This key observation explains why the

CA activation intermediate was captured in the crystal even though the LBDs were occupied by DNQX: the A and C subunits must be held open for crosslinking, whereas the B and D subunits are Wnt inhibitor free to close without disturbing the crosslink. The B and D subunits are therefore likely bound with agonist when the crosslink forms at C665 in the full-length receptor. Given the incomplete inhibition by oxidizing conditions, this partially glutamate-bound configuration probably allows ion conduction, consistent with the notion that closure of the LBDs in the B and D subunits alone is sufficient to activate the receptor (Das et al., 2010). Several of our observations suggest that the

A665C mutant can be trapped, albeit slowly, in other conformational states. Desensitization may promote disulfide bond formation when the receptor is saturated by glutamate, but the geometry of such a desensitized, crosslinked tetramer is expected to be different from that seen in our crystal structure in that the lobe 1 dimer interface would be ruptured (Armstrong et al., 2006). Trapping that we observed in the combined presence of kainate and CTZ suggests that the A665C site moves to a similar position seen in our crystal structure when a dimer is saturated with kainate as when one subunit in a dimer AZD6244 is occupied by glutamate. Stabilizing the LBDs in a nondesensitized, inactive conformation (DNQX plus CTZ) blocked trapping completely in functional experiments. In biochemical experiments, the degree of trapping in DNQX was not significantly different from that for either control (e.g., R661C) or A665C in 500 μM glutamate, suggesting the possibility that oxidizing exposures much longer than those relevant for channel gating could drive the receptor into a conformation resembling the crystallized CA conformation. However, the low signal-to-noise

ratio of our biochemical experiments rules out Thymidine kinase any conclusive interpretation of these data. The selective zinc inhibition of the four triple-substitution mutants that we report, including the HHH mutant, can only occur if lobes 1 of apposed LBD dimers approach sufficiently to create a metal-binding site. Forming this site requires a 16 Å translation of the upper lobes. To our knowledge, such a movement has not been previously documented in the literature. Because the composition and exact geometry of this site seem less important than the presence of three coordinating groups, inhibition due to some local distortion within individual domains seems unlikely. Relatively large OA-to-CA motions therefore occur between dimers as the receptor transitions from the resting state to the fully activated state.

Amplification of cDNA derived

from the papilla using primers designed against chicken prestin produced a band of the correct size (382 nt) identical to a band produced by amplification of plasmid containing chicken prestin (Figure 8A). These results confirm the original cloning of prestin from chicken inner ear (Schaechinger and Oliver, 2007; Tan et al., Protein Tyrosine Kinase inhibitor 2011). Localization to the hair cells was demonstrated by immunolabeling with an antibody against an N-terminal peptide sequence of mammalian prestin. Immunoblots of protein extracts of chicken basilar papilla and mouse cochlea labeled with the antibody displayed a principal band at ∼80 kDa, appropriate for prestin in both animals (mouse, 81.3 kDa; chicken, 81.1 kDa). Similar results were seen in three other blots. When applied to the papilla, the antibody labeled the lateral membrane of SHCs (Figure 8C) and THCs (Figure 8D). Z projections of the stack (Figure 8C) showed the label as a ring around the basolateral Lenvatinib molecular weight aspect of the cell; in some SHCs (Figure 8E, middle) the label was denser

on the side where the top of the cell has a lip projecting toward the neural limb. Hair cell bounds were defined by immunolabeling also for otoferlin which is present in the cell membrane and cytoplasm (Goodyear et al., 2010); comparison with the prestin demonstrated that the prestin label was in the hair cell (Figures 8C and 8E), and none was present in the supporting cells. SHC labeling at other positions confirmed that prestin occurred along the entire epithelium, the label being consistently weaker at the

apex (d = 0.2) and stronger at the base (d = 0.8). We did not quantify the change in labeling intensity with location, but the results suggest a tonotopic gradient in prestin as for other hair cell proteins ( Tan et al., 2013). We investigated likely electromechanical processes in chicken auditory hair cells by measuring “active” hair bundle motion because this might underlie acoustic amplification and extension of the auditory frequency range Rolziracetam in birds. Our main findings were as follows: (1) depolarizing a hair cell elicited biphasic bundle displacements consisting of two processes, one inhibited by MT channel blockers and the other by Na+ salicylate; (2) salicylate had no effect on the maximum current, gating, or adaptation of the MT channels but did block a nonlinear capacitance sensitive to the intracellular chloride concentration; (3) hair bundle deflection with a flexible glass fiber could produce a fast bundle “recoil” or “mechanical twitch” that also appeared to possess two components: one observed in voltage clamp probably reflecting MT channel adaptation (Benser et al., 1996; Ricci et al.

