Focal contacts act as mechanosensors allowing cells to respond to their biomechanical environment. Force transmission through newly formed contact sites is a highly dynamic process requiring a stable link between the intracellular cytoskeleton and the extracellular environment. To simultaneously investigate cellular traction forces in several individual maturing adhesion sites within the same cell, we established a custom-built multiple trap optical tweezers setup. Beads functionalized with fibronectin or RGD-peptides were placed onto the apical surface of a cell and trapped with a maximum force of 160 pN. Cells form adhesion contacts around the beads as demonstrated by vinculin accumulation and start to apply traction forces after 30 seconds. Force transmission was found to strongly depend on bead size, surface density of integrin ligands and bead location on the cell surface. Highest traction forces were measured for beads positioned on the leading edge. For mouse embryonic fibroblasts, traction forces acting on single beads are in the range of 80 pN after 5 minutes. If two beads were positioned parallel to the leading edge and with a center-to-center distance less than 10 µm, traction forces acting on single beads were reduced by 40%. This indicates a spatial and temporal coordination of force development in closely related adhesion sites. We also used our setup to compare traction forces, retrograde transport velocities, and migration velocities between two cell lines (mouse melanoma and fibroblasts) and primary chick fibroblasts. We find that maximal force development differs considerably between the three cell types with the primary cells being the strongest. In addition, we observe a linear relation between force and retrograde transport velocity: a high retrograde transport velocity is associated with strong cellular traction forces. In contrast, migration velocity is inversely related to traction forces and retrograde transport velocity. Force sensing and transmission is a vital process and has various effects on cell morphology, motility, proliferation and physiology Integrin accumulation occurs in response to chemical and mechanical cues in their environment. Their interaction with the ECM leads to signaling cascades which eventually result in the accumulation of intracellular proteins into the cell-matrix contact sites resulting in the constitution and reinforcement of early adhesion sites Cell motility originates in the extension of the actin cytoskeleton by F-actin polymerization in the leading edge where migration is achieved by the exertion of inward facing traction forces The invention of optical tweezers in 1986 by A. Ashkin To study the temporal development and strength of cellular traction forces at an extended number of individual adhesion sites, we established a custom-built multiple trap optical tweezers setup. The multiple trap feature of the optical tweezers system is a valuable tool to derive a force mapping across the entire cell surface. With the existing setup, we positioned up to 5 beads simultaneously on the apical membrane, which enables the coincidental initiation of adhesion sites in distinct locations. This allows the synchronous, time-resolved force mapping in adhesion sites with pN sensitivity. In addition, the influence of geometrical and spatial restrictions such as bead size and spatial relation of bead position was investigated.As cellular forces and retrograde actin flow correlate To investigate the cellular response induced by mechanical stimuli, we established a custom-built multiple trap optical tweezers system  A and prFN functionalized beads were placed with optical traps on the apical cell surface of cells spread on a homogeneous FN-coated substrate to mimic new contact sites  B. For tTo determine the optimal conditions for the optical tweezers force spectroscopy assay, FN functionalized beads of 3.0 and 4.5 µm diameter were positioned by optical traps at the leading edge of mouse embryonic fibroblasts (MEFs) and the force development in the evolving adhesion sites was monitored  C. Both 3.0 µm = 16±1 pN after 5 min, number of independent experiments N = 5, number of examined cells n = 17, F4.5 µm = 83±4 pN, N = 5, n = 14, 2 for 3 µm beads and ≤3.0 µm2 for the 4.5 µm beads were derived. In conclusion these experiments show, that a 1.5 times larger contact area induced a 5-fold increase in force transmission.We obtained strongly reduced forces for 3.0 µm beads compared to forces transmitted onto 4.5 µm beads , FFN,80% = 81±5 pN  and FFN,100% = 134±13 pN  onto the beads. Further enhanced coating densities were not tested with FN as ligand, as the forces applied to 100% FN beads were close to the maximum optical trap counterforces available with the existing setup.For MEF cells in contact with FN beads a dependence of the force-time curves on coating density was observed for membrane/bead interaction times longer than 60s . The evacRGD,50% = 44±7 pN  to FcRGD,80% = 63±9 pN  and FcRGD,100% = 92±11 pN (n = 8) and were discernible after 2 min of membrane-bead contact (p<0.0001). The formation of a second ligand layer on the bead (150% coverage) did not lead to an increased force transmission at the contact sites but resulted in a saturation on the force level observed for 100% coverage ).Identical measurements were performed with beads functionalized with different densities of cRGDfk. Here, an additional bead batch with 150% surface coverage was prepared to test whether a saturation effect occurred. These beads had more ligands attached than required to form a complete monolayer and thus a second peptide layer formed. Data obtained with cRGDfk peptides show a dependence of both, the rate of force increase and the magnitude of forces on the coating density . The evaControl measurements with beads coated solely with PLL (without FN or cRGD) revealed an unspecific bead attachment to the cell surface of a small percentage of beads (about 8%). Although these beads were in contact with the membrane, they did not show rearward translocation and could easily be displaced by the optical traps.Thus, traction forces in the initial 5 min of cell adhesion formation depend on the density of integrins ligands offered on the bead surface. A comparison of cellular traction forces applied to beads covered with different densities of FN and cRGD displays enhanced force transmission at contact sites formed to FN functionalized beads . This diThe optical tweezers setup features a multi trap mode allowing to measure traction forces simultaneously at distinct locations. This enables a force mapping with high spatial and temporal resolution over the whole cell body of a single cell and grants a high accuracy when comparing forces measured within distinct cellular regions. Here, we simultaneously arranged a predefined number of beads on cellular protrusions (area I), the leading edge (area II) and the cell body (area III) of a single cell to estimate the dynamics and adhesion strength occurring during initial force development  A to D. Traction forces were highest in the foremost protrusions, decreased rearwards toward the leading edge and became negligible when beads were placed in the nuclear region or the rear of the cell  D and E.We conducted complementary measurements to evaluate the rate of retrograde bead transport in different cellular areas  B and C.In the cell periphery, cell matrix adhesion sites are often spatially closely related. The results presented so far all considered adhesion sites that were well separated. In the force mapping assay, multiple beads on the cell surface were spatially separated by distances >10 µm and therefore were regarded as independent. Now, we tested the influence of spatially closely related beads and adhesions on force transmission. The beads offering new contact sites for the cells were placed with a distance of 5 µm on the leading edge of the cell . A control was performed with bead spacing larger than 10 µm and yielded the same result as obtained for force transmission on single beads. Two examples of bead spacing were regarded for the acquisition of force-time curves: (i) beads were placed in a radial orientation and (ii) beads were placed in successive order and were aligned normally to the border of the leading edge  C.5 µm = 49±4 pN; N = 7, n = 19) compared to F10 µm = 83±4 pN . The force-time curves show that the force development becomes divergent already after 30 seconds of membrane/bead contact time (p = 0.02).In case (i), a declined force transmission was observed when the spatial separation between beads was reduced from 10 to 5 µm  A to C. 5 µm = 70±4 pN; N = 5, n = 8 and F10 µm = 26±5 pN; N = 4, n = 7).The second case (ii) with a normal bead orientation  B and C In a number of studies, cellular traction forces have been examined using multitudinous approaches The immortalized B16 and MEF cells were of similar size and featured an elongated shape . In contB16 = 42±2 pN , FMEF = 83±4 pN , FPCF = 151±10 pN . B16 cells showed the slowest increase of traction forces over time and after 1 min a significant difference in force transmission was observed in comparison to MEF and PCF cells (p<0.01).Traction forces were measured at the contact site of a 4.5 µm FN functionalized bead over a time course of 300 s. The forces transmitted during the formation of adhesive contacts were clearly distinguishable for the three investigated cell types and after 300 s the following forces resulted  D: FB16 MEF traction forces evolve in a two-step process with a steep force increase in the early adhesion formation  followed by a moderate force development in the second phase. Concerning the entire course of measurements, we derived the fast reinforcement rate for PCF cells. Although PCF and MEF cells showed the same traction force evolution in the first 120 s of bead contact, MEF force enhancement slowed in the following, while PCF cells maintained a linear increase in adhesion strengthening and exerted steadily growing forces onto the beads. The measurement duration was extended to 10 min to determine whether PCF reinforcement continued at the same rate: no decrease in adhesion strengthening was found within the increased measurement interval and after 8 min the cells overcame the optical counterforce and removed the beads from the traps (data not shown).rt resulted in the fastest transport dynamics in the PCF cells, followed by moderate transport rates for MEF cells and slow transport dynamics for B16 cells . A cell type comparative analysis of force transmission and retrograde transport shows a linear correlation of the two values  investigated, our data reveal a cell type independent correlation of traction force generation at adhesion sites, retrograde transport rates and cell migration velocity. B16 melanoma cells developed the weakest forces, which correlated to slow retrograde transport rates. Concomitantly, these cells featured the highest migration velocities of all three cell lines. MEF cells displayed forces, retrograde transport velocities and migration rates in an intermediate regime, while the primary cell line of PCFs exhibited the strongest forces, fastest retrograde transport and slowest migration.A correlation of traction forces and retrograde actin flow has been demonstrated in previous studies Fertilized chick eggs  used for the preparation of primary chick fibroblasts were obtained from a local breeder and experiments were performed according to European (Council Directive 86/609/EEC) and German (Tierschutzgesetz) guidelines for the welfare of experimental animals. Embryos were dissected from eggs after 8 days of breeding in a commercial egg incubator and sacrificed by decapitation prior to skin preparation.2. B16 and MEF cells were maintained in Dulbecco’s modified Eagle’s medium  supplemented with 10% fetal bovine serum  and PCFs were supplied with Kaighn’s modified nutrient mixture (Invitrogen) with 10% FBS and 5% chicken serum. Prior to experiments, cells were plated onto fibronectin (FN) functionalized glass-bottom culture dishes (MatTek) and preincubated for 2 hours to allow cells to spread. 