Physiological Based Simulation of the Immune System
This is an old Physiological simulation of the Immune System, simulating the influenza virus done around 1999 to 2001.
Disclaimer: This article has not been peer reviewed or published. Provided for informational purposes only.
Source Code
- Psim_immune.cpp .cpp file (Physiological simulation of the Immune System source code)
- Psim_immune.h .h file (Physiological simulation of the Immune System source code)
Introduction
This is an old Physiological simulation of the Immune System, simulating the influenza virus done around 1999 to 2001. The model is based on a bronchial tissue model by Bocharov1994 and a immunological model based on the localization-dose-time model of Zinkernagel2000:
Physiological System and Compartments
Schematic of Cardiovascular Compartments
82.5mm3/msec pulmonaryCapillary 82.5mm3/msec (ml/sec)
|------------>------------O--------+-----------O-------->--------------------|
| VenaCava ___|___ aorta|
| | | _______ |
| | lungs | | | |
| |_______| | brain | |
| |_______| |
| 12.49mm3/msec | 12.5mm3/msec|
|------------<------------------------O------------------------O------<------|
| | | cerebralCapillary |
| _________ | __|_________ |
| | | | | | |
| |pituitary| |<-|hypothalamus| |
| |_________| | |____________| |
| 0.01mm3/msec | | |
|-------<----O------------------O------ |
| hypophysealPortal |
| |
| 4.2mm3/msec |
| |----<------------------<---------------------|
| _______ | ____________ |
| | | | | | |
| | liver | | |stomach, si | |
| |_______| | |____________| |
| 21.7mm3/msec | | | 15.0mm3/msec |
|------<----O------------------O----<------O------------------O-----<--------|
| hepaticSinusoid | portalVein |
| | _______ |
| | | | |
| | | spleen| |
| _______ | |_______| |
| | | | | 2.5mm3/msec |
| |kidneys| |----<------O------------------O-----<--------|
| |_______| splenicCapillary |
| 20.0mm3/msec | |
|------<----O------------------O------------------------------------<--------|
| GlomularCapillary |
| _______ _______ _______ _______ |
| | | |adipose| | bone | |other | |
| |muscle | |tissue | |marrow | |tissue | |
| |_______| |_______| |_______| |_______| |
| 28.3mm3/msec | | | | |
|------<----O---------------------------------------------------O---<--------|
genericCapillary
Notes:
- miscellaneous:
- see vessel compartment values table for more information
Schematic of Lymphatic Compartments
Lymph ____________ Blood
125.0ml/hr --> | Lymph |
|---------------------------------->| Junction |---------------------------->|
| ThoracicDuct(2,3,4,5) |____________| VenaCava |
| 1.25e9cells/hr, 3.0e10cells/day |
| |
|ThoracicDuct1 ____________ |
| | |<--------------------------------------------|
| | Hepatic | ______ |
| | Lymph Nodes| 14ml/hr | | |
|<------------------| |<---------------------------|Liver |<--------|
| 14.0ml/hr | 77grams | HepaticAfferent | | |
| (1.4e8cells/hr) |____________| 1.4e7cells/hr |______| |
| ____________ |
| | |<--------------------------------------------|
| |Subcutaneous| ______ |
| | Lymph Nodes| 1.3ml/hr | | |
|<------------------| |<---------------------------| Skin |<--------|
| 1.3ml/hr | 7grams | SubcutaneousAfferent | | |
| (1.3e7cells/hr) |____________| 1.3e6cells/hr |______| |
| ____________ |
| | |<--------------------------------------------|
| | Misc. | ______ |
| | Lymph Nodes| 31.0ml/hr | | |
|<------------------| |<---------------------------| Misc |<--------|
| 31.0ml/hr | 175grams | miscAfferent |Tissue| |
| (3.1e8cells/hr) |____________| 3.1e7cells/hr |______| |
| muscle/kidney/etc |
| +--------------------------------------------|
| ___________ | ______ |
| | | | | nalt | |
| | |<--+ |......| |
| |Mediastinal| | lalt | |
| | Lymph | 30.0ml/hr |......| |
|<----------------| Nodes |<------------------------------|(balt)|<--------|
| 30.0ml/hr | | Mediastinal Afferent | | |
| (3.0e8cells/hr) | | 3.0e7cells/hr |......| |
| | 168grams | |lungs | |
| |___________| |______| |
| respiratory |
| tract |
| ___________ |
| | Test |<-----------------------------------------------|
| |Mediastinal| _______ |
| |Lymph Node | 2.1 ml/hr | Test | |
|<----------------| |<------------------------------|Bronchi|<-------|
| 2.1 ml/hr | 12 grams | Test Mediastinal Afferent |_______| |
| |___________| |
| |
| |
| +-------------------------------+-------------|
| __________ | __________ | ______ |
| | | | | |<--| | | |
| | |<--+ | Peyers | | | | |
| |Mesenteric| |<---| Patch |<----->| | |
| | Lymph | 49.0ml/hr | |__________| | | | |
|<----------------| Nodes |<--------------| __________ | | | |
49.0ml/hr | | Mesenteric | | |<--+ | | |
(4.9e8cells/hr) | | Afferent | | Lamina | | | |
| 273grams | 4.9e7cells/hr |<---| Propria |<----->| | |
|__________| |__________| |______| |
intestine |
|
+------------------------+-------------------------+--------|
| est:2.6e9cells/day| 2.5e11cells/day| |
____________ | ____________ | ____________ | |
| |<--+ | |<--+ | |<--+ |
| Thymus | | Bone | | Spleen | |
| | | Marrow | | | |
|____________|-->| |____________|-->| |____________|-->| |
| | | |
~2.9e9cells/day| ~3.0e10cells/day| | |
+------------------------+-------------------------+--------|
Notes:
- miscellaneous:
- see vessel compartment values table for more information
- References: Zhu1996, Pabst1988, Young1994, Springer1994
- CellFlowPerHour = flow * EfferentConcentration
- thoraticDuctFlow: 125ml/hour = 2-3liters/day = 0.0347mm3/msec = 4.167e4 mm3/20 minutes, Guyton P.194;
- thoraticDuctCellsPerHour = ~0.3e11 cells/day = 1.25e9cells/hour; Pabst1988
- Total exchange from blood is 5.0e11/day, Pabst1988
- Pabst1988: Spleen, Lymph junction flows
- most flow numbers from Zhu1996
- Liver, Small intestine flow cross checked with Young1994
- lymphNode weights proportional to flows. (test mediastinal lymphNode from Bocharov1994)
Lymph Node Flow diagram
Adapted from Young1999, Seabrook1999. 1 gram lymph node receives
0.012% of cardiac output = ~1.2e8 cells/hour (at least 1 in 4 lymphocytes
cross the HEV and enter the lymph node). average transit time
(blood -> efferent) = ~20 hours for lymphNode (6 hrs for spleen), minimum
appearance time = 1-2hours. Total lymph nodes receives 1-2% of cardiac output.
_________
HEV| |
Blood ---------------------->| lymph |
flow = 26e6 cells/hr | node |
(naive > memory) | |-----------> Efferent Lymph
| 1 gram | flow = 30e6 cells/hr (1gram node)
| |
Afferent Lymph ------------->| | 100% lymphocytes
flow = 3e6 cells/hr |_________| 5% produced within node
(memory > naive) (1gram = 2e9 cells) 10% from afferent
85% from blood (HEV)
6-12 afferent/Node
each at 1e6 cells/hour
10-15% macrophage/dendritic, 5-15% dendritic (Fossum1989)
85-90% lymphocytes
Immune System
Overview
The immunological architecture for this design is based on the localization-dose-time model
of Zinkernagel2000:
Briefly stated, the localization-dose-time model proposes that antigen structure, dose, time and the localization of antigen — vis-a-vis the organized lymphoid tissues — determines reactivity as follows:
- Antigen that does not reach secondary lymphoid organs in minimum doses or for sufficiently long time periods is immunologically ignored.
- Antigen that either usually exists in the lymphoid systems or reaches it and persists in excessive amounts for long periods deletes T cells (clonal exhaustion).
- Antigen that is transported to secondary lymphoid organs in sufficient (but not excessive) amounts and for a sufficient time period (but does not persist) induces an effective immune response.
Kinetic data to develop this model is provided by Gudmundsdottir1999 and Iezzi1998 for tCell activation vs. time and antigen dose.
B cell peripheral tolerance is based on the Fulcher1996 article: localization, dosage and lack of tCell help.
This design also builds upon previous mathematical models, in particular: Bocharov1994, for the influenza A bronchial tissue model. And Kesmir1999 for Germinal center kinetic data.
Some Mathematical Modeling References
- Kesmir1999, germinal center kinetics
- Funk1998, Viral immune response
- Rundell1998, Influenza B, primary/secondary response
- Bocharov1994, Influenza A
- Marchuk1991, Hepatitis B, lymphNode data
Some Useful Immunological Reviews
- General Architecture:
- Zinkernagel2000: localization-dose-time model
- Doherty1995: Anatomical environment in immunity. Cognate, milieu, bystander effects
- Matzinger1994: Two-signal “danger” model
- tCell References:
- Doherty2000: virus specific tCell response
- Swain1996: tCell overview
- bCell References:
- Maclennan1997: germinal center
- Maclennan1993: bCell overview
- Liu1991: germinal center
- Peripheral Tolerance References:
- Fulcher1996: bCell tolerance: function of system (dosage, lack of tCell help)
- Goodnow1995: alternative bCell tolerance model: follicular exclusion
- Oral Tolerance:
- Weiner1994: review
- Faria1999: review
- Chung1999: Memory cells refactory to oral tolerance
- Also see: Zinkernagel2000, Matzinger1994 for tCell tolerance
Primary Humoral Immune Response Schematic (influenza):
plasmaCell
...........................||.............................
.INFECTED TISSUE || .
. / antigen .
. infectedCell igA || .
. || []<==igA .
. ||Replication ||neutralization.
. / / .
. antigen Die .
. .
. dendriticImmature macrophage .
. || || .
. []<== antigen []<== antigen .
. || || .
. / / .
. dendriticApc macrophageApc .
. || || .
................||........................||..............
|| ||
..........................||........................||........................
. / / .
. thNaive bCellNaive macrophageApc .
. || || || .
. []<==dendriticApc []<==dendriticApc ||die .
. || || (or antigen) / .
. / / antigen .
. thBlast bCellApc || .
. || || []<==igM .
. []<== il2 []<== thEffector || .
. ||replicate ||activate / .
. || || immuneComplex .
. []<==dendriticApc / .
. ||polarize bCellBlast .
. / || || .
. thEffector ClassSwitch || || .
. || thEffector==>[] / .
. || dendriticApc || bCellPlasmaMedullary==> igM .
. || tZone || .
. ---- || ------------------- || ------------------------------- .
. || || follicle .
. || replicate[] .
. / || .
. thGerminalCenter / .
. bCellCentroblast==> die .
. || dark zone .
. --------------- []duplicate --------------------- .
. || light zone .
. / .
. fdcapc bCellCentrocyteInitial==> die .
. / || || .
. immuneComplex==>[] []==>Antigen==>[] .
. || || || .
. || / / .
. fdc bCellCentrocyteApc==> die .
. || .
. thGerminalCenter==>[] .
. || .
. / .
.LYMPH NODE bCellCentrocyte==> bCellCentroblast .
.or SPLEEN || || (re-entry) .
...................................||.......||................................
/ /
plasmaCell bCellMemory
Immune System Models:
LymphNode/Spleen Common model
Equations common to both lymph node and spleen
TcCell (CD8) (T Zone (pals))
Migration, TcNaiveBlood => TcNaive:
rate = k2 * TcNaiveBlood; TcNaive += rate; TcNaiveBlood -= rate;
k2 Based on flow rate of 0.21 ul/sec-gram (or 1151 ul/sec for spleen, Pabst1988), from rate of thymus generation, tCell half life, size of tCell pool in lymphNode.
