Kang-Ling Liao’s research while affiliated with University of Manitoba and other places

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Publications (9)


Adaptive Immunity Determines the Cancer Treatment Outcome of Oncolytic Virus and Anti-PD-1
  • Article

January 2025

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2 Reads

Bulletin of Mathematical Biology

Kang-Ling Liao

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Kenton D Watt

The immune checkpoint inhibitor, anti-programmed death protein-1 (anti-PD-1), enhances adaptive immunity to kill tumor cells, and the oncolytic virus (OV) triggers innate immunity to clear the infected tumor cells. We create a mathematical model to investigate how the interaction between adaptive and innate immunities under OV and anti-PD-1 affects tumor reduction. For different immunity strength, we create the corresponding virtual baseline patients and cohort patients to decipher the major factors determining the treatment outcome. Global sensitivity analysis indicates that adaptive immunity has more control on the treatment outcome than innate immunity, and whether anti-PD-1 cancels out the OV treatment efficacy depends on the OV dosage and the balance between clearance of infected tumor cells and OV by T cells. The optimal OV infection rate and dosage suggest that OV treatment is more sensitive to adaptive immunity than innate immunity. Our model prediction also indicates that tumor reduction is more sensitive to anti-PD-1 efficacy as adaptive immunity becomes stronger, and anti-PD-1 trends to cancel out the OV treatment efficacy as innate immunity becomes stronger. Based on these results, the recommended treatment protocol for patients with different immunity strength can be determined.





Figure 1. The system network. Tumor cells trigger the immune responses that attract T cells to kill tumor cells. T cells produce IFN-γ, and IFN-γ promotes the production and activation of T cells. IL-27 promotes the activation of T cells and inhibits the production of IFN-γ by T cells. The PD-1-PD-L1 inhibits the activation of T cells and IL-27 promotes the expression of PD-1 and PD-L1 resulting in an increased amount of PD-1-PD-L1. Thus, the increased PD-1-PD-L1 by IL-27 inhibits the immune responses of T cells by tumor cells and the production of T cells by IFN-γ and by IL-27, which are shown by the dashed non-arrow lines and curves. The formation of PD-1-PD-L1 is inhibited by anti-PD-1 (G), due to the binding between anti-PD-1 and free PD-1. Thus, the reactions shown by the dashed non-arrow lines are suppressed by the anti-PD-1. The arrows represent the promotion reaction and the non-arrow lines represent the inhibition reaction.
Figure 2. Dynamics of the model (2.5) under a low dose of IL-27. (A)-(C) show the dynamics of tumor cells, T cells, and IFN-γ of cases (i)-(iv) with the dosage of IL-27 f 0 = 1.1 × 10 −6 g/cm 3 , respectively. The black solid, red dashed, green dashed-dotted, and the blue dotted curves represent the cases (i) Ctrl-IL27/Ctrl-Ab, (ii) Ctrl-IL27/Ab, (iii) IL27/Ctrl-Ab, and (iv) IL27/Ab, respectively. The horizontal axis and vertical axis represent the time with unit days and the density of each variable with unit g/cm 3 , respectively.
Figure 3. Dynamics of the model (2.5) under a high dose of IL-27. (A)-(C) show the dynamics of tumor cells, T cells, and IFN-γ of cases (i)-(iv) with the dosage of IL-27 5f 0 = 5.5 × 10 −6 g/cm 3 , respectively. The black solid, red dashed, green dashed-dotted, and the blue dotted curves represent the case (i) Ctrl-IL27/Ctrl-Ab, (ii) Ctrl-IL27/Ab, (iii) IL27/Ctrl-Ab, and (iv) IL27/Ab, respectively. The horizontal axis and vertical axis account for the time with unit days and the density of each variable with unit g/cm 3 , respectively.
Figure 4. Heat map of R(I 27 , G) for the model (2.5). This figure shows the heat map of the tumor cell density ratio R(I 27 , G) defined as Eq. (3.1), where I 27 ∈ [0, 5.5 × 10 −6 g/cm 3 ] = [0, 5f 0 ] and G ∈ [0, 0.4]. The horizontal and vertical axes represent the values of I 27 with unit f 0 = 1.1 × 10 −6 g/cm 3 and G, respectively. Each point represents the value R(I 27 , G) where the maximum is around 1.16628 and the minimum is around 1.3 × 10 −4 . The colour bar shows the values of R(I 27 , G). The red curves represent the contours and the pink curve displays the critical curve F c (G).
Figure 5. The logarithmic-relative sensitivity curves of model (4.1) for group (I). The first, second, and third rows show the logarithmic-relative sensitivity curves for the model (4.1) with G = 0.1 and I 27 = 0.1f 0 = 1.1 × 10 −7 g/cm 3 (case (I-i)), I 27 = f 0 = 1.1 × 10 −6 g/cm 3 (case (I-ii)), and I 27 = 5f 0 = 5.5 × 10 −6 g/cm 3 (case (I-iii)), respectively, to all parameters p. The first, second, and third columns are the results of p × C p (t)/C(t), p × T p (t)/T (t), and p × I γ (t)/I γ , respectively. The horizontal and vertical axes represent time during [0, 21] days and the normalized value p × X p /X for each parameter p and variable X, respectively.

