Regional structure-function relationships of lumbar cartilage endplates.

Cartilage endplates (CEPs) act as protective mechanical barriers for intervertebral discs (IVDs), yet their heterogeneous structure-function relationships are poorly understood. This study addressed this gap by characterizing and correlating the regional biphasic mechanical properties and biochemical composition of human lumbar CEPs. Samples from central, lateral, anterior, and posterior portions of the disc (n = 8/region) were mechanically tested under confined compression to quantify swelling pressure, equilibrium aggregate modulus, and hydraulic permeability. These properties were correlated with CEP porosity and glycosaminoglycan (s-GAG) content, which were obtained by biochemical assays of the same specimens. Both swelling pressure (142.79 ± 85.89 kPa) and aggregate modulus (1864.10 ± 1240.99 kPa) were found to be regionally dependent (p = 0.0001 and p = 0.0067, respectively) in the CEP and trended lowest in the central location. No significant regional dependence was observed for CEP permeability (1.35 ± 0.97 * 10-16 m4/Ns). Porosity measurements correlated significantly with swelling pressure (r = -0.40, p = 0.0227), aggregate modulus (r = -0.49, p = 0.0046), and permeability (r = 0.36, p = 0.0421), and appeared to be the primary indicator of CEP biphasic mechanical properties. Second harmonic generation microscopy also revealed regional patterns of collagen fiber anchoring, with fibers inserting the CEP perpendicularly in the central region and at off-axial directions in peripheral regions. These results suggest that CEP tissue has regionally dependent mechanical properties which are likely due to the regional variation in porosity and matrix structure. This work advances our understanding of healthy baseline endplate biomechanics and lays a groundwork for further understanding the role of CEPs in IVD degeneration.

TOR signaling regulates GPCR levels on the plasma membrane and suppresses the Saccharomyces cerevisiae mating pathway.

Saccharomyces cerevisiae respond to mating pheromone through the GPCRs Ste2 and Ste3, which promote growth of a mating projection in response to ligand binding. This commitment to mating is nutritionally and energetically taxing, and so we hypothesized that the cell may suppress mating signaling during starvation. We set out to investigate negative regulators of the mating pathway in nutritionally depleted environments. Here, we report that nutrient deprivation led to loss of Ste2 from the plasma membrane. Recapitulating this effect with nitrogen starvation led us to hypothesize that it was due to TORC1 signaling. Rapamycin inhibition of TORC1 impacted membrane levels of all yeast GPCRs. Inhibition of TORC1 also dampened mating pathway output. Deletion analysis revealed that TORC1 repression leads to α-arrestin-directed CME through TORC2-Ypk1 signaling. We then set out to determine whether major downstream effectors of the TOR complexes also downregulate pathway output during mating. We found that autophagy contributes to pathway downregulation through analysis of strains lacking ATG8 . We also show that Ypk1 significantly reduced pathway output. Thus, both autophagy machinery and TORC2-Ypk1 signaling serve as attenuators of pheromone signaling during mating. Altogether, we demonstrate that the stress-responsive TOR complexes coordinate GPCR endocytosis and reduce the magnitude of pheromone signaling, in ligand-independent and ligand-dependent contexts. One Sentence Summary: TOR signaling regulates the localization of all Saccharomyces cerevisiae GPCRs during starvation and suppress the mating pathway in the presence and absence of ligand.

The roles of yeast formins and their regulators Bud6 and Bil2 in the pheromone response.

In response to pheromone Saccharomyces cerevisiae extend a mating projection. This process depends on the formation of polarized actin cables which direct secretion to the mating tip and translocate the nucleus for karyogamy. Here, we demonstrate that proper mating projection formation requires the formin Bni1, as well as the actin nucleation promoting activities of Bud6, but not the formin Bnr1. Further, Bni1 is required for pheromone gradient tracking. Our work also reveals unexpected new functions for Bil2 in the pheromone response. Previously we identified Bil2 as a direct inhibitor of Bnr1 during vegetative cell growth. Here, we show that Bil2 has Bnr1-independent functions in spatially focusing Bni1-GFP at mating projection tips, and in vitro Bil2 and its binding partner Bud6 organize Bni1 into clusters that nucleate actin assembly. bil2∆ cells also display entangled Bni1-generated actin cable arrays and defects in secretory vesicle transport and nuclear positioning. At low pheromone concentrations, bil2∆ cells are delayed in establishing a polarity axis, and at high concentrations they prematurely form a second and a third mating projection. Together, these results suggest that Bil2 promotes the proper formation and timing of mating projections by organizing Bni1 and maintaining a persistent axis of polarized growth.