TcNaive => die:
rate = k2 * TcNaive; TcNaive -= rate;
k2 from: HL = ~27weeks, derived from Berzins1998
Activation (with anergy), TcNaive + professionalAPC => TcBlast:
Based on Zinkernagel2000 localization/time/dosage model:
| Apc type | Apc concentration | Notes | ||
|---|---|---|---|---|
| Low | Medium | High | ||
| Dendritic (with influenza virus) | 1k/ml | 10k/ml | 100k/ml | adapted from Ludewig1998 |
| Dendritic (with rye grass) | 1k/ml | 10k/ml | 100k/ml | adapted from Ludewig1998 |
| bCellMemoryApc (with influenza virus) | 10k/ml | 100k/ml | 1000k/ml | HamiltonEaston1995 (scaled by Ludewig1998) |
also see: Iezzi1998 fig.1
Computer model uses 4 intermediate “activation” states between TcNaive and TcBlast: TcBlastPrecursor1,2,3,4 and also a TcAnergy state
step 1: TcNaive + professionalAPC => TcBlastPrecursor1:
rate = k2 * dendriticApc * tcNaive / (km + dendriticApc); tcBlastPrecursor1 += rate; tcNaive -= rate;
tcNaivehalflife: 3 hours @ high dosage, 10 hours @ low dosage,
and > 98% activated in 20 hours from Gudmundsdottir1999 to match corresponding responder frequency, see step 2
step 2: TcBlastPrecursor1,2,3,4 + professionalAPC => TcBlastPrecursor2,3,4,TcBlast (tcAnergy):
Activation time: Iezzi1998: 10 hours @ high dosage, 30 hours @ Low dosage
Anergy: Gudmundsdottir1999: As the tCell proceeds from TcBlastPrecursor1 to TcBlast, a percentage of tCells will go to the anergy state depending on dosage: 23% anergy (77% responder frequency) @ high dosage, 80% anergy (20% responder frequency) @ Low dosage
repeat every 3 hours {
rate = k2 * dendriticApc * tcBlastPrecursor4 / (km + dendriticApc);
tcBlast += rate;
tcAnergy = tcBlastPrecursor4 - rate;
tcBlastPrecursor4 = 0;
rate = k2 * dendriticApc * tcBlastPrecursor3 / (km + dendriticApc);
tcBlastPrecursor4 += rate;
tcAnergy = tcBlastPrecursor3 - rate;
tcBlastPrecursor3 = 0;
rate = k2 * dendriticApc * tcBlastPrecursor2 / (km + dendriticApc);
tcBlastPrecursor3 += rate;
tcAnergy = tcBlastPrecursor2 - rate;
tcBlastPrecursor2 = 0;
rate = k2 * dendriticApc * tcBlastPrecursor1 / (km + dendriticApc);
tcBlastPrecursor2 += rate;
tcAnergy = tcBlastPrecursor1 - rate;
tcBlastPrecursor1 = 0;
}
Rate = .94 @ high dosage (anergy = 23%), .65 @ low dosage (anergy = 80%)
minimum appearance time (from tcNaive to tcBlast) = 12 hours, average time: 12.8 hours @ rate = .94, 18.5 hours @ rate = .65
TcBlastPrecursor2,3,4,TcBlast => il2:
rate = k2 * TcBlastPrecursor[4,3,2],TcBlast; il2 += rate;
from Cho1999 (fig.2) after 24 hours il2 = ~15ng/ml @ 5.0e5 cells (also see: Zimmermann1999, Hamann1997, Gett1998)
~300 molecules/second; conversion factor: il2: 1ng = 6.5e-8 umoles, 10 units = 1ng
Clonal Expansion, TcBlast + il2 => TcEffector:
- MuraliKrishna1998: (fig.4) 1 tCell increases to ~1.0e5 in ~7days = ~17 repetitions = ~10 hours/rep. (maximum rate = 6-8hours, slowing to 24-30hours as antigen clears);
- MuraliKrishna1998: (fig.4) ~11 replications in 5 days (days 3-8): from day 3 to 5: ~9 replications @ 6-8hours/rep; from day 5 to 8: ~2-3 replications @ 24-30hours/rep; estimate: from day 1 to 3: ~6 replications @ 8hours/rep;
- Gudmundsdottir1999: 7+ repetitions from Blast to Effector, repetition speed is antigen dependent;
- Oehen1998: average 8 hours per repetition;
- Swain1999 (cd4), antigen not needed (revisit this for homeostasis, especially secondary response, ditto th expansion);
- Hamann1997: il2 (or il15 or il4) required for replication;
- Bocharov1994: tcEffector increase = ~10k in 3 days, ~14 repetitions, 1rep each ~five hours,
Computer model uses 15 intermediate states between TcBlast and TcEffector: TcEffectorPrecursor1 to TcEffectorPrecursor15, each state represents 1 replication (also assumes replication rate is dependent on il2, not antigen)
TcBlast,TcEffectorPrecursor[1..15] + il2 => TcEffectorPrecursor[1..15],tcEffector
rateReplication = k2 * il2 / (km + il2);
count += rateReplication;
if(count >= 1.0){
count = 0;
rate = kDispersion * TcEffectorPrecursor15;
tcEffector += 2 * rate;
TcEffectorPrecursor15 -= rate;
rate = kDispersion * TcEffectorPrecursor[14..1];
TcEffectorPrecursor[15..2] += 2 * rate;
TcEffectorPrecursor[14..1] -= rate;
rate = kDispersion * TcBlast;
TcEffectorPrecursor1 += 2 * rate;
TcBlast -= rate;
}
rateReplication (k2,km):
- Cho1999, Gett1998: il2 vs. time/replications
- constraint: averageReplicationTime = 50 hours @ il2 = 0.03 ng/ml
- constraint: averageReplicationTime = 15 hours @ il2 = 0.3 ng/ml
- constraint: averageReplicationTime = 7.5 hours @ il2 = 10.0 ng/ml
- fit k2,km to these constraints (note: multiply by kDispersion to get minimumReplicationTime)
Dispersion (dispersion coefficient):
- MuraliKrishna1998: minimum appearance time is ~72 hours. If assume 16 replications then minimumReplicationTime = 4.5 hours; averageReplicationTime (days 1-5) is ~6-8hours
- kDispersion = minimumReplicationTime / averageReplicationTime = ~4.5/7.5 = 0.6
- derived from: averageReplicationTime = kDispersion * minimumReplicationTime * (1 + 2k + 3k^2 + 4k^3…) = kDispersion * minimumReplicationTime / ((1-k)^2) = kDispersion * minimumReplicationTime / kDispersion^2; (note: k = 1 – kDispersion)
- but see: Hasbold1998: bCell cycle times are all at the same rate, therefore kDispersion = 1.0
TcEffectorPrecursor1,2,3…15 => il2:
totalPrecursor = TcEffectorPrecursor[10..1] rate = k2 * totalPrecursor; il2 += rate;
Cho1999, Gett1998: il2 vs. time/replications
uses same k2 as: TcBlastPrecursor2,3,4,TcBlast => il2
tcEffector Produces minimal il2, Hamann1997, assume cutoff at TcEffectorPrecursor10
il2 + TcEffectorPrecursor1,2,3…15 => autocrine usage:
rate = k2 * il2 * totalPrecursor; il2 -= rate;
uses same totalPrecursor as: TcEffectorPrecursor1,2,3…15 => il2
k2 from: tHalflife = 45 hours @ totalPrecursor = 2.0e7/ml
Assume kinetics similar to ifnAlpha, then from Bocharov1994 each tCell consumes ~50 il2 molecules/min = 1.4e-18 umoles/sec-cell, il2 concentration = 6.5e-6 umoles/ml (~100ng/ml)
TcEffector + il2 => 2TcEffector:
ignore for now, ~10x slower than TcBlast, Hamann1997
Activation, TcMemory + professionalAPC => TcMemoryBlast:
rate = k2 * dendriticApc * tcMemory / (km + dendriticApc); tcMemoryBlast += rate; tcMemory -= rate;
activation time = 6 hours, Lalvani1997
1 hour to activate, Iezzi1998, activates even at low doses
Estimate about 10x primary Curtsinger1998, (Zimmermann1999: memory similar to naive)
TcMemoryBlast => il2:
Similar to naive blast, Hamann1997, table 3 (higher amounts, Zimmermann1999)
Clonal Expansion, TcMemoryBlast + il2 => TcEffector:
MuraliKrishna1998: re-challenge (fig.6b): 1 tCell increases to ~110-300 in ~5days = ~7-9 repetitions (day0-3: 5-6 divisions, day4-5: 2 divisions)
Zimmermann1999 20-50% lower than naive tCells, become effectors more quickly
Flynn1999: 5-10x greater than naive.
Cho1999: requires il15. Kedl1998: effectors within twelve hours. (Homeostatis, “decreasing potential hypothesis”)
TcMemory => die:
long lived?
ThCell (CD4) (T Zone (pals))
Migration, ThNaiveBlood => ThNaive:
ThNaive recirculate blood->lymph organs (high endothelial venules, HEV), Swain1999. Rose p.30: naive tCells usually don’t enter non-lymphoid tissue; CCR7, L-selectin, home to lymph, Lanzavecchia 2000
rate = k2 * ThNaiveBlood; ThNaive += rate; ThNaiveBlood -= rate;
k2 Based on flow rate of 0.35 ul/sec-gram (or 1151 ul/sec for spleen, Pabst1988), from rate of thymus generation, tCell half life, size of tCell pool in lymphNode.
ThNaive => die:
rate = k2 * ThNaive; ThNaive -= rate;
k2 from: HL = ~7weeks, Swain1996, Berzins1998
However, seems to be homeostasis regulated. Sprent1994: tHalfLife = years, if thymus is removed (same for tcNaive)
Activation (with anergy), ThNaive + professionalAPC => ThBlast:
See TcNaive activation (step1: tHalfLife = 3 hours @ high, 10 hours @ low; step2: rate = .94 @ high, .65 @ low)
Based on Zinkernagel2000 localization/time/dosage model
This equation is broken into 2 steps, step 1 is the initial activation from ThNaive to thBlastPrecursor1, and step 2 from tcBlastPrecursor1 to tcBlast, adapted largely from the Gudmundsdottir1999 article.
ThBlastPrecursor3,4,ThBlast => il2:
rate = k2 * ThBlastPrecursor[4,3],ThBlast; il2 += rate;
from Cho1999 (also see: Zimmermann1999, Hamann1997, Gett1998), ~300 molecules/second
Clonal Expansion, ThBlast + il2 => ThEffector:
Assume similar to TcNaive clonal expansion
Overall magnitude and duration at least 3 to 4 fold less than cd8, Doherty2000 p.582
Swain1996: 10reps @10 hours/rep, 4-5 days
Swain1999: antigen not needed, divisions: ~6-8 hours;
Polarization: ThEffectorPrecursor + dendriticApc => ThEffectorPrecursor:
This hypothetical model is based on dendritic cells carrying a “third signal” (derived from the anatomical environment of the tissue of origin) which regulates the th1/th2 cytokine profile. See:
- Kalinski1999, third signal model
- Iwasaki1999
- Secrist1995, ApcType
- MaldonadoLopez1999
- Stumbles1998
- Sangster1997, cytokine profiles
- Everson1996
- Doherty1995, anatomical environment
- Mo1995
- Sarawar1994
The model assumes cognate interactions between thCell and dendritic cell determine polarization (instead of milieu cytokine interactions), from Sangster1997
And from Marshall1999: “Th cells may be imagined as decoding information from DC as to the nature of the antigen they carry and the site of entry, and flexibly “interpreting” this information for antigen-specific B cells in their immediate vicinity.”
Results from influenza studies: Sangster1997, Sarawar1994, Doherty1995 Secrist1995 and Marshall1999 were used to develop and constrain the tCell polarization algorithm as well as the bCell class switching algorithm.
- Influenza cytokine profile: Minimal il4, il5, tnfAlpha. Il2, ifnGamma increase from day 3 through day 7. Il10 remains constant from day 3 through 7. Sarawar1994, Mo1995
- Assume dendritic cells are producing il10 and il12 (il12 polarizes th cells to th1-like cytokine profile: il2, ifnGamma). Sarawar1994, Mo1995
- Initial site anatomy dependent: Same virus injected in 2 different locations generates in one case an igA response and in the other an igG response, Sangster1997
- cognate not milieu or bystander effects: 2 different virus responses in same lymphNode at same time, one is igA, the other is igG, Sangster1997
- lymphNode environment independent: virus specific APC are igA, others are igG, Sangster1997
- igA class switching: il4 or il6 not required, Sangster1997
- class switching possibly dependent on APC and dose (Allergen immunotherapy) Secrist1995
- tMemory => bCellNaive => ig profile, reflects current infection, not the tMemory (old) infection, (re-polarization) Marshall1999
| Dendritic il12 |
thCell Polarization (in %) | Notes | ||
|---|---|---|---|---|
| th0 | th1 | th2 | ||
| 100% | 17 | 83 | 0 | strong th1 Iezzi1999 |
| 0% | 59 | 1 | 40 | strong th2 Iezzi1999 |
Polarization algorithm:
for all ThEffectorPrecursor {
il12 = dendriticApc.profile[IL12] ;
rate = k2th1 * ThEffectorPrecursor.profile[TH0] * il12 / (kmth1 + il12) ;
ThEffectorPrecursor.profile[TH0] -= rate ;
ThEffectorPrecursor.profile[TH1] += rate ;
x1 = 1.0 - il12;
rate = k2th2 * ThEffectorPrecursor.profile[TH0] * x1/ (kmth2 + x1) ;
ThEffectorPrecursor.profile[TH0] -= rate ;
ThEffectorPrecursor.profile[TH2] += rate ;
}
Set k2th1,kmth1, etc. such that at the end of 10 repetitions, th cell profile percentages match table values.