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Combination therapy for cancer with IL-27 and anti-PD-1: A simplified mathematical model: Combination therapy for cancer with IL-27 and anti-PD-1
  • Article
  • Full-text available

December 2022

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66 Reads

Mathematics in Applied Sciences and Engineering

Many experiential and clinical trials in cancer treatment show that a combination of immune checkpoint inhibitor with another agent can improve the tumor reduction. Anti Programmed death 1 (Anti-PD-1) is one of these immune checkpoint inhibitors that re-activate immune cells to inhibit tumor growth. In this work, we consider a combination treatment of anti-PD-1 and Interleukin-27 (IL-27). IL-27 has anti-cancer functions to promote the development of Th1 and CD8+^+ T cells, but it also upregulates the expression of PD-1 and Programmed death ligand 1 (PD-L1) to inactivate these T cells. Thus, the functions of IL-27 in tumor growth is controversial. Hence, we create a simplified mathematical model to investigate whether IL-27 is pro-cancer or anti-cancer in the combination with anti-PD-1 and to what degree anti-PD-1 improves the efficacy of IL-27. Our synergy analysis for the combination treatment of IL-27 and anti-PD-1 shows that (i) ant-PD-1 can efficiently improve the treatment efficacy of IL-27; and (ii) there exists a monotone increasing function Fc(G)F_c(G) depending on the treatment efficacy of anti-PD-1 G such that IL-27 is an efficient anti-cancer agent when its dose is smaller than Fc(G)F_c(G), whereas IL-27 is a pro-cancer agent when its dose is higher than Fc(G)F_c(G). Our analysis also provides the existence and the local stability of the trivial, non-negative, and positive equilibria of the model. Combining with simulation, we discuss the effect of the IL-27 dosage on the equilibria and find that the T cells and IFN-γ\gamma could vanish and tumor cells preserve, when the production rate of T cells by IL-27 is low or the dosage of IL-27 is low.

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Mathematical modeling for the combination treatment of IFN- γ and anti-PD-1 in cancer immunotherapy

September 2022

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17 Reads

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10 Citations

Mathematical Biosciences

When the immune-checkpoint programmed death-1 (PD-1) binds to its ligand programmed death ligand 1 (PD-L1) to form the complex PD-1-PD-L1, this complex inactivates immune cells resulting in cell apoptosis, downregulation of immune reaction, and tumor evasion. The antibody, anti-PD-1 or anti-PD-L1, blocks the PD-1-PD-L1 complex formation to restore the functions of T cells. Combination of anti-PD-1 with other treatment shows promising in different types of cancer treatments. Interferon-gamma (IFN-γ) plays an important role in immune responses. It is mainly regarded as a pro-inflammatory cytokine that promotes the proliferation of CD8+ T cell and cytotoxic T cell, enhances the activation of Th1 cells and CD8+ T cells, and enhances tumor elimination. However, recent studies have been discovering many anti-inflammatory functions of IFN-γ, such as promotion of the PD-L1 expression, T cell apoptosis, and tumor metastasis, as well as inhibition of the immune recognition and the killing rates by T cells. In this work, we construct a mathematical model incorporating pro-inflammatory and anti-inflammatory functions of IFN-γ to capture tumor growth under anti-PD-1 treatment in the wild type and IFN-γ null mutant melanoma. Our simulation results qualitatively fit experimental data that IFN-γ null mutant with anti-PD-1 obtains the highest tumor reduction comparing to IFN-γ null mutant without anti-PD-1 and wild type tumor with anti-PD-1 therapy. Moreover, our synergy analysis indicates that, in the combination treatment, the tumor volume decreases as either the dosage of anti-PD-1 increases or the IFN-γ production efficiency decreases. Thus, the combination of anti-PD-1 and IFN-γ blockade improves the tumor reduction comparing to the monotherapy of anti-PD-1 or the monotherapy of IFN-γ blockade. We also find a threshold curve of the minimal dosage of anti-PD-1 corresponding to the IFN-γ production efficiency to ensure the tumor reduction under the presence of IFN-γ.


