Maximum likelihood estimation of aggregated Markov processes

We present a maximum likelihood method for the modelling of aggregated Markov processes. The method utilizes the joint probability density of the observed dwell time sequence as likelihood. A forward-backward recursive procedure is developed for efficient computation of the likelihood function and its derivatives with respect to the model parameters. Based on the calculated forward and backward vectors, analytical formulae for the derivatives of the likelihood function are derived. The method exploits the variable metric optimizer for search of the likelihood space. It converges rapidly and is numerically stable. Numerical examples are given to show the effectiveness of the method.

Subconductance states of a mutant NMDA receptor channel kinetics, calcium, and voltage dependence

The kinetic properties of main and subconductance states of a mutant mouse N-methyl-D-aspartate (NMDA) receptor channel were examined. Recombinant receptors made of zeta-epsilon 2 (NR1-NR2B) subunits having asparagine-to-glutamine mutations in the M2 segment (zeta N598Q/epsilon 2N589Q) were expressed in Xenopus oocytes. Single channel currents recorded from outside-out patches were analyzed using hidden Markov model techniques. In Ca(2+)-free solutions, an open receptor channel occupies a main conductance (93 pS) and a subconductance (62 pS) with about equal probability. There are both brief and long-lived subconductance states, but only a single main level state. At -80 mV, the lifetime of the main and the longer-lived sub level are both approximately 3.3 ms. The gating of the pore and the transition between conductance levels are essentially independent processes. Surprisingly, hyperpolarization speeds both the sub-to-main and main-to-sub transition rate constants (approximately 120 mV/e-fold change), but does not alter the equilibrium occupancies. Extracellular Ca2+ does not influence the transition rate constants. We conclude that the subconductance levels arise from fluctuations in the energetics of ion permeation through a single pore, and that the voltage dependence of these fluctuations reflects the modulation by the membrane potential of the barrier between the main and subconductance conformations of the pore.

Binding sites contribute unequally to the gating of mouse nicotinic alpha D200N acetylcholine receptors

1. Single channel currents were recorded from HEK 293 cells expressing recombinant mouse adult (alpha 2 beta delta gamma) acetylcholine receptors (AChRs) containing a mutation at residue D200 of the alpha-subunit. Rate and equilibrium constants for AChR activation were estimated from open and closed time obtained over a range of ACh concentrations. 2. Mutation of alpha D200 to asparagine (alpha D200N) dramatically slows the rate constant of channel opening, with adult AChRs slowing 100-fold and embryonic AChRs slowing 400-fold. the rate constant of channel closing increased 3-fold, resulting in a decrease of the gating equilibrium constant of up to 1200-fold. In contrast to channel gating steps, ACh-binding steps are only modestly effected by alpha D200N. 3. Introduction of a potential glycosylation site in alpha D200N cannot account for the effect on channel gating because eliminating the consensus for glycosylation with the mutation alpha D200N + T202V fails to restore efficient gating. Gating is similarly impaired with the substitutions of E, K and Q at position alpha 200. 4. the agonists carbamylcholine and tetramethylammonium also activate the alpha D200N AChR, but with channel opening rates even slower than with ACh. The agonist dependence of the opening rate constant is similar in alpha D200N and wild type AChRs. 5. AChRs containing D200N at just one of the two alpha-subunits show either small or large changes in the gating equilibrium constant, presumably due to the presence of the mutation at either the alpha delta or alpha epsilon/alpha gamma sites. The changes in free energy of channel gating show that the contribution of each binding site is nearly independent. However, the sites do not contribute equally to gating, as an alpha D200N mutation at the alpha epsilon or alpha gamma binding site slows channel opening relatively more than at the alpha delta site.

