🦠 Phage λ Decision Switch

Viral Computational Logic and Binary Decision Making

The Lambda Decision: Biology's Most Famous Switch

Bacteriophage lambda represents one of the most elegant examples of biological computation ever discovered. Upon infection, the virus faces a fundamental binary decision: lyse or lysogenize. This decision involves sophisticated computational logic including bistable switches, competitive inhibition, positive feedback loops, and threshold detection mechanisms.

Computational Significance: The lambda decision switch demonstrates how biological systems implement Boolean logic, digital decision-making, and state memory - fundamental concepts in computer science realized through molecular interactions.

1. Infection → CII Stabilization Logic

The initial computational logic determining CII protein stability and early decision bias toward lysogeny or lysis.

graph TD %% Initial Setup A[Phage Injection] --> B[DNA Circularization] B --> C[Early Transcription] C --> D[CII Protein Synthesis] D --> E{Host Protease Activity?} E -->|High| F[CII Degradation] E -->|Low| G[CII Stabilization] F --> H[Lytic Bias] G --> I[Lysogenic Bias] J[Host Conditions] --> K[Protease Regulation] K --> E L[Multiplicity of Infection] --> M[CII Concentration] M --> N{CII Threshold?} N -->|Above| O[Lysogenic Switch] N -->|Below| P[Lytic Default] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#51cf66,color:#fff style C fill:#51cf66,color:#fff style D fill:#51cf66,color:#fff style E fill:#74c0fc,color:#fff style F fill:#51cf66,color:#fff style G fill:#51cf66,color:#fff style H fill:#b197fc,color:#fff style I fill:#b197fc,color:#fff style J fill:#ff6b6b,color:#fff style K fill:#ffd43b,color:#000 style L fill:#ff6b6b,color:#fff style M fill:#74c0fc,color:#fff style N fill:#74c0fc,color:#fff style O fill:#b197fc,color:#fff style P fill:#ff6b6b,color:#fff
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2. PR/PL Early Gene Control

Computational logic governing early gene expression through the PR and PL promoters, setting up the decision circuitry.

graph TD %% Initial Setup A[Lambda DNA] --> B[PR Promoter] A --> C[PL Promoter] B --> D[cI Gene Transcription] B --> E[cII Gene Transcription] B --> F[cIII Gene Transcription] C --> G[N Protein Synthesis] C --> H[Early Lytic Genes] G --> I[Antitermination] A --> J[Extended Transcription] J --> K[cII/cIII Enhancement] D --> L[CI Repressor] E --> M[CII Activator] F --> N[CIII Protease Inhibitor] L --> O{CI Concentration?} O -->|High| P[PR/PL Repression] O -->|Low| Q[Continued Transcription] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#ffd43b,color:#000 style C fill:#ffd43b,color:#000 style D fill:#51cf66,color:#fff style E fill:#51cf66,color:#fff style F fill:#51cf66,color:#fff style G fill:#51cf66,color:#fff style H fill:#ffd43b,color:#000 style I fill:#51cf66,color:#fff style J fill:#51cf66,color:#fff style K fill:#51cf66,color:#fff style L fill:#ffd43b,color:#000 style M fill:#ffd43b,color:#000 style N fill:#ffd43b,color:#000 style O fill:#74c0fc,color:#fff style P fill:#b197fc,color:#fff style Q fill:#51cf66,color:#fff
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3. CI Auto-regulation

The positive feedback mechanism where CI repressor regulates its own expression, creating a bistable switch for lysogeny maintenance.

graph TD %% Initial Setup A[CI Protein] --> B[OR Operator Binding] B --> C{Operator Occupancy?} C -->|OR1/OR2| D[PRM Activation] C -->|OR3| E[PRM Repression] D --> F[CI Transcription] F --> G[More CI Protein] G --> H[Positive Feedback] H --> B I[Low CI] --> J[OR1 Binding Only] J --> K[PRM Transcription] K --> L[CI Increase] M[High CI] --> N[OR3 Binding] N --> O[PRM Shutoff] O --> P[CI Decrease] Q[Cooperative Binding] --> R[Hill Function] R --> S[Bistable Switch] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#ffd43b,color:#000 style C fill:#74c0fc,color:#fff style D fill:#51cf66,color:#fff style E fill:#b197fc,color:#fff style F fill:#51cf66,color:#fff style G fill:#51cf66,color:#fff style H fill:#b197fc,color:#fff style I fill:#ff6b6b,color:#fff style J fill:#ffd43b,color:#000 style K fill:#51cf66,color:#fff style L fill:#51cf66,color:#fff style M fill:#ff6b6b,color:#fff style N fill:#ffd43b,color:#000 style O fill:#b197fc,color:#fff style P fill:#51cf66,color:#fff style Q fill:#ffd43b,color:#000 style R fill:#51cf66,color:#fff style S fill:#b197fc,color:#fff
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4. Cro Antagonism