Mathematical Modeling and Analysis of CD200–CD200R in Cancer Treatment

August 2022

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20 Reads

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6 Citations

Bulletin of Mathematical Biology

CD200 is a cell membrane protein that binds to its receptor, CD200 receptor (CD200R). The CD200 positive tumor cells inhibit the cellular functions of M1 and M2 macrophages and dendritic cells (DCs) through the CD200–CD200R complex, resulting in downregulation of Interleukin-10 and Interleukin-12 productions and affecting the activation of cytotoxic T lymphocytes. In this work, we provide two ordinary differential equation models, one complete model and one simplified model, to investigate how the binding affinities of CD200R and the populations of M1 and M2 macrophages affect the functions of the CD200–CD200R complex in tumor growth. Our simulations demonstrate that (i) the impact of the CD200–CD200R complex on tumor promotion or inhibition highly depends on the binding affinity of the CD200R on M2 macrophages and DCs to the CD200 on tumor cells, and (ii) a stronger binding affinity of the CD200R on M1 macrophages or DCs to the CD200 on tumor cells induces a higher tumor cell density in the CD200 positive tumor. Thus, the CD200 blockade would be an efficient treatment method in this case. Moreover, the simplified model shows that the binding affinity of CD200R on macrophages is the major factor to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are significantly different to each other. On the other hand, both the binding affinity of CD200R and the population of macrophages are the major factors to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are close to each other. We also analyze the simplified model to investigate the dynamics of the positive and trivial equilibria of the CD200 positive tumor case and the CD200 deficient tumor case. The bifurcation diagrams show that when M1 macrophages dominate the population, the tumor cell density of the CD200 positive tumor is higher than the one of CD200 deficient tumor. Moreover, the dynamics of tumor cell density change from tumor elimination to tumor persistence to oscillation, as the maximal proliferation rate of tumor cells increases.


Mathematical modeling and analysis of the heat shock protein response during thermal stress in fish and HeLa cells

September 2021

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52 Reads

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5 Citations

Mathematical Biosciences

The climate change has the potential to dramatically affect species’ thermal physiology and may change the ecology and evolution of species’ lineages. In this work, we investigated the transition of dynamics in the heat shock response when the thermal stress approaches the upper thermal limits of species to understand how the climate change may affect the heat shock responses in ectotherms and endotherms. The heat shock protein 70, HSP70, prevents protein denaturation or misfolding under thermal stresses. When thermal stress increases, the number of misfolded proteins increases, which leads to high levels of HSP70 protein. However, when temperatures approach limits of thermal tolerance (i.e., the critical thermal maximum, CTmax, for ectotherms and the superior critical temperature, SCT, for endotherms), levels of HSP70 protein synthesis start to decrease. Thus, we hypothesized that the temperature at the first reduction of HSP abundance indicates the thermal limits of the species. In this work, we provide a mathematical model to investigate the behavior of the heat shock responses related to HSP70 protein. This model captures the dynamics of HSP70 protein and Hsp70 mRNA, in HeLa cells (i.e., representative for endotherms) and multiple species of fishes (i.e., representative for ectotherms) with different acclimation histories. Based on our hypothesis of the relationship between the HSP70 protein level and CTmax/SCT, our model provides three methods to predict the CTmax of fishes with varying acclimation temperature and the SCT of HeLa cells. The CTmax increases as the acclimation temperature increases in fishes, however the CTmax plateaus when the acclimation temperature is higher than 20°C in brook trout, a representative cool water salmonid. Our model also captures the situation that the heat shock reaction in fish is more sensitive to the heat shock temperature than HeLa cells, when the heat shock temperature is lower than the upper thermal tolerance. However, both fish and HeLa cells are sensitive to the heat shock temperature when the temperature reaches the thermal tolerance limits. Additionally, our sensitive analysis result indicates that the status of some components in the heat shock reaction changes when the temperature reaches the thermal tolerance resulting in failure in protein refolding in fish and speeding up the refolding process in HeLa cells. Mathematical analysis is also applied on a simplified mathematical model to investigate the detailed dynamics of the model, such as the steady states of the substrate, Hsp70 mRNA, and HSP70 protein, at different thermal stresses. The comparison between the original model and simplified model shows that the inhibition on HSP70 protein transcription by thermal stresses leads to the reduction in HSP70 protein at extreme temperatures.


