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Related Concept Videos

Lytic Cycle of Bacteriophages01:30

Lytic Cycle of Bacteriophages

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Bacteriophages, also known as phages, are specialized viruses that infect bacteria. A key characteristic of phages is their distinctive “head-tail” morphology. A phage begins the infection process (i.e., lytic cycle) by attaching to the outside of a bacterial cell. Attachment is accomplished via proteins in the phage tail that bind to specific receptor proteins on the outer surface of the bacterium. The tail injects the phage’s DNA genome into the bacterial cytoplasm. In the...
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Bacteriophages, or phages, are viruses that specifically infect bacteria. Among them, T-even bacteriophages, such as T4, exhibit a well-characterized lytic replication cycle in Escherichia coli (E. coli). This process ensures the rapid proliferation of the virus while ultimately leading to the destruction of the bacterial host.Attachment and DNA InjectionThe infection process begins with the recognition and binding of the T4 phage to the E. coli cell surface. Tail fibers of the phage...
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Lysogenic Cycle of Bacteriophages00:43

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In contrast to the lytic cycle, phages infecting bacteria via the lysogenic cycle do not immediately kill their host cell. Instead, they combine their genome with the host genome, allowing the bacteria to replicate the phage DNA along with the bacterial genome. The incorporated copy of the phage genome is called the prophage. Some prophages can re-activate and enter the lytic cycle. This often occurs in response to a perturbation, such as DNA damage, but can also transpire in the absence of...
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What are Biogeochemical Cycles?00:54

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The Earth’s hydrosphere includes all of the areas where the storage and movement of water occurs. Since water is the basis of all living processes, the cycling of water is extremely important to ecosystem dynamics.
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Unlike carbon, water, and nitrogen, phosphorus is not present in the atmosphere as a gas. Instead, most phosphorus in the ecosystem exists as compounds, such as phosphate ions (PO43-), found in soil, water, sediment and rocks. Phosphorus is often a limiting nutrient (i.e., in short supply). Consequently, phosphorus is added to most agricultural fertilizers, which can cause environmental problems related to runoff in aquatic ecosystems.
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Related Experiment Video

Updated: Jan 24, 2026

Dissecting Host-virus Interaction in Lytic Replication of a Model Herpesvirus
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Spatial Model for Oncolytic Virotherapy with Lytic Cycle Delay.

Jiantao Zhao1,2, Jianjun Paul Tian3,4

  • 1Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88001, USA.

Bulletin of Mathematical Biology
|May 16, 2019
PubMed
Summary
This summary is machine-generated.

This study models oncolytic virotherapy using partial differential equations, revealing conditions for stable tumor eradication or persistent viral activity. Mathematical analysis and simulations explore virus and tumor cell diffusion dynamics.

Keywords:
Functional reaction–diffusion equationsHopf bifurcationOncolytic virotherapyStability

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Area of Science:

  • Mathematical Biology
  • Oncolytic Virotherapy Modeling
  • Partial Differential Equations

Background:

  • Oncolytic virotherapy uses viruses to selectively destroy cancer cells.
  • Previous models often simplify virus-tumor cell interactions and movement.
  • Incorporating diffusion and lytic cycles is crucial for realistic dynamics.

Purpose of the Study:

  • To develop and analyze a mathematical model for oncolytic virotherapy.
  • To investigate the impact of virus diffusivity, tumor cell diffusion, and viral lytic cycles.
  • To determine conditions for stable tumor eradication and oscillatory dynamics.

Main Methods:

  • Formulation of a functional partial differential equation model.
  • Detailed mathematical analysis of system dynamics.
  • Numerical simulations to validate analytical findings.

Main Results:

  • Established the positive invariant domain for the system's limit set.
  • Identified three spatially homogeneous equilibrium solutions.
  • Proved global asymptotic stability of the virus-free state under specific conditions (viral burst size < critical value).
  • Determined conditions for local asymptotic stability of the virus-present steady state (e.g., diffusion ratio, lytic cycle duration).
  • Identified conditions for Hopf bifurcations leading to stable periodic solutions.

Conclusions:

  • The model provides insights into complex oncolytic virotherapy dynamics.
  • Diffusion and lytic cycle parameters significantly influence treatment outcomes.
  • Results offer implications for designing more effective virotherapy strategies.