 1. For acute exposures The LQ model is based on the curvilinear nature of dose-response curves for the log of cell survivalN factor calculation for PDR-BT appear in literature22, The computation of the GN factor is based on the temporal characteristics of the dose  and the irradiated cells’ repair half-time T1/2. Repair is assumed to follow first-order kinetics and is modelled by a monoexponential function with rate constant μ . 23:For the first pulse the following equation is usedEquation  can be dEquation  is a mod10. The first one updates the state of each GC by applying the rules of the cytokinetic model of Fig. Following tumour initialization (section “The tumour profile concept”), at each subsequent time step the mesh is scanned and the spatiotemporal evolution rules are applied. Each complete scan can be viewed as consisting of two sequential scansA concise description of CERONCO tumour dynamics parameters is given in Table 24. The therapeutic protocol involves EBRT with concomitant cisplatin, followed by two PDR-BT fractions. Follow-up data were not available.Eight patients with squamous cervical carcinoma have been included in our study Midterm (during EBRT)BT0 (before start of BT)BT1 (start of first BT fraction)BT2 (start of second BT fraction)The patient-specific imaging data included T2 weighted MRI-derived 3D reconstructions of the Gross Tumour Volume for up to five time points:These 3D-reconstruction files supply the model with the tumour’s spatial information and correspond to the region of interest onto which the discretizing mesh is superimposed. Each GC of the mesh is labeled as tumour or non/tumour. BT1 and BT2 spatial dose distribution files  are provided as well. For a short outline of the procedure used to create the above files see Supplementary Material Section .EBRT schedule: total dose, number of fractions, fractionation scheme Cisplatin administration schedule (number of cycles − once per week)PDR-BT schedule . The GC pulse dose is derived from the total dose distribution file, by dividing the total dose to the GC by the number of pulses. The interval between successive pulses is 1 hour and the pulse duration is variable (0.2–0.3 hours).Patient-specific treatment data included:All patient information was given in the context of the EU-FP7 project DrTherapat, Grant agreement no. 600852. Patient information was obtained with due observance of the rights of all patients involved and in compliance with all applicable laws and regulations, including the Declaration of Helsinki as revised by the World Medical Assembly, as well as the applicable procedures and the internal guidelines of the institution. Prior to the disclosure of the patient information the clinical institution has obtained appropriate informed consents from all the patients involved, or approval from the applicable ethical review board has been obtained, all in compliance with Applicable Patient Regulations. The patients were accrued at Aarhus University Hospital and the name of the ethical committee is “Videnskabsetisk komité, Region Midt, Denmark”.A new virtual tumour initialization and parameter estimation workflow has been designed.“the tumour profile”:Growth FractionHypoxic FractionDead FractionAdditionally, the user selects:A cisplatin cell kill rate (CKR) value, reflecting the chemosensitivity of cancer cells to cisplatind) value or a series of Td values.A tumour volume doubling time , which in turn are expected to exhibit variable response to therapy and long-term evolution.30, Recently, imaging-based methods have been also reported34. DF estimation can be based on MRI data, as was the case in our study. Similarly, literature abounds with methods for estimation of tumour volume doubling time36.If the user cannot acquire tangible patient-specific information about the tumour features, then they can test candidate scenarios. Otherwise, the available data should be used in order to refine the initialization procedure. GF and HF estimation in cervical cancer has been intensely researched, e.g. through Ki-67 studies and polarographic electrodes, respectively16. Previous model sensitivity analyses indicate that this tumour feature has a profound impact on the result of therapy37. We have therefore decided to expose this crucial tumour characteristic as an adjustable feature of a simulation, in order to offer the possibility of testing several explicit scenarios.In sharp contrast, information about cisplatin chemosensitivity of cervical cancer cells is rather scarce; some efforts have addressed this issue as wellclin, the latter calculated based on the real tumour’s GTV data, at all timepoints for which volumetric data are available. Following initialization, tumour evolution is simulated according to the patient-specific treatment data. When the simulation is complete, the algorithm checks whether there is longitudinal volumetric agreement between the simulated and the clinical tumour, taking into account possible tumour delineation errors. A solution is a