Fix to certain models so they properly simulate

.gitignore

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+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

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+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

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+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions

.gitignore

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+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

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+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

@@ -0,0 +1,186 @@
+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions

.gitignore

@@ -0,0 +1,5 @@
+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

@@ -0,0 +1,3 @@
+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

@@ -0,0 +1,186 @@
+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions

.gitignore

@@ -0,0 +1,5 @@
+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

@@ -0,0 +1,3 @@
+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

@@ -0,0 +1,186 @@
+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions

.gitignore

@@ -0,0 +1,5 @@
+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

@@ -0,0 +1,3 @@
+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

@@ -0,0 +1,186 @@
+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions

.gitignore

@@ -0,0 +1,5 @@
+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

@@ -0,0 +1,3 @@
+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

@@ -0,0 +1,186 @@
+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions

.gitignore

@@ -0,0 +1,5 @@
+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

@@ -0,0 +1,3 @@
+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

@@ -0,0 +1,186 @@
+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions

.gitignore

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+*.net
+*.gdat
+*.cdat
+*.xml
+*.m

Published/Dembo1978/README.md

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+# Dembo 1978
+
+BioNetGen model: Dembo 1978

Published/Dembo1978/blbr_dembo1978.bngl

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+begin model
+
+#@title: |
+# Symmetric bivalent hapten-receptor cross-linking
+# (Dembo and Goldstein, 1978)
+
+#@description: |
+# Network-free (NFsim) kinetic model of symmetric bivalent
+# hapten binding to bivalent cell-surface antibody (IgE),
+# forming linear chains. Three processes: (1) hapten capture
+# from solution — a free bivalent hapten binds a receptor
+# site; (2) receptor cross-linking — a tethered hapten arm
+# binds a free receptor site on a DIFFERENT complex (no
+# intra-complex rings); (3) bond dissociation — any
+# hapten-receptor bond breaks.
+#
+# This is the basic model without ring formation (J1 = J2
+# = 0 in Dembo and Goldstein notation). The equilibrium
+# cross-linking curve (fraction of antibody in polymers,
+# x_poly, vs log hapten concentration) is bell-shaped and
+# symmetric about a_max = 1 (i.e., A_max = 1/H in
+# dimensional terms, corresponding to KC = 1 in Perelson
+# and DeLisi notation). At high and low hapten
+# concentrations, cross-linking approaches zero (prozone
+# effect).
+#
+# The kinetic formulation follows Perelson and DeLisi
+# (1980), who showed that singly-bound and doubly-bound
+# ligand concentrations (m and M) are governed by two
+# coupled ODEs under the equivalent-site hypothesis. Given
+# m(t) and M(t), the full aggregate size distribution can
+# be obtained combinatorially.
+#
+# Default parameterization: KxRT = 5 (dimensionless
+# cross-linking propensity), reproducing moderate
+# cross-linking as in Dembo and Goldstein (1978) Fig. 2
+# (k = 10 case, scaled to KxRT = 5 for tractable
+# simulation).
+
+#@keyword: |
+# bivalent hapten, bivalent receptor, cross-linking,
+# aggregation, prozone effect, bell-shaped dose response,
+# mass action, network-free, NFsim, IgE, basophil,
+# histamine release, equivalent-site hypothesis
+
+#@reference: |
+# Dembo M, Goldstein B (1978). Theory of equilibrium binding
+# of symmetric bivalent haptens to cell surface antibody:
+# application to histamine release from basophils. J Immunol
+# 121:345-353. doi:10.4049/jimmunol.121.1.345
+#
+# Perelson AS, DeLisi C (1980). Receptor clustering on a cell
+# surface. I. Theory of receptor cross-linking by ligands