ThEffector => il2:
th2 generates no il2; estimate th0, th1 generate at ~300 molecules/sec.
il2 + ThEffectorPrecursor => autocrine usage:
See TcEffectorPrecursor autocrine usage
ThEffector => thGerminalCenter:
rate = k2 * ThEffector;
if (thGerminalCenter > thGerminalCenterTarget) {
rate = 0; /* LIMIT FUNCTION */
}
ThEffector -= rate;
thGerminalCenter += rate;
Assume number of thGerminalCenter cells are anatomically constrained to 5-10% of total germinal center cells, Gray1997
Set thGerminalCenterTarget = maximumThGerminalCenter * numberOfGerminalCenters; maximumThGerminalCenter = ~1500 cells/GC
maximum death rate = 0.036 cells/sec, therefore set tHalfLife = ~2 hours
thGerminalCenter => die:
tHalfLife = 8 hours, Kesmir1999
Replication: thGerminalCenter => 2 thGerminalCenter:
GulbransonJudge1997 (nothing for now)
Activation, ThMemory + professionalAPC => ThMemoryBlast:
rate = k2 * dendriticApc * thMemory / (km + dendriticApc); thMemoryBlast += rate; thMemory -= rate;
Assume same as tcMemory
dendritic cell needed for secondary response, Lambrecht1998, Lambrecht2001
ThMemoryBlast => il2:
assume same as naive blast
Clonal Expansion, ThMemoryBlast + il2 => ThEffector:
Assume same as tcMemory
ThMemoryBlast + dendriticApc => ThMemoryBlast re-Polarization:
See Marshall1999 (placeHolder for now), also Kalinski2000 p.1877
ThMemory => die:
long lived?
bCell (T-Zone, Follicles)
Migration, bCellNaiveBlood => bCellNaive:
rate = k2 * bCellNaiveBlood; bCellNaive += rate; bCellNaiveBlood -= rate;
k2 Based on flow rate of 1.15 ul/sec-gram (or 1151 ul/sec for spleen, Pabst1988), from rate of boneMarrow generation, bCell half life, size of bCell pool in lymphNode.
Migration, bCellNaiveRecirculatingBlood => bCellNaiveRecirculating:
migrates: blood -> tzone -> follicules -> lymph -> blood
rate = k2 * bCellNaiveRecirculatingBlood; bCellNaiveRecirculating += rate; bCellNaiveRecirculatingBlood -= rate;
k2 Based on flow rate of 0.24 ul/sec-gram (or 1151 ul/sec for spleen, Pabst1988), from afferent and efferent flow rates, 125ml/hr, 1.25e9 cells/hr = 347222 cells/sec = 34722 bCells/sec = 50bCells/sec-gram.
bCellNaive => (die):
apoptosis ,HL = 3 days, Janeway P.215, Liu1997; MacLennan1997: > 90% die. Also can derive from size of bCellNaive pool, boneMarrow generation and bCellNaiveRecirculating half life.
bCellNaive => bCellNaiveRecirculating:
rate = k2 * bCellNaive / (ki + bCellNaiveRecirculating); bCellNaiveRecirculating += rate; bCellNaive -= rate;
homeostasis equation from MacLennan1997 page 58 item ii
Also see follicular exclusion, Liu1997, Goodnow1995 (peripheral tolerance for auto reactive bCells)
bCellNaiveRecirculating => (die):
rate = k2 * bCellNaive * bCellNaiveRecirculating; bCellNaiveRecirculating -= rate;
homeostasis equation from MacLennan1997: HL (follicles) = 4-5 weeks (page 58, items i, iii)
bCellNaiveRecirculating + dendriticApc => bCellAPC:
rate = k2 * bCellNaiveRecirculating * dendriticApc / (km + dendriticApc); bCellNaiveRecirculating -= rate; bCellAPC += rate;
k2,km from: MacPherson2000: DC/bCell clusters, tHalfLife = ~6 hours at dendriticApc sufficient (1k/ml low-level)
currently antigen is from dendritic cells. from Wykes1998, MacPherson2000. Revisit for free antigen, MacLennan1997
Peripheral Tolerance: bCellAPC => (die):
tHalfLife = 3 days, MacLennan1997 page 58
MacLennan1997: stays in Tcell zone and no longer recirculates, waits for t-cell or dies
Peripheral Tolerance Model from Fulcher1996: bCell tolerance is function of system (dosage and lack of tCell help). Autoreactive cells (lacking tCell help) die here.
(but see: T independent response model — Baumgarth2000)
Activation: bCellAPC + ThEffector => bCellBlast:
rate = k2 * bCellApc * ThEffector / (km + ThEffector); bCellBlast += rate; bCellAPC -= rate;
tActivation = 1-3 hours at ThEffector concentration = 1.0e5/ml (sufficient response) Funk1998
(but see: Baumgarth2000, revisit?)
Germinal Center Formation: bCellBlast => bCellCentroblast:
Liu1991: in each follicle: 3-5 (or 10-20 Liu1997) bCellBlast generate 1.2e4 to 1.5e4 bCellCentroblast in 12 divisions, ~6 hours cycle time = 72 hours total, during the fourth day germinal center develops
Germinal center first appears 4-5 days after antigen, maximum cell numbers at 10-11 days and decline after about 3 weeks, Liu1991
See TcNaive clonal expansion for example code
bCellCentroblastPrecursor[11...1], choose kbCentroblastReplicateInitial such that 95% of bCellBlast take the plasma medullary route, and 5% take the bCellCentroblast route. (See bCellPlasmaMedullary)
bCellCentroblastPrecursor + ThEffector + dendriticApc => classSwitch:
This hypothetical model assumes cognate interactions between bCell and thCell and dendritic cell determine isotype switching. Also see tCell polarization.
Note: class switching also occurs in germinal center, however most before germinal center, Toellner1998, Toellner1996.
| Dendritic il10 |
thCell Profile | Isotype (in %) | Notes | ||||
|---|---|---|---|---|---|---|---|
| th1 ifnGamma |
th2 il4 |
IgA | IgM | IgG | IgE | ||
| 100% | 83% | 0% | 19 | 9 | 72 | 0 | Influenza (live), Sangster1997 |
| 100% | 1% | 40% | 0? | 40 | 40 | 20 | Hasbold1998, il4 |
class switch: 6+ divisions, Deenick1999
dendritic cells (il10) => isotype switch to igA, Fayette1997;
ifnGamma => igG, Snapper1993
Human isotypes: igG1,igG2,igG3,igG4,igA1,igA2,igM,igE, Stavnezer1996
class switch algorithm:
for all bCellCentroblastPrecursor {
ifnGamma = ThEffector.profile[TH1] ;
il4 = ThEffector.profile[TH2] ;
rate = k2igg * bCellCentroblastPrecursor.profile[IGM] * ifnGamma / (kmigg + ifnGamma) ;
bCellCentroblastPrecursor.profile[IGM] -= rate ;
bCellCentroblastPrecursor.profile[IGG] += rate ; (IgG2)
il10 = dendriticApc.profile[IL10] ;
rate = k2iga * bCellCentroblastPrecursor.profile[IGM] * il10 / (kmiga + il10) ;
bCellCentroblastPrecursor.profile[IGM] -= rate ;
bCellCentroblastPrecursor.profile[IGA] += rate ;
rate = k2igg1 * bCellCentroblastPrecursor.profile[IGM] * il4 / (kmigg1 + il4) ;
bCellCentroblastPrecursor.profile[IGM] -= rate ;
bCellCentroblastPrecursor.profile[IGG] += rate ; (IgG1)
rate = k2ige * bCellCentroblastPrecursor.profile[IGG] * il4 / (kmige + il4) ;
bCellCentroblastPrecursor.profile[IGG] -= rate ;
bCellCentroblastPrecursor.profile[IGE] += rate ;
}
empirically adjust k2,km to fit table data.
Germinal Center Overview
The model is based on Liu1991, MacLennan1997. Architecturally similar to the germinal center mathematical model of Kesmir1999
Model assumes germinal center collapse within ~2 days unless continual renewal of bCellCentroblasts from centrocytes (which must undergo cognate interaction with fdc and thGerminalCenter). Cyclic re-entry hypothesis. Maclennan1997, Kesmir1999
Centroblasts have a 6-7 hours cell cycle time, centroblasts don’t increase in numbers, instead they migrate to light zone to become centrocytes, Liu1991
Assume total Centrocyte pool size is 15k, broken down as: bCellCentrocyteInitial = 12k, bCellCentrocyteApc = 2500, bCellCentrocyte = 500
(but see: Camacho1998. Also revisit numbers after adding affinity maturation model, Smith1997)
| source | destination | flow (bCells/sec) | Notes |
|---|---|---|---|
| bCellCentroblast | Die | 0.14 | tHalfLife = ~20 hours, Kesmir1999; bCellCentroblast pool size = ~15k |
| bCellCentroblast | bCellCentrocyteInitial | 0.6 | Liu1991: 6-7hrs cycle time => tHalfLife = 4.85hrs |
| bCellCentrocyteInitial | Die | 0.3 | tHalfLife = 8 hours, Kesmir1999, GulbransonJudge1997 (total die for all Centrocytes = .36/sec (15k @ thl=8hrs)) |
| bCellCentrocyteInitial | bCellCentrocyteApc | 0.3 | derived: tHalfLife = 8 hours |
| bCellCentrocyteApc | Die | 0.06 | tHalfLife = 8 hours |
| bCellCentrocyteApc | bCellCentrocyte | 0.24 | Derived: tHalfLife = 2 hours |
| bCellCentrocyte | bCellCentroblast | 0.14 | must match “bCellCentroblast => die” for stable germinal center, Derived: tHalfLife = 41min |
| bCellCentrocyte | plasmaCell | 0.04 | remainder of budget assigned to plasma and memory, derived: tHalfLife = 2.4hr |
| bCellCentrocyte | bCellMemory (recirculating) | 0.06 | derived: tHalfLife = 1.6hr |
| bCellCentrocyte | bCellMemoryMarginal | 0.002 | derived: tHalfLife = 48hr |
bCellCentroblast => bCellCentrocyteInitial + bCellCentroblast:
See Germinal Center Overview
bCellCentroblast => die:
See Germinal Center Overview
tHalfLife = ~20 hours, Kesmir1999
bCellCentrocyteInitial => die:
See Germinal Center Overview
tHalfLife = 8 hours, Kesmir1999, GulbransonJudge1997
bCellCentrocyteInitial + fdcApc => bCellCentrocyteApc:
Affinity selection ,See Germinal Center Overview
rate = k2 * bCellCentrocyteInitial * fdcApc / (km + fdcApc); bCellCentrocyteApc += rate; bCellCentrocyteInitial -= rate; fdc += kn * rate; fdcApc -= kn * rate;
kn = 0.01, assumes 100 IC (immune complexes) per fdcApc; tHalfLife = 8 hours @ fdcapc saturated.
about 75 fdcApc per Germinal center (GC), Tew1997
(but see: Hannum2000, IC not essential on FDC), Lindhout1998: < 4 hours (1-2 hours) to block apoptosis
bCellCentrocyteApc => die:
See Germinal Center Overview
tHalfLife = 8 hours, Kesmir1999, GulbransonJudge1997
bCellCentrocyteApc + thGerminalCenter => bCellCentrocyte:
“Peripheral Tolerance”, See Germinal Center Overview
rate = k2 * bCellCentrocyteInitial * thGerminalCenter / (km + thGerminalCenter); bCellCentrocyte += rate; bCellCentrocyteApc -= rate;
activation time = 1-3 hours, Funk1998
tHalfLife = 2 hours @ thGerminalCenter saturated
thGerminalCenter quantity = 1500/GC, (5-10% of GC cells), Gray1997
bCellCentrocyte => bCellCentroblast:
See Germinal Center Overview
germinal center, light zone, migrate to dark zone, recirculation hypothesis, McHeyzerWilliams1997 page176
rate = k2 * bCellCentrocyte; [LIMIT FUNCTION (see note)] bCellCentrocyte -= rate; bCellCentroblast += rate; note: limit function: limit rate to amount of cells lost by the "bCellCentroblast => die" equation
Model assumes germinal center size is limited by anatomical constraints. Therefore germinal center size can’t exceed its initial “maximum” size. centrocytes “re-entering” the dark zone to become centroblasts can’t increase the size of the germinal center but only “restore” centroblasts lost due to cell death (apotosis)
Maximum rate should equal the rate of “bCellCentroblast => die” = 0.14 bCells/sec, which gives a tHalfLife = 41min. (set at 28min for extra margin)
bCellCentrocyte => plasmaCell:
See Germinal Center Overview
rate = k2 * bCellCentrocyte; bCellCentrocyte -= rate; plasmaCell += rate;
germinal center, light zone, migrate to boneMarrow, etc. type: IgG, IgA, IgM, IgE, Liu1997, McHeyzerWilliams1997
maximum rate = 0.1 cells/sec-gc (divided between plasma cells and memory cells)
bCellCentrocyte => bCellMemory:
See Germinal Center Overview
rate = k2 * bCellCentrocyte; bCellCentrocyte -= rate; bCellMemory += rate;
less than 5% of peak germinal center bCell number survive as memory cells, Smith1997
marginal zone memory, recirculating memory — McHeyzerWilliams1997
bCellCentrocyte => bCellMemoryMarginal:
See Germinal Center Overview
rate = k2 * bCellCentrocyte; bCellCentrocyte -= rate; bCellMemoryMarginal += rate;
marginal zone memory, recirculating memory — McHeyzerWilliams1997
bCellBlast => bCellPlasmaMedullary:
See TcNaive clonal expansion for example code, dispersion = 0.6
Red pulp / medullary cords
7 repetitions @ 6 hours/rep., peak at 48 hours
| cell | appearance time | peak | ending time |
|---|---|---|---|
| blasts | day 0 | day 2 | day 3 |
| plasmaCell | day 1 | day 2-4 | day 5 |
5 repetitions in 3 days, Sze2000
6-7 divisions, lasts for three days, Maclennan1997
From Sangster1997: plasmaMedullary = 0.2% of spleen
Liu1991: germinal center = 0.3% of spleen (also Smith1997), primary response (~1% or less secondary response, Liu1991)
therefore: ~95% of bCellBlast => plasmaMedullary, ~5% of bCellBlast => germinal center
Selection between plasma and germinal center (alternative theories): BCR driven, DalPorto1998, Smith1997. McHeyzerWilliams2000: b220-, b220+
il12,il6, Dubois1998
bCellPlasmaMedullary => igM, igG, igA, igE:
rate = k2 * bCellPlasmaMedullary; igM,igG += rate;
rate = 2000 igM/sec-cell, Funk1998.