The competitive inhibition logic between CI and Cro proteins for operator binding, implementing mutual exclusion.

graph TD %% Initial Setup A[CI vs Cro Competition] --> B{Operator Binding Affinity?} B -->|CI Higher| C[CI Binds OR1/OR2] B -->|Cro Higher| D[Cro Binds OR3/OR2/OR1] C --> E[PRM Activated] C --> F[PR Repressed] E --> G[More CI] F --> H[Less Cro] D --> I[PR Activated] D --> J[PRM Repressed] I --> K[More Cro] J --> L[Less CI] M[DNA Damage] --> N[RecA Activation] N --> O[CI Cleavage] O --> P[CI Inactivation] P --> Q[Cro Takes Over] R[Competitive Exclusion] --> S[Winner Take All] S --> T[Bistable Outcome] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#74c0fc,color:#fff style C fill:#51cf66,color:#fff style D fill:#51cf66,color:#fff style E fill:#b197fc,color:#fff style F fill:#b197fc,color:#fff style G fill:#51cf66,color:#fff style H fill:#51cf66,color:#fff style I fill:#b197fc,color:#fff style J fill:#b197fc,color:#fff style K fill:#51cf66,color:#fff style L fill:#51cf66,color:#fff style M fill:#ff6b6b,color:#fff style N fill:#51cf66,color:#fff style O fill:#51cf66,color:#fff style P fill:#51cf66,color:#fff style Q fill:#51cf66,color:#fff style R fill:#ffd43b,color:#000 style S fill:#51cf66,color:#fff style T fill:#b197fc,color:#fff
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5. Promoter Occupancy Dynamics

Mathematical modeling of promoter occupancy states and cooperative binding effects that determine transcriptional output.

graph TD %% Initial Setup A[Operator Sites] --> B[OR1 - High CI Affinity] A --> C[OR2 - Medium CI Affinity] A --> D[OR3 - Low CI Affinity] E[Low CI Concentration] --> F[OR1 Occupied Only] F --> G[PRM Activated, PR Active] H[Medium CI Concentration] --> I[OR1 + OR2 Occupied] I --> J[Maximum PRM, PR Repressed] K[High CI Concentration] --> L[All Sites Occupied] L --> M[PRM Repressed, PR Blocked] N[Cooperative Binding] --> O[Hill Coefficient > 1] O --> P[Sigmoidal Response] P --> Q[Sharp Transition] R[Cro Binding Order] --> S[OR3 > OR2 > OR1] S --> T[Opposite CI Pattern] T --> U[Mutual Exclusion] %% Styling - Biological Color Scheme style A fill:#ffd43b,color:#000 style B fill:#ffd43b,color:#000 style C fill:#ffd43b,color:#000 style D fill:#ffd43b,color:#000 style E fill:#ff6b6b,color:#fff style F fill:#74c0fc,color:#fff style G fill:#b197fc,color:#fff style H fill:#ffd43b,color:#000 style I fill:#74c0fc,color:#fff style J fill:#b197fc,color:#fff style K fill:#ffd43b,color:#000 style L fill:#74c0fc,color:#fff style M fill:#b197fc,color:#fff style N fill:#ffd43b,color:#000 style O fill:#51cf66,color:#fff style P fill:#51cf66,color:#fff style Q fill:#b197fc,color:#fff style R fill:#ff6b6b,color:#fff style S fill:#ffd43b,color:#000 style T fill:#51cf66,color:#fff style U fill:#b197fc,color:#fff
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6. Decision Thresholding (Multiplicity of Infection)

How the number of infecting phages (MOI) creates a concentration threshold that biases the lysis/lysogeny decision.

