Article Figures and data Abstract eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract Random search is a behavioral strategy used by organisms from bacteria to humans to locate food that is randomly distributed and undetectable at a distance. We investigated this behavior in the nematode Caenorhabditis elegans, an organism with a small, well-described nervous system. Here we formulate a mathematical model of random search abstracted from the C. elegans connectome and fit to a large-scale kinematic analysis of C. elegans behavior at submicron resolution. The model predicts behavioral effects of neuronal ablations and genetic perturbations, as well as unexpected aspects of wild type behavior. The predictive success of the model indicates that random search in C. elegans can be understood in terms of a neuronal flip-flop circuit involving reciprocal inhibition between two populations of stochastic neurons. Our findings establish a unified theoretical framework for understanding C. elegans locomotion and a testable neuronal model of random search that can be applied to other organisms. https://doi.org/10.7554/eLife.12572.001 eLife digest An animal's ability to rapidly and efficiently locate new sources of food in its environment can mean the difference between life and death. As a result, animals have evolved foraging strategies that are adapted to the distribution and detectability of food sources. Organisms ranging from bacteria to humans use one such strategy, called random search, to locate food that cannot be detected at a distance and that is randomly distributed in their surroundings. The biological mechanisms that underpin random search are relatively well understood in single-cell organisms such as bacteria, but this information tells us little about the mechanisms that are used by animals, which use their nervous system to control their foraging behavior. Roberts et al. have now investigated the biological basis for random search behavior in a tiny roundworm called Caenorhabditis elegans. This worm forages for pockets of bacteria in decaying plant matter and has a simple and well-understood nervous system. Roberts et al. used information on how the cells in this worm's nervous system connect together into so-called "neural circuits" to generate a mathematical model of random searching. The model revealed that the worm's neural circuitry for random searching can be understood in terms of two groups of neuron-like components that switch randomly between "ON" and "OFF" states. While one group promotes forward movement, the other promotes backward movement, which is associated with a change in search direction. These two groups inhibit each other so that only one group usually is active at a given time. By adjusting this model to reproduce the behavioral records of real worms searching for food, Roberts et al. could predict the key neuronal connections involved. These predictions were then confirmed by taking electrical recordings from neurons. The model could also account for the unexpected behavioral effects that are seen when a neuron in one of these groups was destroyed or altered by a genetic mutation. These findings thus reveal a biological mechanism for random search behavior in worms that might operate in other animals as well. The findings might also provide future insight into the neural circuits involved in sleep and wakefulness in mammals, which is organized in a similar way. https://doi.org/10.7554/eLife.12572.002 Introduction Random search is an evolutionarily ancient set of foraging strategies that evolved as an adaptation to environments in which prey items are undetectable at a distance and occur at unpredictable locations. Rather than attempting to exhaustively search a region of interest, the organism samples the environment at randomly selected points. This is achieved by executing a series of straight-line movements, called 'runs,' terminated at random intervals by sampling episodes during which the organism may or may not find prey. Sampling ends in a reorientation event, called a 'turn,' such that the next run is usually in a different direction from the preceding one. In optimal random foraging strategies the probability distribution of run length is matched to the statistical distribution of isolated food patches or prey items (Viswanathan, 2011), with power law distributions predominating when resources are sparsely distributed and exponential distributions predominating when resources are densely distributed (Humphries et al., 2010; Sims et al., 2012; Humphries et al., 2012). Random search has been documented in a wide range of species including microorganisms, nematodes, insects, mollusks, fish, birds, and mammals including humans (Viswanathan, 2011; Berg and Brown, 1972; Pierce-Shimomura et al., 1999). In humans this strategy is observed in diverse contexts, from traditional hunter-gatherer societies (Brown et al., 2007; Humphries and Sims, 2014) to technologically enhanced fishing industries (Bertrand et al., 2007). The formal similarities between random search across widely diverse phyla and spatial scales (Viswanathan, 2011) may point to a common mechanism, even in organisms that are highly cognitive. Despite the universality of random search, little is known about its neuronal basis, in