CiteULike: Author Houk

De Novo Computational Design of Retro-Aldol Enzymes

Lin Jiang — 2008-03-07T02:58:37-00:00

Science, Vol. 319, No. 5868. (7 March 2008), pp. 1387-1391.

The creation of enzymes capable of catalyzing any desired chemical reaction is a grand challenge for computational protein design. Using new algorithms that rely on hashing techniques to construct active sites for multistep reactions, we designed retro-aldolases that use four different catalytic motifs to catalyze the breaking of a carbon-carbon bond in a nonnatural substrate. Of the 72 designs that were experimentally characterized, 32, spanning a range of protein folds, had detectable retro-aldolase activity. Designs that used an explicit water molecule to mediate proton shuffling were significantly more successful, with rate accelerations of up to four orders of magnitude and multiple turnovers, than those involving charged side-chain networks. The atomic accuracy of the design process was confirmed by the x-ray crystal structure of active designs embedded in two protein scaffolds, both of which were nearly superimposable on the design model. 10.1126/science.1152692

Benchmarking the Conductor-like Polarizable Continuum Model (CPCM) for Aqueous Solvation Free Energies of Neutral and Ionic Organic Molecules

Y Takano — 2008-06-30T11:23:48-00:00

J. Chem. Theory Comput., Vol. 1, No. 1. (11 January 2005), pp. 70-77.

Abstract: The conductor-like polarizable continuum model (CPCM) using several cavity models is applied to compute aqueous solvation free energies for a number of organic molecules (30 neutral molecules, 21 anions, and 19 cations). The calculated solvation free energies are compared to the available experimental data from the viewpoint of cavity models, computational methods, calculation time, and aqueous pKa values. The HF/6-31+G(d)//HF/6-31+G(d) and the HF/6-31+G(d)//B3LYP/6-31+G(d) with the UAKS cavities, in which radii are optimized with PBE0/6-31G(d), provide aqueous solvation effects in best agreement with available experimental data. The mean absolute deviations from experiment are 2.6 kcal/mol. The MP2/6-31++G(d,p)//HF/6-31+G(d) with the CPCM-UAKS(HF/6-31+G(d)) calculation is also performed for the base-catalyzed hydrolysis of methyl acetate in water.

Kemp elimination catalysts by computational enzyme design

Daniela Röthlisberger — 2008-03-21T04:33:18-00:00

Nature (19 March 2008)

Benchmarking pKa Prediction Methods for Residues in Proteins

Courtney Stanton — 2008-06-27T10:54:30-00:00

J. Chem. Theory Comput., Vol. 4, No. 6. (10 June 2008), pp. 951-966.

Abstract: Methods for estimation of pKa values of residues in proteins were tested on a set of benchmark proteins with experimentally known pKa values. The benchmark set includes 80 different residues (20 each for Asp, Glu, Lys, and His), half of which consists of significantly variant cases (pKa e 1 pKa unit from the amino acid in solution). The method introduced by Case and co-workers [J. Am. Chem. Soc. 2004, 126, 41674180], referred to as the molecular dynamics/generalized-Born/thermodynamic integration (MD/GB/TI) technique, gives a root-mean-square deviation (rmsd) of 1.4 pKa units on the benchmark set. The use of explicit waters in the immediate region surrounding the residue was shown to generally reduce high errors for this method. Longer simulation time was also shown to increase the accuracy of this method. The empirical approach developed by Jensen and co-workers [Proteins 2005, 61, 704721], PROPKA, also gives an overall rmsd of 1.4 pKa units and is more or less accurate based on residue typethe method does very well for Lys and Glu, but less so for Asp and His. Likewise, the absolute deviation is quite similar for the two methods5.2 for PROPKA and 5.1 for MD/GB/TI. A comparison of these results with several prediction methods from the literature is presented. The error in pKa prediction is analyzed as a function of variation of the pKa from that in water and the solvent accessible surface area (SASA) of the residue. A case study of the catalytic lysine residue in 2-deoxyribose-5-phosphate aldolase (DERA) is also presented.

Model of Cortical-Basal Ganglionic Processing: Encoding the Serial Order of Sensory Events

David Beiser — 2006-06-06T00:26:56-00:00

J Neurophysiol, Vol. 79, No. 6. (1 June 1998), pp. 3168-3188.

