Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation.
(9/3175)
A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819-829) with the following modifications: 1) an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are determined using a simulated annealing algorithm to minimize the error between model responses and various experimental data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents, steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10 degrees C to 25 degrees C. The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening. (+info)
A possible resolution of the gating paradox.
(10/3175)
We introduce a Markov model for the gating of membrane channels. The model features a possible solution to the so-called gating current paradox, namely that the bell-shaped curve that describes the voltage dependence of the kinetics is broader than expected from, and shifted relative to, the sigmoidal curve that describes the voltage dependence of the activation. The model also predicts some temperature dependence of this shift, but presence of the latter has not been tested experimentally so far. (+info)
Energetic and spatial parameters for gating of the bacterial large conductance mechanosensitive channel, MscL.
(11/3175)
MscL is multimeric protein that forms a large conductance mechanosensitive channel in the inner membrane of Escherichia coli. Since MscL is gated by tension transmitted through the lipid bilayer, we have been able to measure its gating parameters as a function of absolute tension. Using purified MscL reconstituted in liposomes, we recorded single channel currents and varied the pressure gradient (P) to vary the tension (T). The tension was calculated from P and the radius of curvature was obtained using video microscopy of the patch. The probability of being open (Po) has a steep sigmoidal dependence on T, with a midpoint (T1/2) of 11.8 dyn/cm. The maximal slope sensitivity of Po/Pc was 0.63 dyn/cm per e-fold. Assuming a Boltzmann distribution, the energy difference between the closed and fully open states in the unstressed membrane was DeltaE = 18.6 kBT. If the mechanosensitivity arises from tension acting on a change of in-plane area (DeltaA), the free energy, TDeltaA, would correspond to DeltaA = 6.5 nm2. MscL is not a binary channel, but has four conducting states and a closed state. Most transition rates are independent of tension, but the rate-limiting step to opening is the transition between the closed state and the lowest conductance substate. This transition thus involves the greatest DeltaA. When summed over all transitions, the in-plane area change from closed to fully open was 6 nm2, agreeing with the value obtained in the two-state analysis. Assuming a cylindrical channel, the dimensions of the (fully open) pore were comparable to DeltaA. Thus, the tension dependence of channel gating is primarily one of increasing the external channel area to accommodate the pore of the smallest conducting state. The higher conducting states appear to involve conformational changes internal to the channel that don't involve changes in area. (+info)
A cost-effectiveness clinical decision analysis model for schizophrenia.
(12/3175)
A model was developed to estimate the medical costs and effectiveness outcomes of three antipsychotic treatments (olanzapine, haloperidol, and risperidone) for patients with schizophrenia. A decision analytic Markov model was used to determine the cost-effectiveness of treatments and outcomes that patients treated for schizophrenia may experience over a 5-year period. Model parameter estimates were based on clinical trial data, published medical literature, and, when needed, clinician judgment. Direct medical costs were incorporated into the model, and outcomes were expressed by using three effectiveness indicators: the Brief Psychiatric Rating Scale, quality-adjusted life years, and lack of relapse. Over a 5-year period, patients on olanzapine had an additional 6.8 months in a disability-free health state based on Brief Psychiatric Rating Scale scores and more than 2 additional months in a disability-free health state based on quality-adjusted life years, and they experienced 13% fewer relapses compared with patients on haloperidol. The estimated 5-year medical cost associated with olanzapine therapy was $1,539 less than that for haloperidol therapy. Compared with risperidone therapy, olanzapine therapy cost $1,875 less over a 5-year period. Patients on olanzapine had approximately 1.6 weeks more time in a disability-free health state (based on Brief Psychiatric Rating Scale scores) and 2% fewer relapses compared with patients on risperidone. Sensitivity analyses indicated the model was sensitive to changes in drug costs and shortened hospital stay. Compared with both haloperidol and risperidone therapy, olanzapine therapy was less expensive and provided superior effectiveness outcomes even with conservative values for key parameters such as relapse and discontinuation rates. (+info)
The cost-effectiveness of treatment with lamivudine and zidovudine compared with zidovudine alone: a comparison of Markov model and trial data estimates.
