Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence

The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all) of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1) separate the data sequence into "pure" subsequences corresponding to constituent Boolean networks; (2) given a subsequence, infer a Boolean network; and (3) infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing which network is to be selected given a switch. Capturing the full dynamic behavior of probabilistic Boolean networks, be they binary or multivalued, will require the use of temporal data, and a great deal of it. This should not be surprising given the complexity of the model and the number of parameters, both transitional and static, that must be estimated. In addition to providing an inference algorithm, this paper demonstrates that the data requirement is much smaller if one does not wish to infer the switching, perturbation, and selection probabilities, and that constituent-network connectivity can be discovered with decent accuracy for relatively small time-course sequences.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]     

Chitosan as a MAMP,searching for a PRR

Chitosan, a deacetylated chitin derivative, behaves like a general elicitor, inducing a non-host resistance and priming a systemic acquired immunity. The defence responses elicited by chitosan include rising of cytosolic H⁺ and Ca²⁺, activation of MAP-kinases, callose apposition, oxidative burst, hypersensitive response (HR), synthesis of abscissic acid (ABA), jasmonate, phytoalexins and pathogenesis related (PR) proteins. Putative receptors for chitosan are a chitosan-binding protein, recently isolated, and possibly the chitin elicitor-binding protein (CEBiP). Nevertheless, it must be pointed out that biological activity of chitosan, besides the plant model, strictly depends on its physicochemical properties (deacetylation degree, molecular weight and viscosity), and that there is a threshold for chitosan concentration able to switch the induction of a cell death programme into necrotic cell death (cytotoxicity).Key words: chitosan, induced resistance, MAMP, PAMP, PCD, PRR, SARRecognition of microbe-associated molecular patterns (MAMPs), by pattern recognition receptors (PRRs), represents the major trait of innate immunity common to plants and animals. In plant immunity, MAMPs, more commonly known as general elicitors, include lipopolysaccharides (LPS), peptidoglycans, flagellin and fungal cell wall fragments (chitin/chitosan oligomers), phospholipids, oxylipins, fatty acids, sterols, proteins, double stranded RNA and methylated DNA, able to elicit a host defence response by binding to specific PRRs. In this view, chitosan, a deacetylated chitin derivative, behaves like a general elicitor, inducing a non-host resistance, by a PRR-mediated recognition, and priming a systemic acquired immunity (or systemic acquired resistance, SAR).¹ The defence responses elicited by chitosan include: raising of cytosolic Ca²⁺, activation of MAP-kinases, callose apposition, oxidative burst, hypersensitive response (HR), synthesis of abscissic acid (ABA), jasmonate, phytoalexins and pathogenesis related proteins (PR) (Fig. 1 and 2^–20Open in a separate windowFigure 1Different responses induced on Phaseolus vulgaris leaves by treatment with solutions of chitosan with 85% deacetylation degree and different molecular weights; all solutions have been prepared at 0.15% w/v in 0.05 M acetic acid and adjusted at pH 5.6. Callose detection with aniline blue (A–C) 12 h after treatment shows that 76 kD-chitosan elicits the formation of a network of small bright yellow fluorescent spots (B) due to callose apposition between the plasmalemma and the cell wall of some mesophyll cells (see the enlargement in the inset), while 6 kD-chitosan induces lesions involving numerous cells fluorescing in yellow-orange, possibly as consequence of the overlap of phenolics autofluorescence and callose fluorescence (see the enlargement in the inset). In 322 kD chitosan-treated leaves numerous green-fluorescent patches (C), due to chitosan deposits, are present on the leaf epidermis along cell walls, but rarely callose apposition is present. Detection of H₂O₂ deposits (as brownish precipitates in D–F) with 3-3′-diaminobenzydine (DAB), 24 h after 6 kD-chitosan treatment, indicates that the lesions in (A) are constituted by necrotizing cells as a consequence of extensive H₂O₂ deposition (D). At the same time, leaves treated with 76 kD-chitosan show moderate H₂O₂ deposits limited to the same mesophyll cells involved in callose apposition, and often localized around the substomatal cavity into which chitosan can permeate (E, arrow). No H₂O₂ deposition is present in 322 kD-chitosan treated plants (F). Evans blue staining to detect dead cells (stained in blue) 24 h after treatment (G–I) shows that the lesions in (A) have already evolved in extensive necrotic cell death, while only some of the cells with callose deposition visible in (B) had turned to programmed cell death (H) (as previously shown with other techniques). No dead cells are present in leaves treated with 322 kD-chitosan (I).