30 min before measurements the standard growth medium was exchanged for CO2 independent medium  Monoclonal mouse anti-vinculin antibodies  were used in combination with Cy3-conjugated goat-anti mouse F(ab’)2 antibodies (Dianova) to mark focal adhesions. The actin cytoskeleton was stained with Alexa488-conjugated phalloidin (Invitrogen) and the nucleus was visualized with DAPI (Sigma Aldrich).6 cells suspended in 250 µl cold electroporation buffer . The cuvette was incubated on ice for 2 min before subjection to an electroporation pulse of 250 V and 60 ms duration . Subsequently the cell suspension was stored on ice for 2 min and cells were mixed with DMEM medium and replated onto cover slips. The transfected cells were incubated for 16 h under routine conditions to express the protein. Subsequently, cell samples were incubated with FN-functionalized beads for 20 min and were fixed to analyze vinculin recruitment at bead contact with a confocal laser scanning microscope .MEF cells were transfected to express full length vinculin-GFP fusion proteins . 2 µg plasmid DNA were transferred into an electroporation cuvette and were mixed with 103-N3, 1 mg/ml). Therefore, beads were incubated with 100 µl Poly-L-Lysine in PBS  for 1 h at room temperature with gentle mixing. The solution was washed 3 times with PBS by centrifugation and varying amounts of FN  or cRGDfk  were added into 100 µl PBS to obtain distinct densities on the bead surface. Beads were incubated with gentle mixing for another hour at room temperature. The amount of ligand attached to the bead surface was determined spectrophotometrically by UV-VIS spectroscopy . Optical density data were obtained from the supernatant of the bead-ligand solution at a wavelength of 260 nm and yielded the concentration cresidue of residual (unattached) ligand. The number of ligand molecules in the supernatant was calculated from the relation Nresidue = cresidue VNA (V denotes the volume of the solution and NA the Avogadro constant). From the number of initially deployed ligand Nini and residual ligand Nresidual, the number of attached ligand molecules per bead Nb was estimated: Nb = (Nini – Nresidue)/nb where nb is the number of beads. The size of an individual 450 kDa FN molecule was determined by scanning electron microscopy 2. For the 1 kDa cRGD tripeptide, a surface coverage of about 0.24 nm2 per molecule was assumed from the relation of FN to cRGD molecular weights. From this calculation, the degree of surface coverage can be estimated. For the presented experiments, bead batches with a surface coverage of 50%, 80% and 100% were prepared for the ligands FN and cRGDfk. An additional sample with 150% coverage was prepared with the cyclic peptide only. Bead-ligand solutions were washed 3 times with PBS to remove residual ligands and were finally stored in 1× PBS at 4°C. Beads were freshly prepared one day prior to the experiments.Carboxylated polystyrene beads of 3.0 µm and 4.5 µm diameter (Polysciences) were homogeneously functionalized either with the extracellular matrix protein FN  or with a cyclic RGD peptide (c(RGDfk)-(Ahx)Glass bottoms of culture dishes (MatTek) were covered with a solution of 50 µl PLL in PBS and incubated for 1 h at room temperature. After rinsing the dishes twice with PBS, 0.5 µl FN diluted in 50 µl PBS were added and dishes were incubated for 1 h at room temperature. Residual FN was removed by rinsing twice with PBS and the culture dishes were stored at 4°C covered with PBS until further use.The laser tweezers setup was based on a two-axis acousto-optical deflection system  which allowed the independent steering and intensity modulation of a large number of quasi static optical traps. Optical traps were operated by an AOD beam steering controller (Aresis), allowing closed-loop operation by relying on the live image of a CCD camera  for positioning of optical traps. Due to the fast access time (6.5 µs) of the deflectors, multiple time-shared traps could be generated within a scan angle of 200×200 µm and operated simultaneously. An infrared diode pumped solid state laser , operating at a wavelength of 1064 nm, was coupled into a custom-built microscope and focused by a high numerical aperture objective to generate the optical traps. The microscope was equipped with epifluorescence optics and a heating unit to maintain a sample temperature of 37°C for live cell force measurements. To manipulate microscopic beads on the cells surface, a water immersion objective  was lowered into the imaging medium within of a glass bottom dish. Imaging was performed with an oil immersion objective  mounted below the sample dish.The optical traps were calibrated using the thermal fluctuation method in combination with video microscopy for trap stiffness and the drag force method for maximum trap force determination U(x) of each trap was derived: 2U(x) = k*Δx(t) where Δx is the bead displacement and k the trap stiffness. The optical potential was calculated separately for forces pointing in x and y direction and showed a circular symmetry. Calibrations were performed close to the apical cell surface. The laser intensity applied to a trap was adjusted by changing the AOD transmission via the software interface Tweez (Aresis). The recorded video frames were submitted to data analysis to obtain the trap stiffness for each trap for varying laser power.Optical trap calibration was performed prior to the experiments in multi trap mode to ensure that no additional losses due to the scanning of the laser beam reduced the effective trap stiffness. Geometrical patterns of four to eight optical traps were generated and calibrated simultaneously  B. Each F = βv = 6πηrv, where β is the drag coefficient, v is the trap velocity, η denotes the fluid viscosity and r the bead radius.To determine the maximal optical force on microscopic beads, the drag force method was applied. A bead was captured in a trap well above the cell surface and moved through the sample plane with a defined trap velocity. The trap velocity was enhanced until the bead was unable to follow the trap. From the recorded escape velocity the maximum trap force was calculated using the Stokes relation F(t) = k*Δx(t) is utilized to determine the traction forces a cell applies to a trapped bead.The linear dependence of trap force on bead displacement Cells were transferred onto FN functionalized glass bottom dishes and were incubated for two to three hours to allow cells to spread. Half an hour before a measurement, the medium was exchanged for F12 imaging medium containing 20 mM Hepes and 2% FBS. FN functionalized beads were applied into the culture dish and 1 to 5 optical traps were activated to capture the beads and position them on the cell. Beads were placed on individual cells with positions varying between cellular protrusions, the leading edge and the cell body. Traps remained active during the complete measurement course of 5 min and images were recorded with a frame rate of 1 Hz with the CCD camera.To characterize the dynamics of retrograde actin flow, the retrograde transport of microscopic beads was monitored. Cells and beads were prepared as described and a predefined number of beads were positioned by optical traps on the cell surface. For the retrograde transport assay, optical traps were switched off immediately after positioning the beads. The bead position was recorded with the CCD camera over a time course of 20 min and with a frame rate of 0.5 Hz. The videos were analyzed with MetaMorph to determine the bead position in each frame and the retrograde transport velocity of the beads was calculated from the derived trajectory data.2 to allow for adhesion and spreading. Subsequently, time lapse movies of migrating cells were recorded  with a rate of 1 frame per minute for 12 hours.To characterize cell motility, cells were sparsely plated onto FN functionalized glass bottom dishes and preincubated for 2 h at 37°C and 5% COTo investigate force development and retrograde transport, time lapse movies were recorded at a frame rate of 1 Hz and analyzed with the object tracking application of MetaMorph (Molecular Devices). In each frame the actual bead position was determined by the software and the bead displacement was calculated as the distance between trap center and actual position.The velocity of migrating cells was derived from the observation of the locomotion of its nucleus. The nucleus was tracked with the manual tracking plugin  and the nuclear velocity was calculated with the chemotaxis and migration plugin (ibidi) for ImageJ.Figure S1DIC images of the three cell types studied. Cells were seeded onto homogeneously fibronectin-functionalized glass cover slips and incubated for 2 hours before fixation. A) Mouse melanoma B16F1 cells, B) mouse embryonic fibroblast (MEF) cells and C) primary chick fibroblast (PCF) cells .(TIF)Click here for additional data file.Figure S2To test whether cells accepted the FN functionalized beads to invoke new adhesion sites on the surface, MEF cells were transfected to express a full length vinculin-GFP fusion protein. In (TIF)Click here for additional data file.Figure S3Averaged force-time curves for each surface density of FN and cRGDfk functionalized beads. A) to C) show the development of cellular traction force exertion onto FN-beads and D) to G) onto cRGDfk-beads .(TIF)Click here for additional data file.