part because of the difficulty of recording and manipulating activity in the brain of an unrestrained animal while it explores a large region of space. The relatively small spatial scale of random search behavior in C. elegans, coupled with the simplicity of its nervous system, provides a unique opportunity to identify the neuronal basis of random search in this species. To the unaided eye, C. elegans search behavior consists of forward runs, each terminated after a variable interval by a briefer period of reverse locomotion, which is also variable in duration (Pierce-Shimomura et al., 1999; Zhao et al., 2003; Wakabayashi et al., 2004), with apparently stochastic switching between these two behavioral states. Reversals are followed by resumption of forward movement that frequently begins with a deep body bend. These bends are highly variable in amplitude and lead to movement in a new direction. Thus, the sequence reverse–forward–deep bend, called a 'pirouette' (Pierce-Shimomura et al., 1999) is the fundamental turning event in C. elegans random search, with functional analogies to tumbles in bacterial chemotaxis (Berg and Brown, 1972). Careful inspection reveals a third state, called "pause," in which locomotion ceases for a fraction of a second or more (Croll, 1975; Shingai, 2000; Stephens et al., 2008; Rakowski et al., 2013; Salvador et al., 2014). Thus, C. elegans locomotion consists of three main behavioral states – forward, reverse, and pause – together with the transitions between them. C. elegans subsists on a diet of bacteria that it finds mainly in rotting plant material (Frézal and Félix, 2015). In the laboratory, search behavior is studied in worms foraging on agar plates containing one or more dense bacterial lawns, analogous to food patches in the ethological literature. Like many other organisms, C. elegans can tune the spatial scale of random search to its physiological state, the availability of food (Wakabayashi et al., 2004; Gray et al., 2005), and prior knowledge of its distribution (Calhoun et al., 2014). The lowest values of search scale are observed during "cropping," (Jander, 1975) the exploitation of a dense food patch. In C. elegans, two substates of cropping have been described: "dwelling," characterized by especially low crawling speed and frequent (presumably short) reversals, and "roaming," characterized by somewhat higher speeds and less frequent reversals. Transitions between dwelling and roaming, like the transitions between forward and reverse locomotion, are stochastic (Ben Arous et al., 2009; Fujiwara et al., 2002; Flavell et al., 2013). Intermediate values of search scale are observed during "local search" (Wakabayashi et al., 2004; Hills et al., 2004) when, for example, the animal is suddenly transferred from a bacterial lawn to a foodless region of the plate. The highest values of search scale are observed during "ranging," when food is exhausted, starvation sets in, and the need to find a new food patch becomes urgent (Wakabayashi et al., 2004; Gray et al., 2005). Worms sometimes spontaneously leave a food patch well before it is exhausted, with leaving rate inversely related to food quality and food density (Shtonda and Avery, 2006; Harvey, 2009), which may reflect a trade-off between exploitation and exploration (Bendesky et al., 2011). At the heart of the C. elegans locomotion circuit are five pairs of premotor 'command' interneurons organized into two functional groups that promote forward and reverse locomotion, respectively (Chalfie et al., 1985; Zheng et al., 1999; Stirman et al., 2010; Schmitt et al., 2012). The two groups are reciprocally connected, and make output synapses onto distinct, non-overlapping sets of motor neurons that control body-wall muscle. The locomotory state (forward or reverse) is believed to be determined mainly by whichever set of motor neurons is more highly activated by input from the command neurons (Kawano et al., 2011; Xie et al., 2013; Gao et al., 2015; Liu et al., 2014). Command neuron activation depends upon influences that are both external and intrinsic to the command neuron network, and appears to have a strong stochastic component that underlies switching between forward and reverse locomotion. Some command neurons are tightly linked both functionally and synaptically to upstream interneurons that also switch state stochastically in concert and counterpoint to them (Gordus et al., 2015), providing a potential additional source of the stochasticity on which random search depends. At least nine classes of chemosensory neurons and twelve classes of upstream interneurons are required for normal regulation of the duration of forward locomotion (Viswanathan, 2011; Gray et al., 2005; Tsalik and Hobert, 2003; Fang-Yen et al., 2015). Input from these neurons onto the command neuron network modulates the mean run length and, thereby, the spatial scale of random search. Search scale also appears to be modulated by neurons that release biogenic amines (serotonin, dopamine, and tyramine) (Flavell et al., 2013; Hills et al., 2004; Bendesky et al., 2011) or peptides (Ben Arous et al., 2009; Flavell et al., 2013; Gloria-Soria and Azevedo, 2008; Styer et al., 2008; Reddy et al., 2009; Bhattacharya et al., 2014). These diverse signaling pathways may provide