The G-alpha Gpa1 directs septin localization in the mating projection of Saccharomyces cerevisiae through its Ubiquitination Domain and Endocytic Machinery.

The yeast mating response uses a G-protein coupled receptor (GPCR), Ste2, to detect mating pheromone and initiate mating projection morphogenesis. The septin cytoskeleton plays a key role in the formation of the mating projection, forming structures at the base of the projection. Desensitization of the Gα, Gpa1, by the Regulator of G-protein Signaling (RGS), Sst2, is required for proper septin organization and morphogenesis. In cells where the Gα is hyperactive, septins are mislocalized to the site of polarity, and the cells are unable to track a pheromone gradient. We set out to identify the proteins that mediate Gα control of septins during the Saccharomyces cerevisiae mating response by making mutations to rescue septin localization in cells expressing the hyperactive Gα mutant gpa1G302S. We found that single deletions of the septin chaperone Gic1, the Cdc42 GAP Bem3, and the epsins Ent1 and Ent2 rescued the polar cap accumulation of septins in the hyperactive Gα. We created an agent-based model of vesicle trafficking that predicts how changes in endocytic cargo licensing alters localization of endocytosis that mirrors the septin localization we see experimentally. We hypothesized that hyperactive Gα may increase the rate of endocytosis of a pheromone responsive cargo, thereby altering where septins are localized. Both the GPCR and the Gα are known to be internalized by clathrin-mediated endocytosis during the pheromone response. Deletion of the GPCR C-terminus to block internalization partially rescued septin organization. However, deletion of the Gpa1 ubiquitination domain required for its endocytosis completely abrogated septin accumulation at the polarity site. Our data support a model where the location of endocytosis serves as a spatial mark for septin structure assembly and that desensitization of the Gα delays its endocytosis sufficiently that septins are placed peripheral to the site of Cdc42 polarity.

N-terminal intrinsic disorder is an ancestral feature of Gγ subunits that influences the balance between different Gßγ signaling axes in yeast.

Activated G protein-coupled receptors promote the dissociation of heterotrimeric G proteins into Gα and Gßγ subunits that bind to effector proteins to drive intracellular signaling responses. In yeast, Gßγ subunits coordinate the simultaneous activation of multiple signaling axes in response to mating pheromones, including MAP kinase (MAPK)-dependent transcription, cell polarization, and cell cycle arrest responses. The Gγ subunit in this complex contains an N-terminal intrinsically disordered region that governs Gßγ-dependent signal transduction in yeast and mammals. Here, we demonstrate that N-terminal intrinsic disorder is likely an ancestral feature that has been conserved across different Gγ subtypes and organisms. To understand the functional contribution of structural disorder in this region, we introduced precise point mutations that produce a stepwise disorder-to-order transition in the N-terminal tail of the canonical yeast Gγ subunit, Ste18. Mutant tail structures were confirmed using circular dichroism and molecular dynamics and then substituted for the wildtype gene in yeast. We find that increasing the number of helix-stabilizing mutations, but not isometric mutation controls, has a negative and proteasome-independent effect on Ste18 protein levels as well as a differential effect on pheromone-induced levels of active MAPK/Fus3, but not MAPK/Kss1. When expressed at wildtype levels, we further show that mutants with an alpha-helical N terminus exhibit a counterintuitive shift in Gßγ signaling that reduces active MAPK/Fus3 levels whilst increasing cell polarization and cell cycle arrest. These data reveal a role for Gγ subunit intrinsically disordered regions in governing the balance between multiple Gßγ signaling axes.

Pre-Operative Substance Use Disorder is Associated with Higher Risk of Long-Term Mortality Following Bariatric Surgery.