DAT1 gene and in the DRD4 gene, respectively, lead to interindividual differences in these error processing correlates. One hundred sixty participants completed a version of the Eriksen Flanker Task while a 26-channel EEG was recorded. The task was slightly modified in order to increase error rates. During data analysis, participants were split into two groups depending on their DAT1 and their DRD4 genotypes, respectively. ERN and Pe amplitudes after correct responses and after errors as well as difference amplitudes between errors and correct responses were analyzed. We found a differential effect of DAT1 genotype on the Pe difference amplitude but not on the ERN difference amplitude, while the reverse was true for DRD4 genotype. These findings are in line with predictions from theoretical models of dopaminergic transmission in the brain. They furthermore tie results from clinical investigations of disorders impacting on the dopamine system to genetic variations known to be at-risk genotypes.Recent studies as well as theoretical models of error processing assign fundamental importance to the brain's dopaminergic system. Research about how the electrophysiological correlates of error processing—the error-related negativity (ERN) and the error positivity (Pe)—are influenced by variations of common dopaminergic genes, however, is still relatively scarce. In the present study, we therefore investigated whether polymorphisms in the  Electrophysiological research extensively investigates the generation of two correlates of error processing: One component, the error-related negativity (ERN), is a defined negative event-related potential (ERP) with an amplitude of up to 10 µV that appears in the response-locked EEG 50 to 100 ms after an erroneous response An influential theoretical model by Holroyd and Coles Given the hypothesized role of DA transmission in the generation of the ERN, several studies investigated error processing in patients with Huntington's Disease (HD) and Parkinson's Disease (PD), both conditions with altered dopaminergic transmission. Beste and colleagues Error processing has also been investigated in patients with psychiatric disorders, with most research focusing on attention deficit hyperactivity disorder (ADHD), a disorder which comprises altered striatal dopamine levels In healthy volunteers, pharmaceutical alteration of dopaminergic transmission in the basal ganglia by a single dose of d-amphetamine resulted in enlarged ERN amplitudes, which was attributed to d-amphetamine's agonistic effect on dopaminergic transmission O-methyltransferase (COMT) polymorphism, for example, is known to influence frontal dopamine levels So far, only few studies of common genotype variations that influence dopaminergic transmission have been reported and these are partly contradictory  was found to possess a genetic variation – a 40 nucleotide variable number of tandem repeats (VNTR) polymorphism in the 3′ untranslated region (UTR) – with two common alleles labelled 9-repeat (9R) and 10-repeat (10R), which supposedly influence gene expression and thereby DA reuptake from extracellular space 9R allele led to increased DAT availability in the participants' striatum 10/10R carriers.The gene encoding the dopamine transporter (DRD4) also possesses a polymorphism with a 48 bp variable number of tandem repeats (VNTR) in exon III, which can vary from 2 to 11 repeats The dopamine D4 receptor gene ; all procedures involved were in accordance with the 2008 Declaration of Helsinki. Participants gave written informed consent after full explanation of the procedures.M) age was 27.02 years, ranging from 20 to 50 years of age (standard deviation SD  = 7.28). All participants were right-handed, without any medication, and never treated for neurologic or psychiatric problems. Results from a subsample (n = 56) have been published elsewhere One hundred sixty subjects  participated in this study. Mean (10/10R group (n = 98) and a group carrying at least one 9R allele  according to their DAT1 VNTR genotype. Additionally, participants were stratified based to their DRD4 VNTR genotype into a 7R group  and a no 7R group (n = 114). DAT1 and DRD4 subgroups did not differ significantly with respect to gender, age, symptoms of depression, reaction time for correct answers, number of errors, and number of trials without artefacts per condition . The severity of ADHD symptoms as assessed with the ADHD Self-Report Scale (ASRS) differed between DAT1 subgroups, with increased values for the 9R group compared to the 10/10R group (t(158) = 2.66, p = .009; see Participants were stratified into a homozygous Participants completed an 18 item screening questionnaire We used a modified version of the Eriksen Flanker Task Event-related potentials were recorded from 26 Ag/AgCl scalp electrodes. Besides the recording sites specified in the 10–20 system, electrodes were placed on Oz, Fpz, under the right eye and on its outer canthus, and on the left and right mastoids. Impedance was kept below 5 kΩ for all electrodes. The ground electrode was placed between Fz and Fpz. Sampling rate was 1000 Hz, with the amplifier band pass filter set to 0.1–70 Hz and the notch filter set to 50 Hz. All data were recorded in relation to a midline reference placed between Cz and Fz and re-referenced offline to an average reference.SD  = 33.01) epochs and for correct responses, an average of 260.80 (SD  = 52.29) epochs were averaged.Eye movement artefacts were corrected Baseline correction based on the mean amplitude from −200 ms to 0 ms was implemented, and the time windows to detect ERN and Pe peaks were subsequently determined based on the grand average time curve over all subjects. The ERN was then automatically identified as the negative peak value between −35 ms and 108 ms over the electrode position Cz; the Pe was analogically detected as the positive peak value between 110 ms and 450 ms.DAT1 (9R group vs. 10/10R group) and DRD4 (no 7R vs. 7R)). Two-sided t-tests were used for post-hoc analyses. For all analyses, p-values below .05 were considered significant.ERP amplitudes were analysed separately for the ERN and the Pe by using an analysis of variance (ANOVA) with the factors condition  and genotype (DAT1 VNTR was performed by polymerase chain reaction (PCR) and subsequent gel electrophoresis as published previously DRD4 VNTR was accomplished using standard PCR procedures modified from a previously published protocol Genomic DNA was extracted from whole blood samples by salt precipitation according to standard protocols. Genotyping of the F  = 90.25, p<.001; post-correct responses: M = 452.21 ms, SD = 56.41; post-error responses: M = 476.90 ms, SD = 68.01), showing significant post-error slowing across all genotype groups. There was no main effect of DAT1 genotype  or DRD4 genotype  and no interaction effects.There was a main effect for response time following an erroneous as compared to a correct response (SD = 51.13). There was no main effect of DAT1 genotype  or DRD4 genotype  as well as no interaction effects.Participants gave an average of 267.87 correct responses  with incorrect responses leading to more negative values than correct ones and an interaction effect of condition and DRD4 genotype , which is discussed below. We did not find an interaction effect of condition and DAT1 genotype , or a three-way interaction effect of condition, DAT1 genotype, and DRD4 genotype . In addition, no main effects of DAT1 genotype  or DRD4 genotype  were found.For the ERN, we found a main effect of condition  = −2.18, p = .031; see M, SD, and post-hoc t-tests; The significant interaction effect of condition and F = 197.70, p<.001) with incorrect responses leading to more positive values than correct ones and an interaction effect of condition and DAT1 genotype , which is discussed below. We did not find an interaction effect of condition and DRD4 genotype  or a three-way interaction effect of condition, DAT1 genotype, and DRD4 genotype . Furthermore, no main effects of DAT1 genotype  or DRD4 genotype  were found.For the Pe, we also found a main effect of condition (9R carriers (t(158) = −1.97, p = .051; see 9R carriers (t(158) = 1.77, p = .079; see The significant interaction effect can be described by marginally smaller difference amplitudes between the correct and incorrect response conditions in DRD4 genotype but not to their DAT1 genotype, whereas the reverse was true for the Pe amplitude. It therefore seems that the DRD4 genotype influences the ERN – defined as the difference wave between incorrect and correct responses – but not the Pe. In turn, DAT1 genotype seems to influence the Pe – also defined as the difference wave – but not the ERN.We found the ERN amplitude to be related to participants' According to the model by Holroyd and Coles 7R carriers could result in compensatorily elevated tonic dopamine levels in the striatum. This elevation in tonic striatal dopamine would make 7R carriers less sensitive to changes in phasic dopamine transmission, which could explain their reduced ERN amplitude. A similar argument was proposed by Krämer and colleagues DRD4 SNP -521C/T. However, while the impact of this SNP on gene expression is still under debate Based on Bilder and colleagues' 7R allele 7R carriers.The results can also be supported from a clinical perspective: ERN amplitude has been connected to self-reported impulsivity with highly impulsive individuals showing lower amplitudes DAT1, our findings seem to be at odds with a study in children that found smaller Pe amplitudes in 10/10R carriers 10R allele has been associated with childhood ADHD 9R allele was associated with persistent ADHD and worse cognitive functioning, respectively.Regarding 9R haplotype which showed significantly higher DAT expression than all other investigated haplotypes 9R carriers could mainly be caused by this specific subgroup. It might therefore be interesting and more informative to investigate Pe amplitudes in participants carrying this haplotype and compare them to all other haplotypes.In addition, a recent SPECT study reported a The findings of van de Giessen and colleagues d = .38 were found for the ERN amplitude depending on participants' DRD4 genotype and of d = .32 for the Pe amplitude depending on participants' DAT1 genotype. A post-hoc power calculation (two-tailed) revealed a probability of detecting a true significant difference of 58 and 50 percent, respectively. For the non-significant findings, effect sizes were d≤.06, indicating that these results represent non-meaningful and practically irrelevant effects.Limitations of the present study are linked to the sample size: Although representing a rather large sample in neurophysiological genetic research, power considerations arise from a general genetic research perspective. The sample size seemed sufficient assuming an intermediate effect size, and effect sizes of Cohen's DAT1 and DRD4 groups are very comparable with regard to demographic data, psychiatric symptoms, reaction time, and artefact-free trials. The only group difference was found for the DAT1 9R and 10/10R groups with regard to their symptoms of ADHD. This is in line with the current literature Furthermore, it would have been interesting to investigate gene-gene interactions. However, this procedure would have resulted in four – partly very small – subgroups, which would likely obscure the effects. Even though this could therefore not be implemented, both our Although we did not find any results on the behavioral level, our study is able to link previously observed error processing deficits in impulsive and ADHD participants to genetic variants that are known to contribute to these disorders.