the means by which the worm optimizes its search strategy in response to feeding history (Gray et al., 2005), the quality, density and spatial distribution of food (Shtonda and Avery, 2006; Calhoun et al., 2015), and other factors that constrain survival and reproduction (Gloria-Soria and Azevedo, 2008; Pujol et al., 2001; Pradel et al., 2007; Lipton et al., 2004). Although the neural circuitry for local search has been described in considerable detail, our understanding of the system remains limited, partly for lack of key physiological data, but also for lack of a model in which to interpret the data. Common sense suggests that the forward and reverse command neurons should inhibit each other to minimize simultaneous occurrences of neuronal states for incompatible behaviors (Zheng et al., 1999). A plausible anatomical substrate for such reciprocal inhibitory connections between command neurons exists in the C. elegans connectome (White et al., 1986), but anatomical data do not specify the signs or strengths of synaptic connections. A quantitative model that incorporates physiological properties of the command neurons and their synaptic connections is needed to interpret experimental results, such as the unexpected observation that silencing some of the reverse command neurons causes a reduction in forward dwell time, and conversely for forward command neurons (Rakowski et al., 2013; Zheng et al., 1999). It is also needed to explain complex patterns of changes in dwell times observed across the three locomotory states caused by introducing or eliminating tonic membrane conductances in the command neurons, and to answer basic mechanistic questions about the control of C. elegans locomotion. At present, the experimental data are insufficient for creating a neuron-by-neuron model of the command network that incorporates biophysical details such as synaptic and membrane conductances without introducing a heavy load of unconstrained parameters (Rakowski et al., 2013). Nor would such a mechanistically detailed model necessarily provide the appropriate level of abstraction in which to intuitively understand C. elegans search behaviors, including their strong stochastic component. Instead, we have kept the level of biological detail to the minimum needed to predict the statistical distributions of dwell times in forward, reverse and pause states, and other fundamental aspects of the behavior. Each of the model's three main assumptions remains within the bounds of widely accepted experimental results; our mathematical analysis simply shows what follows necessarily from these assumptions. To provide an empirical basis for the model we quantified C. elegans search behavior in terms of tangential velocity, defined as the speed and direction of worm's movement along its sinuous trajectory, which we recorded at higher resolution than previously possible. Behavioral data were then fit to a four-state hidden Markov model in which each state corresponds to a unique pattern of activation across the command neurons. Importantly, rate constants governing probabilistic transitions between states in the Markov model are expressed in terms of synaptic weights in an analytically tractable version of the model. We were therefore able to validate the model by showing that it correctly predicts phenomena on which it was not fit, such as reciprocal inhibition between forward and reverse command neurons in the biological network and the behavioral effects of perturbations introduced by laser ablations and genetic mutations. Although the model is inherently probabilistic, we found that it also makes accurate predictions concerning deterministic behaviors in C. elegans, indicating a potentially high level of generality. The present findings thus establish a simple theory of C. elegans locomotory control and provide a testable model of random search that can be applied to other organisms. Results A neuronal model of random search in C. elegans is a theory of the relationship between activation states of the command neurons and foraging behavior. Methods presently available for observing neuronal activity in freely behaving C. elegans utilize calcium-sensitive probes that have insufficient temporal resolution to observe the changes in neuronal activity associated with the rapidly changing behavioral states, especially the frequent brief pauses that are an integral part of the behavior. Therefore, as a proxy for command neuron state, we used the worm's tangential velocity, defined as the speed and direction of worm's movement along its sinuous trajectory. We focused on tangential velocity because in sinusoidal locomotion the net reactive forces produced by body-wall muscle contractions acting against the substrate are tangential to the body surface (Gray et al., 2005). Tangential velocity therefore provides the most direct readout of which group of motor neurons and command neurons (forward or reverse) is more active (Qi et al., 2013). Alternative measures of the rate of translation such as centroid velocity (Pierce-Shimomura et al., 1999) or postural phase velocity (Stephens et al., 2011) have a less direct relationship to command neuron state because these measures either depend in complex ways on the shape of the worm, or rely on a representation of