The notion is that in area CA3, synapses forming the recurrent connection from other area CA3 pyramidal cells, and the perforant path input from the entorhinal cortex have their effective strengths reduced, but are rendered more labile. The ability (M) of neuromodulators to control the course of activity by regulating which of a number of gross pathways determines the activity of neurons is a common scheme. There are also other potential neuromodulatory routes for this influence: for instance, ACh helps regulate oscillations ([N], a critical dynamical effect of neuromodulators in many circumstances)

that simultaneously affect multiple sub-regions of the hippocampal formation (Buzsáki, 2002). It has been suggested that different pathways between these regions are Forskolin ic50 dominant at different selleck chemical phases of theta (Hasselmo et al., 2002),

providing a route for neuromodulatory effects. ACh is also capable of influencing shorter-term storage in working memory (Klink and Alonso, 1997; Hasselmo, 2006). The (O) effects of neuromodulators on various timescales of plasticity are among their most influential. Another obvious issue for memory is whether or not an input actually merits long term storage. One way to assess this is to consider its affective consequences, bearing in mind that they may only be evident after some time has passed. Given the evidence adduced above, it should come as no surprise to find that dopamine is implicated in the later phases of hippocampal storage (Lisman et al., 2011), although this is a rather different function from the plasticity engendered by dopaminergically coded prediction errors that we discussed above as underpinning the learning of appetitive predictions. The extended timescale over which such assessments might be relevant could result in findings such as that patterns that are only incidentally correlated with the delivery of unexpected Tryptophan synthase reward are also preferentially stored (Wittmann et al., 2005). Boosted storage can perhaps be seen as

an instance of internal, cognitive, “approach” to a stimulus based on the reward it predicts (Adcock et al., 2006), matching the internal action of storage in working memory to the externally directed engagement actions that we mentioned above. An informationally more complex case for neuromodulatory influences on plasticity comes in the context of animal conditioning experiments (Gallistel and Gibbon, 2000; Pearce and Hall, 1980), which have particularly centered on the model-free Pavlovian case. Psychological notions, such as that the associability of a stimulus varies with the degree of surprise with which it is endowed (Pearce and Hall, 1980), can be translated into computational terms as the relative learning rate of a stimulus being determined by its predictive uncertainty (Dayan et al.

Some evidence in favor of this idea comes from the observations that the effects of GnRH and FMRFamide on retinal activity vary depending on the season; their effects are weaker during periods of sexual inactivity (Stell et al., 1987). “
“Recognizing when the world has changed—and when it has not—is a fundamental yet much ignored component of associative

learning. Imagine relocating to Sydney, Australia. While much there might be familiar, one prominent difference is of life-or-death import: the cars come from the right. If you don’t learn to look right-left-right before crossing, your visit might be quite short. Transferase inhibitor On the other hand, since you plan to venture to proper-side-of-the-road-driving countries periodically, it would behoove you to also maintain your previous left-right-left behavior, applying that when appropriate.

Optimally, rather than overwriting your original strategy for crossing Palbociclib molecular weight the street, upon experiencing the strange driving habits in your new hometown, you would form a new “state” of “I am in Sydney” and learn new mappings from actions to goals (“policies” in the jargon of reinforcement learning, “action-outcome associations” in terms of learning theory) relevant to that state. Linking these learned policies to the new state would, conveniently, protect the old policies linked to the

old state from being secondly overwritten, so that behavior could be modified quickly if the old state were to reappear. As this example illustrates, appropriate recognition of when to form new states to which to attach information is vital to adaptive behavior. In this issue of Neuron, Bradfield and colleagues ( Bradfield et al., 2013) use a series of complex yet highly controlled behavioral manipulations to show that input from a part of the thalamus, the parafascicular nucleus, onto cholinergic interneurons in the posterior compartment of the dorsomedial striatum (pDMS), is critical to the appropriate creation of new states during learning. Note that we use “state” here to refer to a high-order representation of the environment in which actions are being chosen—a notion that encompasses the animal learning theory terms of “context,” “discriminative stimulus,” and “occasion setter” as well as the statistical learning theory term “latent cause” ( Gershman and Niv, 2010), but is different from common usage of the term in reinforcement learning. In the first phase of training, Bradfield et al. (2013) taught rats to associate two levers with two different, but equally valued, rewards (pellets or sucrose).