We used discriminant function analysis to examine how well δ13C and δ15N predict female post-nesting migration destination. The discriminant analysis classified correctly the foraging ground used for all but one individual and was used to predict putative feeding areas of untracked turtles. We provide the first documentation that the continental shelf of the Mid- and South Atlantic Bights are prime foraging areas for a large number (61%) of adult female loggerheads from the largest loggerhead nesting population in the western hemisphere and the second largest in the world. Our findings offer insights for future management efforts and suggest that this technique can be used to infer foraging strategies and residence areas in lieu of more expensive satellite telemetry, enabling sample sizes that are more representative at the population level.In recent years, the use of intrinsic markers such as stable isotopes to link breeding and foraging grounds of migratory species has increased. Nevertheless, several assumptions still must be tested to interpret isotopic patterns found in the marine realm. We used a combination of satellite telemetry and stable isotope analysis to (i) identify key foraging grounds used by female loggerheads nesting in Florida and (ii) examine the relationship between stable isotope ratios and post-nesting migration destinations. We collected tissue samples for stable isotope analysis from 14 females equipped with satellite tags and an additional 57 untracked nesting females. Telemetry identified three post-nesting migratory pathways and associated non-breeding foraging grounds: (1) a seasonal continental shelf–constrained migratory pattern along the northeast U.S. coastline, (2) a non-breeding residency in southern foraging areas and (3) a residency in the waters adjacent to the breeding area. Isotopic variability in both δ The movement of organisms in space and time defines their interaction with the environment and, thus, constitutes a central aspect of their ecology and evolutionary biology Conserving migratory species has become a profound issue in the twenty-first century as habitats worldwide are being reduced in size or quality 15N relative to their food and, consequently, δ15N measurements serve as indicators of a consumer’s trophic position , while δ13C values vary little along the food chain and are mainly used to identify location Our understanding of the ecology and evolution of migrating organisms has been impeded by the inability to observe directly their long distant movements. However, recent advances in satellite telemetry, genetic analysis and stable isotope analysis are unraveling geographical origin, movement patterns and foraging behavior of individual organisms. Until recently, tracking migratory animals involved the use of passive extrinsic markers . In the last decade, stable isotope ratios have been increasingly used as intrinsic markers to trace foraging habits and movements of wildlife populations. Individuals that use geochemically different habitats, or feed on different resources, can be differentiated through use of stable isotope analysis because the isotopic profile of consumers reflects that of their prey in a predictable manner 13C and lower δ15N values in temperate than in higher-latitude ecosystems Isotopic signatures may be influenced by diet, habitat type and geographic location. Differences among and within oceanic regions in nutrient cycling at the base of the food web produce geographical gradients in carbon and nitrogen isotope composition Caretta caretta, L.) are highly migratory organisms with a complex life cycle. Loggerheads exhibit weak connectivity  identified key foraging grounds used by female loggerheads nesting in Florida and (2) examined the relationship between stable isotope ratios and the location of nonbreeding foraging areas. This is the first study integrating satellite telemetry and stable isotope analysis to investigate migratory strategies used by loggerhead females in the Atlantic Ocean. If loggerhead isotopic signatures from distinct foraging areas differ significantly, stable isotope analysis may be considered a viable alternative to satellite telemetry for denoting migratory patterns in the NW Atlantic, as found elsewhere The animal use protocol for this research was reviewed and approved by the University of Central Florida Institutional Animal Care and Use Committee (IACUC protocol #09–22W). Procedures were approved under the Florida Fish and Wildlife Conservation Commission (Marine Turtle Permit #025).st Century highlights the need to identify key foraging grounds and oceanic hotspots to develop informed management plans for the recovery of the species Loggerheads are highly migratory organisms with a complex life cycle where different life stages occupy different ecological environments. They typically switch from an initial oceanic juvenile stage to one in the neritic zone, where maturity is reached. Breeding migrations are subsequently undertaken every two to three years Blood samples were collected for stable isotope analysis from turtles nesting within the 21 km stretch of beach of the Archie Carr National Wildlife Refuge (hereafter Carr NWR) located in southern Brevard County on Florida’s east-central coast. This area hosts the most important loggerhead rookery in the western hemisphere and accounts for approximately 25% of all the loggerhead nests in Florida Between 2008 and 2010, we attached satellite transmitters  to 14 female loggerheads and tracked their post-nesting migration . Half ofTo investigate the relationship between foraging areas identified by telemetry and isotopic signatures of female tissues, we calculated average latitude and longitude of foraging grounds. We define foraging ground as the area where an individual loggerhead resides during the nonbreeding season and migration as the movement between foraging areas . This assumption is commonly used in studies combining telemetry and stable isotope analysis 13C and δ15N groupings and distinct post-nesting migratory destinations, our study will provide further evidence supporting foraging ground philopatry in most adult loggerhead females.Blood samples (4 ml) were collected from the cervical sinus with a 20-gauge needle and syringe 2 and CO2 with an elemental analyzer  and analyzed with a continuous flow isotope ratio mass spectrometer . Isotopic reference materials were interspersed with samples for calibration. Stable isotope ratios were expressed in conventional notation as parts per thousand (‰) according to the following equation:X is 15N or 13C, and R is the corresponding ratio 15N:14N or 13C:12C. The standards used for 15N and 13C were atmospheric nitrogen and Peedee Belemnite, respectively. Precision was 0.07‰ for δ13C measurements and 0.11‰ for δ15N.Sample preparation was done at the Biology Department of the University of Central Florida. Samples were prepared following standard procedure. RBC samples were freeze-dried for 48 h before being homogenized with mortar and pestle. Lipids were removed using a Soxhlet apparatus with petroleum ether as solvent for 12 h. Approximately 0.5 mg of each sample was weighed and sealed in tin capsules. Prepared samples were sent to the Stable Isotope Core Laboratory at Washington State University, where they were converted to N13C and δ15N and mean latitude of foraging ground and distance from shore were explored through multiple regression analysis. Akaike’s Information Criteria (AIC) was used to determine the best fitting regression Relationships between δ13C and δ15N predict the post-nesting foraging grounds used by loggerheads. We used δ13C and δ15N values of the 14 females equipped with satellite tags as training data set  to develop the discriminant functions and the untracked turtles as test data set for the discriminant classification. Untracked turtles are defined as females that were sampled for stable isotope analysis but that were not equipped with satellite tags. Data were analyzed using program R (R Development Core Team 2009), SPSS v. 19, Sigma Plot 10.0 and ArcGIS 10.0. Alpha level was set to 0.05 for all statistical analyses.To test for significant differences in isotopic signatures among foraging areas, we used multivariate analysis of variance (MANOVA) with the Pillai’s trace test. Data were tested for normality and homogeneity of variance using Kolmogorov-Smirnov and Levene’s test, respectively. Data were normal but did not meet the equal variance assumption even after transformation. We chose the Pillai’s trace test because it is the most robust of the tests when the assumption of similar-covariance matrix is not met Loggerheads moved across a wide range of latitudes spanning from the Great Bahamas Bank (23°N) to the offshore waters of Virginia and Delaware (38.6°N). Satellite telemetry identified three migratory pathways and associated foraging grounds : (1) a sAt the end of the nesting season, six individuals departed eastern central Florida and migrated north to seasonal foraging grounds above 35°N in the Mid-Atlantic Bight where they spent the rest of the summer and beginning of fall . By the 13C values of RBCs from tracked female loggerheads ranged from −17.50 ‰ to −10.48 ‰, and δ15N varied between 5.46 ‰ and 14.00 ‰. The multiple regression analysis and AIC model selection revealed that average latitude alone was the best predictor of δ13C values in female tissues for both winter . Likewise, winter feeding area latitude was the best explanatory variable for δ15N .The δh winter  and summh winter  feeding 4, 22 = 4.147, p = 0.012) and, in univariate analysis, both δ13C  and δ15N values  differed among foraging aggregations  to 7.04±1.83‰ . Individuals residing in eastern central Florida exhibited intermediate values between northern and southern loggerheads in both δ13C (−15.35±0.13‰) and δ15N (10.62±0.19‰). Post hoc Games-Howell (GH) multiple comparison tests indicated that the northern aggregation δ13C differed significantly from the resident aggregation (p<0.001) and marginally from the southern (p = 0.054), while resident and southern aggregations did not differ from each other in δ13C (p = 0.222). δ15N signatures of loggerheads using southern foraging areas differed significantly from the northern aggregation (p = 0.013) and marginally from the resident (p = 0.058) group, while northern and resident aggregations did not differ from each other in δ15N (p = 0.336).Females from the three foraging areas segregated by their overall isotopic signatures  = 16.785, p = 0.002. After removal of the first function, the association between