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Cytotoxic T Lymphocytes CTLs can kill virus-infected cells. Here, a CTL (arrow) is attacking and killing a much larger influenza virus-infected target cell. http://www.cellsalive.com/ Models of CTL Response dT/dt = l – dT – kVT dT*/dt = kVT – dVT* - dEET* dV/dt = pT* - cV dE/dt = kEET* - mE CTL Effectors Nowak and Bangham, Science 272, 74 1996 LCMV Infection LCMV Armstrong into BALB/c mice, Ahmed 1998 Simple Model of CD8 Response DeBoer … Perelson, J Virol. 75,10663 (2001), On-Off Model Activation function Ton = recruitment time A(0) = cells recruited Model Predictions Continuous Model Parameter Estimates Simulating CTL Response Low affinity clones sometimes dominate 10 response V Total CTL V □, ∆,◊ are 3 highest affinity clones Modeling the Kinetics of Hepatitis B and C Infections Alan S. Perelson, PhD Theoretical Biology & Biophysics Los Alamos National Laboratory Los Alamos, NM Viral Hepatitis - Overview Type of Hepatitis A Source of virus Route of transmission Chronic infection Prevention feces fecal-oral no B C D blood/ blood/ blood/ blood-derivedblood-derived blood-derived body fluids body fluids body fluids E feces percutaneouspercutaneous percutaneous fecal-oral permucosal permucosal permucosal yes yes yes no pre/postpre/post- blood donor pre/post- ensure safe exposure exposure screening; exposure drinking immunization immunization risk behavior immunization; water modification risk behavior modification Estimates of Acute and Chronic Disease Burden for Viral Hepatitis, United States Acute infections (x 1000)/year* Fulminant deaths/year Chronic infections Chronic liver disease deaths/year HAV HBV HCV HDV 125-200 140-320 35-180 6-13 100 150 ? 35 0 1-1.25 million 3.5 million 70,000 5,000 8-10,000 1,000 0 * Range based on estimated annual incidence, 1984-1994. Hepatitis B and C Virus HBV is a DNA virus – Genome is very small, ~ 3.2kb, – Takes the form of a partially closed circle – Vaccine; therapy to control not cure HCV is a positive strand RNA virus – Genome is about 9.3kb, approximately the same size as HIV – No vaccine; therapy successful in 50% of people treated Mean Decrease in HCV RNA Levels Over First 14 Days of QD IFN- Treatment Days Mean Decrease HCV RNA (Log10 Copies/mL) 0 7 0.5 0 HCV Genotype 1 -0.5 -1 -1.5 -2 -2.5 5MU 10MU 15MU -3 Lam N. DDW. 1998 (abstract L0346). 14 Model of HCV Infection b Infection Rate p Virions/d I Infected Cell T Target Cell d Loss c Clearance What if IFN blocks infection? IFN p virions/d I Infected Cell b d death T Target cell c clearance What if IFN Blocks Production? b IFN I Infected Cell p Virions/d e Target Cell Effectiveness d Death/Loss T c Clearance What if IFN blocks production? If IFN treatment totally blocks virus production, then -ct dV/dt = - cV => V(t)=V0 e Viral load should fall exponentially with slope c. However, data shows an acute exponential fall followed by slower fall. IFN Effectiveness in Blocking Production Let e = effectiveness of IFN in blocking production of virus • e = 1 is 100% effectiveness • e = 0 is 0% effectiveness dV/dt = (1 – e)pI – cV Early Kinetic Analysis Before therapy, assume steady state so that pI0 =cV0. Also, assume at short times, I=constant=I0, so that dV/dt= (1-e)cV0 - cV Model predicts that after therapy is initiated, the viral load will initially change according to: V(t) = V0[1 – e + e exp(-ct)] This equation can be fit to data and c and e estimated. Thus drug effectiveness can be determined within the first few days! 8 Log10 HCV RNA/mL Log10 HCV RNA/mL 10MU 0 15MU 7 7 1 Days 6 5 4 0 1 2 Days 6 5 2 Viral Kinetics of HCV Genotype 1 Viral Clearance Drug Constant Efficacy (1/d) Half-life of Virions (Hours) Production & Clearance Rates (1012 Virions/d) 5MU 81 ± 4% 6.2 ± 0.8 2.7 0.4 ± 0.2 10MU 95 ± 4% 6.3 ± 2.4 2.6 2.3 ± 4 15MU 96 ± 4% 6.1 ± 1.9 2.7 0.6 ± 0.8 Standard Model of HCV Dynamics Equations Parameters dT l dT bVT dt dI b VT d I dt dV (1 e ) pI cV dt l Supply of target cells d Net loss rate of target cells Variables T Target Cell Density I Infected Cell Density V Virus Concentration Initial Conditions T(0) = T0 V(0) = V0 I (0) = I0 β d Infectivity rate constant Infected cell death rate e Drug efficacy p Virion production rate c Virion clearance rate constant Solution: Change in Viral Load Assuming T = constant, 1 c d 2e c l1 (t t0 ) c d 2e c l2 (t t0 ) V (t ) V0 [(1 )e (1 )e ] 2 where 1 l1 (c d ) 2 1 l2 (c d ) 2 (c d ) 2 4(1 e )cd t0 = delay between treatment commencement and onset of effect When c>>δ, λ1 ≈ c and λ2 ≈ εδ 10MU 7 Log10 HCV RNA/mL 8 Log10 HCV RNA/mL 15MU 7 6 5 4 3 0 7 14 Days 6 5 4 0 7 Days 