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K L Magleby

Publications and source records attributed to K L Magleby.

At least 19 recordsLinked to original sources

Dependency plots suggest the kinetic structure of ion channels.

Ion channels are integral membrane proteins that regulate ionic flux through cell membranes by opening and closing (gating) their pores. The gating can be monitored by observing step changes in the current flowing through single channels, and analysis of the observed open and closed interval durations has provided a window to develop kinetic models for the gating process. One difficulty in developing such models has been to determine the connections (transition pathways) among the various kinetic states involved in the gating. To help overcome this difficulty we present a transform (dependency plot) of the single-channel data that can give immediate insight into the connections. A dependency plot is derived by calculating a contingency table from a two-dimensional (joint density) dwell-time distribution of adjacent open and closed intervals by assuming that the two classified criteria are the open and closed durations of each pair of adjacent intervals. A three-dimensional surface plot of the fractional difference between the numbers of observed interval pairs and the numbers expected if the durations of adjacent intervals are independent then gives the dependency plot. An excess of interval pairs in the dependency plot suggests that the open and closed states (or compound states) that give rise to the interval pairs in excess are directly connected. A deficit of interval pairs suggests that the open and closed states (or compound states) that give rise to the interval pairs in deficit are either not directly connected or that there are additional open-closed transition pathways arising from the directly connected states.

Animals

Ion channels. Preventing artifacts and reducing errors in single-channel analysis.

The power of single-channel analysis techniques has rapidly expanded during the past few years, giving investigators increased ability to identify models and estimate parameters while reducing error and artifacts. At present, however, there is no single best method, as even the most advanced techniques have various limitations which depend on the experimental data and models being examined. Consequently, for the examined models and experimental data, the most critical part of single-channel analysis is to estimate errors and evaluate the ability of the methods used to discriminate among possible gating mechanisms. The magnitudes of the errors and the ability to identify models and estimate parameters depend on the models being examined as well as the experimental conditions and data. Consequently, the evaluation of the errors associated with each method needs to be repeated when the experimental data and examined models change.

Artifacts

Voltage-dependent gating mechanism for single fast chloride channels from rat skeletal muscle.

1. A voltage-dependent gating mechanism for the fast Cl- channel was developed from the analysis of single-channel current records obtained with the patch clamp technique from primary cultures of rat skeletal muscle. Up to 10(6) open and shut intervals were analysed from each of five different excised patches of membrane containing a single fast Cl- channel. 2. Rate constants for a kinetic scheme with six closed and two open states (scheme I) were estimated at a given voltage by maximum likelihood fitting of open and closed dwell-time distributions obtained at that voltage. This procedure was then repeated for data obtained at each of three to eight different membrane potentials for each channel. 3. Plots of the estimated rate constants against membrane potential typically appeared linear on semilogarithmic co-ordinates, consistent with rate constants that are exponentially dependent on voltage. 4. Regression analysis of these plots yielded two parameters for each rate constant: the value of the rate constant at -50 mV (B) and its voltage sensitivity (A). The dwell-time distributions predicted with these parameters and scheme I gave a good description of the experimental dwell-time distributions at all the studied voltages, lending further support for an exponential dependence of rate constants on membrane potential. 5. Estimates of A and B were also obtained by simultaneously fitting dwell-time distributions obtained at three to eight different voltages, in order to better define these parameters. Predicted dwell-time distributions obtained with these estimates and scheme I could approach the theoretical best description of the data for discrete-state Markov models. 6. Eight to twelve of the fourteen rate constants in scheme I appeared voltage sensitive, with effective gating charges ranging from about -1.5 to +1.0 units of electronic charge. 7. The estimated rate constants and their voltage sensitivities for the five analysed channels were generally similar, but showed some heterogeneity. 8. Gating mechanisms which had fewer kinetic states than scheme I, or equal and opposite effective gating charges over each transition barrier, or four or five identical and independent voltage-dependent subunits, all gave poorer descriptions of the data than scheme I. These simpler mechanisms were also ranked below scheme I by the Schwarz criterion, which applies a heavy penalty for additional free parameters. 9. These findings indicate that the voltage dependence of the fast Cl- channel is consistent with a kinetic scheme with six closed and two open states, in which a majority of transitions among the states are voltage dependent.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

Accounting for the Ca(2+)-dependent kinetics of single large-conductance Ca(2+)-activated K+ channels in rat skeletal muscle.