The RNA silencing endonuclease Argonaute 2 mediates specific antiviral immunity in Drosophila melanogaster.

RP van Rij — 2008-05-27T21:30:20-00:00

Genes & development, Vol. 20, No. 21. (1 November 2006), pp. 2985-2995.

Most organisms have evolved defense mechanisms to protect themselves from viruses and other pathogens. Arthropods lack the protein-based adaptive immune response found in vertebrates. Here we show that the central catalytic component of the RNA-induced silencing complex (RISC), the nuclease Argonaute 2 (Ago-2), is essential for antiviral defense in adult Drosophila melanogaster. Ago-2-defective flies are hypersensitive to infection with a major fruit fly pathogen, Drosophila C virus (DCV), and with Cricket Paralysis virus (CrPV). Increased mortality in ago-2 mutant flies was associated with a dramatic increase in viral RNA accumulation and virus titers. The physiological significance of this antiviral mechanism is underscored by our finding that DCV encodes a potent suppressor of RNA interference (RNAi). This suppressor binds long double-stranded RNA (dsRNA) and inhibits Dicer-2-mediated processing of dsRNA into short interfering RNA (siRNA), but does not bind short siRNAs or disrupt the microRNA (miRNA) pathway. Based on these results we propose that RNAi is a major antiviral immune defense mechanism in Drosophila.

Reflex Compensation for Variations in the Mechanical Properties of a Muscle

Richard Nichols — 2008-05-09T17:32:16-00:00

Science, Vol. 181, No. 4095. (13 July 1973), pp. 182-184.

Soleus muscles of anesthetized cats were stretched and released by different amounts while their motor axons were stimulated. Muscle force increased, then gave way in response to large stretch. In the presence of active stretch reflexes in decerebrate cats, the give in force was absent. We demonstrate that autogenetic reflexes can compensate for variations in muscular stiffness revealed when responses to stretch and release are compared. 10.1126/science.181.4095.182

Modulation of striatal single units by expected reward: a spiny neuron model displaying dopamine-induced bistability.

AJ Gruber — 2006-11-23T12:37:41-00:00

J Neurophysiol, Vol. 90, No. 2. (August 2003), pp. 1095-1114.

Single-unit activity in the neostriatum of awake monkeys shows a marked dependence on expected reward. Responses to visual cues differ when animals expect primary reinforcements, such as juice rewards, in comparison to secondary reinforcements, such as tones. The mechanism of this reward-dependent modulation has not been established experimentally. To assess the hypothesis that direct neuromodulatory effects of dopamine on spiny neurons can account for this modulation, we develop a computational model based on simplified representations of key ionic currents and their modulation by D1 dopamine receptor activation. This minimal model can be analyzed in detail. We find that D1-mediated increases of inward rectifying potassium and L-type calcium currents cause a bifurcation: the native up/down state behavior of the spiny neuron model becomes truly bistable, which modulates the peak firing rate and the duration of the up state and introduces a dependence of the response on the past state history. These generic consequences of dopamine neuromodulation through bistability can account for both reward-dependent enhancement and suppression of spiny neuron single-unit responses to visual cues. We validate the model by simulating responses to visual targets in a memory-guided saccade task; our results are in close agreement with the main features of the experimental data. Our model provides a conceptual framework for understanding the functional significance of the short-term neuromodulatory actions of dopamine on signal processing in the striatum.

Action selection and refinement in subcortical loops through basal ganglia and cerebellum

JC Houk — 2008-01-17T20:45:36-00:00

Philosophical Transactions of the Royal Society B: Biological Sciences, Vol. 362, No. 1485. (2007), pp. 1573-1583.

Subcortical loops through the basal ganglia and the cerebellum form computationally powerful distributed processing modules (DPMs). This paper relates the computational features of a DPM's loop through the basal ganglia to experimental results for two kinds of natural action selection. First, functional imaging during a serial order recall task was used to study human brain activity during the selection of sequential actions from working memory. Second, microelectrode recordings from monkeys trained in a step-tracking task were used to study the natural selection of corrective submovements. Our DPM-based model assisted in the interpretation of puzzling data from both of these experiments. We come to posit that the many loops through the basal ganglia each regulate the embodiment of pattern formation in a given area of cerebral cortex. This operation serves to instantiate different kinds of action (or thought) mediated by different areas of cerebral cortex. We then use our findings to formulate a model of the aetiology of schizophrenia.