posture that ignores some of the thrust-generating components of the worm's shape that come into play unless the worm is moving along a fairly linear trajectory. To monitor tangential velocity as directly as possible, we painted a microscopic black spot on the worm and used a motorized stage controlled by a computer to keep the spot in the field of view (Figure 1A). The most common alternative method for measuring tangential velocity, tracking virtual points obtained by segmenting the worm's centerline, is subject to segmentation errors introduced by low contrast images of the worm's head and tail (see Cronin et al., 2005) which changes the distance between virtual points. This method can also be compromised by dropped frames when the worm's centerline crosses itself during tight turns. Figure 1 with 2 supplements see all Download asset Open asset Descriptive statistics of wild type worm tracks. (A) (x,y)-coordinates of a worm during 10 min of foraging. Inset: Image of a worm showing the black spot (arrow) used for optical tracking (scale bar = 200 µm). (B) The speed distribution computed from the distance moved between successive video frames had a peak at 180 µm/s, which includes both forward and reverse locomotion. A second peak at 14 µm/s corresponds to pauses. The decreased probability of observing speeds <14 µm/s (<0.47 μm/frame) is due to noise in the position measurement. (C) At least three time constants were required to fit (red) the speed autocovariance function (black; grey shading shows ± 1 sem). (D) The worm's heading remained nearly constant for ~10 s except for a transient peak at 1.4 s (▼), which corresponds to the period of one half cycle of undulation during sinusoidal locomotion. The dashed line shows random reorientation; shading shows ± 1 sem. (E) Example of v(t) showing periods of forward locomotion, reverse locomotion and pauses of various durations. Upward triangles (▲) mark forward-pause-forward (FPF) events; the downward triangle (▼) marks a reverse-pause-reverse (RPR) event. (F) Velocity distributions for the 5 wild type cohorts (5 colors) analyzed in this study. (G) Ensemble-averaged velocity during FPR transitions. All FPR transitions in all wild type cohorts were aligned at the end of forward movement, grouped according to the duration of the pause (2–9 frames), and averaged. Such transitions were defined using a threshold criterion of |v| < 50 μm/s to identify state P (Rakowski et al., 2013). Pauses lasting ≤ 1 frame are not shown because of ambiguity in state identification; pauses lasting ≥ 10 frames are omitted for clarity. (H) Identical to G except RPF transitions are shown. (I) Cumulative probability distributions for dwell time in the pause state defined as in G and H for all FPR and RPF transitions of duration >1 frame in wild type worms. https://doi.org/10.7554/eLife.12572.003 At the start of a 10 min observation period an individual worm was transferred from a food-laden culture plate to a bare agar surface devoid of overt sensory cues, thereby inducing a period of intensive local search behavior (Jander, 1975; Hills et al., 2004). The (x, y)-coordinates of the centroid of the spot were recorded with a temporal resolution of 33 ms (i.e., frame rate = 30 Hz) and a spatial resolution of 0.5 μm that was limited mainly by the precision of the stage position encoder; the optical tracking error was much smaller (Figure 1—figure supplement 1). A spatial resolution of approximately 0.5 μm amounts to an approximately 10-fold improvement over previously published tracking systems (Kocabas et al., 2012); thus worm speed (Figure 1B) could be extracted with unprecedented accuracy. For statistical analysis, worms were grouped into cohorts having the same genotype or neurons ablated (17–31 worms per cohort), which had been reared together and tested in parallel as young adults within the same 2–3 day period. This approach yielded a comprehensive data set containing a total of 8.3 million position measurements from 501 individuals in 20 cohorts. Model-independent identification of locomotory states Figure 1A– D describes important features of search behavior obtained by regarding the worm as a point moving in an external reference frame (allocentric coordinates) without regard to the orientation of the body axis. The speed distribution was bimodal (Figure 1B) with a broad peak around 180 µm/s that includes both forward and reverse motion, and a narrower peak near zero that corresponds to pauses. The speed autocovariance function had multiple exponential components (Figure 1C), suggesting at least three locomotory states. The average change in heading angle (|Δφ|¯), plotted as a function of the intervening time interval (Figure 1D), showed that worms maintained a nearly constant heading for up to 10 s (Stephens et al., 2010; Peliti et al., 2013), but reoriented randomly within ~30 s, establishing the shortest time scale over which the behavior can be considered a Brownian random walk (Figure 1—figure supplement 2), the simplest form of random search. On shorter time scales the path takes on the character of a truncated Lévy flight (Mantegna and Stanley, 1994). For more detailed analysis we distinguished forward from reverse movement by visual inspection of the recorded videos, and defined velocity, V(t) , to