14 Current Therapy: Peg-IFN 2b + RBV Peg-IFN given once a week Major Point: Drug Pharmacokinetics Matters! Pegylated Interferon (Peg-IFN) 21 HIV HCV Co-Infected Patients (A. Talal) Dosing –1.5 μg/kg Peg-IFN a-2b (12 kDa) weekly –1000 or 1200 mg ribavirin daily Talal et al., Hepatology (2006) HCV RNA and PEG-IFN α-2b Talal et al., Hepatol. (2006) PEG HCV Pharmacodynamics Emax Model Drug concentration, C(t), affects efficacy e max C (t ) e (t ) n n EC50 C (t ) n n = Hill coefficient, EC50 = 50% effective conc. = delay between receptor binding and effect PK Model for Absorption & Elimination of Peg-IFN ka Absorption Site Blood absorption X FDe Amount ka t ke elimination dA k a X ke A dt of drug in blood (A), Concentration = A/Vd X = amount of drug remaining at absorption site F = bioavailability D = dose ka = absorption rate constant ke = elimination rate constant Following a single dose FD ka ka t ke t e e C (t ) Vd ke ka PK Model Following multiple doses, Nke ka FD e ket ( e 1) Nke ka ( ke ka ) t ( N 1) ka ke ka C (t ) ( ka )[1 e (1 e ) (e e ) ke e e ] (ke ka )Vd e 1 (e 1) = dosing interval and N = # of doses Vd = volume of distribution PK Model Drug Concentrations Drug Concentration Profile 1400 Drug Concentration (pg/ml) 1200 1000 800 600 400 200 0 0 5 10 15 Days 20 25 30 Drug Efficacy Profile Efficacy Profile 0.9 0.8 0.7 Efficacy 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 Days 20 25 30 Fit of Model to PEG-IFN α-2b Conc. and HCV RNA Data Difference between responders and nonresponders Talal et al., Hepatol. (2006) Average drug conc. - Not different Median EC50 10-fold lower in SVR (0.04 mg/L) than NR (0.45 mg/L), P=0.014 Median efficacy – higher in responders 0.92 vs 0.45 (P=0.02) Median drug conc./EC50 – higher in responders 10.1 vs 1.0 (P=0.012) Conclusions HCV kinetic models can be used to quantitatively estimate the effectiveness of different drug regimes, and help establish appropriating dosing. They can give quantitative insights into biology of viral infection – rates of virion production, clearance, cell loss, etc. When using peg-IFN 2b drug effectiveness can change during the dosing interval and models need to be modified to take this into consideration. Viral dynamics and immune responses in acute hepatitis B infection Stanca M. Ciupe, Ruy M. Ribeiro, Patrick W. Nelson, Alan S. Perelson Patient data (Webster, Lancet 2000; Whalley, Hepatol. 2000) HBV outbreak was identified in the UK in 1998 due to autohemotherapy Serological exposure to the same HBV variant in 57 patients. 7 identified in the preclinical phase and studied here. Biphasic decay of viral load •First phase - span 56 days; - half life 3.4 days; •Second phase - span 148 days; - half life 23 days; Models A number of models of HBV infection exist: Nowak & Thomas, PNAS 1996; Tsiang et al Hepatol., 1999; Levin et al Hepatol. 2001; Murray & Chisari, PNAS 2005. With exception of Murray & Chisari (2005) they were developed to analyze drug therapy and are missing a number of key features of HBV infection that are important during acute infection. Viral Lifecycle • Model continued Here we will consider that almost 100% of hepatocytes are thought be infected at the peak of the infection. Due to this both cytolytic and non-cytolytic mechanisms may be needed to clear the infection. Further, a large amount of hepatocyte proliferation accompanies viral and cccDNA clearance in animal models (woodchuck, duck and chimpanzee) and presumably in human infection. Key Question: As virus is cleared and uninfected hepatocytes replace infected ones, what prevents infection of these newly generated hepatocytes? Model Cytolytic death p1 * 1 T k infection 1 cccDNA cccDNA dilution T cccDNA R 1 E * 2 T 2 E refractory Cytolytic death p2 V virus c clearance activation mE Cytolytic death Virus production z ≥2 cccDNA R mE s E effectors dE 45 Model equations dT T ( rT rT1* )(1 tot ) kVT R R dt Tmax dT1* kVT ( 1E z )T1* mT1* E dt dT2* T rT2* (1 tot ) zT1* 2T2* E mT2* E dt Tmax dV p1T1* p2T2* cV dt dE s (T1* (t ) T2* (t )) E (t ) d E E dt dR T 1T1* E 2T2* E rR(1 tot ) R R m1RE dt Tmax Ttot T T1* T2* R 46 Parameter fitting • Assumptions: some parameter values fixed based on literature x [r , Tmax , c, s, d E ] (McDonald, Tsiang, Hep. 1999, Lau, Hep. 2000, Lewin, Hep. 2001, Ahmed, Science 1996) - initial conditions (Whalley JEM 2001); - incubation time:80-140 days (Bertoletti, Hep. 2003); 47 Others we estimate by Monte Carlo search x [ p1, p2 , r2 , , m , m1, z, , 1, 2 , R ] •Fitness function: f ( x) (log(ViralTitert ) log(Vt )) 2 data •Search within a predefined range for parameters; •Once a good fit is found, search locally. 