Questing for an Optimal, Universal Viral Agent for Oncolytic Virotherapy
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Questing for an optimal, universal viral agent for oncolytic virotherapy L R Paiva,∗ M L Martins,† and S C Ferreira Jr‡ Departamento de F´ısica, Universidade Federal de Vi¸cosa, 36570-000, Vi¸cosa, MG, Brazil (Dated: November 10, 2018) One of the most promising strategies to treat cancer is attacking it with viruses designed to ex- ploit specific altered pathways. Here, the effects of oncolytic virotherapy on tumors having compact, papillary and disconnected morphologies are investigated through computer simulations of a mul- tiscale model coupling macroscopic reaction diffusion equations for the nutrients with microscopic stochastic rules for the actions of individual cells and viruses. The interaction among viruses and tumor cells involves cell infection, intracellular virus replication and release of new viruses in the tissue after cell lysis. The evolution in time of both viral load and cancer cell population, as well as the probabilities for tumor eradication were evaluated for a range of multiplicities of infection, viral entries and burst sizes. It was found that in immunosuppressed hosts, the antitumor efficacy of a virus is primarily determined by its entry efficiency, its replicative capacity within the tumor, and its ability to spread over the tissue. However, the optimal traits for oncolytic viruses depends critically on the tumor growth dynamics and do not necessarily include rapid replication, cytolysis and spreading currently assumed as necessary conditions to a successful therapeutic outcome. Our findings have potential implications on the design of new vectors for the viral therapy of cancer. PACS numbers: 87.19.xj, 87.10.Mn, 87.18.Hf Keywords: multiscale model, virotherapy, cancer therapy I. INTRODUCTION and to select parameter ranges that enhance its therapeu- tic success. Specially because, in face of the nonlinear- Despite the progress that has been made in imag- ities and complexity involved in cancer progression and ing, diagnosis, treatment and understanding of cancer, its interaction with oncolytic viruses, intuitive reason- the survival rates of patients with metastatic or recur- ing alone may be insufficient. The current paradigm is rent neoplasias as well as patients with tumors at un- that the viral life cycle should lead to rapid replication, resectable locations are still poor, and new therapeutic cytolysis and spread [11]. Nonetheless, the limitations strategies are needed [1]. Furthermore, occult dormant and validity of this appealing, intuitive, and seemingly micrometastasis raise new challenges concerning their re- logical paradigm remains unclear. Indeed, at least one activation and evolution into clinically manifested dis- mathematical result [8] indicates that viruses able to de- ease, particularly after primary tumor resection [2]. stroy tumor cells very fast does not necessarily lead to a Oncolytic virotherapy is claimed to be a promising more effective control of tumor growth. More precisely, anti-cancer strategy, because it can provide a locoregional it was shown that a successful virotherapy of compact control or even eradication of tumors without cross- tumors requires both highly spreading viruses and an op- resistance with standard therapies. Oncolytic viruses are timal range of viral cytotoxity, i. e, neither a too short able to selectively infect and kill tumor cells by exploit- nor a very large time for the lysis of cancer cells. How- ing the same cellular defects that promote tumor growth ever, this result was derived assuming that the viruses [3]. To date, several different viruses are known to be are a continuous field whose dynamics is described by a selectively oncolytic [4]. An archetype is the adenovirus reaction-diffusion equation. Furthermore, the changes in commonly used in gene therapy and oncolytic therapy the stationary local concentrations of viruses due to their experiments [5, 6]. Some studies indicate that the virus entry at cell infections were neglected and the viral burst effectiveness strongly depends on the specific cancer cell size used, equal to the initial viral load, was orders of magnitude greater than the larger ones observed for real arXiv:1109.3614v1 [physics.bio-ph] 16 Sep 2011 line [1]. So, one can hypothesize that for each tumor there must exist an oncolytic virus that maximizes the oncolytic viruses. therapeutic success. In the present paper, a multiscale model based on the Several mathematical models have been proposed to approach proposed by Ferreira et al. [12] was modified study virotherapy [7–10]. They emerge as valuable tools to take explicitly into account the individual, discrete to provide quantitative understanding of the major mech- nature of the oncolytic viruses and applied to evaluate anisms that affect anti-cancer treatment based on viruses the efficacy of virotherapy against compact, papillary and diffuse (disconnected) solid tumors. Considering virus as discrete agents provides a more realistic description ∗ [email protected] of virus entry and replication, key processes involved in † [email protected]; National Institute of Science and Technology oncolytic virotherapy. Our main goal is provide useful for Complex Systems, Brazil insights about how to match the oncolytic virus and the ‡ On leave at Departament de F´ısica y Enginyeria Nuclear, Uni- tumor type in order to get the better outcome for the versitat Polit´ecnica de Catalunya, Spain therapy. 