be a signed scalar value that denotes the speed of movement along the worm's track in the direction of the head (+) or tail (-) (Figure 1E; see Materials and methods). The probability distribution of V(t) (Figure 1F) showed two broad peaks that correspond to forward and reverse movement, and a narrow third peak centered at zero that corresponds to pauses. For the initial analysis we defined pauses using a fixed speed threshold of 0.05 mm/sec (Rakowski et al., 2013). Pauses occurred most frequently as transient interruptions of forward locomotion, causing the worm to stutter as it moves (Figure 1E; Video 1); stuttering also occurred, albeit less frequently, during reverse locomotion (Figure 1E; Video 2). Distinct pauses were also observed during transitions from forward to reverse (Figure 1G; Video 3) and from reverse to forward (Figure 1H; Video 4). Most pauses lasted longer than one video frame, indicating the presence of a locomotory state having a detectable dwell time; thus pauses were not merely zero crossings in plots of velocity versus time. We found that pauses during forward to reverse transitions were on average longer in duration than pauses during reverse to forward transitions (Figure 1I; p<10–5 ; Mann-Whitney U-test). These findings are consistent with the predictions of the model presented below, which uses a probabilistic criterion rather than a fixed velocity threshold to identify pauses. Video 1 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Forward-Pause-Forward transition. The worm is crawling on a foodless agar plate. The microscope stage moves continuously to keep the tracking spot near the center of the frame. Stage movement can be assessed by monitoring the white streaks in the background, which are segments of the worm's track at earlier times. Behavioral state is indicated in the upper left corner of the frame. The indicated behavioral transition is shown at normal speed, and slowed down by a factor of 5. The worm is paused when the tracking spot is stationary relative to the streaks. https://doi.org/10.7554/eLife.12572.006 Video 2 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Reverse-Pause-Reverse transition. https://doi.org/10.7554/eLife.12572.007 Video 3 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Forward-Pause-Reverse transition. https://doi.org/10.7554/eLife.12572.008 Video 4 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Reverse-Pause-Forward transition. https://doi.org/10.7554/eLife.12572.009 The stochastic switch model Based on the results presented in Figure 1 and previous studies noted below, we propose a minimal model for the control of random search behavior that involves two opposing neuron-like "units" that can exist in four distinct states corresponding to forward locomotion, reverse locomotion, and two pause states. This model differs from a previous model that represents the worm as a point in "shape space" (Stephens et al., 2008) in that here velocity is measured directly by observing the motion of a point on the body surface relative to the substrate, rather than indirectly by the temporal progression of shape changes. It also differs from previous models (Rakowski et al., 2013; Zheng et al., 1999; Wicks et al., 1996; Kunert et al., 2014) by representing changes in locomotory state as probabilistic transitions in a Markov process. Ablation of individual premotor interneurons (Chalfie et al., 1985) has led to the hypothesis that the direction of locomotion is controlled by a network comprising five pairs of premotor command interneurons organized into two functional groups that promote forward and reverse locomotion, respectively. Although the anatomical pattern of synaptic connectivity among these interneurons has been established (White et al., 1986) (Figure 2A), this information does not yield an intuitive explanation of how the direction of locomotion is regulated. Nor, in our view, does the present state of the anatomical connectivity provide the basis for a neuron-by-neuron simulation of the network (but see Rakowski et al., 2013), as neither signs nor physiological strengths (weights) of synapses in C. elegans can be inferred reliably from anatomical structure or neurotransmitter type, and almost nothing is known about the intrinsic membrane currents of these neurons or how they shape the input-output function of individual command neurons. Figure 2 with 3 supplements see all Download asset Open asset Assumptions with supporting data for the Stochastic Switch Model. (A) Connectivity of forward and reverse command neurons. Arrows with single heads are monosynaptic connections inferred from the C. elegans connectome (White et al., 1986; Varshney et al., 2011) line thickness is proportional to the number of presynaptic specializations seen in the reconstruction of each pairwise connection. Open, double-headed arrows indicate synaptic pathways from or to the indicated pool of neurons outside the network. (B) Voltage recording from the command neuron AVA in the absence of injected current. In this neuron, quasi-stable membrane potentials are seen at -17 and -32 mV. These results differ from previously published AVA recordings, which were made in the presence of hyperpolarizing current (5–10 pA) that kept the membrane potential near -55 mV (Lindsay