set of model parameter values for which the simulated tumour’s Volume Reduction Percentage (VRP)38, several different criteria for volumetric compliance were tested:The deviation thresholds between the clinical and simulated tumour VRPs have been chosen so as to reflect the existence of the abovementioned possible tumour contouring errors. Since the exact magnitude of such errors is unknown38. Depending on the specific value of a tumour’s volume at a particular timepoint, this criterion may be stricter or more lenient than VRP 10.The last criterion has been based on clinical experience with regards to delineation errors for the case of cervical cancerThe described workflow ensures a multi-level compliance of the virtual tumour with: (a) the predefined tumour features, (b) longitudinal volumetric data, (c) any tumour characteristics for which clinical data are available , and (d) biologically plausible value ranges of the model parameters and the derived therefrom tumour characteristics. These have been retrieved from literature for the specific tumour histological type whenever possible.39:The use of a performance criterion serves for quantitatively representing the agreement of a derived solution with the real volumetric data; the error-measure Mean Absolute Error (MAE) was chosenSolutions with lower MAE values imply better agreement with the clinical data.For each patient, and for each tumour profile and CKR value, the parameter estimation algorithm typically identifies a large number of solutions with tumour doubling times within the acceptable value range, which all belong to a particular solution family. We have observed that it is possible to use the members of a specific solution family in order to identify a single parameter value set that could be assigned to a specific patient, tumour profile, and CKR-value combination. This characteristic set is created by assigning to each parameter the mean of the corresponding values in the solution family.mean-value-set: the VRP for the simulated mean value parameter tumour.New simulation runs have been performed using these mean value parameter sets. Their performance in terms of volumetric agreement with the real tumour, and therefore their effectiveness in representing a particular tumour profile of a patient, can be quantified by using the Mean Absolute Error (MAE) of equation :15\documThe mean value derived from equation  for all Figure Since the number of patients was limited, a formal evaluation of the predictive ability of CERONCO was out of the scope of our work. Nevertheless, a set of predictive tests has been performed. These tests are based on the consideration of patient pairs, wherein the mean value set assigned to a specific patient and tumour profile is used to predict the evolution of another patient’s tumour for the same tumour profile (and vice versa).By running simulations for patient B, Profile I, and each CKR value separately, using the corresponding mean value parameter sets of patient A, we can compute the When for a particular profile only one of the two clinical cases of a pair has retrieved solutions, then the MAE value of the single available run is assigned to the pair error. This simplification involves 2 out of the 8 patients, and has been adopted in order to preserve the generality of the pair methodology.A<−>B is, the higher is the similarity in volumetric regression terms between A and B and the bilateral predictive ability of A and B. As exemplified in the following sections, through the pair methodology the similarity of the regression profiles of any two tumours is reflected quantitatively in their We can expect that the lower MAE40 we have considered a relatively low HF value. The cell kill rate of cisplatin has been tested from very low to rather large values (0.0–0.5). The tumour volume doubling times cover the entire value range reported in literature, with an increment of 20 days in the lower Td region, up to 500 days, and an increment of 500 days subsequently.Two tumour profiles have been studied for each patient: {GF = 60%, HF = 30%, DF = 5%} and {GF = 10%, HF = 30%, DF = 5%}. These are two characteristically different regions of the profile space and produce tumours with very different behaviour (a high proliferative vs a low proliferative one). The dead fraction was kept low, since the tumours had no initial necrotic components. The only exception was patient 71, but in this case too the MRI-calculated initial necrotic diameter is very small compared to the entire tumour’s equivalent diameter, and is well in agreement with a DF value of 5%. Since necrotic regions are typically associated with hypoxic regionsSupplementary Table Each solution represents a distinct tumour scenario compatible with the data of a patient. Different solutions imply different constitutions of the initial tumour in terms of the various tumour cell populations. These in turn result to variable post-therapy tumour constitutions, which are expected to display variable tumour regrowth