PURPOSE: Metabolic and bariatric surgery (MBS) has been associated with reduced all-cause mortality. While the number of subjects with substance use disorders (SUD) before MBS has been documented, the impact of pre-operative SUD on long-term mortality following MBS is unknown. This study assessed long-term mortality of patients with and without pre-operative SUD who underwent MBS. MATERIALS AND METHODS: Two statewide databases were used for this study: Utah Bariatric Surgery Registry (UBSR) and the Utah Population Database. Subjects who underwent MBS between 1997 and 2018 were linked to death records (1997-2021) to identify any death and cause for death following MBS. All deaths (internal, external, and unknown reasons), internal deaths, and external deaths were the primary outcomes of the study. External causes of death included death from injury, poisoning, and suicide. Internal causes of death included deaths that were associated with natural causes such as heart disease, cancer, and infections. A total of 17,215 patients were included in the analysis. Cox regression was used to estimate hazard ratios (HR) of controlled covariates, including the pre-operative SUD. RESULTS: The subjects with pre-operative SUD had a 2.47 times higher risk of death as compared to those without SUD (HR = 2.47, p < 0.01). Those with pre-operative SUD had a higher internal cause of death than those without SUD by 129% (HR = 2.29, p < 0.01) and 216% higher external mortality risk than those without pre-operative SUD (HR = 3.16, p < 0.01). CONCLUSION: Pre-operative SUD was associated with higher hazards of all-cause, internal cause, and external cause mortality in patients who undergo bariatric surgery.

Association of Pre-operative Arthritis with Long-Term Mortality Following Bariatric Surgery.

BACKGROUND: Metabolic and bariatric surgery (MBS) is an effective treatment for obesity and may reduce mortality. Several factors are associated with higher mortality following MBS. The purpose of this study was to examine whether pre-operative arthritis was associated with long-term mortality following MBS. METHODS: Using a retrospective cohort design, subjects who underwent MBS were identified from the Utah Bariatric Surgery Registry. These subjects were linked to the Utah Population Database. State death records from 1998 through 2021 were used to identify deaths following MBS. ICD-9/10 diagnosis codes were used to identify a pre-operative diagnosis of arthritis and to classify the cause of death. All causes of death, internal cause of death (e.g., diabetes, heart disease), and external cause of death (e.g., suicide) were defined as outcomes. Entropy balancing (EB) was applied to create weights to balance the baseline characteristics of the two groups. Weighted Cox proportional hazards regression was used to evaluate the association of pre-operative arthritis with long-term mortality following MBS. RESULTS: The final sample included 15,112 patients. Among them, 36% had a pre-operative arthritis diagnosis. Average (SD) age was 48(12) years old at surgery, and 75% were female. Patients with pre-operative arthritis had 25% (p < 0.01) and 26% (p < 0.01) higher risk of all cause of death and internal cause of death, respectively, compared to patients without pre-operative arthritis. CONCLUSION: Individuals with arthritis prior to MBS may have higher hazard of long-term mortality than those without pre-operative arthritis.

Treatment of Pyogenic Flexor Tenosynovitis in the Emergency Department Setting With WALANT Technique.

BACKGROUND: The standard of care for treatment of pyogenic flexor tenosynovitis (PFT) involves antibiotic therapy and prompt irrigation of the flexor tendon sheath, traditionally performed in the operating room. With the acceptance of wide-awake local anesthesia no tourniquet (WALANT) hand surgery and its potential ability to minimize time to flexor tendon sheath irrigation, we sought to determine whether closed irrigation of the flexor tendon sheath could be safely and effectively performed in the emergency department setting with WALANT technique. METHODS: A retrospective review was conducted of the senior author's hand surgery consultations over a 12-month period. Six patients were identified who were diagnosed with PFT and subsequently underwent irrigation of the flexor tendon sheath using WALANT technique. Patient outcomes such as length of hospital stay, need for reoperation, infectious etiology, perioperative complications, and postprocedure range of motion (ROM) were identified. RESULTS: Six patients with diagnosis of PFT underwent irrigation of the flexor tendon sheath in the emergency department with local anesthesia only. The irrigation procedures were all well-tolerated. One patient required reoperation due to lack of appropriate clinical improvement following initial irrigation. Four of 6 patients regained their preinjury ROM while the remaining 2 patients had mild proximal interphalangeal joint extension lag. There were no complications associated with the procedures. CONCLUSIONS: Surgical treatment of PFT with closed irrigation of the flexor tendon sheath in the emergency department utilizing WALANT technique was safe, effective, and well-tolerated. Local anesthesia alone can be used effectively for irrigation procedures of the flexor tendon sheath.