1. The Ca(2+)-dependent kinetics of large-conductance Ca(2+)-activated K+ channels from cultured rat skeletal muscle were studied with the patch clamp technique. Data were collected in the absence of Na+ and Mg2+, which can alter the kinetics. About 2 x 10(5) open and shut intervals were analysed from each of five different excised membrane patches containing a single active channel. Analysis was restricted to activity in the normal mode, which includes 96% of the intervals. 2. The open probability (Popen) and dwell-time distributions of open and shut intervals were obtained at three to four different [Ca2+]i for each of the channels. Popen data were also obtained from some multichannel patches. 3. Increasing [Ca2+]i increased Popen. At a pH of 7.0 the Hill coefficient was 3.7 +/- 0.8 (range of 3.0-5.0) and a Popen of 0.5 occurred at 14 +/- 7 microM [Ca2+]i (K0.5) for data obtained at +30 mV (n = 6). At a pH of 7.2 the Hill coefficient was 3.0 +/- 0.5 (range of 2.2-3.7) and K0.5 was 9 +/- 6 microM-Ca2+ (n = 7). The large standard deviations for K0.5 reflect the observation that fourfold differences in K0.5 could be observed for different channels studied under the same experimental conditions. 4. Hill coefficients that can be greater than 3 suggest that the channel may bind four or more Ca2+ to become fully activated. The binding of four Ca2+ before opening would require a minimum of five shut states. This estimate of the minimum number of shut states is in general agreement with that obtained from the number of exponential components in the dwell-time distributions of shut intervals. Thus, two different methods give similar estimates of the minimum number of shut states. If the channel can open with different numbers of bound Ca2+, then this could give rise to the three to four open states suggested by the three to four exponential components in the open dwell-time distributions. 5. Kinetic schemes consistent with the Ca(2+)-dependent kinetics were developed by simultaneously fitting open and shut dwell-time distributions obtained at three to four different [Ca2+]i, using maximum likelihood techniques and corrections for missed events. Such simultaneous fitting can provide an increased ability to define models and rate constants.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

Identifying kinetic gating mechanisms for ion channels by using two-dimensional distributions of simulated dwell times.

Ion channels are integral membrane proteins that regulate ionic flux through cell membranes by opening and closing (or gating) their pores. The gating can be monitored by observing step changes in the current flowing through single channels. Analysis of the durations of the open and closed intervals and of the correlations among the interval durations can give insight into the gating mechanism. Although it is well known that the correlation information can be essential to distinguish among possible gating mechanisms, it has been difficult to use this information because it has not been possible to correct the predicted correlations for the distortion of the single-channel data because of filtering and noise. To overcome this limitation we present a method based on a comparison of simulated and experimental two-dimensional dwell-time distributions constructed by analysing simulated and experimental single-channel currents in an identical manner. The simulated currents incorporate the true effects of filtering and noise, the two-dimensional distributions retain the correlation information, and the identical analysis allows direct maximum-likelihood comparison of the simulated and experimental two-dimensional distributions. We show that the two-dimensional simulation method has a greatly increased ability to distinguish among models, compared with methods that use one-dimensional distributions.

Animals

Estimating kinetic parameters for single channels with simulation. A general method that resolves the missed event problem and accounts for noise.

Analysis of currents recorded from single channels is complicated by the limited time resolution (filtering) of the data which can prevent the detection of brief intervals. Although a number of approaches have been used to correct for the undetected intervals (missed events) when identifying kinetic models and estimating parameters, none of them provide a general method which takes into account the true effects of noise and limited time resolution. This paper presents such a method. The approach is to use simulated single-channel currents to incorporate the true effects of filtering and noise on missed events and interval durations. The simulated currents are then analyzed in a manner identical to that used to analyze the experimental currents. An iterative search process using likelihood comparison of two-dimensional dwell-time distributions obtained from the simulated and experimental single-channel currents then allows the most likely rate constants to be determined. The large errors and false solutions that can result from the more typically applied assumptions of no noise and an absolute dead time (idealized filtering) are excluded by the iterative simulation method, and the correlation information contained in the two-dimensional distributions should increase the ability to distinguish among different gating mechanisms. The iterative simulation method is generally applicable to channels which typically open to a single conductance level. For these channels the method places no restrictions on the proposed gating mechanism or the form of the predicted dwell-time distributions.