(13/3175)
In this paper, we present a Markov model for estimating the cost-effectiveness of combination therapy with lamivudine (LMV) and zidovudine (ZDV) compared with ZDV alone. We also compare the predictions of the Markov model for the impact of combination therapy on trial period costs with the actual impact of combination therapy on selected trial period costs estimated from data collected during the clinical trials. In the Markov model, disease stages were defined by CD4 cell count. Based on clinical trial data for patients with CD4 counts higher than 100 cells/mm3, the model assumed that the CD4 cell count level could be maintained above the level at the initiation of therapy for 6.5 months with monotherapy and for 18 months with combination therapy. After this period, transition rates for natural disease progression were used. Incremental lifetime costs and quality-adjusted life years gained with LMV/ZDV compared with ZDV alone were estimated for cohorts of patients initiating antiretroviral therapy at four different CD4 cell count stages. Cost per life year gained varied from $10,000 to $18,000, and cost per quality-adjusted life year gained varied from $14,000 to $27,000. In both cases, the combination therapy was more cost-effective when started earlier in disease progression. These estimates were not sensitive to changes in key parameter values. In addition, the model was used to estimate the impact of combination therapy on healthcare costs during the trial period; these estimated costs were compared with data on the cost of resource use collected during the clinical trial for hospital stays, unscheduled visits, medications, and outpatient procedures. Both the Markov model estimates and the trial data estimates for the trial period showed cost savings in other medical costs, though these were not large enough to completely offset the increased cost for antiretroviral therapy. The model estimates were more conservative than the estimates based on the trial data. (+info)
Markov model and markers of small cell lung cancer: assessing the influence of reversible serum NSE, CYFRA 21-1 and TPS levels on prognosis.
(14/3175)
High serum NSE and advanced tumour stage are well-known negative prognostic determinants of small cell lung cancer (SCLC) when observed at presentation. However, such variables are reversible disease indicators as they can change during the course of therapy. The relationship between risk of death and marker level and disease state during treatment of SCLC chemotherapy is not known. A total of 52 patients with SCLC were followed during cisplatin-based chemotherapy (the median number of tumour status and marker level assessments was 4). The time-homogeneous Markov model was used in order to analyse separately the prognostic significance of change in the state of the serum marker level (NSE, CYFRA 21-1, TPS) or the change in tumour status. In this model, transition rate intensities were analysed according to three different states: alive with low marker level (state 0), alive with high marker level (state 1) and dead (absorbing state). The model analysing NSE levels showed that the mean time to move out of state 'high marker level' was short (123 days). There was a 44% probability of the opposite reversible state 'low marker level' being reached, which demonstrated the reversible property of the state 'high marker level'. The relative risk of death from this state 'high marker level' was about 2.24 times greater in comparison with that of state 0 'low marker level' (Wald's test; P < 0.01). For patients in state 'high marker level' at time of sampling, the probability of death increased dramatically, a transition explaining the rapid decrease in the probability of remaining stationary at this state. However, a non-nil probability to change from state 1 'high marker level' to the opposite transient level, state 0 'low marker level', was observed suggesting that, however infrequently, patients in state 1 'high marker level' might still return to state 0 'low marker level'. Almost similar conclusions can be drawn regarding the three-state model constructed using the tumour response status. For the two cytokeratin markers, the Markov model suggests the lack of a true reversible property of these variables as there was only a very weak probability of a patient returning to state 'low marker level' once having entered state 'high marker level'. In conclusion, The Markov model suggests that the observation of an increase in serum NSE level or a lack of response of the disease at any time during follow-up (according to the homogeneous assumption) was strongly associated with a worse prognosis but that the reversion to a low mortality risk state remains possible. (+info)
Relationship estimation by Markov-process models in a sib-pair linkage study.
(15/3175)
The results of sib-pair linkage studies may be compromised if a substantial number of putative sib pairs are not actually sib pairs. For classification of pairs in a sib-pair genome scan, I propose multipoint methods that are based on a Markov-process model of allele sharing along the chromosome. These methods can be implemented by standard algorithms that compute multipoint marker allele-sharing probabilities for sib pairs. When marker data from at least half the genome are used, misclassification rates are small. The methods will be implemented in an upcoming version of the computer software package S.A.G.E. (+info)
Evaluation of screening for nasopharyngeal carcinoma: trial design using Markov chain models.
(16/3175)
In this paper, we develop a Markov chain model to estimate parameters pertaining to the natural history of nasopharyngeal carcinoma (NPC). The model is of progression from no disease to Epstein-Barr virus (EBV) infection, preclinical screen-detectable tumour and clinical tumour. We derive tentative estimates of the parameters of the model, based on limited published data, to assess the efficacy of serum screening in conjunction with clinical assessment (indirect mirror examination for NPC), for example the average duration of the preclinical screen-detectable phase is estimated as 3.1 years. We further apply these parameters to a hypothetical screening trial in the Hong Kong population to assess the efficacy of serum screening with clinical assessment by different combinations of screening regime. Results suggest: (1) there is no substantial difference between 3-yearly and 6-yearly serum screening; and (2) within the same serum screening regime annual and 3-yearly clinical assessment can prevent 33% and 28% of deaths from NPC respectively. Prediction of deaths and surrogate end points can be used to estimate the required sample size and duration for designing a randomized trial of screening for NPC. Based on these findings and power projections, we suggest a design for a randomized trial in a high incidence area such as Hong Kong. (+info)