potential. Such a characteristic example is presented in Supplementary Fig. Supplementary Tables Subsequently, the mean value parameter sets were constructed and new simulation runs have been performed, in order to test their capability to represent each tumour profile/CKR value combination. Figures A special note should be made about patient 86, for which volumetric data were available for two time points only (pre-therapy and BT0) which is equivalent to a more relaxed constraint. As expected, longitudinal model fitting in this case is generally easier compared to the cases where more time-points are available. As a result, the simulation returns a large number of accepted parameter value sets with very small MAE values. It is expected that many of these parameter value sets would be rejected if more time points with volumetric data were available. This observation stresses the importance of acquiring longitudinal volumetric and other data, and reveals the advantage of modeling approaches able to handle such longitudinal data.In order to get tumour scenarios compatible with the clinical data, the low proliferative tumour profile retrieves in general tumour scenarios of higher radiosensitivity and larger tumour doubling times, compared to the high proliferative profile. No important differences are observed with regards to the tumour cell cisplatin chemosensitivity (Supplementary Table −1) (Supplementary Table −1)  that are much closer to the mean values reported in literature compared to the high proliferative one (45–62 h).The constraint of volumetric data coupled with the choice of the highly proliferative profile leads to radiosensitivity values lying close to the lower end of the literature-reported range .A similar observation holds true for the vast majority of pairs incorporating cases 77 or 95. These clinical cases are exceptional because they practically show no tumour shrinkage at the midterm timepoint  and low tumour regression subsequently. This is a highly plausible explanation for their relative inadequacy to predict or be predicted by the other clinical cases; particularly so since their mutual similarity and predictive ability is high.The above constitute a strong indication that the pair methodology, through the use of the mean value sets, is promising in differentiating in a quantifiable way tumours with different regression profiles. The similarity of the regression profiles is reflected in the assigned MAE errors. Pairs formed by cases with similar regression profiles are assigned lower MAE errors compared to pairs formed by tumours with highly divergent regression profiles.One of the main aims of this study was the design of a clinically-meaningful parameterization methodology for the CERvical cancer ONCOsimulator. This was accomplished through a tumour features-based search of the parameter space. The methodology was applied to eight cervical cancer patients.For each patient, the simulations retrieve adaptation solutions, i.e. sets of model parameter values that result in virtual tumours whose evolution is compliant with: (a) the chosen tumour profile, (b) clinical data , and (c) biologically plausible value ranges of the model parameters and virtual tumour features. Each solution belongs to a specific tumour profile family of solutions and represents a distinct tumour scenario compatible with the data.A methodological framework for the predictive use of the model was also sought. As a first step towards this direction, we have studied the solutions of each tumour profile for each patient, and new parameter value sets were created by assigning to each parameter the mean of the corresponding values in the solution family. This part of our study revealed that each profile of each patient can be adequately represented by a single parameter value set for each CKR value tested.A series of predictive investigations was subsequently performed. These were based on the consideration of patient pairs, wherein the single parameter value set assigned to a specific patient and tumour profile is used to predict the volumetric evolution of another patient’s tumour for the same profile (and vice versa). While bearing in mind all the shortcomings resulting from the limited number of patients, the methodology permitted a quantitative estimation of the tumours’ similarity and bilateral predictive ability in terms of their regression profile. Three patients have been identified, anyone of which can be used to predict the evolution of the tumours of the other two with very good results. At the same time, clinical cases with “outlier” regression profiles proved inadequate for the same purpose, supporting the relevance of the approach. Our observations show that the presented approach is promising in differentiating, in a quantifiable way, tumours with different regression profiles, a result that supports the model’s use in a predictive setting.The simulation results indicate the inherent capacity of CERONCO to discern tumour profiles that are