Table 1

Defence responses elicited by chitosan

Streptomyces antibioticalis, a Novel Species from a Sanitary Landfill Soil

A novel isolate belonging to the genus Streptomyces, strain SL-4^T, was isolated from soil sample collected from a sanitary landfill, New Delhi, India. The taxonomic status of this isolate was studied by polyphasic approach including morphological, physiological and chemo-taxonomic characterization. Spore chains of SL-4^T were open loops, hooks or extended spirals of wide diameter (retinaculiperti). The cell wall peptidoglycan of the isolate SL-4^T contained L,L-diaminopimelic acid, suggesting that the strain has a cell wall of chemotype-I. The polar lipid profile of the isolate was of Type II, with phosphatidylglycerol, phosphatidylethanolamine, phosphatidylinositol and phosphatidylinositol mannosides. The 16SrRNA gene sequence similarity between SL-4^T and its phylogenetic relatives Streptomyces atrovirens NRRLB 16357^T ({"type":"entrez-nucleotide","attrs":{"text":"DQ026672","term_id":"68137786","term_text":"DQ026672"}}DQ026672), S. albogriseolus NRRLB 1305^T ({"type":"entrez-nucleotide","attrs":{"text":"AJ494865","term_id":"21742835","term_text":"AJ494865"}}AJ494865), S viridodiastaticus NBRC 13106^T ({"type":"entrez-nucleotide","attrs":{"text":"AB184317","term_id":"90960133","term_text":"AB184317"}}AB184317), S. caelestis NRRL 2418^T ({"type":"entrez-nucleotide","attrs":{"text":"X80824","term_id":"587528","term_text":"X80824"}}X80824), S. flavoviridis NBRC 12772^T ({"type":"entrez-nucleotide","attrs":{"text":"AB184842","term_id":"90960663","term_text":"AB184842"}}AB184842), S. pilosus NBRC 12807^T ({"type":"entrez-nucleotide","attrs":{"text":"AB184161","term_id":"90959977","term_text":"AB184161"}}AB184161) and S. longispororuber NBRC 13488^T ({"type":"entrez-nucleotide","attrs":{"text":"AB184440","term_id":"90960256","term_text":"AB184440"}}AB184440) was 99.65, 99.65, 99.64, 99.23, 99.15, 99.14 and 99.13 % respectively. Subsequent DNA–DNA hybridization experiments with the test strain and its clade members showed 55.27, 44.27, 36.86, and 15.65 % relatedness between SL-4^T and its relatives S. atrovirens,S. albogriseolus, S. viridodiastaticus and S. longispororuber respectively. The genotypic and phenotypic data was analyzed to verify possibility of the isolate SL-4^T representing novel member of the genus Streptomyces, for which the name S. antibioticalis is being proposed. The type strain is SL-4^T (=CCM 7434^T=MTCC 8588^T).     

Forging a biodiversity ethic in a multicultural context

New Zealand belongs to the Pacific region, a part of the world where human impacts have been both very recent and extreme in their effect. The New Zealand natural environment is rich in endemic taxa, but these are poorly equipped to cope with the effects of invasion by humans and exotic animals and plants. Polynesian immigrants brought to New Zealand a distinctive world view which gave rise to both tribal traditions and living traditions of the Maori. The resultant environmental ethic emphasises guardianship and stewardship, establishment of the right to use a resource, kinship obligations, and a balance between pairs of opposites. Nineteenth-century European colonists were ambivalent in their view of the environment, although a world view which emphasises dominion has tended to dominate. Two recent developments which are important factors in development of a multicultural biodiversity ethic are the enactment of the Resource Management Act 1991 and legal recognition of the principles of the Treaty of Waitangi. The intersection of these developments provides an opportunity to develop a new approach to environmental ethics especially in conceptualising significance, consultative processes, and developing a holistic and ecocentric use of resources.     