Deciding when and how to correct a movement: discrete submovements as a decision making process

Fishbach — 2007-02-27T17:55:06-00:00

Experimental Brain Research, Vol. 177, No. 1. (February 2007), pp. 45-63.

Prediction of complex two-dimensional trajectories by a cerebellar model of smooth pursuit eye movement.

RE Kettner — 2007-04-04T17:22:05-00:00

J Neurophysiol, Vol. 77, No. 4. (April 1997), pp. 2115-2130.

A neural network model based on the anatomy and physiology of the cerebellum is presented that can generate both simple and complex predictive pursuit, while also responding in a feedback mode to visual perturbations from an ongoing trajectory. The model allows the prediction of complex movements by adding two features that are not present in other pursuit models: an array of inputs distributed over a range of physiologically justified delays, and a novel, biologically plausible learning rule that generated changes in synaptic strengths in response to retinal slip errors that arrive after long delays. To directly test the model, its output was compared with the behavior of monkeys tracking the same trajectories. There was a close correspondence between model and monkey performance. Complex target trajectories were created by summing two or three sinusoidal components of different frequencies along horizontal and/or vertical axes. Both the model and the monkeys were able to track these complex sum-of-sines trajectories with small phase delays that averaged 8 and 20 ms in magnitude, respectively. Both the model and the monkeys showed a consistent relationship between the high- and low-frequency components of pursuit: high-frequency components were tracked with small phase lags, whereas low-frequency components were tracked with phase leads. The model was also trained to track targets moving along a circular trajectory with infrequent right-angle perturbations that moved the target along a circle meridian. Before the perturbation, the model tracked the target with very small phase differences that averaged 5 ms. After the perturbation, the model overshot the target while continuing along the expected nonperturbed circular trajectory for 80 ms, before it moved toward the new perturbed trajectory. Monkeys showed similar behaviors with an average phase difference of 3 ms during circular pursuit, followed by a perturbation response after 90 ms. In both cases, the delays required to process visual information were much longer than delays associated with nonperturbed circular and sum-of-sines pursuit. This suggests that both the model and the eye make short-term predictions about future events to compensate for visual feedback delays in receiving information about the direction of a target moving along a changing trajectory. In addition, both the eye and the model can adjust to abrupt changes in target direction on the basis of visual feedback, but do so after significant processing delays.

Porphyrin Isomers: Geometry, Tautomerism, Geometrical Isomerism, and Stability

YD Wu — 2007-06-19T13:17:12-00:00

J. Org. Chem., Vol. 62, No. 26. (26 December 1997), pp. 9240-9250.

Abstract: Density functional calculations have been carried out on free-base porphyrin (1) and its seven possible isomers (2-8) with an N4-metal coordination core. A total of 27 structures resulting from geometrical isomerism ((E/Z)-configurations) and NH tautomerism were studied. Geometries were fully optimized with the nonlocal density functional approximation (BLYP) using the 3-21G and 6-31G** basis sets. The calculated geometries compare favorably with the available X-ray crystal structures. Porphycene (2) is predicted to be the most stable among the eight isomers and is about 2 kcal/mol more stable than porphyrin due to its exceptionally strong hydrogen bonding. Compounds 5-8 are much less stable than porphyrin due to severe ring strain in these compounds. When a -(CH)n- linker is in a (Z)-configuration, each compound is planar or nearly planar with significant -delocalization; the corresponding (E)-configured structures are predicted to be somewhat distorted into bowl-like geometries in order to avoid severe steric interactions involving the inner hydrogens.

Agents of the mind

James Houk — 2007-06-07T02:07:36-00:00

Biol. Cybern., Vol. 92, No. 6. (June 2005), pp. 427-437.

The role of the basal ganglia and cerebellum in language processing

James Booth — 2007-03-21T21:05:29-00:00

Brain Research, Vol. 1133, No. 1. (16 February 2007), pp. 136-144.