rate = 14,000 igG/sec-cell, Funk1998
bCellPlasmaMedullary => die:
tHalfLife = ~3 days, Maclennan1997
tHalfLife = 3-5 days, McHeyzerWilliams1997
revisit for long-lived plasma cells??
bCellPlasmaMedullary => plasmaCell:
See Wehrli2001, (assume approximately 10% exit lymphNode).
bCellMemory + dendriticApc => bCellMemoryAPC:
rate = k2 * bCellMemory * dendriticApc / (km + dendriticApc); bCellMemory -= rate; bCellMemoryAPC += rate;
k2,km from: Arpin1997: lower threshold than naive (dendriticApc or antigen, revisit)
bCellMemoryMarginal + antigen => bCellMemoryAPC:
rate = k2 * bCellMemoryMarginal * antigen / (km + antigen); bCellMemoryMarginal -= rate; bCellMemoryAPC += rate;
k2,km from: Arpin1997: lower threshold than naive (antigen, revisit)
Peripheral Tolerance: bCellMemoryAPC => (die):
assume the same as naive: tHalfLife = 3 days
Activation: bCellMemoryAPC + ThEffector => bCellBlastMemory:
rate = k2 * bCellMemoryApc * ThEffector / (km + ThEffector); bCellBlastMemory += rate; bCellMemoryAPC -= rate;
4x more than naive, Liu1997. 10x more than naive McHeyzerWilliams1997
bCellBlastMemory => bCellCentroblast:
see Liu1991 figure 4: initially ~5x primary, dies out more rapidly
bCellBlastMemory => bCellPlasmaMedullary:
see Liu1997 figure 8: 3-5x more than primary. 5-8 fold more plasma cells than primary, (homeostatis, “decreasing potential hypothesis”.) Arpin1997
bCellMemory => die:
long lived?
Miscellaneous (dendritic, macrophage, cytokines…)
il2 => die:
half life = ~45 minutes
dendriticAPC => die:
tHalfLife = 1 day ?? (with tCell interaction), Iezzi1999; waits in lymph node
macrophageApc + TcEffector => die:
rate = k2 * TcEffector * macrophageApc; macrophageApc -= rate; TcEffector -= rate * N;
Estimate: tHalfLife = 20 minutes at TcEffector = 8000/ul, N = 0.1, Bocharov1994
assumes TcEffector cells destroy infected macrophage and dendritic cells.
dendriticApc + TcEffector => die:
rate = k2 * TcEffector * dendriticApc; dendriticApc -= rate; TcEffector -= rate * N;
Estimate: tHalfLife = 20 minutes at TcEffector = 8000/ul, N = 0.1, Bocharov1994, Iezzi1999, Ingulli1997, Knight1997
assumes TcEffector cells destroy infected macrophage and dendritic cells.
macrophageApc => antigen (macrophage die):
rate = k2 * macrophageApc; macrophageApc -= rate; antigen += kn * rate;
Bender1998, tHalfLife = ~24 hours, kn = 2.0 estimate
Assumes macrophages transport antigen from infected tissue to draining lymphNode, die and release antigen for fdc.
antigen + igM => immuneComplex:
rate = k2 * antigen * igM; antigen -= rate; igM -= kn * rate; immuneComplex += rate;
From Tew1997, kn = 1.0 / 6.02e17
tHalfLife = 10 minutes at igM = 1.7e-10umoles/ul (assume tZone), Bocharov1994
(but see Baumgarth2000, Hannum2000)
fdc + immuneComplex => fdcApc:
rate = k2 * fdc * immuneComplex / (km + immuneComplex);
if (fdcApc > fdcApcTarget) {
rate = 0; /* LIMIT FUNCTION */
}
fdc -= rate;
fdcApc += rate;
immuneComplex -= kn * rate;
Assume number of fdcApc cells are anatomically constrained to ~0.5% of total germinal center cells, adapted from Tew1997
maximum fdcApc = ~75 cells/GC; kn = 100.0
immuneComplex trapped in fdc within minutes, Tew1997
Assume km saturated at immuneComplex = fdc * 1000.0
set tHalfLife = ~30 minutes @ saturation
Lymph Node Model
Equations unique to the lymph node, such as afferent lymph input
Migration, bCellNaiveRecirculatingLymphInput => bCellNaiveRecirculating:
Rate = k2 * bCellNaiveRecirculatingLymphInput; bCellNaiveRecirculatingLymphInput -= Rate; bCellNaiveRecirculating += Rate;
flow = 0.05 ul/sec-gram (from 125 ml/hour per 700 grams)
Migration, macrophageApcLymphInput => macrophageApc:
Rate = k2 * macrophageApcLymphInput; macrophageApcLymphInput -= Rate; macrophageApc += Rate;
flow = 0.05 ul/sec-gram (from 125 ml/hour per 700 grams)
Migration, dendriticApcLymphInput => dendriticApc:
Rate = k2 * dendriticApcLymphInput; dendriticApcLymphInput -= Rate; dendriticApc += Rate;
flow = 0.05 ul/sec-gram (from 125 ml/hour per 700 grams)
Migration, bCellNaiveRecirculating => bCellNaiveRecirculatingLymphOutput:
Rate = k2 * bCellNaiveRecirculating; bCellNaiveRecirculating -= Rate; bCellNaiveRecirculatingLymphOutput += Rate;
output formula missing inflammatory response “shut down”, Mackay1992
tHalfLife = 23 days [revisit] (derived to match efferent flow 1.25e9 cells/hour = 347222/sec, 10% bCells = 34722/sec)
Migration, thNaive => thNaiveLymphOutput:
Rate = k2 * thNaive; thNaive -= Rate; thNaiveLymphOutput += Rate;
output formula missing inflammatory response “shut down”, Mackay1992
tHalfLife = 16.3 days [revisit] (derived to match efferent flow)
Migration, tcNaive => tcNaiveLymphOutput:
Rate = k2 * tcNaive; tcNaive -= Rate; tcNaiveLymphOutput += Rate;
output formula missing inflammatory response “shut down”, Mackay1992
tHalfLife = 54.7 days [revisit] (derived to match efferent flow)
Migration, igM => igMLymphOutput:
Migration, plasmaCell => plasmaCellLymphOutput:
Migration, thEffector => thEffectorLymphOutput:
Migration, tcEffector => tcEffectorLymphOutput:
Example: Rate = k2 * tcEffector; tcEffector -= Rate; tcEffectorLymphOutput += Rate;
output formula missing inflammatory response “shut down”, Mackay1992
flow = 0.05 ul/sec-gram, tHalfLife = ~3 hours (from 125 ml/hour per 700 grams)
Migration, bCellMemory => bCellMemoryLymphOutput:
Migration, thMemory => thMemoryLymphOutput:
Migration, tcMemory => tcMemoryLymphOutput:
Example: Rate = k2 * tcMemory; tcMemory -= Rate; tcMemoryLymphOutput += Rate;
tHalfLife = ~23 days, estimates from bCellNaiveRecirculate
Migration, bCellMemoryLymphInput => bCellMemory:
Migration, thMemoryLymphInput => thMemory:
Migration, tcMemoryLymphInput => tcMemory:
Example: Rate = k2 * tcMemoryLymphInput; tcMemory += Rate; tcMemoryLymphInput -= Rate;
flow = 0.05 ul/sec-gram (from 125 ml/hour per 700 grams)
Spleen Model
Equations unique to the spleen, such as blood output and marginal zone
Migration, bCellNaive => bCellNaiveBlood:
Rate = k2 * bCellNaive; bCellNaive -= Rate; bCellNaiveBlood += Rate;
tHalfLife = 1.5 hours (derived to match steady state input flow rate + cell death, Pabst1988)
Migration, bCellNaiveRecirculating => bCellNaiveRecirculatingBlood:
Rate = k2 * bCellNaiveRecirculating; bCellNaiveRecirculating -= Rate; bCellNaiveRecirculatingBlood += Rate;
tHalfLife = 11.7 hours (derived to match steady state input flow rate + cell death, Pabst1988)
Migration, thNaive => thNaiveBlood:
Rate = k2 * thNaive; thNaive -= Rate; thNaiveBlood += Rate;
tHalfLife = 2.5 hours (derived to match steady state input flow rate + cell death, Pabst1988)
Migration, tcNaive => tcNaiveBlood:
Rate = k2 * tcNaive; tcNaive -= Rate; tcNaiveBlood += Rate;
tHalfLife = 2.1 hours (derived to match steady state input flow rate + cell death, Pabst1988)
bCellNaiveRecirculating => bCellNaiveMarginalZone:
Rate = k2 / (ki + bCellNaiveMarginalZone; bCellNaiveRecirculating -= Rate; bCellNaiveMarginalZone += Rate;
Assume anatomically limited and at steady state, rate matches loss rate, Maclennan1997, Maclennan1993
bCellNaiveMarginalZone => die:
Rate = k2 * bCellNaive; bCellNaiveRecirculating -= Rate;
tHalfLife = 3-5 weeks. Maclennan1997, Maclennan1993, extended indefinitely if no new naive cells.
bloodRbc => die:
tHalfLife = ~120 days, 0.36ul/sec Guyton page 425
platelets => die:
tHalfLife = ~8-12 days, 6.84ul/sec ,Guyton page 436
Migration, monocyteBlood => macrophage:
Migration, monocyteBlood => dendriticImmature:
macrophage => 2 * macrophage:
macrophage => die:
See General Tissue Model
Migration, bCellMemory => bCellMemoryBlood:
Migration, thMemory => thMemoryBlood:
Migration, tcMemory => tcMemoryBlood:
Example: Rate = k2 * tcMemory; tcMemory -= Rate; tcMemoryBlood += Rate;
tHalfLife = ~2.5 hours, estimates from thNaive
Migration, bCellMemoryBlood => bCellMemory:
Migration, thMemoryBlood => thMemory:
Migration, tcMemoryBlood => tcMemory:
Example: Rate = k2 * tcMemoryBlood; tcMemory += Rate; tcMemoryBlood -= Rate;
k2 Based on flow rate of 1151 ul/sec for spleen, Pabst1988
Bronchial Test model
Influenza A model:
From Bocharov1994: “Human influenza is an infection of the upper respiratory tract and
the major central airways.
As the virus multiplies in the epithelium throughout the respiratory tract it causes
degeneration and necrosis.
The pathology, characterized by desquamation of the epithelium, involves the nasal mucosa,
larynx and tracheobronchial tree.
Infection with influenza A virus can result in a spectrum of clinical responses
ranging from an asymptomatic infection to a primary viral pneumonia that rapidly
progresses to a fatal outcome.