Ion Channel Gating

Voltage dependence and stability of the gating kinetics of the fast chloride channel from rat skeletal muscle.

1. The voltage dependence and stability of the gating kinetics of the fast Cl-channel in excised patches of membrane from cultured rat skeletal muscle were studied with the patch clamp technique. Up to 10(6) open and shut intervals were analysed from each of five different patches containing a single fast Cl-channel. 2. To test for kinetic stability, plots of the mean durations of consecutive groups of 5-500 open and shut intervals were examined at each voltage. After excluding infrequent entries into both an apparent subconductance state and a long-lived (inactive) shut state, there were no abrupt and sustained changes in the moving means, indicating the absence of obvious shifts to other kinetic modes. The moving means did, however, fluctuate about the overall mean. 3. A comparison of experimental and simulated data indicated that most, but not all, of the fluctuation in the moving means was due to the stochastic variation inherent in the gating process. The fluctuation not accounted for by stochastic variation was mainly expressed as a slow, low-amplitude, component of drift about the mean. This slow component was unlikely to have arisen from measurement errors. 4. To examine whether the slow drift reflected detectable changes in kinetic modes, the data were divided into consecutive groups of 50,000 intervals. The exponential components describing the distributions were remarkably similar among the different groups, with stochastic variation accounting for most of the observed differences. This finding implies a single kinetic mode throughout the experiment. Thus, any changes in channel activity associated with the slow drift would have little effect on the analysis of gating kinetics presented here. 5. Depolarization increased channel open probability, Popen, for all five channels. This increase had a voltage sensitivity of 17 +/- 4 mV per e-fold change (effective gating charge of 1.6 +/- 0.32 electronic charges at 23 degrees C). Popen was 0.5 at -31 +/- 4 mV. 6. The depolarization-induced increase in Popen typically arose from a decrease in the mean shut time (19 +/- 4 mV per e-fold change; effective gating charge of 1.3 +/- 0.3 at 23 degrees C) and an increase in the mean open time (109 +/- 61 mV per e-fold change; effective gating charge of -0.24 +/- 0.13). 7. Neither plots of Popen versus voltage nor plots of the mean open and mean shut time versus voltage were completely described by a single Boltzmann distribution, suggesting multiple voltage-sensitive steps in channel gating.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

Kinetic time constants independent of previous single-channel activity suggest Markov gating for a large conductance Ca-activated K channel.

Models for the gating of ion channels usually assume that the rate constants for leaving any given kinetic state are independent of previous channel activity. Although such discrete Markov models have been successful in describing channel gating, there is little direct evidence for the Markov assumption of time-invariant rate constants for constant conditions. This paper tests the Markov assumption by determining whether the single-channel kinetics of the large conductance Ca-activated K channel in cultured rat skeletal muscle are independent of previous single-channel activity. The experimental approach is to examine dwell-time distributions conditional on adjacent interval durations. The time constants of the exponential components describing the distributions are found to be independent of adjacent interval duration, and hence, previous channel activity. In contrast, the areas of the different components can change. Since the observed time constants are a function of the underlying rate constants for transitions among the kinetic states, the observation of time constants independent of previous channel activity suggests that the rate constants are also independent of previous channel activity. Thus, the channel kinetics are consistent with Markov gating. An observed dependent (inverse) relationship between durations of adjacent open and shut intervals together with Markov gating indicates that there are two or more independent transition pathways connecting open and shut states. Finally, no evidence is found to suggest that gating is not at thermodynamic equilibrium: the inverse relationship was independent of the time direction of analysis.

Animals

Adjacent interval analysis distinguishes among gating mechanisms for the fast chloride channel from rat skeletal muscle.