Development of dementia in patients who underwent bariatric surgery.

BACKGROUND: Dementia, including Alzheimer's disease, interfere with daily function and are one of the major causes of disability, institutionalization, and death. Obesity is associated with an increased risk of dementia. However, the effect of significant and sustained weight loss following bariatric surgery on dementia is not known. The purpose of this study was to assess the long-term risk of dementia following bariatric surgery. METHODS: A surgical cohort was identified from the Utah Bariatric Surgery Registry and was linked to the Utah Population Database that includes electronic medical records, death records, and State Facility data. Adult subjects (≥ 18 years old) at time of surgery (1996-2016) were matched with non-surgical subjects. The final sample included 51,078 subjects (1:2 matching); surgery group n = 17,026; non-surgery subjects n = 34,052). Dementia were identified by ICD-9/10 diagnosis codes following surgery year or matched baseline year. Cox proportional hazard model was used to calculate the hazard ratio in the outcome between the groups. RESULTS: Average (SD) age of the subjects was 42 (12) years old at surgery or matched baseline year, 78% were female and mean follow-up time was 10.5 years. 1.4% of the surgery group and 0.5% of the control group had an incidence of dementia. Controlling the covariates in the Cox regression, the surgery group had a higher risk for dementia incidence than the matched non-surgery subjects (HR = 1.33, p = 0.02). CONCLUSIONS: The study showed an increased hazard for dementia in individuals who underwent bariatric surgery compared to matched non-surgical subjects. Additional long-term data is needed to verify this association.

Phosphorylation of RGS regulates MAP kinase localization and promotes completion of cytokinesis.

Yeast use the G-protein-coupled receptor signaling pathway to detect and track the mating pheromone. The G-protein-coupled receptor pathway is inhibited by the regulator of G-protein signaling (RGS) Sst2 which induces Gα GTPase activity and inactivation of downstream signaling. G-protein signaling activates the MAPK Fus3, which phosphorylates the RGS; however, the role of this modification is unknown. We found that pheromone-induced RGS phosphorylation peaks early; the phospho-state of RGS controls its localization and influences MAPK spatial distribution. Surprisingly, phosphorylation of the RGS promotes completion of cytokinesis before pheromone-induced growth. Completion of cytokinesis in the presence of pheromone is promoted by the kelch-repeat protein, Kel1 and antagonized by the formin Bni1. We found that RGS complexes with Kel1 and prefers the unphosphorylatable RGS mutant. We also found overexpression of unphosphorylatable RGS exacerbates cytokinetic defects, whereas they are rescued by overexpression of Kel1. These data lead us to a model where Kel1 promotes completion of cytokinesis before pheromone-induced polarity but is inhibited by unphosphorylated RGS binding.

Depression and Anxiety Incidence During Pregnancy Between Bariatric Surgery Patients and Matched Control Subjects.

PURPOSE: Obesity is a well-known risk factor for depression and mental illnesses. Metabolic and bariatric surgery (MBS) is a common treatment for individuals with severe obesity. Studies suggest that MBS is associated with increased risk of depression. However, little is known if pregnant women following MBS have greater incidence of depression/anxiety than non-surgical pregnant women with severe obesity. MATERIALS AND METHODS: Utah Bariatric Surgery Registry (UBSR) was used to identify subjects who underwent bariatric surgery between 1996 and 2016 and were matched (1:2 matching) to subjects with severe obesity from the Utah Population Database (UPDB). Depression and anxiety diagnoses during pregnancy were identified from birth records and electronic medical records (EMRs) during 10 months before birth. A multivariate logistic regression with clustering due to same subjects with multiple births was used. RESULTS: Patients included 1427 MBS women (associated 2492 births) and 2854 non-surgical women (associated 4984 births). In the surgical group, 24.4% of the pregnancies had diagnosed depression/anxiety, while 14.3% of the pregnancies in the control group had depression/anxiety (p < 0.01). The surgery group had 1.51 times higher odds of depression and/or anxiety during pregnancy than the control group after controlling for covariates (OR = 1.51, p < 0.01). CONCLUSION: The present study provides evidence that women who previously underwent MBS have higher odds of depression/anxiety during pregnancy than women with obesity who did not undergo MBS.

Beneficial impacts of neuromuscular electrical stimulation on muscle structure and function in the zebrafish model of Duchenne muscular dystrophy.