After center fixation for 400 ms, the monkeys were presented with a central cue that was identical to the search target. The cue stayed on for 200–2500 ms randomly, after which time a search array with 20 stimuli was presented, and the center cue was replaced by the center fixation spot. Monkeys were required to hold fixation at the center of the screen before the search array onset. click here After the onset, monkeys had 4 s to find the target that was the same as

the central cue. No constraints were placed on their search behavior in order to allow them to conduct the search naturally. Monkeys were required to fixate the target stimulus for 700 ms continuously to receive a juice reward. The position of the target on the screen was changed randomly from trial to trial. A memory-guided saccade task was used to determine a cell’s RF and stimulus selectivity. Briefly, the trial started with the monkey fixating a central spot. A peripheral stimulus flashed for 100 ms in one of the stimulus positions used in the search array. After a random period between 500 and 1500 ms, the central spot was extinguished, and the monkey was rewarded for making a saccade to the memorized position of the peripheral stimulus. Before the offset of the fixation Topoisomerase inhibitor spot, monkeys were required to maintain

center fixation. Eleven locations, including nine in the contralateral visual field and two on the vertical middle line, were used, which comprised 11 of the 20 locations used in the search array. Firing rates were compared between the prestimulus period, 200–0 ms before stimulus flash onset, and the poststimulus period, 50–250 ms after the flash onset, using the Wilcoxon rank-sum test, and stimulus locations with significant increased responses (p < 0.05)

were defined to be in the RF. Sites with RFs extending into both hemisfields were rarely found and were excluded from further analyses after a preliminary RF mapping. Multiunit spikes and local field potentials (LFPs) were recorded from the FEF and V4 simultaneously using a Multichannel Acquisition Processor system by Plexon. On a given day, up to four tungsten microelectrodes (FHC) were advanced through the dura in each area. Electrodes within an area were spaced 650 or 900 μm apart. Neural signals were filtered between 250 Hz and 8 Rolziracetam kHz and amplified and digitized at 40 kHz to obtain spike data. The location of recordings in both the FEF and V4 was verified with MRI. In both monkeys, we electrically (<50 μA) stimulated in the FEF and elicited eye movements. Eye movements were recorded by an infrared eye tracking system (Eye Link II, SR Research) at a sampling rate of 500 Hz. Recording sites that showed a significant visual response (Wilcoxon rank-sum test, p < 0.05) were included for analysis. The intervals used for this statistical comparison were as described before. Firing rates were calculated with 10 ms nonoverlapping bins.

, 2010) and took pictures using a Yokogawa CSU-XA1 spinning-disc confocal microscope with a Photometrics Cascade II EMCCD camera (1024 × 1024), controlled by μManager (http://www.micro-manager.org). One image was taken right before axotomy, and images were collected every 9 s for 7 min postaxotomy. To visualize the axons for laser axotomy in GFP-DLK-1L/S dynamic experiments, we used 0.5 s exposure time, which was much longer than in the localization analysis in Figure 5. The

fluorescence intensity of the first 3 μm axon fragments near cut sites was measured using MetaMorph (Molecular Devices). A comparable nonaxonal region of interest was also measured as background. For the quantification of GFP-DLK-1L/S protein level after axotomy, the intensity of each time point (Ft = Fi − Fb; Ft, fluorescence intensity at time point t; Fi, fluorescence intensity of the region buy PLX3397 of interest; Fb, intensity of the background) was normalized by the intensity at axotomy (F0). In comparisons of measurement of axonal regrowth in Figure 6, we used one-tailed Student’s t test. Comparisons involving multiple groups used one-way ANOVA and Bonferroni posttests in Graphpad Prism (GraphPad Software). To compare variables such as axon termination proportions in Figure 1, 2, and 4, we used Fisher’s exact