Voltage dependence of mouse acetylcholine receptor gating: different charge movements in di-, mono- and unliganded receptors

1. The voltage dependence of binding and gating in wild-type and mutant recombinant mouse nicotinic acetylcholine receptors (AChRs) was examined at the single-channel level. 2. The closing rate constant of diliganded receptors decreased e-fold with approximately 66 mV hyperpolarization in both wild-type (adult and embryonic) and mutant receptors. The opening rate constant of a mutant receptor (alpha Y93F) was not voltage dependent. 3. The voltage dependence of closing in monoliganded receptors was examined in several receptors having a mutation in the binding site (alpha G153S) or pore region (alpha L251C and epsilon T264P). The closing rate constant of these monoliganded receptors decreased e-fold with approximately 124 mV hyperpolarization. 4. The voltage dependence of closing and opening in unliganded receptors was examined in two receptors having a mutation in the pore region (alpha L251C and epsilon T264P). Neither the closing nor the opening rate constants of unliganded receptors were voltage dependent. 5. If z if the amount of charge that moves during channel closure and delta is the distance (as a fraction of the electric field) that the charge moves, we conclude that z delta = 0.4 in diliganded receptors, 0.2 in monoliganded receptors, and 0.0 in unliganded receptors. It is likely that charges on the protein, rather than the agonist molecule, move z delta = 0.2 after each ACh molecule has bound. 6. The results suggest that unliganded openings arise from a local, concerted change in the structure of the pore (channel opening) that does not involve the net movement of charged residues. We speculate that as a consequence of agonist binding, charged moieties in the protein change their disposition so that they move with respect to the electric field when the channel gates. The results are consistent with the idea that there is semi-independent movement of distinct domains during AChR gating.

Inorganic, monovalent cations compete with agonists for the transmitter binding site of nicotinic acetylcholine receptors

The properties of adult mouse recombinant nicotinic acetylcholine receptors activated by acetylcholine (ACh+) or tetramethylammonium (TMA+) were examined at the single-channel level. The midpoint of the dose-response curve depended on the type of monovalent cation present in the extracellular solution. The shifts in the midpoint were apparent with both inward and outward currents, suggesting that the salient interaction is with the extracellular domain of the receptor. Kinetic modeling was used to estimate the rate constants for agonist binding and channel gating in both wild-type and mutant receptors exposed to Na+, K+, or Cs+. The results indicate that in adult receptors, the two binding sites have the same equilibrium dissociation constant for agonists. The agonist association rate constant was influenced by the ionic composition of the extracellular solution whereas the rate constants for agonist dissociation, channel opening, and channel closing were not. In low-ionic-strength solutions the apparent association rate constant increased in a manner that suggests that inorganic cations are competitive inhibitors of ACh+ binding. There was no evidence of an electrostatic potential at the transmitter binding site. The equilibrium dissociation constants for inorganic ions (Na+, 151 mM; K+, 92 mM; Cs+, 38 mM) and agonists (TMA+, 0.5 mM) indicate that the transmitter binding site is hydrophobic. Under physiological conditions, about half of the binding sites in resting receptors are occupied by Na+.

Identification of a high affinity divalent cation binding site near the entrance of the NMDA receptor channel

Single channel currents from recombinant N-methyl-D-aspartate (NMDA) receptors having an N-to-Q mutation in M2 reveal a divalent cation binding site that is near the entrance of the pore (approximately 0.2 through the electric field). Ca2+ rapidly binds to this site and readily permeates the channel, while Mg2+ binds more slowly and does not permeate as readily. In wild-type receptors, Mg2+ also blocks the current by occupying a site that is approximately 0.6 through the field. When the more external site is occupied by Ca2+, the conductance of the pore to NA+ is reduced but not abolished, perhaps by an electrostatic blocking mechanism. The site serves to enrich the fraction of NMDA receptor current carried by CA2+.

Inactivation of Fac in mice produces inducible chromosomal instability and reduced fertility reminiscent of Fanconi anaemia

Fanconi anaemia (FA) is an autosomal recessive disease characterized by bone marrow failure, variable congenital malformations and predisposition to malignancies. Cells derived from FA patients show elevated levels of chromosomal breakage and an increased sensitivity to bifunctional alkylating agents such as mitomycin C (MMC) and diepoxybutane (DEB). Five complementation groups have been identified by somatic cell methods, and we have cloned the gene defective in group C (FAC)(7). To understand the in vivo role of this gene, we have disrupted murine Fac and generated mice homozygous for the targeted allele. The -/- mice did not exhibit developmental abnormalities nor haematologic defects up to 9 months of age. However, their spleen cells had dramatically increased numbers of chromosomal aberrations in response to MMC and DEB. Homozygous male and female mice also had compromised gametogenesis, leading to markedly impaired fertility, a characteristic of FA patients. Thus, inactivation of Fac replicates some of the features of the human disease.