compatible with the actual evolution of a clinical tumour from incompatible ones, thereby complementing the characterization of a tumour when experimental/clinical information is lacking. When many different scenarios are in accordance with the observed tumour behaviour, CERONCO can specify which clinical/experimental information could be sought to narrow down the number of compatible tumour scenarios. It can also suggest plausible value ranges for currently unidentified parameters.Our results also show that agreement with clinical data in volumetric terms alone may mask tumours with radically different characteristics and, hence, prognosis. This can be illustrated intuitively in the form of tumour relapse experiments, where tumours of different profiles, all compliant with the longitudinal volumetric data, may have a very different constitution in terms of the distinct tumour cell subpopulations having survived the treatment. These different post-therapy tumour constitutions are expected to display variable tumour regrowth potential. Such studies with CERONCO are ongoing and planned to form the subject of a dedicated publication.Parameter estimation:training set), using a dense search of the tumour profile space. The number of candidate profiles can be reduced if specific information about the tumour profile or other features is available, through imaging or other studies, as well as if follow-up data are made available.CERONCO parameter estimation for a subset of patients .Classifier construction:Use of machine learning approaches for the identification of features that can define different patient classes. The goal will be to derive triple combinations of the form: patient class/tumour profile/assigned parameter value set.Validation:validation set) to evaluate predictive simulations, based on each patient’s class .Use of an independent set of patients (All these observations carry important implications for the future clinical validation of CERONCO. A formal validation framework can be briefly outlined as follows:Clinical validation of complex multiscale models is a demanding long-term process, presupposing extensive interdisciplinary effort to overcome numerous challenges. The presented proof-of-concept results lend support to the possibility of using CERONCO for the prediction of response of cervical tumours to the considered treatment protocol, provided that rich clinical datasets are made available. It should be noted that the core modeling algorithms and the presented methodology is fairly easily applicable to other types of cancer as well.Supplementary Material for revised manuscript


A high HLA expression in uveal melanoma (UM) is part of the prognostically unfavorable inflammatory phenotype. We wondered whether the presence of soluble HLA (sHLA) in the aqueous humour is associated with clinical, histopathological or genetic tumour characteristics, and represents tumour HLA expression and intratumoural inflammation. Aqueous humour from 108 UM patients was analysed for the presence of sHLA, using a Luminex assay specific for HLA Class I. Clinical and genetic parameters were compared between sHLA-positive and negative eyes. A qPCR analysis was performed on tumour tissue using a Fluidigm assay. In 19/108 UM-containing eyes, the sHLA level in the aqueous was above the detection limit. Tumours in sHLA-positive eyes were significantly larger, more frequently involved the ciliary body, and more often showed monosomy 3, gain of chromosome 8q and loss of BAP1 staining. Melanoma-related survival was worse in patients with sHLA-positive aqueous humour. sHLA in the aqueous did not represent the tumour’s HLA expression and did not relate to immune cell infiltration in the tumour. We conclude that UM-containing eyes may contain sHLA in the aqueous humour, where it is a prognostically-unfavourable sign and may influence local immune responses. Although rare, with an incidence varying between 5.0 per million in the United States of America to 9.5 per million in Northern Europe, uveal melanoma (UM) is the most common primary ocular malignancy in adults ,2. The mPrognostically-infaust tumours often carry an inflammatory phenotype, which is characterised by infiltrating lymphocytes and macrophages and a high expression of HLA Class I ,12,13. TInformation regarding the HLA expression level of the tumour might be obtained by studying the non-cell bound or soluble version of HLA (sHLA) in the aqueous humour. The presence of soluble HLA was first found in plasma of healthy HLA-A2 positive individuals in a study in 1970 in Leiden, The Netherlands . The sHLSince its discovery, sHLA has been determined in different body fluids, including blood, plasma, amniotic fluid, seminal plasma, synovial fluid, sweat, urine and peritoneal dialysate. Levels of sHLA have been studied in the context of acute and chronic graft-versus-host disease, preeclampsia, rheumatoid arthritis and chronic renal failure ,24,25,26For enucleated UM patients, prognostic information comes from