The roles of the cerebellum and basal ganglia have typically been confined in the literature to motor planning and control. However, mounting evidence suggests that these structures are involved in more cognitive domains such as language processing. In the current study, we looked at effective connectivity (the influence that one brain region has on another) of the cerebellum and basal ganglia with regions thought to be involved in phonological processing, i.e. left inferior frontal gyrus and left lateral temporal cortex. We analyzed functional magnetic resonance imaging data (fMRI) obtained during a rhyming judgment task in adults using dynamic causal modeling (DCM). The results showed that the cerebellum has reciprocal connections with both left inferior frontal gyrus and left lateral temporal cortex, whereas the putamen has unidirectional connections into these two brain regions. Furthermore, the connections between cerebellum and these phonological processing areas were stronger than the connections between putamen and these areas. This pattern of results suggests that the putamen and cerebellum may have distinct roles in language processing. Based on research in the motor planning and control literature, we argue that the putamen engages in cortical initiation while the cerebellum amplifies and refines this signal to facilitate correct decision making.

A model of the motor servo: incorporating nonlinear spindle receptor and muscle mechanical properties.

CC Gielen — 2007-03-02T17:13:13-00:00

Biol Cybern, Vol. 57, No. 4-5. (1987), pp. 217-231.

A model for the stretch reflex is proposed incorporating a nonlinear description of muscle receptor behavior, a delay in the reflex loop and a model of muscle mechanical properties. The model adequately describes the nonlinear response properties of EMG and force to constant ramps in loading and unloading direction. The EMG responses during the ramp and at ramp plateau could be simulated adequately for all ramp velocities except for high stretch velocities where EMG activity appeared in bursts, presumably due to spinal nonlinearities. Force responses during ramp stretches could be simulated except at ramp plateau, where the measured force response decayed slower than the simulated responses. The model also explained that EMG and force responses during ramp stretches after a displacement of about 1 cm could be approximately described by a product relationship between a position-related term and a low-fractional power of velocity. During unloading ramps the model did not predict a clear velocity dependence in agreement with the data.

Cooperative hydrogen bonding effects are key determinants of backbone amide proton chemical shifts in proteins.

LL Parker — 2007-01-18T08:33:19-00:00

J Am Chem Soc, Vol. 128, No. 30. (2 August 2006), pp. 9863-9872.

A computational methodology for backbone amide proton chemical shift (delta(H)) predictions based on ab initio quantum mechanical treatment of part of the protein is presented. The method is used to predict and interpret 13 delta(H) values in protein G and ubiquitin. The predicted amide-amide delta(H) values are within 0.6 ppm of experiment, with a root-mean-square deviation (RMSD) of 0.3 ppm. We show that while the hydrogen bond geometry is the most important delta(H)-determinant, longer-range cooperative effects of extended hydrogen networks make significant contributions to delta(H). We present a simple model that accurately relates the protein structure to delta(H).

Network models of the basal ganglia.

DG Beiser — 2006-11-23T12:34:21-00:00

Curr Opin Neurobiol, Vol. 7, No. 2. (April 1997), pp. 185-190.

Over the past year, a number of conceptual and mathematical models of the basal ganglia and their interactions with other areas of the brain have appeared in the literature. Even though the models each differ in significant ways, several computational principles, such as convergence, recurrence and competition, appear to have emerged as common themes of information processing in the basal ganglia. Simulation studies of these models have provoked new types of questions at the many levels of inquiry linking biophysics to behavior.

Structural basis for antibody catalysis of a disfavored ring closure reaction.

K Gruber — 2006-11-01T16:49:46-00:00

Biochemistry, Vol. 38, No. 22. (1 June 1999), pp. 7062-7074.

The catalysis of disfavored chemical reactions, especially those with no known natural enzyme counterparts, is one of the most promising achievements of catalytic antibody research. Antibodies 5C8, 14B9, 17F6, and 26D9, elicited by two different transition-state analogues, catalyze disfavored endo-tet cyclization reactions of trans-epoxy alcohols, in formal violation of Baldwin's rules for ring closure. Thus far, neither chemical nor enzyme catalysis has been capable of emulating the extraordinary activity and specificity of these antibodies. X-ray structures of two complexes of Fab 5C8 with the original hapten and with an inhibitor have been determined to 2.0 A resolution. The Fab structure has an active site that contains a putative catalytic diad, consisting of AspH95 and HisL89, capable of general acid/base catalysis. The stabilization of a positive charge that develops along the reaction coordinate appears to be an important factor for rate enhancement and for directing the reaction along the otherwise disfavored pathway. Sequence analysis of the four catalytic antibodies, as well as four inactive antibodies that strongly bind the transition-state analogues, suggests a conserved catalytic mechanism. The occurrence of the putative base HisL89 in all active antibodies, its absence in three out of the four analyzed inactive antibodies, and the rarity of a histidine at this position in immunoglobulins support an important catalytic role for this residue.