Estimating single-channel kinetic parameters from idealized patch-clamp data containing missed events

We present here a maximal likelihood algorithm for estimating single-channel kinetic parameters from idealized patch-clamp data. The algorithm takes into account missed events caused by limited time resolution of the recording system. Assuming a fixed dead time, we derive an explicit expression for the corrected transition rate matrix by generalizing the theory of Roux and Sauve (1985, Biophys. J. 48:149-158) to the case of multiple conductance levels. We use a variable metric optimizer with analytical derivatives for rapidly maximizing the likelihood. The algorithm is applicable to data containing substates and multiple identical or nonidentical channels. It allows multiple data sets obtained under different experimental conditions, e.g., concentration, voltage, and force, to be fit simultaneously. It also permits a variety of constraints on rate constants and provides standard errors for all estimates of model parameters. The algorithm has been tested extensively on a variety of kinetic models with both simulated and experimental data. It is very efficient and robust; rate constants for a multistate model can often be extracted in a processing time of approximately 1 min, largely independent of the starting values.

Activation kinetics of recombinant mouse nicotinic acetylcholine receptors: mutations of alpha-subunit tyrosine 190 affect both binding and gating

Affinity labeling and mutagenesis studies have demonstrated that the conserved tyrosine Y190 of the acetylcholine receptor (AChR) alpha-subunit is a key determinant of the agonist binding site. Here we describe the binding and gating kinetics of embryonic mouse AChRs with mutations at Y190. In Y190F the dissociation constant for ACh binding to closed channels was reduced approximately 35-fold at the first binding site and only approximately 2-fold at the second site. At both binding sites the association and dissociation rate constants were decreased by the mutation. Compared with wildtype AChRs, doubly-liganded alpha Y190F receptors open 400 times more slowly but close only 2 times more rapidly. Considering the overall activation reaction (vacant-closed to fully occupied-open), there is an increase of approximately 6.4 kcal/mol caused by the Y-to-F mutation, of which at least 2.1 and 0.3 kcal/mol comes from altered agonist binding to the first and second binding sites, respectively. The closing rate constant of alpha Y190F receptors was the same with ACh, carbamoylcholine, or tetramethylammonium as the agonist. This rate constant was approximately 3 times faster in ACh-activated S, W, and T mutants. The equilibrium dissociation constant for channel block by ACh was approximately 2-fold lower in alpha Y190F receptors compared with in wildtype receptors, suggesting that there are changes in the pore region of the receptor as a consequence of the mutation. The activation reaction is discussed with regard to energy provided by agonist-receptor binding contacts, and by the intrinsic folding energy of the receptor.

Mutation of the acetylcholine receptor alpha subunit causes a slow-channel myasthenic syndrome by enhancing agonist binding affinity

In five members of a family and another unrelated person affected by a slow-channel congenital myasthenic syndrome (SCCMS), molecular genetic analysis of acetylcholine receptor (AChR) subunit genes revealed a heterozygous G to A mutation at nucleotide 457 of the alpha subunit, converting codon 153 from glycine to serine (alpha G153S). Electrophysiologic analysis of SCCMS end plates revealed prolonged decay of miniature end plate currents and prolonged activation episodes of single AChR channels. Engineered mutant AChR expressed in HEK fibroblasts exhibited prolonged activation episodes strikingly similar to those observed at the SCCMS end plates. Single-channel kinetic analysis of engineered alpha G153S AChR revealed a markedly decreased rate of ACh dissociation, which causes the mutant AChR to open repeatedly during ACh occupancy. In addition, ACh binding measurements combined with the kinetic analysis indicated increased desensitization of the mutant AChR. Thus, ACh binding affinity can dictate the time course of the synaptic response, and alpha G153 contributes to the low binding affinity for ACh needed to speed the decay of the synaptic response.

