DPRESS: Localizing estimates of predictive uncertainty

<p>Abstract</p> <p>Background</p> <p>The need to have a quantitative estimate of the uncertainty of prediction for QSAR models is steadily increasing, in part because such predictions are being widely distributed as tabulated values disconnected from the models used to generate them. Classical statistical theory assumes that the error in the population being modeled is independent and identically distributed (IID), but this is often not actually the case. Such inhomogeneous error (heteroskedasticity) can be addressed by providing an individualized estimate of predictive uncertainty for each particular new object <it>u</it>: the standard error of prediction <it>s</it>_ucan be estimated as the non-cross-validated error <it>s</it>_t*for the closest object <it>t</it>* in the training set adjusted for its separation <it>d </it>from <it>u </it>in the descriptor space relative to the size of the training set.</p> <p><display-formula><graphic file="1758-2946-1-11-i1.gif"/></display-formula></p> <p>The predictive uncertainty factor <it>γ</it>_t*is obtained by distributing the internal predictive error sum of squares across objects in the training set based on the distances between them, hence the acronym: <it>D</it>istributed <it>PR</it>edictive <it>E</it>rror <it>S</it>um of <it>S</it>quares (DPRESS). Note that <it>s</it>_t*and <it>γ</it>_t*are characteristic of each training set compound contributing to the model of interest.</p> <p>Results</p> <p>The method was applied to partial least-squares models built using 2D (molecular hologram) or 3D (molecular field) descriptors applied to mid-sized training sets (<it>N </it>= 75) drawn from a large (<it>N </it>= 304), well-characterized pool of cyclooxygenase inhibitors. The observed variation in predictive error for the external 229 compound test sets was compared with the uncertainty estimates from DPRESS. Good qualitative and quantitative agreement was seen between the distributions of predictive error observed and those predicted using DPRESS. Inclusion of the distance-dependent term was essential to getting good agreement between the estimated uncertainties and the observed distributions of predictive error. The uncertainty estimates derived by DPRESS were conservative even when the training set was biased, but not excessively so.</p> <p>Conclusion</p> <p>DPRESS is a straightforward and powerful way to reliably estimate individual predictive uncertainties for compounds outside the training set based on their distance to the training set and the internal predictive uncertainty associated with its nearest neighbor in that set. It represents a sample-based, <it>a posteriori </it>approach to defining applicability domains in terms of localized uncertainty.</p

Low potency toxins reveal dense interaction networks in metabolism

Background The chemicals of metabolism are constructed of a small set of atoms and bonds. This may be because chemical structures outside the chemical space in which life operates are incompatible with biochemistry, or because mechanisms to make or utilize such excluded structures has not evolved. In this paper I address the extent to which biochemistry is restricted to a small fraction of the chemical space of possible chemicals, a restricted subset that I call Biochemical Space. I explore evidence that this restriction is at least in part due to selection again specific structures, and suggest a mechanism by which this occurs. Results Chemicals that contain structures that our outside Biochemical Space (UnBiological groups) are more likely to be toxic to a wide range of organisms, even though they have no specifically toxic groups and no obvious mechanism of toxicity. This correlation of UnBiological with toxicity is stronger for low potency (millimolar) toxins. I relate this to the observation that most chemicals interact with many biological structures at low millimolar toxicity. I hypothesise that life has to select its components not only to have a specific set of functions but also to avoid interactions with all the other components of life that might degrade their function. Conclusions The chemistry of life has to form a dense, self-consistent network of chemical structures, and cannot easily be arbitrarily extended. The toxicity of arbitrary chemicals is a reflection of the disruption to that network occasioned by trying to insert a chemical into it without also selecting all the other components to tolerate that chemical. This suggests new ways to test for the toxicity of chemicals, and that engineering organisms to make high concentrations of materials such as chemical precursors or fuels may require more substantial engineering than just of the synthetic pathways involved