Free radical biology and medicine: it's a gas, man!

WA Pryor — 2006-08-21T03:10:31-00:00

Am J Physiol Regul Integr Comp Physiol, Vol. 291, No. 3. (September 2006)

We review gases that can affect oxidative stress and that themselves may be radicals. We discuss O(2) toxicity, invoking superoxide, hydrogen peroxide, and the hydroxyl radical. We also discuss superoxide dismutase (SOD) and both ground-state, triplet oxygen ((3)O(2)), and the more energetic, reactive singlet oxygen ((1)O(2)). Nitric oxide ((.)NO) is a free radical with cell signaling functions. Besides its role as a vasorelaxant, (.)NO and related species have other functions. Other endogenously produced gases include carbon monoxide (CO), carbon dioxide (CO(2)), and hydrogen sulfide (H(2)S). Like (.)NO, these species impact free radical biochemistry. The coordinated regulation of these species suggests that they all are used in cell signaling. Nitric oxide, nitrogen dioxide, and the carbonate radical (CO(3)(.-)) react selectively at moderate rates with nonradicals, but react fast with a second radical. These reactions establish "cross talk" between reactive oxygen (ROS) and reactive nitrogen species (RNS). Some of these species can react to produce nitrated proteins and nitrolipids. It has been suggested that ozone is formed in vivo. However, the biomarkers that were used to probe for ozone reactions may be formed by non-ozone-dependent reactions. We discuss this fascinating problem in the section on ozone. Very low levels of ROS or RNS may be mitogenic, but very high levels cause an oxidative stress that can result in growth arrest (transient or permanent), apoptosis, or necrosis. Between these extremes, many of the gasses discussed in this review will induce transient adaptive responses in gene expression that enable cells and tissues to survive. Such adaptive mechanisms are thought to be of evolutionary importance.

A cerebellar model of timing and prediction in the control of reaching.

AG Barto — 2005-12-19T22:41:18-00:00

Neural Comput, Vol. 11, No. 3. (1 April 1999), pp. 565-594.

A simplified model of the cerebellum was developed to explore its potential for adaptive, predictive control based on delayed feedback information. An abstract representation of a single Purkinje cell with multistable properties was interfaced, using a formalized premotor network, with a simulated single degree-of-freedom limb. The limb actuator was a nonlinear spring-mass system based on the nonlinear velocity dependence of the stretch reflex. By including realistic mossy fiber signals, as well as realistic conduction delays in afferent and efferent pathways, the model allowed the investigation of timing and predictive processes relevant to cerebellar involvement in the control of movement. The model regulates movement by learning to react in an anticipatory fashion to sensory feedback. Learning depends on training information generated from corrective movements and uses a temporally asymmetric form of plasticity for the parallel fiber synapses on Purkinje cells.

The use of overlapping submovements in the control of rapid hand movements.

KE Novak — 2005-12-19T22:26:04-00:00

Exp Brain Res, Vol. 144, No. 3. (June 2002), pp. 351-364.

Rapid targeted movements are subject to special control considerations, since there may be inadequate time available for either visual or somatosensory feedback to be effective. In our experiments, subjects rapidly rotated a knob to align a pointer to one of several targets. We recognized three different types of movement segments: the primary movement, and two types of submovement, which frequently followed. The submovements were initiated either before or after the end of the primary movement. The former, or "overlapping" type of submovement altered the kinematics of the overall movement and was consequently difficult to detect. We used a direct, objective test of movement regularity to detect overlapping submovements, namely, examining the number of jerk and snap zero crossings during the second half of a movement. Any overlapping submovements were parsed from the overall movement by subtracting the velocity profile of the primary movement. The velocity profiles of the extracted submovements had near-symmetric bell shapes, similar to the shapes of both pure primary movements and nonoverlapping submovements. This suggests that the same neural control mechanisms may be responsible for producing all three types of movement segments. Overlapping submovements corrected for errors in the amplitude of the primary movement. Furthermore, they may account for the previously observed, speed-dependent asymmetry of the velocity profile. We used a nonlinear model of the musculoskeletal system to explain most of the kinematic features of these rapid hand movements, including how discrete submovements are superimposed on a primary movement. Finally, we present a plausible scheme for how the central nervous system may generate the commands to control these rapid hand movements.