test. For expression studies in 293 T cells, full-length dlk-1L and dlk-1S cDNAs were cloned into pcDNA3-HA or pcDNA-FLAG to generate pCZGY1711(FLAG-DLK-1 L), pCZGY1710(HA-DLK1L), pCZGY1709(HA-DLK-1S), pCZGY1708(FLAG-DLK-1L(Δ856–881)), and pCZGY1707(HA-DLK-1L(Δ856–881)). Cells were cultured using standard procedures in Dulbecco’s modified Eagle’s medium found ( Nakata et al., 2005). Lipofectamine selleck kinase inhibitor 2000 (Invitrogen) was used in cell transfection. One day after transfection, cells were treated with 3 μM Ionomycin (Cell Signaling Technology, 9995) with or without BAPTA-AM (10 mM) (Sigma, 126150-97-8) for 15 min and lysed using radioimmunoprecipitation buffer (25 mM Tris-HCl [pH 7.4], 150 mM KCl, 5 mM EDTA, 1% NP-40, 0.5% sodium deoxycholate, and 0.1%

SDS, and protease inhibitor cocktail; Roche Applied Science). Equivalent amounts of lysates were incubated with rabbit anti-FLAG (Sigma, F7425) for 6–8 hr at 4°C. Immune complexes were precipitated with protein A agarose (GE Healthcare) for 1 hr at 4°C, washed four times with lysis buffer, and eluted by heating to 95°C for 5 min in SDS sample buffer containing 1 mM DTT. Blots were probed with rabbit anti-FLAG antibodies (Sigma, F7425) or a mouse anti-HA monoclonal antibody (Cell Signaling, 2367). The blot was visualized with Amersham HRP-conjugated anti-rabbit or anti-mouse secondary antibodies at 1:5,000 (Amersham) using the SuperSignal West Femto kit (Pierce). Yeast two-hybrid assays were performed using pACT2 and pBTM166 vectors (Clontech). DLK-1 cDNAs encoding full-length or fragment of the protein were fused to the GAL4 DNA binding domain in pACT2 or the GAL4 activation domain in pBTM166.

Functional connectivity within cortical networks has traditionally been investigated by measuring the cross-correlation between the spike trains of pairs of neurons (Douglas et al., 1989 and Douglas and Martin, 1991). Still, little is known about functional

connectivity under sensory stimulation or about the role of inhibition in the cortical network. We combine multiple computational approaches with optogenetic activation of PV+ neurons to determine how inhibitory activity modulates network connectivity within and across layers and columns of the cortex. We targeted expression of the light-sensitive ON-01910 research buy channel channelrhodopsin-2 (ChR2) to PV+ neurons in the mouse auditory cortex (Figure 1A), using a Cre-dependent adeno-associated virus (Sohal et al., 2009). One month posttransfection, we recorded neural responses with a 4 × 4 polytrode in putative L2/3 through L4 of the primary auditory cortex (Figure 1B) while playing pure tones to the contralateral ear and stimulating PV+ cells with blue light (Figure 1C). Functional connectivity between the recorded sites this website was quantified using Ising models, which

have previously been used to model neural interactions in many different systems (Ganmor et al., 2011a, Ganmor et al., 2011b, Köster et al., 2012, Marre et al., 2009, Ohiorhenuan et al., 2010, Roudi et al., 2009a, Schaub and Schultz, 2012, Schneidman et al., 2006, Shlens et al., 2006, Shlens et al., 2009 and Tang et al., 2008). The Ising model describes the coupling (a measure of functional connectivity) between pairs of recording sites and between recording sites and external stimuli based on observed population firing patterns and corresponding stimuli (Figures 1B and 1C). Because all pairwise interactions are fitted simultaneously, Ising models are less prone to false-positive interactions

that are inherent to traditional correlation analysis (Schneidman et al., 2006). For example, in a Megestrol Acetate fully connected Ising model (see Experimental Procedures), the strongest coupling to sounds occurred in rows 3 and 4 (Figure 2A), corresponding to the thalamorecipient layers. By contrast, traditional correlation analysis indicated strong connectivity between sounds and sites in all rows (Figure 2B). This false-positive connectivity between sounds and activity in rows 1 and 2 is due to the absence of site-to-site interactions in the correlation analysis. In a reduced Ising model where recording sites were coupled to sound but not to each other, which we call the independent neurons model, positive couplings between neural activity and the sound stimulus were also present in all recorded layers and did not differ across depth (Figure 2C; p = 0.55, Kruskal-Wallis analysis of variance [ANOVA]).