Kinetic properties of NMDA receptors in embryonic Xenopus spinal neurons

1. The kinetic properties of embryonic Xenopus spinal cord neuron N-methyl-D-aspartate (NMDA)-activated receptors (NMDAR) were examined at the single-channel level. These receptors have a main conductance state of 50 pS and make occasional sojourns to a subconductance level of approximately 40 pS. The open channel lifetime is 1.3 ms at -80 mV and in 1 mM Ca(2+)-, Mg(2+)-free solution. Extracellular Mg2+ blocks the channel at a rate of 2.9 x 10(8) M-1 s-1 and with a Kd of approximately 20 microM at -80 mV. In patches with only one channel active, the closed interval duration distribution requires at least four exponentials to be fit. The time constant of one closed interval component decreases with increasing NMDA concentration. Kinetic modeling indicates that these NMDA receptors open at a rate of 230 s-1 and close at a rate of 167 s-1, that in the absence of desensitization the maximum probability of being open is approximately 0.5, and that this probability is half-maximal at approximately 150 microM NMDA.

Activation of recombinant mouse acetylcholine receptors by acetylcholine, carbamylcholine and tetramethylammonium

1. The kinetic properties of cloned mouse embryonic nicotinic acetylcholine receptors (AChRs) expressed in HEK 293 cells or Xenopus oocytes were examined using high concentrations of acetylcholine (ACh), carbamylcholine (CCh), or tetramethylammonium (TMA). The rate constants of agonist binding and channel gating were estimated by fitting kinetic models to idealized open and closed intervals over a range of agonist concentrations. 2. Once doubly liganded, TMA-activated receptors open at approximately 3000 s-1. The equilibrium binding constants for TMA are 525 and 12,800 microM. Doubly liganded CCh-activated receptors open at approximately 11,500 s-1; the equilibrium binding constants for this agonist are 14 and 570 microM. If we assume that doubly liganded, ACh-activated receptors open at 60,000 s-1, then the equilibrium binding constants for ACh are 20 and > 650 microM, similar to those for CCh. For all three agonists the higher affinity site both binds and releases agonists more slowly than does the lower affinity site. 3. ACh and CCh bind to the two sites equally rapidly, at approximately 2 x 10(7) and 4 x 10(7) M-1 s-1 at the first and second binding sites, respectively. Compared with ACh, the TMA association rate is approximately 100 times slower at the first binding site, and approximately 30 times slower at the second binding site. These results indicate that at both binding sites the association rate of TMA is not limited by diffusional or steric factors. 4. All three agonists dissociate from the receptor binding sites at similar rates. The dissociation rate for all agonists was approximately 40 times slower at the first binding site than at the second. These results suggest that the interaction of the quarternary amine moiety with the receptor determines the rate of release of the agonist, and that the nature of this interaction is quite different at the two binding sites. 5. Although the channel opening rates for the three agonists varied approximately 20-fold, the channel closing rates were not strongly agonist dependent, and varied less than 3-fold. We speculate that the ester moiety of the agonist promotes both rapid binding and fast opening of the ligand receptors, and that interactions of the quarternary amine moiety of the agonist with the receptor determine the channel closing rate constant.

A large-scale gene-trap screen for insertional mutations in developmentally regulated genes in mice

We have used a gene-trap vector and mouse embryonic stem (ES) cells to screen for insertional mutations in genes developmentally regulated at 8.5 days of embryogenesis (dpc). From 38,730 cell lines with vector insertions, 393 clonal integrations had disrupted active transcription units, as assayed by beta-galactosidase reporter gene expression. From these lines, 290 clones were recovered and injected into blastocysts to assay for reporter gene expression in 8.5-dpc chimeric mouse embryos. Of these, 279 clones provided a sufficient number of chimeric embryos for analysis. Thirty-six (13%) showed restricted patterns of reporter-gene expression, 88 (32%) showed widespread expression and 155 (55%) failed to show detectable levels of expression. Further analysis showed that approximately one-third of the clones that did not express detectable levels of the reporter gene at 8.5 dpc displayed reporter gene activity at 12.5 dpc. Thus, a large proportion of the genes that are expressed in ES cells are either temporally or spatially regulated during embryogenesis. These results indicate that gene-trap mutageneses in embryonic stem cells provide an effective approach for isolating mutations in a large number of developmentally regulated genes.