groups (foraging areas) and predictors (δ13C and δ15N) became not significant Χ2 (1) = 0.867, p = 0.352. The first discriminant function accounted for 97.6% of the between-group variability. Overall the discriminant analysis of the training data set was able to correctly classify the foraging ground used for all but one individual . The only misclassified loggerhead was assigned to the resident aggregation, while satellite telemetry indicated this loggerhead belonged to the southern aggregation as it migrated to the SE Gulf of Mexico. The stability of the classification procedure was checked by a leave-one-out cross validation, which classified 92.9% of the test data set correctly. In the untracked females, RBC δ13C ranged from −19.36 ‰ to −9.72 ‰ and δ15N varied between 2.79 ‰ and 14.00 ‰. Putative foraging ground was predicted for 57 untracked turtles in the test data set and was based on the above classification functions. The discrimination analysis assigned 15 of the 57 untracked individuals (26.3%) to the northern aggregation, 20 females (35.1%) to the resident group and 22 females (38.6%) to the southern aggregation  was significant (P> Wilks’ Lambda <0.002). Two discriminant functions were calculated, with a combined Χregation , Table 4Our telemetry data identified new foraging areas used by female loggerheads of the NWA Florida Peninsular Recovery Unit. Six of the 14 individuals we tracked moved north and four resided in eastern central Florida, demonstrating for the first time that the Mid- and South-Atlantic Bights, respectively, provide important foraging grounds for adult females of this Recovery Unit. This result is a major difference from the results of prior satellite tracking studies. Overall there are published tracking data for 47 females of the NWA Florida Peninsular Recovery Unit The Mid- and South- Atlantic Bights are known to be important foraging areas for adult females of the NWA North Recovery Unit, which comprises loggerheads nesting from the Florida/Georgia border to southern Virginia Prior to our study, the documentation that adult females of the NWA Florida Peninsular Recovery Unit used Mid- and South- Atlantic Bights were limited to few flipper tag returns We can think of three plausible explanations for the novelty of our tracking data: (1) the high use of Mid- and South- Atlantic Bights may be a new phenomenon, (2) sample size of telemetry studies is small and our results, as well as prior studies’, may be due to chance, (3) Mid- and South- Atlantic Bights have always been important foraging grounds for the Florida Peninsular Recovery Unit but the importance was not detected with prior technology such as flipper tag return. Even though considerable progress has been made into understanding sea turtle migration using recovery of flipper-tagged individuals 13C and δ15N allowed us to identify three distinct foraging aggregations. Four gradients from enriched to depleted δ13C in marine habitats 13C we observed: (1) nearshore/offshore, (2) benthic/pelagic, (3) enriched/depleted δ13C food webs and (4) low/high latitudes.The variability we found among individuals in both δ13C are due to a neritic/oceanic gradient because all the loggerheads we tracked stayed on the continental shelf (within the 200 m isobaths), thus in neritic habitat. Our data did not allow testing the benthic/pelagic gradient because we only have dive profile data for four (of the 14) loggerheads we tracked. Bathymetry is not a good proxy to investigate the benthic/pelagic gradient because individuals may use the water column differently and these differences can only be detected if diving profiles are available. Adult loggerheads are known to feed mostly on benthic invertebrates such as crabs and mollusks 13C among loggerheads. The benthic/pelagic and the enriched/depleted food web gradients are tightly connected. Benthic organisms will most likely feed on seagrass or algae-based webs that are enriched in δ13C compared to pelagic environment based on phytoplankton food webs 13C is the latitudinal gradient. Latitudinal differences in δ13C are due to temperature, surface water CO2 concentrations and differences in plankton biosynthesis or metabolism 13C isotopic values of our satellite-tracked loggerheads, with northern individuals being more depleted in 13C, support the conclusion that a latitudinal gradient is the main driver of the variation in δ13C we observed. This conclusion agrees with previous studies in several marine taxa  loggerheads at different latitudes forage at different trophic levels, (2) the differences in RBC δ15N are a consequence of primary producers’ baseline shift in nitrogen values associated with prevailing N cycling regimes that are maintained and amplified higher up the food chain and (3) a combination of the two hypotheses. The nitrogen stable isotope ratios of primary producers define the δ15N value at the base of the food web and are a function of the δ15N values of their nutrient sources , subsequent biological transformation  and isotopic fractionation 15N support a gradient in the NWA, with δ15N values becoming progressively more enriched from the subtropics as we move north along the U.S. coastline  has δ15N values ranging from 9.74 to 10.28 ‰ (10.07±0.29‰), while the second group (n = 3) δ15N values range from 13.77 to 14‰ (13.87±0.12‰). These values suggest that females of the two clusters forage at different trophic levels. Despite previous paradigms that all turtles are benthic foragers, we suspect that the depleted group has a diet based mostly on jellyfish, while the enriched group forages mostly on benthos (crustacean and mollusks). These conclusions are supported by video footage of loggerheads foraging on sea scallop beds in the Mid-Atlantic . Intraspecific variability in foraging preference in adult female loggerheads has been demonstrated using series of scute samples 15N between the two groups may reflect an anthropogenic effect. Recently McKinney et al. 15N of particulate matter available to primary producers from estuaries (more enriched) to nearshore (average 30 km offshore) to mid-shelf (average 90 km offshore) in six locations at the same latitude (in the Mid Atlantic Bight). Our two groups of northern females also followed this pattern, with the enriched group residing an average of 17 km from shore (range = 10–29 km) and depleted group 71 km (range = 67–76 km) from shore. Thus, both groups may forage at the same trophic level and the differences in δ15N may be attributed to agriculture runoff and anthropogenic waste that increase δ15N in nearshore compared to mid-shelf ecosystems There also may be some individual variability in foraging preference, as reflected in our data on females using northern feeding areas. Within the northern aggregation, our δOur use of the isotopic patterns identified in the 14 loggerheads equipped with satellite tags to assign putative post-nesting migration destinations of the remaining 57 untracked females allowed us to scale up the information obtained with satellite telemetry, gain a better idea at the population level and begin to understand relative importance of foraging grounds. Telemetry and assignment results were similar and highlighted a similar relative importance of foraging grounds. However, it should be noted that while telemetry results were obtained over the course of several years , all the untracked turtles analyzed were sampled in 2010. Therefore, our analysis does not take into consideration remigration interval, which may affect the relative importance of each foraging area on a year-to-year basis.15N to be informative in the Mediterranean, our study in the NW Atlantic, as well as Hatase et al. 13C and δ15N to assign post-nesting migration destinations. Interestingly, Hatase et al. 13C and δ15N to be caused by a neritic/oceanic gradient, while we found them to be associated with a latitudinal gradient. Therefore, while we support the use of stable isotope analysis in lieu of more expensive satellite tags, we emphasize the need to validate the use of isotopic signatures with satellite telemetry on a subsample of individuals because oceanographic processes that affect baseline stable isotope ratios differ among ocean basins and geographical regions and, thus, data interpretations without validation can be misleading.Several authors The Carr NWR hosts approximately 25% of all the nests laid by the NWA loggerhead Florida Peninsular Recovery Unit, which in turn makes up the greatest majority of the NWA female population. Therefore, to identify key foraging areas used by females nesting at Carr NWR is particularly important for the persistence of the species as a whole. Using a combination of satellite telemetry and stable isotope analysis we not only identified prime foraging areas -whose importance was previously unknown- but also validated the use of stable isotope analysis as a tool to derive post-nesting migration destinations for the most important breeding aggregation of this Recovery Unit. We provided the first documentation that the continental shelf of the Mid- and South Atlantic Bights offer essential foraging areas for a large number (61%) of adult female loggerheads of the NWA Florida Peninsular Recovery Unit. These same areas have been found to be extremely important for loggerheads of the NWA Northern Recovery Unit sensu Norris After validating stable isotope analysis with satellite tracking, we suggest using isotopic signatures to assign turtles to foraging regions to scale up knowledge obtained from a limited number of individuals equipped with satellite tags to sample sizes that are more representative at the population level. Regular monitoring of foraging locations for nesting females will open new opportunities to investigate carry-over effects . Phases of migration are represented by rapid changes in displacement distance; summer and winter foraging areas can be seen where displacement values plateau. Note differences in y-axis scale among (TIF)Click here for additional data file.Figure S2Displacement from release site plot of loggerheads equipped with satellite tags that resided in eastern central Florida (turtle g–j).(TIF)Click here for additional data file.Figure S3Displacement from release site plot of loggerheads equipped with satellite tags that followed the southern strategy and took up year-round residence in southern foraging grounds (turtle k–n). Phases of migration are represented by rapid changes in displacement distance. Year-round foraging areas can be seen where displacement values plateau.(TIF)Click here for additional data file.


