Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

The Role of Computational Methods in the Identification of Bioactive Compounds

Computational methods play an ever increasing role in lead finding. A vast repertoire of molecular design and virtual screening methods emerged in the past two decades and are today routinely used. There is increasing awareness that there is no single best computational protocol and correspondingly there is a shift recommending the combination of complementary methods. A promising trend for the application of computational methods in lead finding is to take advantage of the vast amounts of HTS (High Throughput Screening) data to allow lead assessment by detailed systems-based data analysis, especially for phenotypic screens where the identification of compound-target pairs is the primary goal. Herein, we review trends and provide examples of successful applications of computational methods in lead finding

A 3D similarity method for scaffold hopping from known drugs or natural ligands to new chemotypes.

A primary goal of 3D similarity searching is to find compounds with similar bioactivity to a reference ligand but with different chemotypes, i.e., "scaffold hopping". However, an adequate description of chemical structures in 3D conformational space is difficult due to the high-dimensionality of the problem. We present an automated method that simplifies flexible 3D chemical descriptions in which clustering techniques traditionally used in data mining are exploited to create "fuzzy" molecular representations called FEPOPS (feature point pharmacophores). The representations can be used for flexible 3D similarity searching given one or more active compounds without a priori knowledge of bioactive conformations or pharmacophores. We demonstrate that similarity searching with FEPOPS significantly enriches for actives taken from in-house high-throughput screening datasets and from MDDR activity classes COX-2, 5-HT3A, and HIV-RT, while also scaffold or ring-system hopping to new chemical frameworks. Further, inhibitors of target proteins (dopamine 2 and retinoic acid receptor) are recalled by FEPOPS by scaffold hopping from their associated endogenous ligands (dopamine and retinoic acid). Importantly, the method excels in comparison to commonly used 2D similarity methods (DAYLIGHT, MACCS, Pipeline Pilot fingerprints) and a commercial 3D method (Pharmacophore Distance Triplets) at finding novel scaffold classes given a single query molecule

Combination of a naive Bayes classifier with consensus scoring improves enrichment of high-throughput docking results.

We have previously shown that a machine learning technique can improve the enrichment of high-throughput docking (HTD) results. In the previous cases studied, however, the application of a naive Bayes classifier failed to improve enrichment for instances where HTD alone was unable to generate an acceptable enrichment. We present here a protocol to rescue poor docking results a priori using a combination of rank-by-median consensus scoring and naive Bayesian categorization

Streamlining lead discovery by aligning in silico and high-throughput screening.

Lead discovery in the pharmaceutical environment is largely an industrial-scale process in which it is typical to screen 1-5 million compounds in a matter of weeks using High Throughput Screening (HTS). This process is a very costly endeavor. Typically a HTS campaign of 1 million compounds will cost anywhere from $500000 to$1000000. There is consequently a great deal of pressure to maximize the return on investment by finding fast and more effective ways to screen. A panacea that has emerged over the past few years to help address this issue is in silico screening. In silico screening is now incorporated in all areas of lead discovery; from target identification and library design, to hit analysis and compound profiling. However, as lead discovery has evolved over the past few years, so has the role of in silico screening

Bioturbo Similarity Searching: Combining Chemical and Biological Similarity to Discover Structurally Diverse Bioactive Molecules

Virtual screening using bioactivity profiles has become an integral part of currently applied hit finding methods in pharmaceutical industry. However, a significant drawback of this approach is that it is only applicable to compounds that have been biologically tested in the past and have sufficient activity annotations for meaningful profile comparisons. Although bioactivity data generated in pharmaceutical institutions is growing on an unprecedented scale, the number of biologically annotated compounds still covers only a minuscule fraction of chemical space. For a newly synthesized compound or an isolated natural product to be biologically characterized across multiple assays, it may take a considerable amount of time. Consequently, this chemical matter will not be included in virtual screening campaigns based on bioactivity profiles. To overcome this problem, we herein introduce bioturbo similarity searching that uses chemical similarity to map molecules without biological annotations into bioactivity space and then searches for biologically similar compounds in this reference system. In benchmark calculations on primary screening data, we demonstrate that our approach generally achieves higher hit rates and identifies structurally more diverse compounds than approaches using chemical information only. Furthermore, our method is able to discover hits with novel modes of inhibition that traditional 2D and 3D similarity approaches are unlikely to discover. Test calculations on a set of natural products reveal the practical utility of the approach for identifying novel and synthetically more accessible chemical matter

Application of machine learning to improve the results of high-throughput docking against the HIV-1 protease.

We have previously reported that the application of a Laplacian-modified naive Bayesian (NB) classifier may be used to improve the ranking of known inhibitors from a random database of compounds after High-Throughput Docking (HTD). The method relies upon the frequency of substructural features among the active and inactive compounds from 2D fingerprint information of the compounds. Here we present an investigation of the role of extended connectivity fingerprints in training the NB classifier against HTD studies on the HIV-1 protease using three docking programs: Glide, FlexX, and GOLD. The results show that the performance of the NB classifier is due to the presence of a large number of features common to the set of known active compounds rather than a single structural or substructural scaffold. We demonstrate that the Laplacian-modified naive Bayesian classifier trained with data from high-throughput docking is superior at identifying active compounds from a target database in comparison to conventional two-dimensional substructure search methods alone