1. The durations of adjacent open and shut intervals, obtained with the patch-clamp technique from fast Cl- channels in tissue-cultured rat skeletal muscle, were analysed to distinguish among eight previously considered gating mechanisms for the channel which differed in the connections among the states. 2. Open intervals were separated into groups based on the duration of the shut intervals which occurred before or after each open interval. Fitting these conditional open distributions with sums of exponentials indicated that they were described by two exponential components. 3. The time constants of the two components in the conditional open distributions were independent of the adjacent shut interval durations. The observation of invariant time constants is consistent with gating mechanisms in which the rate constants for transitions among the states remain constant with time (discrete Markov process). 4. In contrast to the invariant time constants, the areas of the two components in the conditional open distributions were dependent on the adjacent shut interval durations. The area of the fast open component increased, and the area of the slow open component decreased, as the duration of adjacent shut intervals increased. Thus, it is changes in areas, rather than time constants, which give rise to the observed inverse relationship between the durations of adjacent open and shut intervals. 5. The findings in summary statements 2-4 indicate that at least two open states are connected by independent pathways to different shut states; the open state associated with the fast open component is connected to a shut state (or compound shut state) of longer effective lifetime, and the open state associated with the slow open component is connected to a shut state (or compound shut state) of briefer effective lifetime. 6. Seven of the eight previously considered gating mechanisms were rejected because they did not account for the observed relationships between the durations of adjacent open and shut intervals, when analysed in terms of either conditional open distributions or conditional mean open interval durations. 7. The seven rejected gating mechanisms also did not account for the observed correlations between interval durations, when analysed in terms of correlation coefficients. Adjacent interval and correlation analysis thus provided a means to distinguish among the gating mechanisms.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

Gating scheme for single GABA-activated Cl- channels determined from stability plots, dwell-time distributions, and adjacent-interval durations.

To study the gating of a GABA-activated Cl- channel, currents from single channels activated by 1.0 microM GABA were examined in patches of membrane excised from cultured chick cerebral neurons. The distributions of open and shut interval durations were each described by the sum of 3 exponential components, suggesting that the channel normally enters at least 3 open and 3 shut states. Five different 6-state gating schemes were found that could describe, all equally well, the observed distributions of open and shut interval durations. Plots of the mean duration of open intervals adjacent to shut intervals of specified durations revealed that, on the average, openings of brief duration were adjacent to closings of long duration. This observation indicated 2 or more independent transition pathways between the open and shut states. Examination of the distributions of open intervals adjacent to shut intervals of specified durations revealed that the time constants of the exponential components describing these conditional open-interval distributions were independent of the durations of the adjacent shut intervals. In contrast, the areas changed in a manner consistent with open states of briefer mean lifetimes typically making transitions to shut states of longer mean lifetimes. Four of the 5 gating schemes considered were rejected because they did not predict the relationship between adjacent intervals or because they predicted that the channel should switch between 2 gating modes with markedly different mean open and shut times, which was not a characteristic of the experimental data. The single remaining kinetic scheme could account for the observed kinetic properties of the GABA channel.

Animals

Fractal models are inadequate for the kinetics of four different ion channels.

The gating kinetics of single ion channels have been well described by models which assume that channels exist in a number of discrete kinetic states, with the rate constants for transitions among the states remaining constant in time. In contrast to such discrete Markov models, it has recently been considered whether gating might arise from transitions among a continuum of states, with the effective rate constants for leaving the collections of states given by a fractal scaling equation (Liebovitch, L.S., J. Fischbarg, J.P. Koniarek, I. Todorova, and M. Wang. 1987. Biochim. Biophys. Acta. 896:173-180; Liebovitch, L.S., and J.M. Sullivan. 1987. Biophys. J. 52:979-988). The present study compares discrete Markov with fractal continuum models to determine which best describes the gating kinetics of four different ion channels: GABA-activated Cl channels, ACh-activated end-plate channels, large conductance Ca-activated K (BK) channels, and fast Cl channels. Discrete Markov models always gave excellent descriptions of the distributions of open and shut times for all four channels. Fractal continuum models typically gave very poor descriptions of the shut times for all four channels, and also of the open times from end-plate and BK channels. The descriptions of the open times from GABA-activated and fast Cl channels by the fractal and Markov models were usually not significantly different. If the same model accounts for gating motions in proteins for both the open and shut states, then the Markov model ranked above the fractal model in 35 of 36 data sets of combined open and shut intervals, with the Markov model being tens to thousands of orders of magnitude more probable. We suggest that the examined fractal continuum model is unlikely to serve as a general mechanism for the gating of these four ion channels.