Km, kcat, Ki values, enzyme half-life, product•enzyme dissociation constant, and the rate constant for the reversed reaction) has been developed. This tool provides comparison of the progress of uninhibited versus inhibited reactions for common inhibitory mechanisms, and guides the tuning of reaction conditions. Possible applications include: analysis of substrate turnover, identification of the point of maximum difference in product concentration (Δmax[P]) between inhibited and uninhibited reactions, determination of an optimal observation window unbiased for inhibitor mechanisms or potency, and interpretation of observed inhibition in terms of true inhibition. An important observation that can be utilized to improve assay signal strength and resolution is that Δmax[P] occurs at a high degree of substrate consumption (commonly >75%) and that observation close to this point does not adversely affect observed inhibition or IC50 values.A difficulty associated with high throughput screening for enzyme inhibitors is to establish reaction conditions that maximize the sensitivity and resolution of the assay. Deduction of information from end-point assays at single concentrations requires a detailed understanding of the time progress of the enzymatic reaction, an essential but often difficult process to model. A tool to simulate the time progress of enzyme catalyzed reactions and allows adjustment of reactant concentrations and parameters (initial concentrations,  With low substrate concentrations it often becomes necessary to allow reactions to proceed until a large proportion of substrate becomes depleted in order to obtain sufficiently high signals (i.e. a high S/B ratio). While such extended incubation times may obscure the effect of weak inhibitors, shorter incubation times give weaker signals that may adversely affect assay performance. Different modes of inhibition (e.g. uncompetitive and non-competitive) further complicates data interpretation and assay design. A further difficulty is that the underlying theory, which is based on rate-law equations for initial reaction velocity, becomes violated at extended reaction times and thus complicates data interpretation, particularly the relation between observed and true inhibitor potency A common experimental condition in HTS for enzyme inhibitors is to use low substrate concentrations ( equation 1). In practice, initial reaction rates can only be approximated since the real measurable quantity represents a concentration at a given time-point . With small enough time intervals, which is commonly used when determining kinetic parameters, the approximation improves, and for many experiments this is not a problem. However, conditions such as those commonly applied to HTS for enzyme inhibitors often violate this approximation and make interpretations based on the MM equation for initial reaction velocity less reliable. Furthermore, such assays are often associated with a high enough level of substrate turnover to render the phenomenon of product inhibition  significant, thus complicating interpretation of observed inhibition further. Consequently, interpretation of data from experiments such as HTS, as well as the design of HTS assay conditions, should ideally be founded on progress curve analysis. Since the MM rate law cannot be analytically integrated to explicitly express product concentration as a function of time and in terms of catk and Km, this has to be achieved by numeric approaches In experimental deduction of kinetic parameters, the initial reaction rate at different substrate concentrations is measured and data obtained fitted to the Michaelis-Menten (MM) rate law equation (Simulation Tool S1), or obtained from the author. Reaction variables  and parameters , enzyme half life) can be adjusted and the effects of entered values are directly coupled to graphs displaying the formation of product as a function of time ( & S1). The modes of inhibition included are; competitive (inhibitor·enzyme dissociation constant Kic), uncompetitive (inhibitor·enzyme dissociation constant Kiu), and mixed inhibition . This allows for non-competitive inhibition to be accounted for by setting the two inhibitor·enzyme dissociation constants for mixed inhibition to equal values (i.e. Kic = Kiu). The graphs also display the difference in product concentration between inhibited and uninhibited reactions (Δ[P]) as a function of time for the different types of inhibition, which is particularly useful for estimation of when the maximum difference in product concentration (Δmax[P]) occurs between uninhibited and inhibited reactions. For simple comparison, the time progress of Δ[P] is also shown in a separate graph for all three types of inhibition (P] as a function of inhibition (%) as the reaction proceeds, and Δ[P] as a function of the degree of substrate conversion .A tool in spreadsheet format in which progress curves of inhibited and uninhibited reversible enzyme reactions can be interactively adjusted and compared for various types of inhibition was developed. The tool can be downloaded as supplementary material  at that point, the associated amount of substrate conversion (%), and the value of Δmax[P] (µM) are given . There is also a possibility to directly enter specific time-points to see the resulting Δ[P], the percentage substrate conversion, and the degree of inhibition (%). Entered time points are coupled to two graphs displaying the degree of inhibition (%) as a function of time and substrate conversion (50) as a function of substrate consumption (Keq = VfKmb/VbKmf) is automatically deduced.Key data are extracted from the curves and presented in table format. For each type of inhibition the time point of Δnversion Fig. 2. S] = 2Km and [I] = 2Kic) and competitive inhibition the effect of different incubation times can be studied , Δ[P] is 19 µM, substrate conversion 24% (uninhibited reference reaction), and the observed inhibition 40%. Since the degree of inhibition is similar at these two points, but Δ[P] is more than doubled at Δmax[P], a time point closer to Δmax[P] is appropriate for read-out.Prior to experimentation, specific reaction conditions can be studied and compared by feeding different reaction parameters into the simulation tool. With a given set of conditions , the observed inhibition 32%, and substrate conversion 33%. Thus, the assay resolution becomes lower under these conditions.The effect of lowering substrate concentration to kcat = 1 s−1, Km = 1 mM and Ki = 200 nM), a good correlation between observed and simulated data was obtained; Δmax[P] was predicted to 1.23 mM and its time point to 77 minutes, which only deviates slightly from the observed Δmax[P] of 1.18 mM after 73–74 minutes. This demonstrates how a reasonable estimate of the progress curves can be directly obtained by using kinetic parameters pre-determined in an initial rate experiment, or based on literature values. It should be noted that full determination of kinetic parameters, inhibition mechanism, and error estimates, by progress curve analysis requires more data at different [S] and [I], as in initial rate experiments Km, the underlying rate constants, i.e. (k−1+kcat)/k1 = Km, remains undetermined if not other types of kinetic data is available. Furthermore, as for any method relying on progress curve analysis, the linearity and range of the response must be accounted for when interpreting and comparing experimental data with simulated data.Comparison with experimentally generated progress curves for LTA4H catalyzed peptide hydrolysis, with or without the competitive inhibitor bestatin, showed that simulated and experimental curves are in agreement. This suggests that predictions based on the simulation tool have significance Fig. 4. Km was determined to be 3.6 µM and kcat to be 0.43 sec−1 by progress curves analysis and to be 3.9 µM and 0.45 sec−1 by the initial rate method. (One reason for the successful determination of Km by the progress curve method was the possibility to use a relatively high [So] of ∼5 Km.) Comparing the experimentally observed Δmax[P] and the time point when it occurred, with the corresponding values predicted by the tool, gave deviations of only 0.17 µM (2%) and a 90 seconds (3%), respectively.To further evaluate the validity of the simulations, progress curves were also collected for another enzyme system, peptidolysis by presequence peptidase, with and without bestatin as an inhibitor Fig. 4. max[P] along with the associated time point, % Substrate, % Inhibition, and IC'50) that are automatically deduced in response to adjusted parameters. The corresponding data at defined time points can also be extracted by entering time points in the column headers of an adjacent table . This helps the user to identify an optimal window of observation. For each type of inhibition the corresponding reaction equations are given. Non-competitive inhibition is not directly included but can be accounted for setting Kic = Kiu, realizing that this is a special case of mixed inhibition.In the tool the user is presented to three differently colored blocks  in which reactions parameters and variables can be adjusted Fig. 5. Simulation Tool S1) or obtained from the author. The tool provides accurate simulation of experimental progress curves . The associated degree of substrate consumption is normally above 70% and is rather insensitive to changes in substrate and inhibitor concentrations. Furthermore, the observed inhibition does not significantly deviate from initial conditions until the substrate is almost completely depleted (>80%). An ideal point of observation should therefore be within a window of about 50–75% substrate consumption, which is in contrast to the common recommendation of <20% substrate depletion for determination of kinetic parameters.A general observation that emerges when using the simulation tool is that Δ50) as a function of substrate consumption  to true inhibition (IC50) at specific reaction conditions.Since interpretation of observed inhibition in terms of true inhibition can become confused at such high levels of substrate depletion, the tool clearly visualizes observed inhibition (%) and inhibitor potency . The fact that non-competitive and mixed inhibitors have two Ki values augmenting each other explains this effect. Consequently, identification of non-competitive and mixed inhibitors are generally favored.Comparing different modes of inhibition at corresponding reaction conditions indicates that non-competitive and mixed inhibition exhibit the largest Δ.As outlined above, an observation window close to the time point of Δvelocity Fig. 2, e.g. no more than 20 percent substrate conversion, or substrate conversion should be within the linear range, or substrate concentration must equal Km. Such rules may sometimes limit the successful design of experiments by giving low signal windows. Many of the rules that guide the set-up of HTS assays stem from a fear of violating MM conditions and the underlying assumptions for steady state kinetics. Comparative analysis of progress curves of uninhibited versus inhibited