48 Model gives biphasic decay of viral load Best fit of model to data Patient 7 is the only patient not to clear HBV ALT and Effector cells hepatocytes E ALT ALT=alanine aminotransferase ALT ALT and Effector cells E Cytolytic and Noncytolytic Immune Responses cytolytic cytolytic Non-cytolytic Non-cytolytic • Noncytolytic response occurs early followed by the cytolytic one 3-4 weeks later • Weak CTL response in patient7 who does not clear infection. Cytolytic vs non-cytolytic Model Results 99% hepatocytes are infected cells at the peak * T Viral production by 1 is estimated to be approximately half the production by T2* .This suggests that all cccDNAs may not be good replicative templates. Needs to be examined experimentally. Refractory cells refractory R infected • Prevent the rekindling of the viral infection • Slow transition back into the target population, although when virus is cleared and cytokine milieu changes this rate may increase. Are all model assumptions needed? This model is very complicated and involves four features not present in the drug therapy models used so far to fit HBV DNA data: – Proliferation of infected and uninfected hepatocytes – with no proliferation hepatocyte mass decreases substantially during the course of infection if a cytolytic response occurs. Also, proliferation contributes to loss of cccDNA by dilution and allows uninfected cells to repopulate the liver as infected ones are killed. Model includes a cytolytic response – This is required to obtain the two phase HBV DNA decay seen in the data – However, model suggests a strong enough noncytolytic response could do the job of clearing infection. Thus, whether a cytolytic response is truly required to clear infection in not certain. With CTL response model gives biphasic decay of viral load Best fit of model to data Patient 7 is the only patient not to clear HBV No CTL response No CTL response Is non-cytolytic response needed? Model has a non-cytolytic response that converts infected cells into cells refractory to infection. In the absence of a non-cytolytic response, the system must rely on a cytolytic response to clear infection. This requires massive loss of hepatocytes. Further, proliferation of uninfected cells to replace cells that are killed, generates new targets and rekindles the infection. No non-cytolytic response hepatocyte loss infection rekindles No non-cytolytic response Assumption about R cells If the noncytolytic response simply “cures” cells, then again new targets are generated that rekindle the infection No R cells; direct transition of infected cells into uninfected cells No R, direct transition into target population Can antibodies replace R cells and prevent re-establishment of infection? If an anti-HbsAg response occurs, then these antibodies may neutralize remaining virus and prevent reestablishment of infection as infected cells are replaced by uninfected ones. Antibodies Anti-HBs antibodies are detectable, but after the resolution of acute infection. Acute Hepatitis B Virus Infection with Recovery Typical Serologic Course Symptoms HBeAg anti-HBe Total anti-HBc Titer HBsAg 0 4 8 anti-HBs IgM anti-HBc 12 16 20 24 28 32 36 52 Weeks after Exposure 100 Hepatitis B Virus Model of Ab response We consider: -the production of free antibodies by plasma cells. -attachment of antibody to both subgenomic and infectious viral particles. -allow antibodies to neutralize the virus, i.e. reduce the infectivity rate k depending on the amount of antibody bound. Effect of anti HBV Ab Model can not generate a high enough concentration of Ab to fully block infection HbsAg positive subgenomic particles bind the majority of Ab Model predicts viral rebound in most patients at the end of the second phase 10 7 Antibody Summary Have developed a model of acute HBV infection that reproduces the observed HBV DNA and ALT kinetic patterns Model suggests that both cytolytic and noncytolytic responses play a role in viral clearance. The model also reveals that as infected cells are cleared and replaced by uninfected ones a mechanism is needed to prevent the infection of these cells. We have postulated that these newly generated cells are temporarily refractory to new infection. This could be due to a sustained “antiviral” state established by a noncytolytic response or due to selection of cells that have reduced levels of the cell surface receptors HBV uses to enter cells. Anti-HbsAg antibodies could play a similar role, but ongoing modeling suggests that the great excess of subgenomic particles prevents effective antibody neutralization of the virus.