Polymerization of a monomeric guanosine derivative in a hydrogen-bonded aggregate

Summary The adduct IIa, in which glycine is linked to the 3-amino group of 3-amino-3-deoxyguanosine-5-phosphate, condenses very efficientlyin aqueous solution when treated with a watersoluble carbodiimide to give long oligomeric products. The corresponding cytidine derivative IIb yields a complex mixture of very short oligomers. We believe that the efficient condensation reaction occurs in a hydrogen-bonded tetrahelical aggregate of a type that is known to form with many guanosine derivatives.     

Isolation of a halobacterial phage with a fully cytosine-methylated genome

Summary A new bacteriophage from Halobacterium halobium has been isolated and partially characterized. It is not homologous to the phage H (Schnabel, et al. 1982) which infects the same bacterium, though it appeared spontaneously in a culture of H adapted to H. halobium NRL/JW. The size and morphology of N are comparable to that of other known halophages. The genome of N consists of linear double-stranded DNA, 56 kb in size, whose dCMP is totally replaced by 5-methyl-dCMP. This is the second case of a fully cytosine-methylated genome, the bacteriophage XP12 from Xanthomonas oryzae, being so far the only one reported. Like H, the N, genome seems to have terminal redundancy and circular permutation. N is the first halobacterial phage which survives prolonged exposure to low ionic strength environments. After 48 h incubation in distilled water a loss in infectivity of less than 50% is observed.     

Neither a mentalist nor a reductionist be!

There is basis for concern that applied psychophysiology, if not the field of biofeedback, is being coopted by, and merged into, a reborn inner model, with the return of cognition to preeminence in the psych and neuro disciplines. Despite currently fashionable views that such mentalistic inventions and neuro/psychological developments somehow illuminate behavior or offer simpler accounts of behavioral facts, there is little or no evidence that any such construction has ever told us anything new about behavior.Preparation of this article was supported in part by the following PHHS Grants: NHLBI HL 34034, NIDA DA 03476, NIDA DA 04130, NIDA DA 02490, NIDA DA 04133, NIDA DA 01147, NIDA DA 04731, and NIDA contract 271-86-8113.     

Neither a mentalist nor a reductionist be!

There is basis for concern that applied psychophysiology, if not the field of biofeedback, is being coopted by, and merged into, a reborn "inner" model, with the return of "cognition" to preeminence in the "psych" and "neuro" disciplines. Despite currently fashionable views that such mentalistic inventions and neuro/psychological developments somehow illuminate behavior or offer simpler accounts of behavioral facts, there is little or no evidence that any such construction has ever told us anything new about behavior.     

Lateralization in Paridae: comparison of a storing and a non-storing species on a one-trial associative memory task

Summary We present evidence of a difference between a storing and non-storing species in lateralization and transfer of spatial memory processing. Using the technique of monocular occlusion, we compared the performance of a food-storing species, the marsh tit (Parus palustris), with a closely related species that does not store food, the blue tit (P. caeruleus), on a task which relies on one-trial learning for the spatial location of hidden food items. In this one-trial associative learning task, the birds had to return to sites in phase II of a trial where they had been allowed to eat some, but not all, of a piece of peanut in phase I. In the first experiment, in which the birds did not wear eye caps, marsh tits required fewer looks in phase II to find the hidden peanut than blue tits. By categorising the sites as seeded, unseeded or not visited in phase I, further analysis suggested that the two species also differ in the way they behave towards the 3 types of site. Marsh tits appear to distinguish between seeded and other sites, irrespective of whether the other sites were known to be empty (unseeded) or not (not visited); whereas blue tits preferentially returned to those sites that have been visited in phase I, irrespective of whether they contained a seed or not. In the second experiment, all birds wore an eye cap on the left or right eye for phase I and II of each trial. For both species, it was demonstrated that although the visual systems fed by both the right and left eye are involved in short-term storage, the right eye system is associated also with long-term storage. Thus, lateralization was found in both blue tits and marsh tits. However, unilateral transfer of these memories was found only in marsh tits, suggesting that there may be a difference between storers and non-storers in the mechanism of memory processing.     