Neuromuscular electrical stimulation (NMES) allows activation of muscle fibers in the absence of voluntary force generation. NMES could have the potential to promote muscle homeostasis in the context of muscle disease, but the impacts of NMES on diseased muscle are not well understood. We used the zebrafish Duchenne muscular dystrophy (dmd) mutant and a longitudinal design to elucidate the consequences of NMES on muscle health. We designed four neuromuscular stimulation paradigms loosely based on weightlifting regimens. Each paradigm differentially affected neuromuscular structure, function, and survival. Only endurance neuromuscular stimulation (eNMES) improved all outcome measures. We found that eNMES improves muscle and neuromuscular junction morphology, swimming, and survival. Heme oxygenase and integrin alpha7 are required for eNMES-mediated improvement. Our data indicate that neuromuscular stimulation can be beneficial, suggesting that the right type of activity may benefit patients with muscle disease.

Variable penetrance of Nab3 granule accumulation quantified by a new tool for high-throughput single-cell granule analysis.

Reorganization of cellular proteins into subcellular compartments, such as the concentration of RNA-binding proteins into cytoplasmic stress granules and P-bodies, is a well-recognized, widely studied physiological process currently under intense investigation. One example of this is the induction of the yeast Nab3 transcription termination factor to rearrange from its pan-nucleoplasmic distribution to a granule at the nuclear periphery in response to nutrient limitation. Recent work in many cell types has shown that protein condensation in the nucleus is functionally important for transcription initiation, RNA processing, and termination. However, little is known about how subnuclear compartments form. Here, we have quantitatively analyzed this dynamic process in living yeast using a high-throughput computational tool and fluorescence microscopy. This analysis revealed that Nab3 granule accumulation varies in penetrance across yeast strains. A concentrated single granule is formed from at least a quarter of the nuclear Nab3 drawn from the rest of the nucleus. Levels of granule accumulation were inversely correlated with a growth defect in the absence of glucose. Importantly, the basis for some of the variation in penetrance was attributable to a defect in mitochondrial function. This publicly available computational tool provides a rigorous, reproducible, and unbiased examination of Nab3 granule accumulation that should be widely applicable to a variety of fluorescent images. Thousands of live cells can be readily examined enabling rigorous statistical verification of significance. With it, we describe a new feature of inducible subnuclear compartment formation for RNA-binding transcription factors and an important determinant of granule biogenesis.

Metformin and leucine increase satellite cells and collagen remodeling during disuse and recovery in aged muscle.

Loss of muscle mass and strength after disuse followed by impaired muscle recovery commonly occurs with aging. Metformin (MET) and leucine (LEU) individually have shown positive effects in skeletal muscle during atrophy conditions but have not been evaluated in combination nor tested as a remedy to enhance muscle recovery following disuse atrophy in aging. The purpose of this study was to determine if a dual treatment of metformin and leucine (MET + LEU) would prevent disuse-induced atrophy and/or promote muscle recovery in aged mice and if these muscle responses correspond to changes in satellite cells and collagen remodeling. Aged mice (22-24 months) underwent 14 days of hindlimb unloading (HU) followed by 7 or 14 days of reloading (7 or 14 days RL). MET, LEU, or MET + LEU was administered via drinking water and were compared to Vehicle (standard drinking water) and ambulatory baseline. We observed that during HU, MET + LEU resolved whole body grip strength and soleus muscle specific force decrements caused by HU. Gastrocnemius satellite cell abundance was increased with MET + LEU treatment but did not alter muscle size during disuse or recovery conditions. Moreover, MET + LEU treatment alleviated gastrocnemius collagen accumulation caused by HU and increased collagen turnover during 7 and 14 days RL driven by a decrease in collagen IV content. Transcriptional pathway analysis revealed that MET + LEU altered muscle hallmark pathways related to inflammation and myogenesis during HU. Together, the dual treatment of MET and LEU was able to increase muscle function, satellite cell content, and reduce collagen accumulation, thus improving muscle quality during disuse and recovery in aging.

Gradient Tracking by Yeast GPCRs in a Microfluidics Chamber.