The typical uncomplicated influenza syndrome is tracheobronchitis with the additional
involvement of small airways.”
inject => antigenBal:
antigenBal += infectionDose (at time 0);
influenza infectionDose = 2.9e7 particles/ml; equals approximately 10% of epithelia cells in bronchial test region), Bocharov1994
antigenBal => die:
tHalfLife = 14 hours, mucociliary Clearance, Bocharov1994
antigenBal + igABal => die:
rate = k2 * igABal * antigenBal; antigenBal -= rate; igABal -= N * rate; (neutralize)
tHalfLifeAntigenBal = 68 min @ igABal = 1.7e-10 umole/ul; N = 10 molecules, Bocharov1994 (rate constant = 8.6e9-8.6e12 ul/umole-day, use 8.6e10)
igABal => die:
tHalfLife = 6 days
Epithelium equations
epitheliaDead => epitheliaCell:
tissue regeneration, fibroblasts. Assumes epithelia region is anatomically constrained. New epithelia cells can only replace dead cells
rate = k2 * epitheliaDead; epitheliaCell += rate; epitheliaDead -= rate;
tHalfLife: 5 hours, Bocharov1994
epitheliaCell + antigenBal => epitheliaApc:
Infection
rate = k2 * epitheliaCell * antigenBal; epitheliaApc += rate; epitheliaCell -= rate; antigenBal -= N * rate;
N = 10; tHalfLife = 1.7 hours at antigenBal = 1.0e7 particles/ul, Bocharov1994 (rate constant = 5.9e11 ul/umole-day)
epitheliaCell + interferonAlpha => epitheliaResistive:
Rate = K2 * epitheliaCell * interferonAlpha; epitheliaResistive += Rate; epitheliaCell -= Rate; interferonAlpha -= N * rate;
N = 10 molecules = 1.3e-7 iu; tHalfLife = 1 hours at interferonAlpha = 0.05 iu/ul, from Bocharov1994 (tc->tr = 1 hour, nsufi = 10-100 iu/ml)
epitheliaCell => die:
rate = k2 * epitheliaCell; epitheliaCell -= rate; epitheliaDead += rate;
k2 from: HL = ~30hours, Stites 678,679
epitheliaResistive => epitheliaCell:
Rate = K2 * epitheliaResistive; epitheliaResistive -= Rate; epitheliaCell += Rate;
tHalfLife = ~24 hours, Bocharov1994
epitheliaApc => epitheliaDead:
rate = k2 * epitheliaApc; epitheliaApc -= rate; epitheliaDead += rate;
tHalfLife = ~16 hours, Bocharov1994
epitheliaApc => antigenBal:
virus replication
rate = k2 * epitheliaApc; antigenBal += rate;
production rate = ~7000 virus particles/day-cell, Bocharov1994 (6000/day)
epitheliaApc + TcEffector => die:
rate = k2 * TcEffector * epitheliaApc; epitheliaApc -= rate; epitheliaDead += rate; TcEffector -= rate * N;
tHalfLife = 20 minutes at TcEffector = 8000/ul, N = 0.05, adapted from Bocharov1994
TcEffector => die:
ThEffector => die:
rate = k2 * TcEffector; TcEffector -= rate;
tHalfLife = 20 hours, AICD, placeHolder for now, revisit… Swain1996
macrophage + antigenBal => macrophageApc:
rate = k2 * macrophage * antigenBal; macrophageApc += rate; macrophage -= rate; antigenBal -= N * rate;
N = 5; tHalfLife = 1 hours at antigenBal = 1.0e7 particles/ul, Bocharov1994 (rate constant = 1.4e13-1.4e11 ul/umole-day)
macrophageApc => interferonAlpha:
Rate = k2 * macrophageApc; interferonAlpha += Rate;
generation, 2.0e-4 iu/day-cell, Bocharov1994 (0.17 molecules/sec), 0.15 molecules/sec Lehmann1996
interferonAlpha => die:
tHalfLife = ~42 minutes
macrophageApc => tnfAlpha:
Rate = k2 * macrophageApc; tnfAlpha += Rate;
generation, 155 molecules/sec-cell, Lehmann1996
tnfAlpha => die:
tHalfLife = ~45 minutes, estimate
Interstitium equations
Activation/Polarization: dendriticImmature + antigenBal => dendriticAPC:
Hypothetical third signal model algorithm. Kalinski1999. See tCell polarization.
| Antigen | il12 | il10 |
|---|---|---|
| influenza | 100% | 100% |
| Ryegrass | 0% | 100% |
rate = k2 * dendriticImmature * antigenBal; dendriticApc += rate; dendriticImmature -= rate; antigenBal -= N * rate;
N = 5; tHalfLife = 1 hours at antigenBal = 1.0e7 particles/ul, assumes same as macrophage
plasmaCell => igABal,igE:
rate = k2 * plasmaCell.profile[IGA]; igABal += rate;
generation, igA = 13,000 molecules/sec-cell, Funk1998
igE = 11,000 molecules/sec-cell, extrapolated from Funk1998
igE => die:
tHalfLife = 2 days
plasmaCell => die:
tHalfLife = 3 weeks, Maclennan1997
TcEffector + !dendriticApc => TcMemory:
rate = k2 * TcEffector / (1.0 + dendriticApc / km); TcEffector -= rate; TcMemory += rate;
MuraliKrishna1998: only about 1% survive. (also see Zinkernagel1996)
tHalfLife = estimate 1000 hours. km = 10k/ml estimate.
thBlast + !dendriticApc => ThMemory:
ThEffector + !dendriticApc => ThMemory:
rate = k2 * ThEffector / (1.0 + dendriticApc / km); ThEffector -= rate; ThMemory += rate;
Assume same as tcMemory.
Activation, ThMemory + dendriticApc => thBlast:
rate = k2 * dendriticApc * thMemory / (km + dendriticApc); thBlast += rate;
See tcMemory activation (lymphNode).
1-6 hours, activation time, Lalvani1997, Iezzi1998
thBlast + dendriticApc => il5:
rate = k2 * dendriticApc * thBlast; il5 += rate;
9600 molecules/sec @ dendriticApc = 1000/ml, loosely adapted from Swain1996, Horie1996, and asthma timelines
asthma: il5: 80% tCell, 15% eosinophil, 11% mast, Moqbel1994
thBlast + dendriticApc => il3:
rate = k2 * dendriticApc * thBlast; il3 += rate;
6000 molecules/sec @ dendriticApc = 1000/ml (placeHolder, adapted from il5)
macrophageApc => bloodGmcsf:
Rate = k2 * macrophageApc; bloodGmcsf += Rate;
generation, 1.3e4 molecules/sec-cell, adapted from Petros1992 (assume at serum = 1ng/ml, MW=~50k, thl=2 hours, #macrophageApc = ~500k)
macrophageApc => die:
tHalfLife = ~24 hours, Bender1998
macrophageApc => macrophageApcLymphOutput:
Rate = k2 * macrophageApc; macrophageApc -= Rate; macrophageApcLymphOutput += Rate;
flow = 6.25e-3 ul/sec
dendriticApc => dendriticApcLymphOutput:
Rate = k2 * dendriticApc * (inflammatoryOutputRate?); dendriticApc -= Rate; dendriticApcLymphOutput += Rate;
flow = 6.25e-3 ul/sec, from lymphatics compartment schematic, (30ml/hr (lungs) * 7.5e-4 (bronchial test portion))
increased by inflammatoryOutputRate? Revisit
macrophageApc + TcEffector => die:
rate = k2 * TcEffector * macrophageApc; macrophageApc -= rate; TcEffector -= rate * N;
Estimate: tHalfLife = 20 minutes at TcEffector = 8000/ul, N = 0.1, Bocharov1994
assumes TcEffector cells destroy infected macrophage and dendritic cells.
dendriticApc + TcEffector => die:
rate = k2 * TcEffector * dendriticApc; dendriticApc -= rate; TcEffector -= rate * N;
Estimate: tHalfLife = 20 minutes at TcEffector = 8000/ul, N = 0.1, Bocharov1994, Iezzi1999, Ingulli1997, Knight1997
assumes TcEffector cells destroy infected macrophage and dendritic cells.
mastNaive + igE => mastCell:
rate = k2 * mastNaive * igE; mastCell += rate mastNaive -= rate; igE -= rate * N;
N = 300k/6.02e17 umoles, Metcalfe1997, 300k receptors/cell
k2 from tHalfLife = 68 minutes @ igE = 1.7e-10 umoles/ul adapted from Bocharov1994
mastCell + antigen => mastCellDegranulated,histamine:
rate = k2 * mastCell * antigen; mastCellDegranulated += rate mastNaive -= rate; histamine += rate * N1; antigen -= rate * N2;
N1 = 1.6e10/6.02e17 umoles, Metcalfe1997, 3-8pg histamine/cell, molecular weight = 111 (c5h9n3)
N2 = 30k particles, Metcalfe1997, maximum histamine release at 30k receptors/cell occupied. (minimal at 100 receptors), internalized within 6-10 minutes
k2 from: high affinity = 8.6e11 ul/umoles-day => tHalfLife = 5.8 minutes @ antigen = 1.2e8 particles/ul adapted from Bocharov1994
histamine => die:
tHalfLife = 15 minutes, 13-96minutes, Erjavec1986, Irmanflorjanc1994
mastCellDegranulated => die:
tHalfLife = 1 day, placeHolder
mastNaive => die:
tHalfLife = 20 days, Kiernan1979
mastCell => die:
tHalfLife = 20 days, Kiernan1979
eosinophil + il5 => ltc4:
rate = k2 * eosinophil * il5^4; ltc4 += rate
k2 from: 200 molecules/second @ il5 = 12 ng/ml (adapted from Wenzel1990, also see Horie1996, Moqbel1994)
ltc4 molecular weight = 625, Murphy1982 p.201
currently placeHolder equation “curve-fit” to match late response timelines. Hill equation with N > 1
revisit: see Laviolette1995
eosinophil => die:
tHalfLife = 11 weeks, Weller1991, (but see Yamaguchi1994, half life vs. il5)
ltc4 => die:
tHalfLife = 20 minutes, 10-20 minutes estimate, Wenzel1990
il3 => die:
tHalfLife = ~35 minutes, Khwaja1994
il5 => die:
tHalfLife = ~45 minutes
Migration, il3 => il3Blood:
Migration, il5 => il5Blood:
Rate = k2 * il3; il3 -= Rate; il3 += Rate;
tHalfLife = ~15 minutes, placeHolder
Inflammatory Response:
for inflamed tissues generating tnfAlpha from macrophages
inflammatoryRate = 1.0 + kn * tnfAlpha / (km + tnfAlpha);
kn = 160, adapted from McWilliam1994, Flynn1999, (9x VanFurth1989)
km = 3.0e-7 umoles/ml (6ng/ml), adjusted to match Flynn1999 data
Inflammatory Output Response:
for inflamed tissues generating tnfAlpha from macrophages
inflammatoryOutputRate = 1.0 + kn * tnfAlpha / (km + tnfAlpha);
kn = 9 estimate, McWilliam1994
km = 3.0e-7 umoles/ml (6ng/ml)
Inflammatory il3 Response:
il3inflammatoryRate = 1.0 + kn * il3
kn = 4.0 @ il3 = 1.1e-7 umoles/ml, placeHolder
Inflammatory il5 Response:
il5inflammatoryRate = 1.0 + kn * il5
kn = 5.0 @ il5 = 3.3e-8 umoles/ml, placeHolder
Migration, eosinophilBlood => eosinophil:
Rate = k2 * eosinophilBlood * il5inflammatoryRate; eosinophilBlood -= Rate; eosinophil += Rate;
Also See General Tissue Model
Migration, mastCellBlood => mastNaive:
Rate = k2 * mastCellBlood * il3inflammatoryRate; mastCellBlood -= Rate; mastCell += Rate;
Also See General Tissue Model
Migration, bCellNaiveRecirculatingBlood => bCellNaiveRecirculating:
Migration, ThEffectorBlood => ThEffector:
Migration, TcEffectorBlood => TcEffector:
Migration, plasmaCellBlood => plasmaCell:
Rate = k2 * plasmaCellBlood * inflammatoryRate; plasmaCellBlood -= Rate; plasmaCell += Rate;
Also See General Tissue Model
Migration, bCellNaiveRecirculating => bCellNaiveRecirculatingLymphOutput:
Rate = k2 * bCellNaiveRecirculating * inflammatoryRate; bCellNaiveRecirculating -= Rate; bCellNaiveRecirculatingLymphOutput += Rate;
Also See General Tissue Model
Migration, monocyteBlood => dendriticImmature:
Migration, monocyteBlood => macrophage:
Rate = k2 * monocyte * inflammatoryRate; monocyte -= Rate; macrophage += Rate;
Also See General Tissue Model
Migration, thBlast => thMemoryLymphOutput: (assume same as thMemory)
Migration, bCellMemory => bCellMemoryLymphOutput:
Migration, thMemory => thMemoryLymphOutput:
Migration, tcMemory => tcMemoryLymphOutput:
Example: Rate = k2 * tcMemory * inflammatoryOutputRate; tcMemory -= Rate; tcMemoryLymphOutput += Rate;
Also See General Tissue Model
Migration, bCellMemoryBlood => bCellMemory:
Migration, thMemoryBlood => thMemory:
Migration, tcMemoryBlood => tcMemory:
Example: Rate = k2 * tcMemoryBlood * inflammatoryRate; tcMemory += Rate; tcMemoryBlood -= Rate;
Also See General Tissue Model
macrophage => 2 * macrophage:
dendriticImmature => 2 * dendriticImmature:
Example:
if ((macrophage + macrophageApc) < macrophageInitial) {
Rate = k2 * macrophage;
macrophage += Rate;
} /* if */
Assume anatomically constrained, revisit?