Suppression of a Morphogenic Mutant in Rous Sarcoma Virus Capsid Protein by a Second-Site Mutation: a Cryoelectron Tomography Study

Retrovirus assembly is driven by polymerization of the Gag polyprotein as nascent virions bud from host cells. Gag is then processed proteolytically, releasing the capsid protein (CA) to assemble de novo inside maturing virions. CA has N-terminal and C-terminal domains (NTDs and CTDs, respectively) whose folds are conserved, although their sequences are divergent except in the 20-residue major homology region (MHR) in the CTD. The MHR is thought to play an important role in assembly, and some mutations affecting it, including the F167Y substitution, are lethal. A temperature-sensitive second-site suppressor mutation in the NTD, A38V, restores infectivity. We have used cryoelectron tomography to investigate the morphotypes of this double mutant. Virions produced at the nonpermissive temperature do not assemble capsids, although Gag is processed normally; moreover, they are more variable in size than the wild type and have fewer glycoprotein spikes. At the permissive temperature, virions are similar in size and spike content as in the wild type and capsid assembly is restored, albeit with altered polymorphisms. The mutation F167Y-A38V (referred to as FY/AV in this paper) produces fewer tubular capsids than wild type and more irregular polyhedra, which tend to be larger than in the wild type, containing ∼30% more CA subunits. It follows that FY/AV CA assembles more efficiently in situ than in the wild type and has a lower critical concentration, reflecting altered nucleation properties. However, its infectivity is lower than that of the wild type, due to a 4-fold-lower budding efficiency. We conclude that the wild-type CA protein sequence represents an evolutionary compromise between competing requirements for optimization of Gag assembly (of the immature virion) and CA assembly (in the maturing virion).In the first step of retrovirus maturation, the Gag precursor polyprotein is processed into three main components: the matrix (MA), capsid (CA), and nucleocapsid (NC). Of these, ∼1,000 to 2,000 copies of CA assemble into a capsid shell, enclosing the dimeric RNA genome and viral replication enzymes, while leaving a sizable population of unassembled CA subunits (5, 24). A properly formed capsid is thought to be essential for infectivity. The CA proteins of different retroviruses are quite uniform in size, ∼230 to 240 amino acids, but exhibit little sequence similarity except in the major homology region (MHR). Nevertheless, they share a structure with two domains (the N-terminal and C-terminal domains [NTDs and CTDs, respectively]) of conserved folds, connected by a short linker (2, 3, 8, 12, 17, 21, 22, 28). The NTDs form hexameric and pentameric rings that associate via homodimeric interactions between CTDs present in neighboring rings. Recently, structural evidence for a third interaction between the NTDs and the CTDs has been presented (10, 16, 31).The observed conservation of the MHR sequence points to its functional importance; in particular, the MHR is thought to play key roles, both in Gag assembly to produce immature virions and subsequently in the assembly of capsids within maturing virions. Consistent with this, several studies have reported adverse effects of point mutations in the MHR: certain mutations block the assembly of Gag proteins, whereas others have no evident effect on Gag assembly, genome incorporation, or budding but yield virus-like particles that are noninfectious or poorly infectious (1, 7, 13, 26, 30, 35-37). Starting with mutations of the latter kind, a series of second-site suppressors have been isolated that partially restore infectivity. Of these, two mapped in the NTD (A38V and P65Q), three in the dimerization helix in the CTD (F193L, R185W, and I190V), and one in the cleavage site between CA and the downstream peptide (S241L) (4, 7, 13, 25). The rescue of the MHR mutants by suppressing mutations was found not to be allele specific (25). The lack of allele specificity and the temperature sensitivity of some MHR mutations and their suppressors suggest that the affected residues are important for achieving a conformation(s) needed for proper assembly.In a previous study, we used cryoelectron tomography (cryo-ET) to characterize the pleiomorphic variability of wild-type Rous sarcoma virions (6, 20). Some 80% of them were found to contain capsids, which could be tubular, irregular polyhedra, or “continuous curvature” capsids, lacking angular vertices. The capsid type was found to correlate with the number of glycoprotein spikes per virion and with the efficiency of assembly, or conversely, the size of the pool of unassembled CA subunits contained within a virion. Based on these observations, we posited that in capsid assembly in situ, which is necessarily a nucleated process, different kinds of nucleation complexes initiate assembly of the various kinds of capsids. We also observed that tubular and some continuous curvature capsids had little internal material, suggesting that packaging of the viral ribonucleoprotein (RNP) had failed. Accordingly, and to accommodate the extensive polymorphism that was observed, we posited that a viable core is one with a closed capsid (of any morphology) that has successfully packaged its RNP. Subsequent in vitro studies have supported and clarified the perception of CA assembly as a variably nucleated process. Specifically, (i) it has been demonstrated that CA protein can assemble in a nucleation-driven manner into a variety of capsid-related structures (32, 33), and (ii) the mutation F167Y has been found to hamper nucleation of CA assembly in vitro, while the A38V suppressor strongly promotes assembly. Thus, CA-A38V assembles exceedingly rapidly, and in the double mutant, the A38V change overcomes the nucleation defect caused by F167Y.We have now further investigated the relationships among capsid morphology, nucleated assembly, and infectivity by performing a cryo-ET analysis of virions produced by the temperature-sensitive double mutant in which F167Y is complemented with the suppressor A38V; at the permissive temperature, the infectivity of the double mutant is restored to about 70% of wild type (25). Prior observations (32, 33) allowed the prediction that capsid assembly in vivo would be impaired in initiation for F167Y and for F167Y-A38V (abbreviated hereafter as FY/AV) at the nonpermissive temperature. Expectations for the double mutant at the permissive temperature were less clear: capsids should be produced, but this process might be altered in some way, as infectivity is lower than in the wild type. Because infectivity as measured could also be affected by Gag-related functions occurring earlier in the replication pathway, i.e., in viral budding or in proteolytic processing, we also compared the rates of virus growth, terminal Gag cleavage, and budding efficiency under these conditions for both the mutants and the wild-type virus.     