Mathematical modeling of the eyespots in butterfly wings

September 2021

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86 Reads

Journal of Theoretical Biology

Butterfly wing color patterns are a representative model system for studying biological pattern formation, due to their two-dimensional simple structural and high inter- and intra-specific variabilities. Moreover, butterfly color patterns have demonstrated roles in mate choice, thermoregulation, and predator avoidance via disruptive coloration, attack deflection, aposematism, mimicry, and masquerade. Because of the importance of color patterns to many aspects of butterfly biology and their apparent tractability for study, color patterns have been the subjects of many attempts to model their development. Early attempts focused on generalized mechanisms of pattern formation such as reaction-diffusion, diffusion gradient, lateral inhibition, and threshold responses, without reference to any specific gene products. As candidate genes with expression patterns that resembled incipient color patterns were identified, genetic regulatory networks were proposed for color pattern formation based on gene functions inferred from other insects with wings, such as Drosophila. Particularly detailed networks incorporating the gene products, Distal-less (Dll), Engrailed (En), Hedgehog (Hh), Cubitus interruptus (Ci), Transforming growth factor-β (TGF-β), and Wingless (Wg), have been proposed for butterfly border ocelli (eyespots) which helps the investigation of the formation of these patterns. Thus, in this work, we develop a mathematical model including the gene products En, Hh, Ci, TGF-β, and Wg to mimic and investigate the eyespot formation in butterflies. Our simulations show that the level of En has peaks in the inner and outer rings and the level of Ci has peaks in the inner and middle rings. The interactions among these peaks activate cells to produce white, black, and yellow pigments in the inner, middle, and outer rings, respectively, which captures the eyespot pattern of wild type Bicyclus anynana butterflies. Additionally, our simulations suggest that lack of En generates a single black spot and lack of Hh or Ci generates a single white spot, and a deficiency of TGF-β or Wg will cause the loss of the outer yellow ring. These deficient patterns are similar to those observed in the eyespots of Vanessa atalanta, Vanessa altissima, and Chlosyne nycteis. Thus, our model also provides a hypothesis to explain the mechanism of generating the deficient patterns in these species.

Citations (5)


... Both genes appear to be involved in the modulation of an inflammatory response to radiation. Transcription factor EC (TFEC) regulates a variety of cytokines capable of cancer stem cell promotion [53][54][55], while the pro-cancer or anti-cancer role of Epstein-Barr virus-induced gene 3 (EBI3) is less clearly understood [56]. ...

Reference:

NF-κB in the Radiation Response of A549 Non-Small Cell Lung Cancer Cells to X-rays and Carbon Ions under Hypoxia
IL-27 in combination with anti-PD-1 can be anti-cancer or pro-cancer
  • Citing Article
  • December 2023

Journal of Theoretical Biology

... For the immunotherapy and biological therapy of female GTMM, some patients may benefit from long-term remission (16), but large-scale studies are still needed to confirm this. Some research (6,17,18) suggests that antiprogrammed cell death protein 1 therapy is more effective for improving overall survival in patients with advanced or recurrent GTMM. In summary, the treatment approach tends not to be standardized and is rather individualized according to the characteristics of the disease and the patient. ...

Different mechanisms of CD200-CD200R induce diverse outcomes in cancer treatment
  • Citing Article
  • September 2023

Mathematical Biosciences

... Studies have shown that high Th1 cell (13) or low TNF (14) recruiting score is related to the poor prognosis of KIRC patients. Previously, PD-L1 has been reported to act as an accurate biomarker for KIRC, and the agents targeting PD-L1 have had promising effects in renal cell carcinoma (15,16). In this study, the negative regulation of immune response was obviously activated in the low-score group. ...

Mathematical modeling for the combination treatment of IFN- γ and anti-PD-1 in cancer immunotherapy
  • Citing Article
  • September 2022

Mathematical Biosciences

... At the microscopic scale, differential equations are used to model intracellular signaling networks (1)(2)(3), including cancer signaling pathways (4), epithelial-mesenchymal transitions (5), single-cell RNA velocity (6)(7)(8), and morphogen gradients involved in cell development (9)(10)(11)(12). At the mesoscopic scale, ordinary differential equations (ODEs) are frequently applied to simulate cancer-immune (13)(14)(15) and virus-host immune interactions (16,17), aiding in the prediction of disease progression. At the macroscopic scale, partial differential equations (PDEs) are employed to describe cell movement and spatial cell-cell interactions, such as tumor cell invasion (18)(19)(20) and spatial interactions of immune cells (21,22), facilitating predictions of cancer development and cardiovascular disease progression (23)(24)(25). ...

Mathematical Modeling and Analysis of CD200–CD200R in Cancer Treatment
  • Citing Article
  • August 2022

Bulletin of Mathematical Biology

... Fortunately, we identified two genes directly related to heat shock response (Dnajc17 and Dnaja1) on chromosome 02, which is another kind of balance, maintaining pathways activated by different stressors and generally accompanied by the increased expression of heat shock proteins [72,73]. The Dnaj family is a subfamily of Hsp40 that typically functions as accessory proteins to HSP70, assisting in the folding, stabilization, and unfolding of client proteins [74]. ...

Mathematical modeling and analysis of the heat shock protein response during thermal stress in fish and HeLa cells
  • Citing Article
  • September 2021

Mathematical Biosciences