the tumour’s size, and its chromosome and mutation status. Knowledge regarding the immune status of the tumour and its HLA expression may one day be useful in deciding whether immunotherapy may be appropriate as adjuvant therapy to prevent metastases. We developed and optimised an assay to assess sHLA Class I in small amounts of anterior chamber fluid and determined whether we can detect this in the aqueous humour of UM-containing eyes. The assay recognises the soluble version of HLA Class I. Our data show that it is possible to determine sHLA Class I levels in the aqueous humour of UM eyes, and that the presence of sHLA is related to survival, but that this is more related to the presence of a large, anteriorly-located tumour than to the expression of HLA on the tumour cells.A high expression of HLA antigens on UM cells is an indicator of inflammation and of a bad prognosis. We wondered whether analysis of sHLA molecules in aqueous humour can be used to indirectly determine HLA expression as an indicator of the presence of an inflammatory phenotype in the tumour, and whether sHLA expression in the aqueous humour is higher in eyes with a high-risk UM. Using a newly-developed Luminex assay, we measured sHLA in aqueous humour samples of 108 UM-containing eyes and observed measurable levels in 19/108 (18%). We compared the characteristics of these 19 sHLA-positive cases with those of the 89 sHLA-negative cases (see p < 0.001), and more often involved the ciliary body (p < 0.001). Tumours from the sHLA-positive group belonged to higher American Joint Committee on Cancer (AJCC) stages (p < 0.001).The tumours in the sHLA-positive group were thicker, with a mean tumour prominence of 9.8 mm (SD = 2.2 mm) versus a mean prominence of 7.0 mm (SD = 2.9 mm) in the sHLA-negative group (p = 0.034). Additionally, the sHLA-positive group more frequently showed gain of 8q  as opposed to the sHLA-negative group , but no difference was observed with regard to chromosome 6p (p = 0.98). A total of 16/18 (89%) of the tumours in the sHLA-positive group had lost BAP1 staining, which was significantly different from the 50/79 (63%) tumours in the sHLA-negative group (p = 0.036).With regard to chromosome status, the sHLA-positive group showed significantly more often monosomy 3  compared to the sHLA-negative group    patients developing metastases versus 36/88 (41%) patients in the negative group (= 0.025) .2M expression between the sHLA-negative and sHLA-positive groups, no significant differences were found   .p = 0.38, p = 0.73, p = 0.52, p = 0.78, p = 0.52 and p = 1.00, respectively)  (Mann–Whitney U test), no significant difference between the two groups was observed (ctively) . This imp = 0.02 and p = 0.003, respectively).We found no correlation between the tumour’s HLA expression and the presence of sHLA in the aqueous humour, nor any evidence for a relation between the tumour’s infiltrate profile and the presence of sHLA in aqueous humour. This made us wonder what else might determine the presence of sHLA. We already noticed that several clinical and genetic prognostic parameters were strongly associated with the presence of sHLA. We performed a multivariate regression analysis with data on chromosome 3 status, tumour prominence and involvement of the ciliary body, to see which characteristic is predominant in determining the presence of sHLA in the aqueous humour . When coThis is the first study describing the presence of sHLA in fluid of the anterior chamber. Due to the prognostic importance of an inflammatory phenotype in UM, we focused on determining whether the soluble form of cell-bound HLA Class I exists in the aqueous humour, and whether it corresponds to HLA expression on the tumor itself, and which clinical and histopathological characteristics of the UM determine its presence. We found measurable levels of sHLA in 19/108 of the aqueous humour samples from UM eyes, but no correlation with the level of expression of HLA in the primary tumour. However, there were other clear correlations; e.g., between tumour size and location, and with genetics: The sHLA-positive eyes contained tumours with a significantly larger prominence, which were more often located in the ciliary body and had a higher AJCC stage. With regard to chromosome status, the sHLA-positive eyes were significantly more often M3 tumours, with a gain of 8q, and loss of BAP1 protein expression. The association between involvement of the ciliary body and M3 is well known . HLA expMost studies on the presence of sHLA, in serum samples from metastatic cutaneous malignant melanoma patients, focus on the sHLA form of HLA-G and not on HLA-A/B . StudiesCurrent treatment options for metastatic UM are limited, but new therapies based on immunologic principles are being developed. One study on glioblastoma describes the potential of sHLA as the basis to identify potential biomarkers for disease detection and treatment . sHLA mo+ T lymphocytes [Other studies focus on the mechanism by which sHLA plays a