Human physiologically based pharmacokinetic model for propofol

BACKGROUND: Propofol is widely used for both short-term anesthesia and long-term sedation. It has unusual pharmacokinetics because of its high lipid solubility. The standard approach to describing the pharmacokinetics is by a multi-compartmental model. This paper presents the first detailed human physiologically based pharmacokinetic (PBPK) model for propofol. METHODS: PKQuest, a freely distributed software routine , was used for all the calculations. The "standard human" PBPK parameters developed in previous applications is used. It is assumed that the blood and tissue binding is determined by simple partition into the tissue lipid, which is characterized by two previously determined set of parameters: 1) the value of the propofol oil/water partition coefficient; 2) the lipid fraction in the blood and tissues. The model was fit to the individual experimental data of Schnider et. al., Anesthesiology, 1998; 88:1170 in which an initial bolus dose was followed 60 minutes later by a one hour constant infusion. RESULTS: The PBPK model provides a good description of the experimental data over a large range of input dosage, subject age and fat fraction. Only one adjustable parameter (the liver clearance) is required to describe the constant infusion phase for each individual subject. In order to fit the bolus injection phase, for 10 or the 24 subjects it was necessary to assume that a fraction of the bolus dose was sequestered and then slowly released from the lungs (characterized by two additional parameters). The average weighted residual error (WRE) of the PBPK model fit to the both the bolus and infusion phases was 15%; similar to the WRE for just the constant infusion phase obtained by Schnider et. al. using a 6-parameter NONMEM compartmental model. CONCLUSION: A PBPK model using standard human parameters and a simple description of tissue binding provides a good description of human propofol kinetics. The major advantage of a PBPK model is that it can be used to predict the changes in kinetics produced by variations in physiological parameters. As one example, the model simulation of the changes in pharmacokinetics for morbidly obese subjects is discussed

The role of ligand efficiency metrics in drug discovery

The judicious application of ligand or binding efficiencies, which quantify the molecular properties required to gain binding affinity for a drug target, is gaining traction in the selection and optimisation of fragments, hits, and leads. Retrospective analysis of recently marketed oral drugs shows that they frequently have highly optimised ligand efficiency values for their target. Optimising ligand efficiencies based on both molecular size and lipophilicity, when set in the context of the specific target, has the potential to ameliorate the molecular inflation that pervades current practice in medicinal chemistry, and to increase the developability of drug candidates

Continuous-wave two-photon spectroscopy of the 1S-2S transition in hydrogen.

We have observed the 1S-2S transition in atomic hydrogen gas with a resolution of 5 parts in 109 by Doppler-free two-photon spectroscopy, using multimilliwatt cw radiation near 243 nm generated by sum-frequency mixing. The experiment opens the way to substantial increases in the accuracy of the Rydberg constant, the electron/proton mass ratio, and the Lamb shift of the hydrogen 1S ground state. © 1985 The American Physical Society

Simultaneous magneto-optical trapping of three atomic species

10.1103/PhysRevA.73.011402PHYSICAL REVIEW A73

Mid-infrared dual-comb spectroscopy with 2.4 mu m Cr2+:ZnSe femtosecond lasers

The mid-infrared part of the electromagnetic spectrum is the so-called molecular fingerprint region because gases have tell-tale absorption features associated with molecular rovibrations. This region can be for instance exploited to detect small traces of environmental and toxic vapors in atmospheric and industrial applications. Novel Fourier-transform spectroscopy without moving parts, based on time-domain interferences between two comb sources, can in particular benefit optical diagnostics and precision spectroscopy. To date, high-resolution and -sensitivity proof-of-principle experiments have only been reported in the near-infrared region where frequency-comb oscillators are conveniently available. However, as most of the molecular transitions in this region are due to weak overtone bands, this spectral domain is not ideal for sensitive and rapid detection. Here we present a proof-of-principle experiment of frequency-comb Fourier-transform spectroscopy with two Cr2+:ZnSe femtosecond oscillators directly emitting in the 2.4 μm mid-infrared region. The acetylene absorption spectrum in the region of the n1+n511+51 band, extending from 2370 to 2525 nm, could be recorded within a 10 μs acquisition time without averaging with 12 GHz resolution