+# bearing two chemically identical functional groups. Math
+# Biosci 48:71-110. doi:10.1016/0025-5564(80)90017-6
+
+#@note: |
+# Network generation is not feasible because bivalent-
+# bivalent cross-linking produces an unbounded set of chain
+# species. NFsim is used with -bscb (block same-complex
+# binding, which implies complex bookkeeping).
+#
+# Mapping to Dembo and Goldstein (1978) notation:
+# H = 2 * Ka (twice the single-site association constant)
+# K = cross-linking constant (units of area)
+# k = K * X_T (dimensionless, here KxRT)
+# a = H * A (dimensionless hapten concentration)
+# a_max = 1 (when b = 0, i.e., no monovalent hapten)
+# x_poly = fraction of antibody in polymers of size >= 2
+#
+# Mapping to Perelson and DeLisi (1980) notation:
+# K = k1/k-1 (association constant for whole ligand)
+# K2 = k2/k-2 (cross-linking association constant)
+# beta = KC/(1+KC) (dimensionless concentration)
+# delta = beta*(1-beta)*K2*S0 (cross-linking parameter)
+# M_bar = S0 * (1+2*delta - sqrt(1+4*delta)) / (4*delta)
+
+begin parameters
+
+ # Physical constants
+ NA 6.02214076e23 # /mol
+
+ # Experimental conditions
+ V_cell 1e-9 # L/cell
+ R_per_cell 3e5 # molecules/cell
+
+ # SSA/NFsim scaling
+ f 0.01 # dimensionless
+ V_sim V_cell*f # L
+
+ # Scaled molecule counts
+ RT R_per_cell*f # molecules (= 3000)
+
+ # Total bivalent hapten (ligand)
+ # Default: 10x receptor count (near optimal cross-linking)
+ LT_per_cell 3e6 # molecules/cell
+ LT LT_per_cell*f # molecules
+
+ # Single-site kinetic rate constants
+ # K = kon/koff = 1e8 /M (intrinsic affinity for one site)
+ kon 1e6 # /M/s
+ koff 0.01 # /s
+
+ # Dimensionless cross-linking propensity
+ # k = K * X_T in Dembo notation; KxRT here
+ KxRT 5 # dimensionless
+
+ # Stochastic rate constants (single-site, per molecule pair)
+ kf kon/(NA*V_sim) # /(molecule*s)
+ kxf KxRT/RT*koff # /(molecule*s)
+
+end parameters
+
+begin molecule types
+ # Bivalent hapten (ligand): two identical receptor-binding sites
+ L(r,r)
+ # Bivalent receptor (antibody/IgE): two identical hapten-binding sites
+ R(l,l)
+end molecule types
+
+begin seed species
+ L(r,r) LT # molecules
+ R(l,l) RT # molecules
+end seed species
+
+begin observables
+ # Free hapten (both sites unbound)
+ Species Obs_Free_L L(r,r)
+ # Free receptor (both sites unbound)
+ Species Obs_Free_R R(l,l)
+ # Total hapten-receptor bonds
+ Molecules Obs_Bonds L(r!1).R(l!1)
+ # Free hapten sites (on any hapten molecule)
+ Molecules Obs_Free_L_sites L(r)
+ # Free receptor sites (on any receptor molecule)
+ Molecules Obs_Free_R_sites R(l)
+end observables
+
+begin reaction rules
+
+ # ================================================================
+ # Hapten capture: free hapten binds a receptor site
+ # ================================================================
+ # Corresponds to R1 in Perelson and DeLisi (1980): a free ligand
+ # from solution binds a free receptor site with rate constant k1.
+ R_capture: L(r,r) + R(l) -> L(r!1,r).R(l!1) kf
+
+ # ================================================================
+ # Cross-linking: tethered hapten arm binds DIFFERENT complex
+ # ================================================================
+ # Corresponds to R2 in Perelson and DeLisi (1980): the free arm
+ # of a singly-bound hapten binds a receptor site on a different
+ # complex. The "+" between reactants with -bscb flag enforces
+ # inter-complex binding (no intra-complex rings).
+ R_crosslink: L(r!+,r) + R(l) -> L(r!+,r!1).R(l!1) kxf
+
+ # ================================================================
+ # Bond dissociation: any hapten-receptor bond breaks
+ # ================================================================
+ # Corresponds to reverse of R1/R2: any bond between hapten
+ # and receptor dissociates with rate constant k_off.
+ R_dissoc: L(r!1).R(l!1) -> L(r) + R(l) koff
+
+end reaction rules
+
+end model
+
+begin actions
+
+ #@note: |
+ # Network generation is infeasible (unbounded chains).
+ # NFsim flags:
+ # -bscb block same-complex binding (implies -cb)
+
+ # Equilibration kinetics
+
+ #@protocol: |
+ # Simulate from all-free initial conditions to equilibrium
+ # (3000 s). Cross-links build up and reach steady state as
+ # hapten captures and cross-links balance dissociation.
+
+ simulate({method=>"nf",suffix=>"nfr",t_start=>0,\
+ t_end=>3000,n_steps=>300,gml=>2147483647,\
+ param=>"-bscb"})
+
+end actions