part in tumor-escape. It is thought that sHLA Class I molecules induce apoptosis of cytolytic effector cells; e.g., Natural Killer (NK) cells and CD8phocytes ,38,39.A limitation of this study is the absence of a comparison of aqueous humor of UM eyes to normal eyes and eyes with other conditions. We tested a limited number of ocular fluids from normal eyes that underwent cataract surgery, and obtained negative results, which was expected as previous studies have shown low or undetectable levels of a wide range of cytokines in the normal aqueous humor . Now thaAnother limitation of this study is that the aqueous samples were only acquired from enucleated eyes, of which the tumours are usually large. It would be interesting to expand this analysis to eyes undergoing irradiation treatment. Additionally, as this assay detects the backbone of the HLA Class I molecule, while another addition would be to expand the assay to detect different HLA alleles to see whether they are expressed at the same level.This study was conducted at the department of Ophthalmology, Leiden University Medical Center (LUMC), Leiden, The Netherlands. Aqueous humour samples were obtained from eyes of 108 UM patients who had been enucleated at the LUMC, between 1999 and 2017. Clinical patient information and data on survival were obtained from patient charts and the Dutch National Cancer Registry, and collected in a database. Follow-up time was defined as the time period between the date of enucleation and the moment of death or the last recorded follow-up moment. Data was updated in June 2019. Of the 108 patients, 45 had died from metastases, 19 from other causes and 44 were still alive at the end of follow-up.Enucleated eyes underwent conventional histopathological evaluation by a pathologist specialised in ocular pathology. Tumour, lymph node and metastases (TNM) were staged in accordance with the 8th edition of the American Joint Committee on Cancer (AJCC) staging manual .Directly following enucleation, an anterior chamber puncture was performed to collect a sample of aqueous humour, using a 23 Gauge needle, and samples were directly stored at −80 °C. Additionally, a tumour sample was collected for cytogenetic analysis, as well as for DNA and/or mRNA analysis. Tumour tissue was fixed in 4% neutral buffered formalin for at least 48 h, dehydrated and embedded in paraffin.2M-PE . The Bio-Plex LuminexTM system  was used for read-out.Soluble HLA Class I in the anterior chamber fluid was measured using an in-house developed assay and optimised for use with aqueous humour. This assay uses magnetic beads coupled to anti-HLA-Class I directed, and purified W6/32 antibody , and the detection antibody anti- βMeasuring the levels of sHLA in aqueous humour by magnetic Luminex assay was newly developed, and is based on a previously-described assay . First, As this was the first time that aqueous humour samples were tested, optimal dilutions were determined first. The test values were interpolated in the calibration line. Samples below the lower limit of quantification were categorised as negative.For the 108 samples included in this study, three different cytogenetic tests were performed to determine the tumours’ chromosome statuses. On 36/108 tumours, both karyotyping and fluorescence in situ hybridisation (FISH) analysis with the use of DNA probes designed specifically for the centromere of chromosome 3, were performed. Twenty-three Tumours were analysed using a genome wide micro-array analysis of single-nucleotide polymorphisms (SNPs), performed with the Affymetrix 250K Nsp array , as previously described . A totalA qPCR Fluidigm 96.96 dynamic array  was performed on tissue from 94 tumours. RNA isolation and quality checks were performed as previously described . Total Rp values of <0.05 were considered statistically significant. Statistical analyses were performed using SPSS software . The Pearson chi-square test was used to analyse categorical data and a Linear-by-Linear Association was used in case of more than two categories. The Mann–Whitney U Test was used as a non-parametric test to compare two groups. For multivariate analysis, a multivariate linear regression was conducted. Kaplan–Meier curves were made to analyse survival, with the log rank test to compare groups and were drawn using GraphPad Prism version 5.00 for Windows, GraphPad Software, La Jolla, CA, USA. This study was approved by the Biobank Committee of the LUMC . The research adhered to Dutch law and the tenets of the Declaration of Helsinki .Soluble HLA is especially present in the aqueous humour of large tumours, which display ciliary body involvement, loss of chromosome 3, and negative BAP1 staining, and which have a higher chance of developing metastases. As sHLA is related to metastasis development, the presence of detectable levels of sHLA in the aqueous humour may aid in selecting cases for future adjuvant trials or aid in prognostication, without having to take tumour material from mateiral or a tumour biopsy.