Prostatectomy in a county hospital; a review of 677 cases in a six-year period

Transurethral procedures were used in 620 of 677 cases in which prostatectomy was done (principally by residents supervised by a urologist) at a county hospital in a six-year period. Open operations were used in the other 57 cases. Results were classified as "excellent" in 46.8 per cent of the transurethral cases and as "good" in 36.3 per cent.     

Isolation and Characterization of a Novel Lysine Racemase from a Soil Metagenomic Library

A lysine racemase (lyr) gene was isolated from a soil metagenome by functional complementation for the first time by using Escherichia coli BCRC 51734 cells as the host and d-lysine as the selection agent. The lyr gene consisted of a 1,182-bp nucleotide sequence encoding a protein of 393 amino acids with a molecular mass of about 42.7 kDa. The enzyme exhibited higher specific activity toward lysine in the l-lysine-to-d-lysine direction than in the reverse reaction.Amino acids are the building blocks of proteins and play an important role in the regulation of the metabolism of living organisms. Among two enantiomers of naturally occurring amino acids, l-amino acids are predominant in living organisms, while d-amino acids are found in both free and bound states in various organisms like bacteria (36), yeasts (35), plants (47), insects (11), mammals (17), bivalves (39), and fish (28). The d-amino acids are mostly endogenous and produced by racemization from their counterparts by the action of a racemase. Thus, the amino acid racemases are involved in d-amino acid metabolism (29, 46). Since the discovery of alanine racemase in 1951 (42), several racemases toward amino acids, such as those for glutamate, threonine, serine, aspartate, methionine, proline, arginine, and phenylalanine, have been reported in bacteria, archaea, and eukaryotes, including mammals (1, 2, 15, 30, 31, 44). They are classified into two groups: pyridoxal 5′-phosphate (PLP)-dependent and PLP-independent enzymes (9, 36).Lysine racemase (Lyr, EC 5.1.1.5) was first reported in Proteus vulgaris ATCC 4669 (19) and proposed to be involved in the lysine degradation of bacterial cells (5, 19). Catabolism of lysine occurs via two parallel pathways. In one of the pathways, δ-aminovalerate is the key metabolite, whereas in the other l-lysine is racemized to d-lysine, and l-pipecolate and α-aminoadipate (AMA) are the key metabolites (5). d-Lysine catabolism proceeds through a series of cyclized intermediates which are necessary to regenerate an α-amino acid and comprise the following metabolites (AMA pathway): d-lysine→α-keto-ɛ-amino caproate→Δ¹-piperideine-2-carboxylate→pipecolate→Δ¹-piperideine-6-carboxylate→α-amino-δ-formylcaproate→α-AMA→α-ketoadipate (6, 7, 12, 27). The final product is converted to α-ketoglutarate via a series of coenzyme A derivatives and subsequently participates as an intermediate in the Krebs cycle. This pathway suggests that the biological function of d-lysine in the bacteria is that of a carbon or nitrogen source. Racemization of added l-lysine to d-lysine by whole cells of Proteus spp. and Escherichia spp. (19) and by the cell extract of Pseudomonas putida ATCC 15070 (5, 20) has been found. However, the enzyme has not been purified to homogeneity, and thus, its molecular and catalytic characteristics, including its gene structure, have not been elucidated. In this study, we explored a metagenomic library constructed from a garden soil to isolate a novel Lyr enzyme. After expression in Escherichia coli, the purified enzyme was characterized in terms of optimal pH and temperature, thermal stability, and racemization activity.     