graph TD %% Initial Setup A[Multiplicity of Infection] --> B{MOI Level?} B -->|Low MOI| C[Single Infection] B -->|High MOI| D[Multiple Infections] C --> E[Limited CII] C --> F[Lytic Tendency] E --> G[Insufficient Lysogeny Signal] D --> H[Additive CII] D --> I[Lysogenic Tendency] H --> J[Threshold Exceeded] K[CII Threshold Model] --> L[Sigmoid Function] L --> M[Probability Distribution] M --> N[Decision Statistics] O[Environmental Stress] --> P[Protease Activity] P --> Q[CII Stability] Q --> R[Threshold Modulation] S[Population Heterogeneity] --> T[Bet Hedging] T --> U[Mixed Outcomes] U --> V[Evolutionary Strategy] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#74c0fc,color:#fff style C fill:#ffd43b,color:#000 style D fill:#ffd43b,color:#000 style E fill:#51cf66,color:#fff style F fill:#ff6b6b,color:#fff style G fill:#51cf66,color:#fff style H fill:#51cf66,color:#fff style I fill:#b197fc,color:#fff style J fill:#51cf66,color:#fff style K fill:#ffd43b,color:#000 style L fill:#51cf66,color:#fff style M fill:#51cf66,color:#fff style N fill:#b197fc,color:#fff style O fill:#ff6b6b,color:#fff style P fill:#51cf66,color:#fff style Q fill:#51cf66,color:#fff style R fill:#51cf66,color:#fff style S fill:#ff6b6b,color:#fff style T fill:#51cf66,color:#fff style U fill:#51cf66,color:#fff style V fill:#b197fc,color:#fff
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7. Maintenance of Lysogeny

The stable memory state maintained by CI auto-regulation, implementing biological digital memory.

graph TD %% Initial Setup A[Established Lysogen] --> B[CI Repressor Present] B --> C[PR/PL Repression] C --> D[Lytic Genes Silent] E[PRM Promoter] --> F[CI Auto-regulation] F --> G[Homeostatic Control] G --> H[Stable CI Levels] I[OR1/OR2 Occupancy] --> J[Optimal PRM Activity] J --> K[CI Maintenance] K --> L[Memory Persistence] M[Perturbations] --> N{CI Disruption?} N -->|Minor| O[Self-Correction] N -->|Major| P[Memory Loss] O --> Q[Return to Stability] P --> R[Lytic Induction] S[Heritability] --> T[Daughter Cell Inheritance] T --> U[Epigenetic Memory] U --> V[Stable Lysogeny] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#ffd43b,color:#000 style C fill:#51cf66,color:#fff style D fill:#b197fc,color:#fff style E fill:#ffd43b,color:#000 style F fill:#51cf66,color:#fff style G fill:#51cf66,color:#fff style H fill:#b197fc,color:#fff style I fill:#ffd43b,color:#000 style J fill:#51cf66,color:#fff style K fill:#51cf66,color:#fff style L fill:#b197fc,color:#fff style M fill:#ff6b6b,color:#fff style N fill:#74c0fc,color:#fff style O fill:#51cf66,color:#fff style P fill:#51cf66,color:#fff style Q fill:#51cf66,color:#fff style R fill:#b197fc,color:#fff style S fill:#ff6b6b,color:#fff style T fill:#51cf66,color:#fff style U fill:#51cf66,color:#fff style V fill:#b197fc,color:#fff
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8. Induction by DNA Damage

The signal transduction pathway that converts DNA damage into CI inactivation, triggering lytic development.

graph TD %% Initial Setup A[DNA Damage] --> B[RecA Activation] B --> C[RecA* Formation] C --> D[CI Cleavage Activity] D --> E[CI Auto-proteolysis] E --> F[CI Inactivation] F --> G[OR Operator Release] G --> H[PR Promoter Activation] H --> I[Cro Expression] I --> J[Lytic Gene Cascade] K[UV Radiation] --> L[Thymine Dimers] L --> M[Replication Block] M --> N[ssDNA Formation] N --> B O[SOS Response] --> P[RecA Induction] P --> Q[Amplified Signal] Q --> R[Rapid CI Clearance] S[Timing Control] --> T[CI Half-life] T --> U[Induction Kinetics] U --> V[Lytic Commitment] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#51cf66,color:#fff style C fill:#51cf66,color:#fff style D fill:#51cf66,color:#fff style E fill:#51cf66,color:#fff style F fill:#51cf66,color:#fff style G fill:#74c0fc,color:#fff style H fill:#51cf66,color:#fff style I fill:#b197fc,color:#fff style J fill:#b197fc,color:#fff style K fill:#ff6b6b,color:#fff style L fill:#51cf66,color:#fff style M fill:#51cf66,color:#fff style N fill:#74c0fc,color:#fff style O fill:#ff6b6b,color:#fff style P fill:#51cf66,color:#fff style Q fill:#51cf66,color:#fff style R fill:#51cf66,color:#fff style S fill:#ffd43b,color:#000 style T fill:#51cf66,color:#fff style U fill:#51cf66,color:#fff style V fill:#b197fc,color:#fff
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9. Lytic Late Gene Cascade