Cells typically exist in a highly dynamic environment, which cannot easily be recreated in culture dishes or microwell plates. Microfluidic devices can provide precise control of the time, dose, and orientation of a stimulus, while simultaneously capturing quantitative single-cell data. The approach is particularly powerful when combined with the genetically tractable yeast model organism. The GPCR pathway in yeast is structurally conserved and functionally interchangeable with those in humans. We describe the implementation of a microfluidic device to investigate morphological and transcriptional responses of yeast to a gradient or pulse administration of a GPCR ligand, the peptide mating pheromone α-factor.

Cytoskeletal diversification across 1 billion years: What red algae can teach us about the cytoskeleton, and vice versa.

The cytoskeleton has a central role in eukaryotic biology, enabling cells to organize internally, polarize, and translocate. Studying cytoskeletal machinery across the tree of life can identify common elements, illuminate fundamental mechanisms, and provide insight into processes specific to less-characterized organisms. Red algae represent an ancient lineage that is diverse, ecologically significant, and biomedically relevant. Recent genomic analysis shows that red algae have a surprising paucity of cytoskeletal elements, particularly molecular motors. Here, we review the genomic and cell biological evidence and propose testable models of how red algal cells might perform processes including cell motility, cytokinesis, intracellular transport, and secretion, given their reduced cytoskeletons. In addition to enhancing understanding of red algae and lineages that evolved from red algal endosymbioses (e.g., apicomplexan parasites), these ideas may also provide insight into cytoskeletal processes in animal cells.

Temporal dynamics of viral load and false negative rate influence the levels of testing necessary to combat COVID-19 spread.

Colleges and other organizations are considering testing plans to return to operation as the COVID-19 pandemic continues. Pre-symptomatic spread and high false negative rates for testing may make it difficult to stop viral spread. Here, we develop a stochastic agent-based model of COVID-19 in a university sized population, considering the dynamics of both viral load and false negative rate of tests on the ability of testing to combat viral spread. Reported dynamics of SARS-CoV-2 can lead to an apparent false negative rate from ~ 17 to ~ 48%. Nonuniform distributions of viral load and false negative rate lead to higher requirements for frequency and fraction of population tested in order to bring the apparent Reproduction number (Rt) below 1. Thus, it is important to consider non-uniform dynamics of viral spread and false negative rate in order to model effective testing plans.

Acute Effects of Cheddar Cheese Consumption on Circulating Amino Acids and Human Skeletal Muscle.

Cheddar cheese is a protein-dense whole food and high in leucine content. However, no information is known about the acute blood amino acid kinetics and protein anabolic effects in skeletal muscle in healthy adults. Therefore, we conducted a crossover study in which men and women (n = 24; ~27 years, ~23 kg/m2) consumed cheese (20 g protein) or an isonitrogenous amount of milk. Blood and skeletal muscle biopsies were taken before and during the post absorptive period following ingestion. We evaluated circulating essential and non-essential amino acids, insulin, and free fatty acids and examined skeletal muscle anabolism by mTORC1 cellular localization, intracellular signaling, and ribosomal profiling. We found that cheese ingestion had a slower yet more sustained branched-chain amino acid circulation appearance over the postprandial period peaking at ~120 min. Cheese also modestly stimulated mTORC1 signaling and increased membrane localization. Using ribosomal profiling we found that, though both milk and cheese stimulated a muscle anabolic program associated with mTORC1 signaling that was more evident with milk, mTORC1 signaling persisted with cheese while also inducing a lower insulinogenic response. We conclude that Cheddar cheese induced a sustained blood amino acid and moderate muscle mTORC1 response yet had a lower glycemic profile compared to milk.

Temporal Dynamics of Viral Load and False negative Rate Influence the Levels of Testing Necessary to Combat COVID19 Spread.

Colleges and other organizations are considering testing plans to return to operation as the COVID19 pandemic continues. Pre-symptomatic spread and high false negative rates for testing may make it difficult to stop viral spread. Here, we develop a stochastic agent-based model of COVID19 in a university sized population, considering the dynamics of both viral load and false negative rate of tests on the ability of testing to combat viral spread. Reported dynamics of SARS-CoV-2 can lead to an apparent false negative rate from ~17% to ~48%. Nonuniform distributions of viral load and false negative rate lead to higher requirements for frequency and fraction of population tested in order to bring the apparent Reproduction number (Rt) below 1. Thus, it is important to consider non-uniform dynamics of viral spread and false negative rate in order to model effective testing plans.