il4 based? Bertorelli2000
Also See General Tissue Model
macrophage => die:
dendriticImmature => die:
See General Tissue Model
General Tissue Model
Equations for tissues not under investigation (mostly migration)
Migration, bCellNaiveRecirculatingBlood => bCellNaiveRecirculating:
Migration, ThEffectorBlood => ThEffector:
Migration, TcEffectorBlood => TcEffector:
Migration, plasmaCellBlood => plasmaCell:
| tissue | Effector cells: ThEffectorBlood, TcEffectorBlood, plasmaCellBlood | bCellNaiveRecirculatingBlood | |
|---|---|---|---|
| ul/sec Note1 | %total Note1 | ul/sec Note2 | |
| Liver | 5.2 | 15 | 77 * 11.3 / 700 |
| Skin | 3.5 | 10 | 7 * 11.3 / 700 |
| Miscellaneous | 5.2 | 15 | 175 * 11.3 / 700 |
| Respiratory Tract | 6.9 | 20 | 168 * 11.3 / 700 |
| Bronchial Test | 6.9 * 7.5e-4 | 168 * 7.5e-4 * 11.3 / 700 | |
| Intestines | 6.9 | 20 | 273 * 11.3 / 700 |
| boneMarrow | 6.9 | 20 | |
Note1: Effector Cells: From Binns1992: percentage of 125 ml/hr, (see migration pattern worksheet, and lymphatic compartments schematic)
Note2: total all tissues = 11.3 ul/sec, derived to match afferent flow concentration to draining lymph node. (see lymphatic compartments schematic)
Rate = k2 * plasmaCellBlood; plasmaCellBlood -= Rate; plasmaCell += Rate;
Migration, bCellNaiveRecirculating => bCellNaiveRecirculatingLymphOutput:
| tissue | flow ul/sec | volume ul | cells/sec | tHalfLife days |
|---|---|---|---|---|
| Liver | 2.3 | 1,600,000 total | 231 | 5.6 |
| Skin | 10.5 | 3,800,000 total | 21 | 3.1 |
| Miscellaneous | - | - | 525 | 306 |
| Respiratory Tract | 0.36 | 640,000 interstitium | 0.38 | 17.5 |
| Bronchial Test | 0.36 | 480 interstitium | 0.38 | 17.5 |
| Intestines | - | - | 819 | 133.0 |
| boneMarrow | - | - | - | - |
Rate = k2 * bCellNaiveRecirculating; bCellNaiveRecirculating -= Rate; bCellNaiveRecirculatingLymphOutput += Rate;
Derived to match blood -> internal cell flows at steady state. Revisit, as the numbers for miscellaneous and intestines look incorrect.
Migration, mastCellBlood => mastNaive:
Migration, eosinophilBlood => eosinophil:
Migration, monocyteBlood => dendriticImmature:
Migration, monocyteBlood => macrophage:
| tissue | macrophage | dendritic | Mast | Eos | |
|---|---|---|---|---|---|
| ul/sec Note1 | %total Note1 | ul/sec Note2 | ul/sec | ul/sec Note3 | |
| Liver | 50 | 53 | - | - | - |
| Skin | - | - | - | - | - |
| Miscellaneous | - | - | - | - | 104.8 |
| Respiratory Tract | 14 | 15 | - | 267 | 0.13 |
| Bronchial Test | 14 * 7.5e-4 | 0.14 * 7.5e-4 | 267 * 7.5e-4 | 0.13 * 7.5e-4 | |
| Intestines | 7 | 7 | - | - | - |
| boneMarrow | - | - | - | - | - |
| Spleen | 24 | 25 | - | - | - |
| lymphNode | - | - | - | - | - |
Rate = k2 * monocyteBlood; monocyteBlood -= Rate; macrophage += Rate;
Note1: From VanFurth1989: percentage of 95 ul/sec, (4465 cells/sec)
Note2: matches steady state, revisit
Note3: 105ul/sec total
macrophage => 2 * macrophage:
tHalfLife = 1 days (anatomically constrained?) (respiratory tract, bronchial test, intestines) otherwise zero, adapted from VanFurth1989
macrophage => die:
tHalfLife = 4 days, adapted from VanFurth1989
dendriticImmature => 2 * dendriticImmature:
tHalfLife = 1 days (anatomically constrained? ) (respiratory tract, bronchial test, intestines) otherwise zero, adapted from Lambrecht1998
il4 based? Bertorelli2000
dendriticImmature => die:
tHalfLife = 3 days, adapted from Lambrecht1998
plasmaCell => die:
tHalfLife = 3 weeks, Maclennan1997; 3-6 weeks, McHeyzerWilliams1997
ThEffector => die:
TcEffector => die:
rate = k2 * TcEffector; TcEffector -= rate;
tHalfLife = 20 hours, AICD, placeHolder, revisit… Swain1996
ThEffector + !dendriticApc => ThMemory:
TcEffector + !dendriticApc => TcMemory:
rate = k2 * TcEffector / (1.0 + dendriticApc / km); TcEffector -= rate; TcMemory += rate;
MuraliKrishna1998: only about 1% survive. (also see Zinkernagel1996)
tHalfLife = estimate 1000 hours. km = 10k/ml estimate.
Migration, bCellMemory => bCellMemoryLymphOutput:
Migration, thMemory => thMemoryLymphOutput:
Migration, tcMemory => tcMemoryLymphOutput:
Example: Rate = k2 * tcMemory; tcMemory -= Rate; tcMemoryLymphOutput += Rate;
tHalfLife = ~4 days estimate
Migration, bCellMemoryBlood => bCellMemory:
Migration, thMemoryBlood => thMemory:
Migration, tcMemoryBlood => tcMemory:
Example: Rate = k2 * tcMemoryBlood; tcMemory += Rate; tcMemoryBlood -= Rate;
Estimate: k2 Based on flow rate of effector cells.
boneMarrow/thymus Model
bloodGmcsf => die:
tHalfLife = ~2 hours, Petros1992, (actually 5 minutes in blood, 2 hours in tissue)
bloodil3 => die:
tHalfLife = ~35 minutes, Khwaja1994
bloodil5 => die:
tHalfLife = ~45 minutes
boneMarrow => mastCellBlood:
rate = k2 * (1.0 + kn * bloodil3 / (km + bloodil3)); mastCellBlood += rate;
generation/migration, k2 => tHalfLife blood = 3.9 hours, 160/sec
km = 2ng/ml, estimated from Khwaja1994
kn = 1.0, placeHolder for now
boneMarrow => eosinophilBlood:
rate = k2 * (1.0 + kn * bloodil5 / (km + bloodil5)); eosinophil += rate;
generation/migration, k2 => tHalfLife blood = 9 hours, 21393/sec (from Stites p.184; Weller1991: tHalfLife = 11 weeks, tissue levels = several hundred times blood level)
km = 1ng/ml, placeHolder
kn = 3.0, placeHolder for now
boneMarrow => monocyteBlood:
rate = k2 * (1.0 + kn * bloodgmcsf / (km + bloodgmcsf)); monocyteBlood += rate;
generation/migration, k2 => tHalfLife = 10-12 hours, 4446/sec
kn = 2 (3x increase in 24 hours, normal at 96 hours, VanFurth1989, McWilliam1994)
km = 2.0e-9 umole/ml, assume saturated at gmcsf = 1ng/ml, Petros1992
boneMarrow => rbcBlood:
rate = k2; rbcBlood += rate;
generation/migration, tHalfLife = ~120 days, 1.8e6/sec
boneMarrow => plateletsBlood:
rate = k2; plateletsBlood += rate;
generation/migration, thl = 8-12days, 1.9e6/sec
boneMarrow => bCellNaiveBlood:
rate = k2; bCellNaiveBlood += rate;
generation/migration
estimate 5-10% of total b lymphocyte population/day = ~3e10 cells/day, Janeway P. 214
Thymus => ThNaiveBlood:
rate = k2; ThNaiveBlood += rate;
Berzins1998: total tCell rate = ~.7% of total tCell population per day (thymus generation: cd4/cd8 ratio = ~3.5/1; in periphery cd4/cd8 ratio = ~2/1 typical) (thNaive generation: .78 * .007 * 1.2e12/day), (tcNaive generation: .22 * .007 * 1.2e12/day)
Thymus => TcNaiveBlood (thymus):
rate = k2; TcNaiveBlood += rate;
see ThNaiveBlood
Migration, plasmaCellBlood => plasmaCell:
rate = k2 * plasmaCellBlood; plasmaCell += rate; plasmaCellBlood -= rate;
in boneMarrow, MacLennan1997
up to 90% of IgG production from boneMarrow, Janeway P.219, see General tissue
plasmaCell => IgGBlood:
rate = k2 * plasmaCell.profile[IGG]; IgGBlood += rate;
generation, 14,000/sec
plasmaCell => die:
tHalfLife = 3-6 weeks, McHeyzerWilliams1997
plasmaCell => IgMBlood:
rate = k2 * plasmaCell.profile[IGM]; IgMBlood += rate;
generation, 2,000/sec
IgMBlood => die:
tHalfLife = 5 days
IgGBlood => die:
tHalfLife = 23 days
ThEffector + !dendriticApc => ThMemory:
TcEffector + !dendriticApc => TcMemory:
See General Tissue Model
Results:
Influenza A (primary and secondary response) Results:
This initial simulation studies the kinetic characteristics of an “uncomplicated” influenza A virus infection.
See Bocharov1994.
Influenza A Primary Response simulation output, starting with an initial infectious dose of 2.9e7 particles/ml.
Infection was cleared in approximately 9 days, which matches Flynn1999.
From simulation results, viral clearance appears to be quite sensitive to migration kinetics.
The “inflammationRate” variable
from tnfAlpha (see inflammationRate, Bronchial Tissue model, inflammatory response)
was “curve fit” to match the Flynn1999 data. The current value needs to be re-visited.
Influenza A Secondary Response simulation output.
Continuing from the primary response, on day 28, plasma cells and igA were removed from tissues.
And an infectious dose of 2.9e7 virus particles/ml was added.
Infection was cleared in approximately 7 days, which matches Flynn1999.
Encouragingly, in both the primary and secondary responses, the “qualitative” shape/timeline
of the germinal center response curves match the Liu1991 data.
Hopefully indicating that the lymph node model is generally correct.
As with the primary response various variables (inflammationOutputRate, bCellPlasmaMedullary => plasmaCell rate coefficient)
were “curve fit” to match the Flynn1999 data.
The secondary response model is still incomplete. Unresolved is the homeostatsis of memory cells.
Why doesn’t a particular strain overwhelm the memory repertoire, or die out? Also, recirculating memory cells
appear to be insufficient to generate a secondary response. It was necessary to add a bCellMemoryMarginal pool
in order to generate a sufficient bCell response. The tCell response also required adjustment.
tCellEffector -> tCellMemory was adjusted to generate a sufficient tCell response.
Do memory cells, upon activation in tissues, replicate? Currently they only replicate in lymph nodes, as this generates a timeline which matches the Flynn1999 data.
If memory cells replicate in tissues it would appear to cause viral elimination much earlier than the Flynn data would seem to indicate.