We studied DIV10 cultured cortical neurons from GluN2B+/+ and GluN2B2A(CTR)/2A(CTR) littermates. These cultures exhibited similar levels of basal viability and levels of synaptic connectivity and strength, as measured by mini EPSC frequency/size, spontaneous EPSC frequency, and AMPA receptor currents ( Figures S2A–S2D), as well as unaltered cell capacitance ( Figure S2E). Whole-cell and extrasynaptic NMDAR currents in both GluN2B+/+ DAPT mouse and GluN2B2A(CTR)/2A(CTR) neurons were found to be similarly sensitive to the GluN2B-specific antagonist ifenprodil. In neurons

of both genotypes, we observed a blockade of around 60% ( Figure 2B), indicative of a high (∼80%) level of GluN1/GluN2B heterodimeric receptors. Moreover, the proportion of extrasynaptic NMDARs was found to be the same for GluN2B2A(CTR)/2A(CTR)

and GluN2B+/+ neurons ( Figure 2C). Thus, any differential CTD subtype-specific effects on excitotoxicity could be studied without the potentially confounding factor of altered NMDAR location. We also investigated whether any differences in use-dependent run-down of whole-cell NMDAR currents were observed because this may be relevant to long-term exposure to NMDA. Having measured baseline whole-cell NMDAR currents, ten further 10 s CH5424802 chemical structure applications of NMDA were applied over a 10 min period. We found no difference in run-down of steady-state NMDAR currents in GluN2B+/+ and GluN2B2A(CTR)/2A(CTR) neurons (around 3% per application;

Figure S2F). We also examined NMDAR single-channel properties. We excised outside-out patches from DIV9 GluN2B+/+ and GluN2B2A(CTR)/2A(CTR) neurons and measured NMDA-evoked unitary currents, finding no difference in their mean single-channel conductance of approximately 50 pS, which is typical for GluN2B-containing NMDARs ( Figure S2G). Despite the aforementioned similarities, we found one important difference; whole-cell NMDAR currents in Thymidine kinase GluN2B2A(CTR)/2A(CTR) neurons were around 30% lower than GluN2B+/+ ( Figure 2D). Levels of GluN2B protein were lower in DIV10 GluN2B2A(CTR)/2A(CTR) cortical neurons ( Figure S2H) and in P7 cortical protein extracts ( Figure S2I; ruling out the possibility of an in vitro artifact). An explanation for this difference was found when we looked at GluN2B2A(CTR) mRNA levels, which were lower both in DIV10 GluN2B2A(CTR)/2A(CTR) cortical neurons and in P7 cortical extracts ( Figures S2H and S2I). However, this decrement appeared to be a developmental-stage-dependent effect because by adulthood, levels of forebrain GluN2B mRNA ( Figure 3A) and protein (p = 0.51, n = 5,5) were unaltered in GluN2B+/+ versus GluN2B2A(CTR)/2A(CTR) mice. We hypothesize that GluN2B2A(CTR), compared to wild-type GluN2B, may be transcribed, processed, or exported slightly less efficiently, which manifests itself in a mRNA decrement in development when expression of many genes, including those encoding NMDAR subunits, is changing rapidly.

However, despite the increase in accuracy compared to the interleaved condition, odor sampling durations remained identical between the two conditions (Figure 5C; Table 1). The improvement in accuracy on blocked

stimuli developed rapidly (within 20 trials; data not shown) and consisted of both a transient component that disappeared Quisinostat concentration when returning to interleaved conditions (about 2/3 of the total) and a long-lasting component that persisted (about 1/3) (Figure 5A; compare first and last sets of interleaved sessions). This experiment implies that the performance accuracy benefits observed in previous go-signal tasks compared to RT tasks are simply due to testing with blocked stimuli. To test this directly, the same