Animals

Kinetic states and modes of single large-conductance calcium-activated potassium channels in cultured rat skeletal muscle.

1. Kinetic states and modes of a large-conductance Ca2+-activated K+ channel in excised patches of membrane from cultured rat skeletal muscle were studied with the patch clamp technique. Up to 10(6) open and shut intervals were analysed from each of seven different excised membrane patches containing a single channel. 2. Plots of the mean durations of consecutive groups of ten to fifty open and shut intervals were made to assess kinetic stability of the channel. Occasional abrupt decreases in the mean open interval duration from normal to different distinct levels, which were maintained for hundreds to thousands of consecutive intervals, indicated entry of the channel into different modes. 3. Four different kinetic modes were identified: normal mode, which included 96% of the intervals; intermediate open mode with 3.2% of the intervals; brief open mode with 0.5% of the intervals; and buzz mode with 0.1% of the intervals. The mean open interval durations were 61% of normal during the intermediate open mode, 12% of normal during the brief open mode, and 2.6% of normal during the buzz mode. 4. Most mode transitions were observed from the normal mode to one of the other modes and then back to normal. Sojourns in the normal mode lasted 5-1000 s. Sojourns in the intermediate open, brief open, and buzz modes lasted 1.5-150, 1-7, and 0.01-1 s, respectively. 5. During normal activity the distributions of interval durations were typically described by the sum of three to four exponential components for the open intervals and six to eight exponential components for the shut intervals, and this was the case for data obtained over a wide range of open channel probability resulting from different Ca2+i. These observations suggest that the channel can enter at least three to four open and six to eight shut states during normal activity. 6. The numbers of detected states for data sets of different sample sizes drawn from normal activity agreed with theoretical predictions, and were essentially independent of the segment of normal activity from which the data sets were drawn. These observations are consistent with relative stability of channel kinetics during normal activity. Detection of each additional open or shut state after the first was found to require a 3- to 10-fold increase in the number of analysed events. 7. The intermediate open mode differed from the normal mode in that the longest open component of the four normal open components was absent.

Action Potentials

Sampling, log binning, fitting, and plotting durations of open and shut intervals from single channels and the effects of noise.

(1) Analysis of the durations of open and shut intervals measured from single channels currents provides a means to investigate the mechanisms of channel gating. Durations of open and shut intervals are conveniently measured from single channel data by using a threshold level to indicate transitions between open and shut states. This paper presents a detailed characterization of sampling, binning, and noise errors associated with 50% threshold analysis, provides criteria to reduce these errors, methods to correct for them, and presents an efficient means of data handling for binning and plotting interval durations. (2) Measuring interval durations by sampling at a fixed rate introduces two types of errors, (a) the number of intervals of a given measured duration are increased (promoted) over that expected in the absence of sampling, producing a sampling promotion error, (b) sampling decreases the total fraction of true intervals that are detected, producing a sampling detection error. Sampling errors can be reduced to negligible levels if the actual or effective (after interpolation) sampling period is less than 10-20% of both the dead time and fastest time constant in the distribution of intervals. Dead time is given by the duration of a true interval that has a filtered amplitude equal to 50% of the true amplitude. (3) Methods are presented to correct for sampling promotion error during least squares and maximum likelihood fitting. Sampling detection error is more difficult to correct, but an empirical description of the sampling detection error can be used to calculate the effective fraction of detected events with sampling. (4) Noise in the single channel current record can produce two types of error. (a) If noise peaks in the absence of channel activity exceed the threshold for detection, then false channel events of brief duration are produced. Sufficient filtering will prevent this type of error. (b) Noise can also increase the total fraction of true intervals that are detected, producing a noise detection error. Increased filtering over that required to prevent false events is not necessarily the best method for reducing noise detection error, as increased filtering can prevent detection of the faster exponential components. (5) Noise detection error can be reduced in two ways: (a) an empirical description of the noise detection error can be used to calculate the effective fraction of detected events in the presence of noise. (b) The sampling period can be selected so that the sampling detection error cancels the noise detection error.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

Correcting single channel data for missed events.