Appendix A: Tables
| Compartment Name | volume liters |
% of Body Weight | % Of Total Body Water | |
|---|---|---|---|---|
| Extracellular | total | 14 | 20% | 33% |
| Blood Total | 5.4 | |||
| Blood Plasma | 3.0 | (4.3%) | (7%) | |
| Blood Erythrocytes | 2.4 | |||
| Interstital | 11 | (15.7%) | (26%) | |
| Intracellular | 28 | 40% | 67% | |
| Total Body Water | 42 | 60% | 100% | |
Notes:
- Guyton P.306: extracellular = 16liters, intracellar = 32 liters, total body = 48 liters
- Vander P.7: extracellular = 14liters (interstital = 11L, plasma = 3L), intracellar = 28 liters, total body = 42 liters (60% body weight)
- Vander P.372: hemocrit = 45% men, 42% women, blood total = 5.4L, erythrocytes = 2.4L
- Shargel page.52
| Cardiovascular vessels | |||
|---|---|---|---|
| compartment Name | Flow, mm3/msec | Volume, mm3 | |
| Total | Plasma | ||
| Pulmonary Capillary | 82.5 | 864000 | 475200 |
| Vena Cava | 82.5 | 3432792 | 1888036 |
| Aorta | 82.5 | 702000 | 361100 |
| Cerebral capillary | 12.5 | 55621 | 30592 |
| Hypophyseal portal | 0.01 | 118 | 65 |
| Hepatic sinusoid | 21.7 | 105458 | 58002 |
| Portal Vein | 17.5 | 23090 | 12700 |
| Splenic Capillary | 2.5 | 6075 | 3341 |
| Glomular Capillary | 20.0 | 88994 | 40047 |
| Generic Capillary | 28.3 | 119852 | 65919 |
| Blood reservoir | 5400000 | 2970000 | |
| Total | 82.5 | 5400000 | 2970000 |
| Lymphatic vessels | |||
| compartment Name | Flow, ml/hour | Volume, mm3 | |
| Total | |||
| Thoratic Duct 5 | 125.0 | 200000 | |
| Thoratic Duct 4 | 125.0 | 100000 | |
| Thoratic Duct 3 | 125.0 | 100000 | |
| Thoratic Duct 2 | 125.0 | 100000 | |
| Thoratic Duct 1 | 125.0 | 100000 | |
| HepaticAfferent | 14.0 | 362000 | |
| SubcutaneousAfferent | 1.3 | 227000 | |
| MiscAfferent | 31.0 | 9.7e6 | |
| MediastinalAfferent | 30.0 | 300000 | |
| TestMediastinalAfferent | 2.1 | 225? 21000? | |
| MesentericAfferent | 49.0 | 372000 | |
| Interstitial reservoir | 11500000 | ||
| Total | 125.0 | 11500000 | |
Notes:
- cardiovascular:
- total flow: 75bpm 66ml stroke vol. = 4.9L/min = 82500 mm^3/sec, (actually derived from Guyton P. Page162, aorta: cross-sectional area,velocity)
- references: flow information: Guyton P.200, Greger P.2439, (hypophyseal portal: Greenspan P.97-99)
- references: volume information: Guyton P.162, pulmonary:9%, heart:7% (note:combine heart with pulmonary), arteries:13%, capillary:7%, veins:64%, total:5.4e6mm3
hemocrit = 45% => plasma volume = 5.4e6 * .55 = 2.97e6 - blood reservoir: “temporary placeHolder” common pool for blood cells etc. (for now, speeds up simulation)
- lymphatic:
- References: see Schematic of Lymphatic compartments
- Chylomicron lymph flow latency: approximately 2 hours
- Efferent volume: .6? liters lymph, derived from simulation: ~9hours to remove chylomicrons from lymph
- assume Afferent volume = interstital fluid, see organ compartment values table (below)
- peritoneal cavity = ~2-3 liters, estimate from Yuan1994
- thoratic duct volume numbers are rough “place holders” for now
- Interstitial reservoir: “temporary placeHolder” for glucose, tsh, etc.
| Compartment Name | Weight kilograms |
Total volume ml |
blood flow ml/min |
lymphatic flow ml/hour |
interstital volume ml |
vascular volume ml |
|
|---|---|---|---|---|---|---|---|
| Spleen | total | 0.150 | 150 | 150 | 0 | ? | |
| tZone (pals) | 0.021 | - | - | - | - | ||
| follicle | 0.006 | - | - | - | - | ||
| Marginal Zone | 0.011 | - | - | - | - | ||
| red pulp | 0.112 | - | - | - | - | ||
| Lymph Nodes | total | 0.7 | 700.0 | 125 | ? | ||
| tZone (pals) | 79% | - | - | - | - | ||
| follicle | 21% | - | - | - | - | ||
| Small Intestine | Total | 1.6 | 2147 | 45 | 372 | ||
| Epithelium | - | - | - | - | - | ||
| Lamina propria | - | - | - | - | - | ||
| Peyer’s patches | - | - | - | - | - | ||
| Lung | Total | 1.1 | 999 | 4950 | 30 | 300 | |
| Broncho Alveolar space (BAL) | - | 560 | - | - | - | - | |
| Epithelium | - | 800 | - | - | - | - | |
| Interstitium | - | 640 | - | - | - | - | |
| Bronchial test segment | Total | 2.1 | 21? | ||||
| Broncho Alveolar space (BAL) | - | 0.42 | - | - | - | - | |
| Epithelium | - | 0.6 | - | - | - | - | |
| Interstitium | - | 0.48 | - | - | - | - | |
| Bone / Bone Marrow | 9.8 | 279 | |||||
| Skin | 4.0 | 3.8e3 | 500 | 1.3 | 227 | ||
| Liver | 1.6 | 1809 | 1300 | 14 | 362 | ||
| Thymus | |||||||
| Brain | 1.4 | 750 | |||||
| Heart | 0.3 | 300 | 250 | 43 | |||
| Kidneys | 0.3 | 284 | 1200 | 97 | |||
| Skeletal Muscle | 35.0 | 2.6e4 | 1000 | 4558 | |||
| Fat | 10.0 | ||||||
| connective tissue | 4.9 | ||||||
| adrenals | 0.014 | ||||||
| thyroid | 0.028 | ||||||
| Total Body | 70.0 | 4950 | 125 | 11000 | |||
Notes:
- miscellaneous:
- References:
- References: Greger p.2439 (Blood flows, weights)
- Shargel page 68
- Zhu1996, volumes
- References lymphatic flows: see Schematic of Lymphatic compartments
- References:
- Compartment:
- spleen:
- Chadburn2000: spleen volume: 75% red pulp, 25% white pulp
- volumes derived from cell distribution (percentage of white pulp): tzone = 55%, follicle = 16%, marginal zone = 28%, 1.8e9 lymphocytes/gram of white pulp
- lymphNode:
- Marchuk1991
- 600-800grams, 1% of body mass, 500-1000 lymph nodes in body
- volumes derived from cell distribution: tzone = 79%, follicle = 21%
- Small Intestine:
- surfaceArea = ~100m2, Pabst1987, 200m2 Shargel p.when 13 ,300m2 Faria1999, 1e11 Lymphoid cells/meter Faria 1999
- 13-20 intra-epithelia lymphocytes per 100 epithelia cells, Pabst1987 = 2.7e11 epithelia cells in small Intestine
- bacteria = ~1.0e12/gram-stool ? Faria 1999?
- Lung:
- Bocharov1994, Crapo1982
- surfaceArea = 70-90m2 = 8.0e7mm2
- bal thickness = 7um, volume = 560ml
- epithelium thickness = 10um, volume = 800ml
- interstitium thickness = 8um (placeHolder), volume = 640ml
- surfaceArea of epithelia cell = 500um2, ~2000 epithelia cells / mm2; total epithelia cells in lung: 1.6e11
- bronchial test segment:
- Bocharov1994
- surfaceArea = 6.0e4 mm2 = 0.075% of lung; (scale lungs values by 7.5e-4)
- bal thickness = 7um, volume = .42ml
- epithelium thickness = 10um, volume = .6ml
- interstitium thickness = 8um (placeHolder), volume = .48ml
- Skin:
- Goldsmith1990
- surfaceArea = weight^.425 * height^.725 * 71.84; averageSurfaceArea = 1.7 square meters
- average thickness = 2.23mm; density = 1.102 gm/ml (assumes skin is 70% water + 30% protein)
- spleen:
| Pool | Total Cells | Subset | Plasma | B1 (cd5) | ||||
|---|---|---|---|---|---|---|---|---|
| Total | Naive % |
Recir. % |
Memory % |
|||||
| Blood | 3.4e9 | 3.4e9 | 65 | 30 | 5 | 0 | ||
| Lymph Fluid | efferent | 5.0e8 | 5.0e8 | 0 | ||||
| afferent | 4.7e8 | 4.7e8 | 0 | |||||
| Peritoneal Cavity | 8.3e7 | 8.3e7 | 0 | |||||
| Spleen | total | 3.5e10 | ? | |||||
| tZone (pals) | 7.0e9 | 50 | 50? | |||||
| follicle | 1.3e10 | 100 | ||||||
| Marginal Zone | 1.5e10 | 100 | ||||||
| red pulp | ||||||||
| Lymph Nodes | 2.3e11 | 2.1e11 | 52 | 48 | 2.1e10 | |||
| Bone Marrow | 4.5e10 | 2.5e10 | total:2.0e10 IgA:4.4e9 IgM:4.3e9 IgG:1.1e10 |
|||||
| Small Intestine | Total | |||||||
| Epithelium | 1.0e8 | 1.0e8 | 0 | |||||
| Lamina propria | 3.5e10 | 7.5e9 | total:2.8e10 IgA:1.3e10 IgM:9.5e9 IgG:5.4e9 |
|||||
| Peyer’s patches | 6.0e9 | 6.0e9 | 0 | |||||
| Lung | Total | |||||||
| BronchoAlveolar space (BAL) | 4.8e5 | 0 | ||||||
| Epithelium | 2.4e8 | 0 | ||||||
| Interstitium | 9.0e8 | ? | ||||||
| Skin | 8.0e6 | 8.0e6 | 0 | |||||
| Liver | 1.6e8 | 1.6e8 | 0 | |||||
| Thymus | 5.0e8 | 5.0e8 | 0 | |||||
| Misc Tissue | 2.0e10 | 2.0e10 | 0 | |||||
| Total Body | 3.7e11 | |||||||
Notes:
- miscellaneous:
- References:
- Adapted from Westermann1992 fig.2, table1 (except for below, especially lymphNode)
- Seabrook1999: Afferent lymph composition = interstitial fluid composition
- Others: Guyton, Janeway, Pabst1988, Pabst1995
- Plasma Cells:
- Funk1998
- 1 igA plasma cell generates: ~13,000 molecules/second
- 1 igG plasma cell generates: ~14,000 molecules/second
- 1 igM plasma cell generates: ~2,000 molecules/second
- individual strains:
- Janeway p. 404,311
- bCells: 1:1.0e4 to 1:1.0e6
- tCells: 1:1.0e4 to 1:1.0e6
- Pool:
- Blood: 5.4L blood * 2544cells/ul = 1.37e10 cells, Janeway P.67; naive vs. recirculating % loosely derived from Young1999
- Lymph Fluid:
- EfferentConcentration = 1.0e7 cells/ml = thoraticDuctCellsPerHour / thoraticDuctFlow
- AfferentLymphConcentration = 1.0e6 cells/ml (Seabrook1999)
- Percentages between afferent (85%), PeritonealCavity (15%) estimate from Yuan1994
- Spleen: Percentages from: MacLennan1993: 20% tZone, 36% follicle, 44% marginal zone
- lymphNode:
- Marchuk1991: germinal center diameter = .1 to .3 mm
- Marchuk1991: cells/gram of lymphNode: bCells: 3.0e8; plasma: 3.0e7; tCells: 1.4e9 (th:7.0e8, tc:7.0e8, thfollicle:1.0e7); macrophage: 3.3e6; macrophageApc: 2-8e5, idc=1.6e7; dendritic:1.6e7
- boneMarrow: plasma cells: quantities to generate average Ig blood levels.
- Small Intestine:
- Percentages between Epithelium (60%), LaminaPropria (25%), PeyersPatches (15%), Pabst1987?
