Advanced Hepatitis C Virus Replication PDE Models within a Realistic Intracellular Geometric Environment

Abstract

The hepatitis C virus (HCV) RNA replication cycle is a dynamic intracellular process occurring in three-dimensional space (3D), which is difficult both to capture experimentally and to visualize conceptually. HCV-generated replication factories are housed within virus-induced intracellular structures termed membranous webs (MW), which are derived from the Endoplasmatic Reticulum (ER). Recently, we published 3D spatiotemporal resolved diffusion–reaction models of the HCV RNA replication cycle by means of surface partial differential equation (sPDE) descriptions. We distinguished between the basic components of the HCV RNA replication cycle, namely HCV RNA, non-structural viral proteins (NSPs), and a host factor. In particular, we evaluated the sPDE models upon realistic reconstructed intracellular compartments (ER/MW). In this paper, we propose a significant extension of the model based upon two additional parameters: different aggregate states of HCV RNA and NSPs, and population dynamics inspired diffusion and reaction coefficients instead of multilinear ones. The combination of both aspects enables realistic modeling of viral replication at all scales. Specifically, we describe a replication complex state consisting of HCV RNA together with a defined amount of NSPs. As a result of the combination of spatial resolution and different aggregate states, the new model mimics a cis requirement for HCV RNA replication. We used heuristic parameters for our simulations, which were run only on a subsection of the ER. Nevertheless, this was sufficient to allow the fitting of core aspects of virus reproduction, at least qualitatively. Our findings should help stimulate new model approaches and experimental directions for virology.

Spatio-Temporal Modeling of Immune Response to SARS-CoV-2 Infection

“…Building on some biological observations and mathematical models (temporal approaches) [7,8,[10][11][12][13]16,22,28,[30][31][32][33][34][35][36], we develop a new spatio-temporal mathematical model to explore the interactions between the most essential components of the immune system and SARS-CoV-2 particles within a cellular perspective. This dynamical interaction occurs on a spatial domain ℵ ∈ R 2 over a time interval [0, T] and it involves the healthy host cells h(t, x), viral-infected cells i(t, x), SARS-CoV-2 molecules v(t, x), chemokines c(t, x), the effector T cells f (t, x), the regulatory T cells r(t, x), B-lymphocytes cells β(t, x) and antibodies α(t, x).…”

“…where the differential operator (K) of order 2 will be explained in detail in the following context. Host h(t, x) & Infected cells i(t, x) Following biological observations and spatiotemporal mathematical approach that have been taken from various experimental studies for similar infectious diseases such as [31,32], we suppose that both type of cells are exercising a random motility on the spatial domain ℵ at rates D h > 0 and D i > 0, respectively. The density of the host cells is assumed to be produced logistically at a rate µ h , while the decay of its density comes from many reasons at a rate δ 11 .…”

Spatio-Temporal Analysis of Infectious Diseases

“…These articles provide novel insights into the interaction between space and time in the context of each specific infectious disease, providing new perspectives in the understanding of these pathologies and their extent. A total of 11 manuscripts [1,2,3,4,5,6,7,8,9,10,11] were accepted after a single-blind review process by at least two international experts using the journal-specific review guidelines.…”

“…The different works corresponding to these articles were carried out in different geographical areas of several countries: China [2,5,6,7,8,10], Colombia [4], Ecuador [3], Korea [9], and Taiwan [1]. One of the studies deals with the analysis of an intracellular geometric model [11].…”

“…Several infectious diseases are addressed by studying their differentiated characteristics and relating them to relevant explanatory variables. The list of diseases studied includes typhoid and paratyphoid fevers [10]; Middle East respiratory syndrome-related coronavirus (MERS-CoV) [9]; tuberculosis [8]; bacillary dysentery [7]; cystic echinococcosis [6]; hand, foot, and mouth disease [5]; zika virus disease (ZVD) [4]; dengue [1,3,4]; and hepatitis [2,11].…”