2 II. MODEL that increases with the scarcity of nutrients φ2 essential to sustain the cell metabolism. Figure 1 illustrates the multiple agents and processes 3-Migration, with a probability involved in the model at distinct time and length scales. The tissue is modelled by a square lattice fed through a 2 single capillary vessel at its top. Four different cell types φ2 Pmov =1 − exp −σc , (4) (normal and dead cells, uninfected and infected tumor " θmov # cells) and an oncolytic virus are considered. These indi- vidual agents are described by their populations σn, σd, that increases with the local population of cancer cells σc, and σv, respectively, at every site x. In contrast to and the nutrient concentration per cell. A probability the normal and dead cells, one or more uninfected or in- increasing with the nutrient concentration is justified by fected cancer cells can pile up in a given site, reflecting the necessity of nutrients for cell motility and, in ad- the fact that the division of tumor cells is not constrained dition, by the degradation of the extracellular matrix by contact inhibition. In turn, since the viruses are very nearby the tumor surface that releases several chemicals small particles in comparison with cells, there is no con- which promote cell migration and proliferation. This hy- straint on their population. pothesis is consistent with experimental data in multi- The nutrients, diffusing from the capillary vessel cellular tumor spheroids [14] and was previously used in throughout the tissue, are divided into two groups: those other mathematical models [15, 16]. The migrating cell that limits cell replication but are not demanded for cell moves to one of its nearest-neighbor sites chosen at ran- survival (j = 1) and those essential to maintain the basic dom, interchanging its position with a normal or necrotic cell functions and whose deprivation can induce death cell if there exists any. If the interchanged normal or (j = 2). Both nutrient types are described by contin- necrotic cell moved to a site still occupied by other can- uous fields φj (~x, t), which evolve in space and time ac- cer cells, it is eliminated. These rules for cancer growth cording the simplest (linear with constant coefficients) are similar to those used by Scalerandi et al. [17] in a dimensionless reaction-diffusion equations deterministic model with collective cell actions controlled by threshold (step) functions of the nutrient concentra- tion per cancer cell. ∂φj 2 2 2 = ∇ φj − α φj σn − λj α φj σc. (1) Become infected ∂t 4- with a probability The factors λj take into account distinct nutrient uptake 2 rates for normal and cancer cells. The parameter α sets σv up a characteristic length scale for nutrient diffusion in Pinf =1 − exp − , (5) σcθinf the normal tissue (see reference [13] for the complete vari- " # able transformations leading to this dimensionless equa- an increasing function of the local viral load per cell, tion). Eq. (1) obeys a periodic boundary condition along controlled by the parameter θ . The model assumes the direction parallel to the capillary and a Neumann inf perfect viral selectivity for cancer cells, thereby the in- boundary condition at the border of the tissue. At the fection of normal cells by oncolytic viruses is neglected. capillary vessel the nutrient concentrations are φ = 1 j The number of viruses n that infect a given cell is se- (continuous and fixed supply). v lected from a Poisson distribution, Each uninfected cancer cell, randomly selected with equal probability, can carry out one of four actions: 1-Mitotic replication, with a probability knv e−k P (nv)= , (6) nv! 2 φ1 P =1 − exp − , (2) where k is the typical viral entry. This Poisson law has div θ σ " div c # been observed in cell cultures as a function of the mul- tiplicity of infection (MOI), defined as the ratio between an increasing function of the concentration per cancer cell the total viral load injected in the system and the num- of the nutrients φ1. The daughter cell randomly occupies ber of target cells [18]. The model assumes that an in- one of their normal or necrotic nearest neighbor sites, fected cancer cell does not divide nor migrate because its whether there exists any, or piles up at its mother site. slaved cellular machinery is focused on virus replication. In the simulations, we observed at most three or four It is also assumed that infected cancer cells sustain their cancer cells at the same site simultaneously. metabolism until lysis and die only by lysis. The death 2-Death, with a probability by lysis occurs with a probability 2 φ2 − Tinf Pdel = exp , (3) Plysis =1 − exp − , (7) " θdelσc # T l 3 where Tinf is the time elapsed since the cell infection most probable prognosis after the treatment as well as the and Tl is the characteristic time for cell lysis.