The temporal program of lytic development, implementing a genetic timer and developmental cascade.

graph TD %% Initial Setup A[Lytic Commitment] --> B[Early Lytic Genes] B --> C[N Antitermination] C --> D[Q Protein Expression] D --> E[Late Gene Activation] F[DNA Replication] --> G[Replication Timing] G --> H[Late Promoter Activation] H --> I[Structural Proteins] J[Head Proteins] --> K[Capsid Assembly] L[Tail Proteins] --> M[Tail Assembly] N[DNA Packaging] --> O[Progeny Assembly] P[Lysis Proteins] --> Q[Holin Expression] Q --> R[Membrane Permeabilization] R --> S[Endolysin Release] S --> T[Cell Wall Digestion] T --> U[Cell Lysis] V[Temporal Control] --> W[Regulatory Cascade] W --> X[Ordered Expression] X --> Y[Efficient Assembly] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#51cf66,color:#fff style C fill:#51cf66,color:#fff style D fill:#51cf66,color:#fff style E fill:#51cf66,color:#fff style F fill:#ff6b6b,color:#fff style G fill:#51cf66,color:#fff style H fill:#51cf66,color:#fff style I fill:#ffd43b,color:#000 style J fill:#ffd43b,color:#000 style K fill:#51cf66,color:#fff style L fill:#ffd43b,color:#000 style M fill:#51cf66,color:#fff style N fill:#ffd43b,color:#000 style O fill:#51cf66,color:#fff style P fill:#ffd43b,color:#000 style Q fill:#51cf66,color:#fff style R fill:#51cf66,color:#fff style S fill:#51cf66,color:#fff style T fill:#51cf66,color:#fff style U fill:#b197fc,color:#fff style V fill:#ffd43b,color:#000 style W fill:#51cf66,color:#fff style X fill:#51cf66,color:#fff style Y fill:#b197fc,color:#fff
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10. Decision Integration Logic

The master control logic integrating all decision inputs into the final binary choice between lysis and lysogeny.

graph TD %% Initial Setup A[Multiple Inputs] --> B[CII Stabilization] A --> C[Host Conditions] A --> D[MOI Signal] A --> E[DNA Damage Status] B --> F[Lysogenic Bias Weight] C --> G[Environmental Weight] D --> H[Population Weight] E --> I[Stress Weight] J[Integration Function] --> K{Weighted Sum > Threshold?} K -->|Yes| L[Lysogenic Decision] K -->|No| M[Lytic Decision] L --> N[CI Dominance] N --> O[Stable Repression] O --> P[Integrated Prophage] M --> Q[Cro Dominance] Q --> R[Lytic Program] R --> S[Progeny Production] T[Decision Memory] --> U[State Maintenance] U --> V[Switch Stability] V --> W[Biological Computing] %% Styling - Biological Color Scheme style A fill:#ff6b6b,color:#fff style B fill:#51cf66,color:#fff style C fill:#ff6b6b,color:#fff style D fill:#ff6b6b,color:#fff style E fill:#ff6b6b,color:#fff style F fill:#51cf66,color:#fff style G fill:#51cf66,color:#fff style H fill:#51cf66,color:#fff style I fill:#51cf66,color:#fff style J fill:#ffd43b,color:#000 style K fill:#74c0fc,color:#fff style L fill:#51cf66,color:#fff style M fill:#51cf66,color:#fff style N fill:#ffd43b,color:#000 style O fill:#51cf66,color:#fff style P fill:#b197fc,color:#fff style Q fill:#ffd43b,color:#000 style R fill:#51cf66,color:#fff style S fill:#b197fc,color:#fff style T fill:#ffd43b,color:#000 style U fill:#51cf66,color:#fff style V fill:#51cf66,color:#fff style W fill:#b197fc,color:#fff
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