- LaminaPropria: plasma cells: derived from Elson1997 (3-4 grams IgA produced/day): igA: 70-90%, IgM: 5-15%, igG: 3-5%
- Lung:
- BAL concentrations (Velluti1984): macrophage:138k/ml, lymphocytes:17k/ml, neutrophil:1.3k/ml, eosinophils:0.7k/ml
- BAL (9.5e6 lymphocytes), Epithelium (2.4e10 lymphocytes (Westermann1992: 15lymphocytes/100 epithelia cells)), Interstitium (6.0e9)
- Skin: 8.0e8 cells = 2.0e5 cells/gram (Seabrook1999) * 4000 grams
- Liver: .5e9 / 35% (derived from Westermann1992, NT cells) = 1.4e9 cells
- MiscTissue: Percentages between bCells (50%), tCells (50%) are place holders for now
- Total Body: lymphocytes = order of 1.0e12 cells, Stites page 43. Total bCells: ~9.0e11, Rolink1993
| Pool | Total Cells | Th (cd4) | Tc (cd8) | Gamma Sigma |
|||||
|---|---|---|---|---|---|---|---|---|---|
| Total | Naive % |
Memory % |
Total | Naive % |
Memory % |
||||
| Blood | 1.0e10 | 6.9e9 | 23 | 77 | 3.4e9 | 0.0 | |||
| Lymph Fluid | efferent | 4.8e9 | 3.3e9 | 85 | 15 | 1.0e9 | 5.0e8 | ||
| afferent | 7.0e9 | 3.7e9 | 1.9e9 | 1.4e9 | |||||
| Peritoneal Cavity | 1.6e9 | 4.1e8 | 9.9e8 | 1.7e8 | |||||
| Spleen | Total | 3.5e10 | 69 | 31 | 0.0 | ||||
| tZone (pals) | 3.0e10 | 2.3e10 | 7.0e9 | ||||||
| follicle | 1.0e9 | 1.0e9 | 0 | ||||||
| Marginal Zone | 4.0e9 | 3.3e9 | 7.0e8 | ||||||
| red pulp | |||||||||
| Lymph Nodes | 9.8e11 | 4.9e11 | 90 | 10 | 4.9e11 | 9.5e9 | |||
| Bone Marrow | 2.5e10 | 1.0e10 | 0 | 100 | 1.5e10 | 0.0 | |||
| Small Intestine | Total | 3.5e10 | |||||||
| Epithelium | 1.0e10 | 1.5e9 | 33 | 67 | 8.5e9 | 0.0 | |||
| Lamina propria | 1.8e10 | 1.3e10 | 33 | 67 | 5.0e9 | 0.0 | |||
| Peyer’s patches | 6.8e9 | 4.5e9 | 100 | 0 | 1.5e9 | 7.5e8 | |||
| Lung | Total | ||||||||
| BronchoAlveolar space (BAL) | 9.0e6 | 5.6e6 | 15 | 85 | 3.4e6 | 15 | 85 | 6.0e7 | |
| Epithelium | 2.4e10 | 7.2e9 | 15 | 85 | 1.7e10 | 15 | 85 | 2.0e8 | |
| Interstitium | 5.0e9 | 2.5e9 | 15 | 85 | 2.5e9 | 15 | 85 | 0.0 | |
| Skin | 7.2e8 | 3.6e8 | 3.6e8 | 0.0 | |||||
| Liver | 9.6e8 | 4.0e8 | 31 | 69 | 5.6e8 | 0.0 | |||
| Thymus | 5.1e10 | 2.3e10 | 0 | 100 | 2.3e10 | 4.5e9 | |||
| Misc Tissue | 2.0e10 | 1.0e10 | 1.0e10 | 0.0 | |||||
| Total Body | 1.2e12 | 1.7e10 | |||||||
Notes:
- miscellaneous:
- See bCells pools worksheet
- Th: percentages between Naive and Memory adapted from Swain1996
- Pool:
- MiscTissue: Percentages between Th (50%), Tc (50%) are place holders for now
- Lymph efferent: Farstad1997
| Pool | Macrophage | Neutrophil | Dendritic cells | Eos | Baso | Mast cells | NK | |
|---|---|---|---|---|---|---|---|---|
| Blood | 0 | 4200/ul | 0 | 203/ul | 7/ul | 0.6/ul | 0 | |
| Lymph Fluid | efferent | 0 | 0 | 2.5e8 | ||||
| afferent | 5-15e4/ml | 1.9e9 | ||||||
| Peritoneal Cavity | 0 | |||||||
| Spleen | 4.6e10 | 0 | ||||||
| Lymph Nodes | 2.5e9 | 2.2e10 | 3.8e8 | |||||
| Bone Marrow | 0 | 1.0e8 | ||||||
| Small Intestine | total | 2.8e10 | 9.3e8 | 0 | ||||
| Epithelium | 0 | |||||||
| Lamina propria | 0 | |||||||
| Peyer’s patches | 7.5e8 | |||||||
| Lung | total | 2.3e10 | 2.3e8 | 0 | ||||
| BronchoAlveolar space (BAL) | 7.7e7 | 1.3e6 | 6.2e5 | 2.7e4 | ||||
| Epithelium | 2.3e10 | 2.3e8 | 6.0e6 | 1.0e7 | 2.5e9 | |||
| Interstitium | 8.0e7 | 1.6e8 | 2.4e8 | 4.0e8 | 5.0e8 | |||
| Skin | 1.0e9 | 4.0e7 | ||||||
| Liver | 1.0e11 | 4.8e8 | ||||||
| Thymus | 0 | |||||||
| Misc Tissue | ~2.0e11 | 0 | ||||||
| Total Body | 1.7e10 | |||||||
Notes:
Pool:
- Blood:
- mast cells: Metcalfe1997
- Monocytes: not listed, blood only
- Lymph Fluid:
- Dendritic cells: Fossum1989
- Spleen:
- macrophage: VanFurth1989, rough estimate
- platelets: 30% of total
- number of germinal centers = ((initialStrain * 5%) * 4096 / 3%) / 15,000
- very rough estimate: fdc = 5.6e6 total, estimate: ~75k follicles total
- lymphNode:
- Marchuk1991
- very rough estimate: fdc = 1.5e5/gram, estimate: follicles = ~2000/gram
- Small Intestine:
- macrophage: VanFurth1989, rough estimate
- neutrophil: Pabst1987
- Lung:
- macrophage total: Crapo1982
- dendritic total: xia1995: < 1%, (but Holt1994: 500-800dc/mm2 * 8e7mm2 = 4.8e10)
- interstitium: Jeffery1989: neutrophil, eosinophils, mast
- epithelium: Djukanovic1990, Pesci1993, Laitinen1993: eosinophils
- BAL: Velluti1984: macrophage
- BAL: Liu1991b: neutrophil, eosinophils, mast
- BAL: iga: .9mg/ml, igg: .17mg/ml, ige: 77.2ng/ml, Reynolds_1976
- skin:
- dendritic: Banchereau1998
- Liver:
- macrophage: VanFurth1989, also from web: 1600grams * 1.0e7 kupfer/gram
- miscellaneous tissue:
- Eos: Weller1991
| Destination | Source | |||||
|---|---|---|---|---|---|---|
| Lymphoblasts | Non-Blasts | |||||
| Lymph Node | Spleen | Lungs | Gut | skin | ||
| Bone Marrow | 27 | 20 | 20 | 30 | ||
| Muscle | 10 | 25 | 8 | 3 | ||
| Skin | 12 | 10 | 5 | 1 | ||
| Lungs | 8 | 8 | 20 | 10 | ||
| Liver | 8 | 8 | 15 | 30 | ||
| Gut | 15 | 15 | 20 | 2 | ||
| Lymph Nodes | 4 | 3 | 5 | 10 | ||
| Spleen | 2 | 2 | 2 | 8 | ||
| Misc | 14 | 9 | 5 | 6 | ||
| Total | 100% | 100% | 100% | 100% | ||
Notes:
- miscellaneous:
- adapted from Binns1992
| homing receptor | vascular addressin | destination |
|---|---|---|
| L-selectin (cd62L) | cd34, glyCAM-1 | naive => lymphNode |
| L-selectin (cd62L) | MAdCAM | naive => peyersPatches |
| alpha4Beta7 | MAdCAM | naive => peyersPatches memory/effector => Lamina Propria of GI tract |
| CLA | E-selectin | memory/effector => skin |
| VLA-4 | VCAM-1 | lymphoblasts => inflammation site memory/effector => inflammation site |
| cd44 | hyaluronate | lymphoblasts => inflammation site |
Notes:
- References: Farber2000, Springer1994, Stites p.61
| Marker | Naive | effector | Central Memory | Memory |
|---|---|---|---|---|
| cd45ro | - | + | + | + |
| cd45ra | high | high | low | low |
| cd29 | low | high | high | high |
| cd25 (il2r) | low | high | low | low |
| cd28 | high | |||
| cd2 | low | high | ||
| cd44 | low | high |
Notes:
- References: Farber2000, Springer1994, Lanzavecchia2000
- cd5, cd3+, cd4, cd8
| Cell name | Diameter | Half Life | Rate | Default Concentration | Reference |
|---|---|---|---|---|---|
| RBC | 7.8um | life span = ~120days | 1.6e11/day | 5.0e6 cells/ul blood | Guyton P.425 |
| platelets | 2-3um | life span = 8-12 days | 30k/day/mm3, 1.62e11/day | 250e3 cells/ul blood | Guyton P.435, 436, 463 |
| neutrophils | 10-15um | circulation: 12 hours, tissue: 2 days | ~1.0e9/kg-day = ~7.0e10/day | 4200 cells/ul blood | Guyton P.435, Stites p.32, storage in boneMarrow = 5x blood, eats 5 to 20 bacteria before dies; Benestad1989: migration to inflamed tissue (skin .5cm2) = ~2e6/hr |
| eosinophils | 15-20um | 30min circulation, 12days tissue | 203 cells/ul blood | Guyton P.435; for each in circulation: 500 in connective tissue, 200 in bone marrow | |
| basophils | 7 cells/ul blood | Guyton P.435 | |||
| monocytes | 12-15um | 10-12 hours in blood | 42 cells/ul blood | Guyton P.435, 436 | |
| bCells | 5-12um | 620 cells/ul blood | Janeway P.67, 214, Westermann1992, Stites p.43 | ||
| helper tCells | 5-12um | 1278 cells/ul blood | Janeway P.67, Stites P.49,43, Westermann1992 | ||
| cytotoxic tCells | 5-12um | 620 cells/ul blood | Janeway P.67, Stites P.49, 43, Westermann1992 | ||
| Dendritic cells | ~3 days | ? cells/ul | Ruedl2,000 | ||
| Mast cells | 10-15um | ? cells/ul | |||
| Macrophage | 20-50um | ? cells/ul | Guyton 439: eats ~100 bacteria before dies | ||
| NK cells | ? cells/ul |
| Cytokine | Molecular Weight | Half Life | Rate | Default Conc. | Cells | Reference |
|---|---|---|---|---|---|---|
| gcsf | 18k | Benestad1989 | ||||
| gmcsf | 19k-90k, 22k Benestad1989 | HL = 5 min. blood, HL = 1-3 hours tissue | 1ng/ml blood | macrophage, tCells | Petros1992 | |
| il-1 | 17000 | HL < 1hr | macrophage | Mondino1996; Stites; inflammatory | ||
| il-2 | 15400 | HL < 1hr | activated Th1 produces, co-stimulus for tCell expansion, autocrine, paracrine | Stites | ||
| il-3 | 18k | 35 min | Mast, eos growth | Benestad1989, Khwaja1994 | ||
| il-4 | 15000 | HL < 1hr | Stites; immunosuppressive | |||
| il-5 | 30,000 | HL < 1hr | Th2 produces, eosinophil growth | Portanova1995 | ||
| il-6 | 22000 – 30000 | HL < 1hr | Stites; inflammatory | |||
| il-10 | 18000 | HL < 1hr | Th2, CD8+, macrophage, monocytes, dendritic, bCells, eosinohil, mast cells… | Mondino1996; Stites; immunosuppressive | ||
| il-12 | 35000 – 40000 | HL < 1hr | macrophage, dendriticMature | Lanzavecchia2000; Stites | ||
| il-15 | HL < 1hr | |||||
| il-18 | HL < 1hr | dendriticMature | Lanzavecchia2000 | |||
| ifn-alpha | 16000 – 27500, 17k | HL = 42min | dendriticMature | Lanzavecchia2000; Stites; type1; (note: 8e-5iu = 6e3 molecules, conversion factor = 7.5e7) | ||
| ifn-gamma | 18000 | HL < 1hr | Th1 produces, activates macrophage, iG class switching (igG2a in mouse, igG2a: fix complement, macrophage Fc receptors), cd8 | Stites; type2 | ||
| mif | HL < 1hr | activates macrophages | macrophage inhibition factor | |||
| tnf-alpha | ~20k | HL < 1hr | macrophage | Mondino1996; inflammatory | ||
| tgf-beta | HL < 1hr | Mondino1996; immunosuppressive |
Notes:
- miscellaneous:
- References: Janeway p.588; Stites p.16, ch 10
| Extracellular Fluid | triglycerides (grams) |
fatty acids (grams) |
glucose (grams) |
protein (grams) |
|---|---|---|---|---|
| Blood plasma | 3, note c | .3-.45, note d | 2.7, note b | 219, note e |
| Interstitial fluid | 10.0, note b | 280, note e |
Notes:
- Stryer P. 771, Voet P.792
- in lipoproteins,Voet P. 792
- free fatty acids, Guyton P. 866, Voet P.792
- 7.3grams/dl * 3liters = 219grams, 2.5g/dl interstitial, Guyton P.190, Voet P.375
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Books/Monographs
- Berne, Levy – Physiology, 4th ed
- Brooks – Exercise Physiology, 3rd ed
- Greenspan – Basic and Clinical Endocrinology 5th ed
- Greger – Comprehensive Human Physiology (vol I,II), 1996
- Guyton and Hall – Textbook of medical physiology, 9th ed
- Janeway – Immunobiology 4th ed, 1999
- Lehninger – Principles of Biochemistry, 2nd ed
- Mims – Medical Microbiology 2nd ed, 1998
- Rose – The Autoimmune Diseases 3rd ed, 1998
- Salway – Metabolism at a Glance, 1994
- Shargel – Applied biopharmaceutics and pharmacokinetics, fourth ed
- Stites – Medical Immunology 9th ed, 1993
- Stryer – Biochemistry, 4th ed
- Vander – Human physiology, 7th ed
- Voet & Voet – Biochemistry, 2nd ed
- Abramson – blood vessels and lymphatics in organ systems (flow data for organs)
- Alberts – Molecular Biology of the Cell, 3rd ed
- Berne P.,Levy – Cardiovascular physiology
- Fung – Biomechanics, circulation
- Johnson – Gastrointestinal Physiology
- Netter – Atlas of human anatomy
- Segel – Enzyme Kinetics, 1993
Web Sites