four subjects that were tested on the go-signal task with blocked odor pairs (Figure 4) were subsequently trained to asymptotic performance in the learn more RT paradigm also using blocked odor pairs (Figures 6A and 6B, phase IV). The stimulus difficulty was increased over consecutive days. Accuracy on the most difficult stimulus pair (12% mixture contrast) improved remarkably, from <70% on the interleaved condition to 91% ± 1% in the blocked condition (Figures 6A and 6C). We therefore introduced two successively more difficult problems: 4% and 2% mixture contrast, both obtained by using liquid dilutions of the 12% mixture stimuli (see Experimental Procedures for details). Accuracy on these stimuli, more difficult than any used previously by our group or others, was significantly above chance (Figures 6A and 6C) but was not associated with an increase in OSD (Figures 6B and 6D). Finally, we reintroduced a go signal at a fixed delay of 1 s (Figures 6A and 6B,

phase why V). The duration was fixed in order to allow optimal anticipation and subjects were trained for 5–6 sessions. Despite much longer OSD compared to the RT condition (Figures 6B and 6D) there was no significant difference in accuracy (p = 0.91, two-way ANOVA for difficulty and OSD instruction) (Figure 6E). Thus, maximal odor categorization accuracy was achieved by rats in self-paced conditions with <300 ms odor sampling time and could not be further improved by providing additional time for stimulus integration. The only impact of the go signal was to decrease performance when it was not fully anticipated, as can be seen by comparing accuracy in Figure 4B and Figure 6C (12% contrast). Studying rats performing an odor categorization task, we found that accuracy improves with stimulus sampling time only up to about 300 ms, consistent with previous studies showing rapid olfactory decisions (Karpov, 1980; Laing, 1985, 1986; Uchida and Mainen, 2003; Wesson et al., 2008). Using reward (and punishment) manipulations (Figures 1 and 2) and a response go signal (Figure 3), we were able to increase rats’ sampling time, but this failed to improve accuracy.

All other unlabeled chemicals and reagents were analytical graded. A. bisporus (AB) were commercially purchased from Cuddalore in vegetable markets, Tamil Nadu. A voucher specimen (No. 217) was deposited in Department of Botany, Annamalai University. Powder of AB (50 g) were extracted by stirring with 500 ml of ethanol (30 °C) at 150 rpm for 24 h

and filtered through Whatman No. 4 filter paper. The residues of ethanol extract was then rotary evaporated at 40 °C to dryness, re-dissolved in ethanol to a concentration of 10 mg/ml and stored at 4 °C for further use. The terpenoids content of the A. bisporus extracts were determined by the method of Puncal D Test. The flavonoid content of the sample were detected with few ml of ammonia shows the presence of fluorescence http://www.selleckchem.com/products/BKM-120.html learn more at 366 nm indicates the presence of flavonoids. The steroids content of the sample were detected by added a few ml of concentrated sulfuric acid solution to the extract. Formation of green color indicates the presence of steroids. The Carbohydrates and Sugars content of the sample were detected by added a few ml of concentrated sulfuric acid solution to the extract and heated formation of charring indicates the presence of carbohydrates. The alkaloids content of the sample were detected by the method of Dragandorff’s test. The

proteins content of the sample were detected by the method of Ninhydrin test. The Tannins content of the sample were detected by 1 ml of

Aluminum chloride. The total phenolic concentration in ABE and ABCNPs was expressed as gallic acid equivalents and was measured according to the method described by Bandoniene et al8 with slight modifications. The Total flavonoid contents (TFC) of the A. bisporus were extracted with 5% NaNO2, 10% AlCl3 and 1 M NaOH were measured at 510 nm with a known quercetin concentration as a standard. The results were expressed as milligrams of quercetin equivalents (CE) per gram of sample. AB loaded chitosan nanoparticles were synthesized by ionic gelation method using tripolyphosphate as a gelating agent. A known amount of chitosan was dissolved in 1% (v/v) acetic acid and allowed to stir for 1 h 3 mg/ml AB ethanol of extract have Libraries prepared already was then added to the freshly prepared chitosan dispersion. The pH of the medium was maintained at 5.0 using 1 M NaOH and then further stirred for 1 h. Finally, 1 mg/ml of TPP was added to the chitosan- AB ethanol extract under mild magnetic stirring. The resulting mixture was allowed to stir for 2 h to form AB encapsulated chitosan nanoparticles. The AB loaded chitosan nanoparticles were collected after the centrifugation of 10,000 rpm for 45 min with 4 °C.9 The powdered samples were collected with the help of lyophilizer and stored at 4 °C for further use. The ABE and ABCNPs were used for analyzing their DPPH radical scavenging activities where determined by the method of Chen.