reactions helps to better understand when, and to what extent, these concerns should be accounted for and also helps in the final data interpretation. The tool presented here aids in this process and provides accurate simulations of experimental progress curves.In summary, HTS assays are often designed with a set of common rules of thumb in mind, Purified LTA4 hydrolase was a gift from Dr. Agnes Rinaldo Mattis, Karolinska Institute. Presequence peptidase was a gift from Prof. Elzbieta Glaser, Stockholm University. Mca-R-P-P-G-F-S-A-F-K(Dnp)-OH was from R&D Systems, UK. Alanine-4-nitroanlide and other standard chemicals were from Sigma-Aldrich, Sweden. equation 2) was numerically integrated according to Euler's method with an integration time step of 1 second ( equation 3). A function to estimate enzyme half life was also included as a mechanism-free model that accounts for enzyme inactivation by reducing its concentration with respect to its half-life ( equation 4). Because product inhibition and the reversed reaction may be prevalent as product accumulates, these phenomena were also taken into account in all rate equations ( equations 2 & 5–7). For inhibited reaction progress curves, the same approach was applied on the rate laws for the three common types of inhibition ( equations 5–7). Additional equations used in the simulation tool are shown in Equations S1 (equations 8–13).To simulate reaction progress curves expressing product concentration as a function of time, the reversible MM rate law for initial reaction velocity . Moreover, HTS assays are typically performed with [E] at orders of magnitude lower than [S]. A level with [S] approaching [E] is thus equivalent with almost complete substrate depletion and will therefore contribute very weakly to the overall reaction rate. For the reversed reaction, the equivalent condition is most pronounced at the very beginning of the reaction. However, since the product level at this stage is very low the overall contribution to the reaction rate will be small. Another reason to work with very low [E] is imposed by the fact that IC50 values lower than one-half of the [E] cannot be measured. Since compounds are typically screened at 1–100 µM it is common to work with [E] around 100 nM, which in most cases is much lower than [S].The underlying assumption is that the rapid equilibrium approximations holds true throughout the complete reaction and that the reactions are pseudo-first-order in  between inhibited and uninhibited reactions as a function of substrate conversion (left) or observed inhibition (right) for four types of inhibition: competitive (yellow trace), uncompetitive (green trace), non-competitive (orange trace), and mixed (blue trace). In the simulation tool, the graphs are directly coupled to user entered reaction parameters and variables. Entered reaction conditions were: [S] = Km = 0.25Kmp = 10[I] = 400[Eo] = 100 µM; [Po] = 0 µM; kcat = 0.5 s−1; enzyme t(1/2) = 24 hours; Kic = Kiu = Ki-non = 5 µM for competitive, uncompetitive, and non-competitive inhibition; and Kiu = 5Kic = 15 µM for mixed inhibition. Substrate conversion refers to the uninhibited reference reaction (left). Note the reversed x-axis (right).(TIF)Click here for additional data file.Figure S3Δ[P50 .] between inhibited and uninhibited reactions for competitive (yellow), uncompetitive (green), non-competitive (orange), and mixed (blue) inhibition as a function of IC' At initial reaction conditions, IC'50 equals IC50. In the tool, the graph is directly coupled to user adjustable reaction variables and parameters. Entered reaction conditions were: [S] = Km = 0.25Kmp = 10[I] = 400[Eo] = 100 µM; [Po] = 0 µM; kcat = 0.5 s−1; enzyme t(1/2) = 24 hours; Kic = Kiu = Ki-non = 5 µM for competitive, uncompetitive, and non-competitive inhibition; and Kiu = 5Kic = 15 µM for mixed inhibition.(TIF)Click here for additional data file.Figure S4Asymptotic behaviour of the Z-factor. The Z-factor is plotted as a function of the S/B ratio at different coefficients of variation (CV). The asymptotes are shown as horizontal dashed lines. Corresponding curves, asymptotes, and CV values are in identical colors. For a specific CV the Z-factor can only be improved by increasing the S/B ratio, with an upper bond defined by the asymptote.(TIF)Click here for additional data file.Figure S5Differences between progress curves generated from pseudo-first order and second order rate equations. Curves generated from the pseudo-first-order model are shown as thick lines and curves generated with the second-order model are shown as thin lines. A) Progress curves (solid lines) are plotted against the left Y-axis and the differences between the models (dotted lines) are plotted against the right Y-axis. Progress curves were generated by numeric integration of equation a and b for different Km values, as indicated in the graph. Other variables and parameters were as follows: [So] = 100 µM, [Etot] = 100 nM and kcat = 0.5 s−1. Differences between the two models are below 1% for the Km values tested. B) Progress curves  were generated by numeric integration of equation a and b for different values of [So], as indicated in the graph, and with other parameters as follows: Km = 20 µM, [Etot] = 100 nM and kcat = 0.5 s−1. Differences between the two models  are below 3% for the values tested. The results shown in A) and B) demonstrate that differences between progress curves generated from pseudo-first order and second order rate equations are small at conditions normally applied in HTS. The differences are of the same magnitude or smaller as experimental noise and should therefore only have a limited effect on the quality of predictions made by the tool. 1. Morrison JF (1969) Kinetics of the reversible inhibition of enzyme-catalysed reactions by tight-binding inhibitors. Biochim Biophys Acta 185: 269–286.(TIF)Click here for additional data file.Simulation Tool S1The simulation tool in Microsoft Excel binary format.(XLSB)Click here for additional data file.


We show that changing environmental colour from white to red with 1/f models, and from white to red or blue with AR(1) models, generates coloured environmental series that are not normally distributed at finite time-scales, potentially confounding comparison with normally distributed white noise models. Increasing variability of sample Skewness and Kurtosis and decreasing mean Kurtosis of these series alter the frequency distribution shape of the realised values of the coloured stochastic processes. These changes in distribution shape alter patterns in the probability of single and series of extreme conditions. We show that the reduced extinction risk for undercompensating (slow growing) populations in red environments previously predicted with traditional 1/f methods is an artefact of changes in the distribution shapes of the environmental series. This is demonstrated by comparison with coloured series controlled to be normally distributed using spectral mimicry. Changes in the distribution shape that arise using traditional methods lead to underestimation of extinction risk in normally distributed, red 1/f environments. AR(1) methods also underestimate extinction risks in traditionally generated red environments. This work synthesises previous results and provides further insight into the processes driving extinction risk in model populations. We must let the characteristics of known natural environmental covariates  guide us in our choice of how to best model the impact of coloured environmental variation on population dynamics.The colour of environmental variability influences the size of population fluctuations when filtered through density dependent dynamics, driving extinction risk through dynamical resonance. Slow fluctuations (low frequencies) dominate in red environments, rapid fluctuations (high frequencies) in blue environments and white environments are purely random (no frequencies dominate). Two methods are commonly employed to generate the coloured spatial and/or temporal stochastic  series used in combination with population  models: autoregressive [AR(1)] and sinusoidal (1/ There is considerable interest in the importance of coloured stochastic processes (sometimes termed “noise”) across a wide range of scientific disciplines, from engineering and physics to evolutionary ecology and genetics f) methods The colour of species’ responses to environmental variation has repeatedly been found to have an important impact on population extinction risk in simple, unstructured and more complex, structured dynamical models  noise is normally distributed (Gaussian), and comparison between different environmental colours is generally based on the implicit assumption that normality is retained as noise colour varies f coloured stochastic processes, comparing coloured series with normally distributed, white series. We show that coloured series tend to deviate from the normal distribution, which may have a confounding effect in studies using these methods. We then investigate population variability as a proxy for extinction risk in undercompensatory populations forced by environmental variation that either has a normal distribution for all colours, or where distribution shape varies with colour. We compare 1/f and AR(1) methods over a wider parameter space than previously studied for AR(1) noise We examine the frequency distribution of AR(1) and 1/ε) is found over consecutive time steps (t) as a function of the desired temporal autocorrelation φ (with mean 0 and standard deviation 1). The square root term is usually included to maintain a constant variance (over infinite series) independently of α to distinguish them from the value of the coefficient used to generate the series, A simple, first-order autoregressive model was used to generate AR(1) coloured environmental time-series as follows:f) environmental noise time-series were generated with the spectral synthesis method β) were generated and sent to an inverse fast Fourier transform. In order to generate these time series (tε), n random phases fθ were generated from a uniform distribution with limits , as well as n normally distributed random variables fω, with 0 mean and unit variance. To generate the amplitudes for a desired spectral exponent (fω) was multiplied by af. The complex coefficients (CC) were found as CC = fa exp(iθ), from which an inverse fast Fourier transform was taken. The real parts of this transform comprised the 1/f environmental noise time series (tε). The desired spectral exponent defining time series colour, was initially varied across 21 evenly spaced values between , producing blue (negatively autocorrelated) and strongly reddened, or brown (positively autocorrelated) noise, respectively. This range of spectral exponents can also be approximately generated with AR(1) methods. We also examined alternative methods for generating 1/f signals, including those that generate spatio-temporally structured coloured series Sinusoidal  and 1/f series, then tested the normality of each series with a Jarque-Bera test. This compares the sample skewness and kurtosis statistics against the null hypothesis of those from series that are normally distributed . We recorded whether or not each series failed the normality test at significance level a = 0.05.We generated 1,000 replicate series of f stochastic series also leads to a change in the distribution shape. White series are normally distributed (fail to reject the null hypothesis of the Jarque-Bera test), while reddened AR(1) or 1/f series tend not to be. There is an increasing probability that blue AR(1) series fail the normality test. These results were driven by changes in the variance of the sample skewness and kurtosis statistics with colour (f models (7 steps) and shorter (100 steps) series.f models . These qf methods generate non-normally distributed coloured series over finite time-scales, we used spectral mimicry X and Y, and reorders one series (Y) to generate a third series (Z) that approximates the temporal characteristics (colour) of the other (X). For each replicate here, a traditional coloured series (X) was generated as described above, with an independent, random series (Y) drawn from a standard normal distribution . Only random series, Y, that failed to reject the null hypothesis of a Jarque-Bera statistical test  were selected for further use. The elements of X were ranked in increasing value, with their order statistics recorded from the original series. Series Z is then generated from Y “by replacing each element of Y by the corresponding order statistic of X.”  and 1/c of X.”  p. 433. ned here .