Essential role of Mash-2 in extraembryonic development

The outer layer of the blastocyst, or trophectoderm, is the first cell lineage to differentiate in the mouse embryo, but little is known about the genetic control of its development. Lineage-specific transcription factors may be important in lineage specification, and the product of the Mash-2 gene fulfils the criteria for such a factor. Mash-2 is a mammalian member of the achaete-scute family which encodes basic-helix-loop-helix transcription factors and is strongly expressed in the extraembryonic trophoblast lineage. Mash-2 transcripts are found in the female germ line and in the embryo throughout preimplantation development, but are highly expressed later only in the ectoplacental cone, the chorion and their derivatives in the placenta. Mash-2 transcripts are not found in primary and secondary giant cells, yolk sac or allantois at any post-implantation stage, and are present only transiently and at low levels in the embryo during gastrulation. To analyse the role of Mash-2 in development, we have used gene targeting to generate mice having no Mash-2 function. We report here that Mash-2-/- embryos die from placental failure at 10 days postcoitum. In mutant placentas, spongiotrophoblast cells and their precursors are absent and chorionic ectoderm is reduced. We have rescued this placental mutant phenotype by constructing chimaeras with tetraploid wild-type embryos which contribute almost exclusively to extraembryonic tissues. Mash-2-/- embryos developed normally and adult Mash-2-/- mice were viable, demonstrating that Mash-2 has no major role in the embryo itself. Mash-2 is the first transcription factor shown to play a critical part in the development of the mammalian trophoblast lineage.

Dominant-negative and targeted null mutations in the endothelial receptor tyrosine kinase, tek, reveal a critical role in vasculogenesis of the embryo

The receptor tyrosine kinases (RTKs) expressed on the surface of endothelial cells are likely to play key roles in initiating the program of endothelial cell growth during development and subsequent vascularization during wound healing and tumorigenesis. Expression of the Tek RTK during mouse development is restricted primarily to endothelial cells and their progenitors, the angioblasts, suggesting that Tek is a key participant in vasculogenesis. To investigate the role that Tek plays within the endothelial cell lineage, we have disrupted the Tek signaling pathway using two different genetic approaches. First, we constructed transgenic mice expressing a dominant-negative form of the Tek receptor. Second, we created a null allele of the tek gene by homologous recombination in embryonic stem (ES) cells. Transgenic mice expressing dominant-negative alleles of Tek or homozygous for a null allele of the tek locus both died in utero with similar defects in the integrity of their endothelium. By crossing transgenic mice that express the lacZ reporter gene under the transcriptional control of the endothelial cell-specific tek promoter, we found that the extraembryonic and embryonic vasculature was patterned correctly. However, homozygous tek embryos had approximately 30% and 75% fewer endothelial cells at day 8.5 and 9.0, respectively. Homozygous null embryos also displayed abnormalities in heart development, consistent with the conclusion that Tek is necessary for endocardial/myocardial interactions during development. On the basis of the analysis of mice carrying either dominant-negative or null mutations of the tek gene, these observations demonstrate that the Tek signaling pathway plays a critical role in the differentiation, proliferation, and survival of endothelial cells in the mouse embryo.

Mammalian achaete-scute homolog 1 is required for the early development of olfactory and autonomic neurons

The mouse Mash-1 gene, like its Drosophila homologs of the achaete-scute complex (AS-C), encodes a transcription factor expressed in neural precursors. We created a null allele of this gene by homologous recombination in embryonic stem cells. Mice homozygous for the mutation die at birth with apparent breathing and feeding defects. The brain and spinal cord of the mutants appear normal, but their olfactory epithelium and sympathetic, parasympathetic, and enteric ganglia are severely affected. In the olfactory epithelium, neuronal progenitors die at an early stage, whereas the nonneuronal supporting cells are present. In sympathetic ganglia, the mutation arrests the development of neuronal precursors, preventing the generation of sympathetic neurons, but does not affect glial precursor cells. These observations suggest that Mash-1, like its Drosophila homologs of the AS-C, controls a basic operation in development of neuronal progenitors in distinct neural lineages.

Non-injection methods for the production of embryonic stem cell-embryo chimaeras

The simple aggregation of pluripotent ES cells with morulae-stage embryos can result in viable chimaeras at a similar frequency to that of blastocyst injection. The savings in time and equipment inherent in the aggregation techniques, however, make this approach well worth considering.