et al., 2011). (C) Neuronal representation of the Stochastic Switch Model. Forward and reverse command neurons are represented as single binary neuron-like units ℱ and ℛ, respectively. Arrows depicting cross connections (Wℱℛ, Wℛℱ) represent functional (net mono- and polysynaptic) connections between forward and reverse units. Self-connections (Wℱℱ, Wℛℛ) represent synaptic connections between neurons comprising a given unit, voltage dependent currents in these neurons, and polysynaptic recurrent pathways involving non-command neurons. Downward arrows (hℱ, hℛ) represent the combined effects of input from presynaptic neurons, including sensory neurons, and neuromodulation. (D) Markov model representation of the command neuron network. The color of a unit indicates its state of activation (red on, white off). In addition to the forward state F and the reverse state R, there are two pause states, X and Y. Arrows, with their associated rate constants, indicate transitions in which a single unit changes state. Transitions in which two units change state simultaneously have probability zero because single-unit transitions are assumed to be statistically independent. (E) The most likely sequence of states in the hidden Markov model (computed using the Viterbi algorithm) for a representative data segment. https://doi.org/10.7554/eLife.12572.010 To establish a mathematically tractable framework for understanding how the command network functions during search behavior, we created a minimal model based on three simplifying assumptions, each of which was biologically motivated. (i) Command neurons act like binary units (Hopfield, 1982). This assumption was based on voltage recordings from command neurons in which we regularly observed two stable membrane potentials with rapid transitions between them (Figure 2B; also see Kato et al., 2015). It is also supported by the observation of a bimodal distribution of calcium activity in AVA neurons and their upstream partners AIB and RIM (Gordus et al., 2015), and the report of distinct up and down states in voltage recordings from motor neruons (Liu et al., 2014). (i
Plants synthesize several classes of small heat shock proteins ranging in size from 15 to 30 kDa. Two conserved classes, designated class I and class II, are localized to the cytosol. Recombinant HSP18.1 and HSP17.7, representing class I and class II proteins from pea, respectively, were expressed in Escherichia coli and purified. Non-denaturing polyacrylamide gel electrophoresis and electron microscopy demonstrated that the purified proteins formed discretely sized, high molecular weight complexes. Sedimentation equilibrium analytical ultracentrifugation revealed that the HSP18.1 and HSP17.7 complexes were composed of approximately 12 subunits. Both proteins were able to enhance the refolding of chemically denatured citrate synthase and lactate dehydrogenase at stoichiometric levels in an ATP-independent manner. Furthermore, HSP18.1 and HSP17.7 prevented aggregation of citrate synthase at 45°C and irreversible inactivation of citrate synthase at 38°C. HSP18.1 also suppressed aggregation of lactate dehydrogenase at 55°C. These findings demonstrate that HSP18.1 and HSP17.7 can function as molecular chaperones in vitro. Plants synthesize several classes of small heat shock proteins ranging in size from 15 to 30 kDa. Two conserved classes, designated class I and class II, are localized to the cytosol. Recombinant HSP18.1 and HSP17.7, representing class I and class II proteins from pea, respectively, were expressed in Escherichia coli and purified. Non-denaturing polyacrylamide gel electrophoresis and electron microscopy demonstrated that the purified proteins formed discretely sized, high molecular weight complexes. Sedimentation equilibrium analytical ultracentrifugation revealed that the HSP18.1 and HSP17.7 complexes were composed of approximately 12 subunits. Both proteins were able to enhance the refolding of chemically denatured citrate synthase and lactate dehydrogenase at stoichiometric levels in an ATP-independent manner. Furthermore, HSP18.1 and HSP17.7 prevented aggregation of citrate synthase at 45°C and irreversible inactivation of citrate synthase at 38°C. HSP18.1 also suppressed aggregation of lactate dehydrogenase at 55°C. These findings demonstrate that HSP18.1 and HSP17.7 can function as molecular chaperones in vitro.
Electrostatics and solvation energies are important for defining protein stability, structural specificity, and molecular recognition. Because these energies are difficult to compute quickly and accurately, they are often ignored or modeled very crudely in computational protein design. To address this problem, we have developed a simple, fast, and accurate approximation for calculating Born radii in the context of protein design calculations. When these approximate Born radii are used with the generalized Born continuum dielectric model, energies calculated by the 10(6)-fold slower finite difference Poisson-Boltzmann model are faithfully reproduced. A similar approach can be used for estimating solvent-accessible surface areas (SASAs). As an independent test, we show that these approximations can be used to accurately predict the experimentally determined pK(a)s of >200 ionizable groups from 15 proteins.