ε = X) were generated with T = 10,000 steps for each desired value of ε = Z) were generated for each replicate using spectral mimicry. All series were rescaled to zero mean and desired variance at the given time scale, following the methods set out in εσ2 = 0.01, 0.1 and 0.5, to investigate any interaction between the size of environmental fluctuations and the non-linear deterministic population model . These analyses demonstrate that previous results based on traditionally generated AR(1) methods, showing changes in the probability of single or series of extreme events with colour f methods. Single extreme events do not become less likely as the environment reddens  if coloured series are controlled to be normally distributed. Likewise, series of extreme events do not become less likely in red environments . These series were used to force a simple population growth function, the commonly used discrete-time theta-logistic (Ricker) function, which models population density (N) over consecutive time steps (t) as.r is the intrinsic growth rate (r = 1.5), K is the carrying capacity  and b describes the shape of density dependence (b = 0.1). These parameter values result in undercompensatory (slow) population dynamics, allowing comparison with previous work  or 1/f processes, or through spectral mimicry based on random, Gaussian processes as described above.Traditional and ‘control’ AR(1) or 1/see also . The poptN+1 as the expected value of a Poisson random process to model demographic stochasticity and explicit extinction events, coupled with stochastic fluctuations entering through the carrying capacity, tK = K0+ tεtKtK≥0 to avoid biologically unfeasible  dynamics. This earlier work considered environmental fluctuations with very high variance, leading to high probabilities of negative tK values unless truncated. For example, the cumulative probability of tK≤5 is ∼0.07 in coloured series with K0 = 100, εσ2 = 4140 , assuming a normal frequency distribution. To avoid these issues, we considered the more general case where environmental variation affected per capita growth rate (pgr) additively and recorded the Coefficient of Variation of population fluctuations, NCV = Nσ/Nµ. While this did not generate explicit extinction events across the range of εσ2 values considered here, results based on NCV captured important features of those models based on traditional methods of generating environmental fluctuations that incorporated explicit extinctions. Therefore, NCV is used here as a proxy for extinction risk. While other methods exist for estimating population extinction risk (reviewed in NCV), as this is easily obtained from and commonly used in empirical time series analysis Previous work has used α) or spectral exponents (β) from each environmental time-series, rather than the desired (input) values  autocorrelation coefficients ≥0.1] generated with traditional methods, environmental reddening initially leads to an increase, followed by a decrease in the size of population fluctuations (NCV) for both 1/f and AR(1) methods  = 0.01] in both AR(1) and 1/f models.When the deterministic undercompensatory population model  is force methods . This cof environments and a relatively small decline under very red AR(1) environments. Extinction risk was slightly overestimated in blue environments (β → 1) generated with traditional methods  from white to pink environments in all cases. The decrease in NCV under intermediate and strong (εσ2≥0.1) traditional pink to red environments occurs as Nσ declines, despite the simultaneous decrease of mean population density in red 1/f environments and asymptote of Nµ in red AR(1) environments. No such declines in Nσ are present in pink to red environments controlled to have a normal distribution (Differences in N and µN : σN incrribution .K = 100) when εσ2≥0.1 (per-capita growth rates decline rapidly from high densities (tN>K) but increase relatively slowly from very low densities (tN<K).While mean population density tends to increase with environmental reddening, median densities are generally below the carrying capacity  series cause underestimation of extinction risk in reddened environments through changes in the distribution shape of the environmental signal, rather than colour f methods for generating coloured stochastic  series also tend to produce coloured series that are not normally distributed over finite lengths , even though they do generate normally distributed white series. These changes in distribution shape confound the effect of colour on population dynamics in unexpected ways, leading to an underestimation of extinction risk in red (slowly changing) environments.We have shown here that traditional AR(1) and 1/N;CVUsing only normally distributed environmental series removes the confounding effect of two contrasting components of environmental variability present in very red environments generated with traditional methods: the patterns in the probability of single and series of poor conditions with environmental reddening , Fig. S1f environmental models. Results presented here illustrate that (i) contrary to previous predictions (β>1.5) and (ii) these reduced extinction risks are largely driven by changes in frequency distribution shape, rather than environmental reddening per se. The second result is confirmed by modelling normally distributed environmental fluctuations with the spectral mimicry method Cuddington and Yodzis dictions , environtφ is arbitrary in the AR(1) generating method  processes. Do these particular differences result in qualitatively different effects when filtered through density dependent [AR(1)] population dynamics? Results here suggest any qualitative differences are reduced, or disappear, when normally distributed fluctuations are filtered through undercompensating population dynamics . This does not imply that model results based on longer time-scales are not relevant, however. Empirical data limitations should not be confused with long-term natural population behaviours.AR(1) and 1/dynamics . Many ofThe power-law relationship between temporal lags and autocorrelation coefficients has been suggested as a proxy for the memory of a time series, another potential factor that can help explain persistence time and the pattern of time-series fluctuations Other model assumptions can also make comparison between studies awkward. For example, the form of the deterministic population model can have important effects, particularly under the influence of relatively strong environmental variability. The theta-Ricker model we used here has also been used in earlier studies on the impact of coloured noise The probability and frequency of catastrophic events is of great relevance to conservation biology. Catastrophic events can be thought of as representing the ‘tails’ of a distribution of population or environmental fluctuations α|, |β| → 0).The structure of stochastic  variation has implications across a variety of areas within population biology and beyond Further research is needed to fully understand the mechanisms driving extinctions in natural populations and the importance of coloured noise filtering through biological processes to drive population fluctuations. Results here show that previously reported patterns of extinction risk in density dependent population models can arise as an artefact of changes in the distribution shape of environmental fluctuations, rather than environmental colour. We can now interpret previous and future theoretical results in a new light, accounting for the effects of changes in the underlying distribution of environmental covariates as well as the environment’s temporal structure.Figure S1Skewness and Kurtosis measures from  AR(1) and  1/f coloured stochastic series . Reddened series  show an increased variance in both Skewness and Kurtosis values (blue line = mean), with a reduced mean Kurtosis for very red and blue AR(1) and pink to red 1/f models. AR(1) models also show increased variance for Kurtosis under blue noise (α<0).(PDF)Click here for additional data file.Figure S2Comparing the expected  and observed  colour statistics  in stochastic series generated using 1/f (left column) and AR(1) (right column) models. Each black point represents the relationship between expected and observed colour statistic for a single replicate. The blue line shows the 1∶1 relationship.(PDF)Click here for additional data file.Figure S3The probability of single and runs of n extreme values (tε≤−2.5) occurring in AR(1) and 1/f coloured environmental series varies with environmental reddening , for 21 values of α between the limits  or β∼.  Probability of a single value tε ≤ –2.5 in coloured series scaled to εσ2(T∞) = 1 (solid lines) or εσ2(T500) = 1 (dashed lines) in a 500 step sequence . Panels (c–f) show the probability of finding n =  consecutive values of tε ≤ –2.5 in a 500 step sequence scaled to εσ2(T500) = 1 using  traditional or  spectral mimicry methods.(PDF)Click here for additional data file.Figure S4Per-capita growth rates for two different population models with the same carrying capacity (K = 100). Based on (A) the original parameter values for the theta-Ricker model  or MSS model by Schwager et al.  and (B) parameter values chosen to maintain identical behaviour around the equilibrium point for both models: theta-Ricker , MSS . Scaling parameter values to give identical dynamics around the equilibrium does not ensure that dynamics will be similar elsewhere in the population phase space.(PDF)Click here for additional data file.Text S1(DOC)Click here for additional data file.