Interpretation of currents recorded from single ion channels in cellular membranes or lipid bilayers is complicated by the necessarily limited time resolution of the recording and detection systems. All intervals less than a certain duration, depending on the frequency response of the system, are not detected. Such missed events produce increases in the durations of observed open and shut intervals. In order to obtain the true kinetic scheme and rate constants underlying the observed activity, it is necessary to take into account missed events. We develop methods to correct for missed events for models with two or more states, including models with multiple open and shut states, compound states, and loops. Our methods can be used in a forward direction to predict observed distributions of open and shut intervals for a given kinetic scheme and time resolution. They can also be used in a backwards direction with iterative methods to determine rate constants consistent with the observed distributions. While a given kinetic scheme with rate constants predicts unique observed distributions of open and shut intervals, rate constants determined from observed distributions are not necessarily unique. Using these correction methods, we examine the effects of missed events for a five-state model consistent with some properties of large conductance Ca-activated K channels.

Ion Channels

Quantitative description of three modes of activity of fast chloride channels from rat skeletal muscle.

The steady-state kinetic properties of single Cl- channels with fast kinetics active at resting membrane potentials in cultured rat skeletal muscle were studied using the patch-clamp technique. Membrane patches containing single active Cl- channels were often observed, and binomial analysis of the percentage open time in membrane patches containing several Cl- channels indicated that the channels did not occur as obligatory dimers and that they gated independently of one another. Channel activity could be divided into three categories: normal, which included about 99% of the openings and closings; buzz mode, which included about 1% and consisted of bursts of about 50 brief open and shut intervals; and inactivated shut states which included about 0.01% of the shut intervals and lasted for seconds, and occasionally minutes. The method of maximum likelihood was used to determine the number of significant exponential components required to fit the distributions of open and shut intervals during normal activity. Open interval distributions required at least two components, with time constants of 0.52 and 1.5 ms at -40 mV and 7.6 degrees C. Shut interval distributions required at least five exponential components, with time constants of 0.064, 0.72, 1.9, 12.3 and 350 ms. Kinetic reaction schemes were developed for the normal and buzz mode using maximum likelihood techniques to determine the most likely models and rate constants. In developing these models the effects of limited time resolution and missed events were taken into account. Each model tested typically had two or more sets of equally likely rate constants. Incorrect sets of rate constants resulting from the effect of missed events could be eliminated by analysis of the data with different time resolutions. Normal activity could be accounted for by several different seven-state models with two open and five shut states. As different models could be found that gave identical descriptions of the data, the distributions of open and shut intervals were not sufficient to define a unique model. It was established that no other seven-state models would be found that describe the distributions of open and shut intervals during normal activity better than the most likely presented models.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials

Single chloride-selective channels active at resting membrane potentials in cultured rat skeletal muscle.

The patch-clamp technique was used to characterize channels that could contribute to the resting Cl-conductance in the surface membrane of cultured rat skeletal muscle. Two Cl- -selective channels, in addition to the Cl- -selective channel of large conductance described previously (Blatz and Magleby, 1983), were observed. One of these channels had fast kinetics and a conductance of 45 +/- 1.8 pS (SE) in symmetrical 100 mM KCl. The other had slow kinetics and a conductance of 61 +/- 2.4 pS. The channel with fast kinetics typically closed within 1 ms after opening and flickered between the open and shut states. The channel with slow kinetics typically closed within 10 ms after opening and displayed less flickering. Both channels were active in excised patches of membrane held at potentials similar to resting membrane potentials in intact cells, and both were open a greater percentage of time with depolarization. Under conditions of high ion concentrations, both channels exhibited nonideal selectivity for Cl- over K+ with the permeability ratio PK/PCl of 0.15-0.2. Additional experiments on the fast Cl- channel indicated that its activity decreased with lowered pHi and that SO2-4 and CH3SO-4 were ineffective charge carriers. These findings, plus the observation that the fast Cl- channel was also active in membrane patches on intact cells, suggest that the fast Cl- channel provides a molecular basis for at least some of the resting Cl- conductance. The extent to which the slow Cl- channel contributes is less clear as it was typically active only after excised patches of membrane had been exposed to high concentrations of KCl at the inner membrane surface.

Animals