Four-Point Bending as a Method for Quantitatively Evaluating Spinal Arthrodesis in a Rat Model

The most common method of evaluating the success (or failure) of rat spinal fusion procedures is manual palpation testing. Whereas manual palpation provides only a subjective binary answer (fused or not fused) regarding the success of a fusion surgery, mechanical testing can provide more quantitative data by assessing variations in strength among treatment groups. We here describe a mechanical testing method to quantitatively assess single-level spinal fusion in a rat model, to improve on the binary and subjective nature of manual palpation as an end point for fusion-related studies. We tested explanted lumbar segments from Sprague–Dawley rat spines after single-level posterolateral fusion procedures at L4–L5. Segments were classified as ‘not fused,’ ‘restricted motion,’ or ‘fused’ by using manual palpation testing. After thorough dissection and potting of the spine, 4-point bending in flexion then was applied to the L4–L5 motion segment, and stiffness was measured as the slope of the moment–displacement curve. Results demonstrated statistically significant differences in stiffness among all groups, which were consistent with preliminary grading according to manual palpation. In addition, the 4-point bending results provided quantitative information regarding the quality of the bony union formed and therefore enabled the comparison of fused specimens. Our results demonstrate that 4-point bending is a simple, reliable, and effective way to describe and compare results among rat spines after fusion surgery.Lower back pain has several etiologies and affects approximately 70% to 80% of American adults at some point in their lives.¹⁰ Spinal fusion and its clinical goal of reducing or eliminating motion remains the surgical ‘gold standard’ of care for patients, with rates of surgery increasing dramatically in recent years.^6,22 Although successful fusion can greatly benefit patients, unsuccessful fusion (pseudoarthrosis) can result in significant morbidity and costly reoperation procedures.²⁰ Consequently, research regarding fusion procedures and associated grafting technology is ongoing. According to a 2013 systematic review of bone-graft alternatives, approximately 1400 products are available on the international market, with rates of successful bony union ranging from 45% to 100% depending on the grafting material, spinal instrumentation, patient population, and operative procedure used.⁹ In addition, biologics such as bone morphogenetic protein,^3,14,23 demineralized bone-matrix-based products,¹¹ parathyroid hormone,^13,18,21 stem cells,^1,8,16 and vitamin D¹⁵ are under investigation to determine each compound''s ability to enhance bone formation after a spinal fusion procedure. Fusion procedures typically are performed in rat models to evaluate the preclinical efficacy, safety, and rate of bony union among these various bone-forming adjuvants.^{1-3,5,7,8,13-19,21,23-25}The most common method of evaluating the success (or failure) of rat spinal fusion procedures is manual palpation testing. However, the resultant data are subjective, binary, and do not provide any measurable information on the strength of the subsequent union (fusion). In an effort to provide quantitative data, previous studies have used a variety of mechanical testing methods in addition to manual palpation. The approaches used in these studies vary and are either inappropriate, difficult to replicate, or require an intricate experimental setup.^7,19,25 One such method is 3-point bending, a common and simple means of mechanically testing the strength of materials. By definition, 3-point bending creates combined bending and significant shear stress at the midpoint of specimens with high thickness-to-span ratios. For this reason, a specimen length-to-thickness ratio of at least 20:1 has been suggested to ensure that shear stresses are relatively insignificant when compared with the bending stresses.⁴ Conforming to this stipulation is possible for protocols testing long bones, such as the femur, but becomes impractical when examining the small span of a single-level (that is, L4–L5) fusion segment of a rat spine.The goal of this study, therefore, was to develop a mechanical testing method to quantitatively assess single-level spinal fusion in a rat model, thereby improving on the binary and subjective nature of manual palpation as an end point for fusion-related studies. We hypothesized that the resistance generated during 4-point bending would confirm the results obtained through manual palpation and, more importantly, would provide additional insight into the overall strength of the fusion formed.