Kinematic properties of on-line error corrections in the monkey.

A Fishbach — 2005-12-19T22:25:16-00:00

Exp Brain Res, Vol. 164, No. 4. (August 2005), pp. 442-457.

Despite the abundant experimental evidence for the irregular, multipeaked velocity profiles that often characterize rapid human limb movements, there is currently little agreement on how to interpret these phenomena. While in some studies these irregularities have been interpreted as reflecting a continuous control process, in others the irregularities are considered to be evidence for the existence of discrete movement primitives that are initiated by an intermittent controller. Here we introduce a novel "soft symmetry" method for analyzing irregular movements and decomposing them into their discrete movement primitives. We applied this method to analyze rapid pronation/supination wrist movements in monkeys during a one-dimensional tracking task. We showed that the properties of the extracted overlapping submovements (OSMs) were very similar to those of single, regular movements, despite the fact that the decomposition algorithm did not restrict the extracted submovements to a particular shape. In addition we showed that the movement primitives corrected preceding primitives and that the correction initiation time was highly variable, and thus could not be explained by the relatively fixed sensorimotor delay. These results argue against the interpretation of movement irregularities as reflecting a continuous control process and reinforce the hypothesis that movement irregularities result from an intermittent control mechanism. Demonstrating these phenomena in non-human primates will allow neurophysiological investigation of the neural mechanisms involved in these corrections.

Features of motor performance that drive adaptation in rapid hand movements.

KE Novak — 2005-11-11T15:12:19-00:00

Exp Brain Res, Vol. 148, No. 3. (February 2003), pp. 388-400.

In order to explore how subjects correct for errors in movement and adapt their motor programs, we studied rapid hand movements. Subjects grasped a grooved knob and made brisk turning movements to various targets, similar to tuning a radio dial. A motor attached to the knob shaft was configured to apply a destabilizing negative viscous perturbation. Following a period of practice with no perturbations, the negative viscosity was engaged, which caused a large change in overall kinematics: the peak velocity increased, the movement amplitude was too large, and discrete corrective submovements were generated to bring the pointer back onto the target. After about an hour and nearly 1000 trials, subjects learned to move accurately in the new dynamic environment, returning their overall kinematics near to previous levels. Measures of performance included the endpoint error of the primary movement (the initial movement segment), the frequency and amplitude of corrective submovements, task success rate, mean squared jerk, and deviation from a "normal" angular velocity temporal profile. Both the amplitude and frequency of corrective submovements decreased progressively during adaptation as the subjects made fewer target overshoot errors. These results are consistent with motor learning schemes in which adaptation of the motor controller is driven by an attempt to reduce the endpoint error of the primary movement. While there have been many theories regarding what is being optimized in motor control, in general, biologically plausible mechanisms for implementing these schemes have not been described. A biologically plausible optimization criterion is the minimization of the occurrence and amplitude of corrective submovements, since the latter have been proposed as realistic climbing fiber training signals for adaptive changes in the cerebellum. We postulate that the other criteria that have been proposed are instead secondary to an increased accuracy of the primary movement and a corresponding decrease in the occurrence and amplitude of corrective submovements.

Binding affinities of host-guest, protein-ligand, and protein-transition-state complexes.

KN Houk — 2005-05-13T08:16:57-00:00

Angew Chem Int Ed Engl, Vol. 42, No. 40. (20 October 2003), pp. 4872-4897.

The affinities of hosts-ranging from small synthetic cavitands to large proteins-for organic molecules are well documented. The average association constants for the binding of organic molecules by cyclodextrins, synthetic hosts, and albumins in water, as well as of catalytic antibodies or enzymes for substrates are 10(3.5+/-2.5) M(-1). Binding affinities are elevated to 10(8+/-2) M(-1) for the complexation of transition states and biological antigens by antibodies or inhibitors by enzymes, and to 10(16+/-4) M(-1) for transition states with enzymes. The origins of the distributions of association constants observed for the broad range of host-guest systems are explored in this Review, and typical approaches to compute and analyze host-guest binding in solution are discussed. In many classes of complexes a rough correlation is found between the binding affinity and the surface area that is buried upon complexation. Enzymes transcend this effect and achieve transition-state binding much greater than is expected from the surface areas.