Hitchhiking and severe bottleneck effects have impact on the dynamics of genetic diversity of a population by inducing homogenization at a single locus and at the genome-wide scale, respectively. As a result, identification and differentiation of the signatures of such events from DNA sequence data at a single locus is challenging. This paper develops an analytical framework for identifying and differentiating recent homogenization events at multiple neutral loci in low recombination regions. The dynamics of genetic diversity at a locus after a recent homogenization event is modeled according to the infinite-sites mutation model and the Wright-Fisher model of reproduction with constant population size. In this setting, I derive analytical expressions for the distribution, mean, and variance of the number of polymorphic sites in a random sample of DNA sequences from a locus affected by a recent homogenization event. Based on this framework, three likelihood-ratio based tests are presented for identifying and differentiating recent homogenization events at multiple loci. Lastly, I apply the framework to two data sets. First, I consider human DNA sequences from four non-coding loci on different chromosomes for inferring evolutionary history of modern human populations. The results suggest, in particular, that recent homogenization events at the loci are identifiable when the effective human population size is 50000 or greater in contrast to 10000, and the estimates of the recent homogenization events are agree with the “Out of Africa” hypothesis. Second, I use HIV DNA sequences from HIV-1-infected patients to infer the times of HIV seroconversions. The estimates are contrasted with other estimates derived as the mid-time point between the last HIV-negative and first HIV-positive screening tests. The results show that significant discrepancies can exist between the estimates. Hitchhiking and severe bottleneck effects have similar signatures on the population genome by reseting the molecular clock. However, their impacts at the genome level are on different scales. The hitchhiking effect has a local signature because recombination breaks down linkage disequilibrium between sites on the genome; consequently, the locus completely linked to a site under a positive selection becomes homogenous in the population After a recent homogenization event at a neutral locus, the accumulated genetic diversity at the locus and the elapsed time are positively correlated when assuming constant molecular clock. To quantify the relation between genetic diversity at the neutral locus in a low recombination region and the time elapsed since a recent homogenization event, Griffiths Simulation based inference methods have been developed for the same problem to include an exponential population growth model and full polymorphism data in samples of DNA sequences I consider the same setting as in Genetic diversity at a neutral locus, in a low recombination region, affected by a recent homogenization event is a result of mutations accumulated at the locus since the homogenization event. To model the dynamics of genetic diversity at such a locus after the homogenization event, this paper combines the infinite-sites mutation model and the Wright-Fisher reproduction model with constant population size. The parameters in the model represent the effective population size Variation in a sample of DNA sequences drawn from a population evolving according to this model can be described as a combination of genealogical and mutation processes. The genealogical process traces ancestral lineages of the sample back in time until the recent homogenization event at time Under the model described above, the probability distribution of the number of polymorphic sites Griffiths Lemma 1The moment generating functioncan be represented aswhereThe coefficients  are determined by the following recurrence relations with initial conditions:The prove of Lemma 1 is provided in the Note that the coefficients Expression (3) is used to derive expressions for the derivatives of MathematicaMathematica's ability of doing exact computations with fractions, as a result avoiding numerical instability issues. The program is available from the author on request.To derive a numerically stable expression for Note that when In previous studies Using the probabilistic framework developed above, three likelihood-ratio based tests are considered in this section for identifying and differentiating recent homogenization events at independently evolving multiple neutral loci in low recombination regions.To identify a recent homogenization event at a locus based on the number of polymorphic sites in a sample of DNA sequences, the hypothesis Note that Suppose we know, for example, from other studies, that a recent homogenization event occurred at time Based on this approximation, for each For a case of The following steps can be taken to infer the time To estimate a Homo sapiens (ancestors of modern humans) emerged in Africa between 150,000 and 200,000 years ago (kya) and dispersed to other regions of the world sometimes before 50,000 years before present (yr B.P.). Studies based on mitochondrial and Y-chromosome support this hypothesis Anthropological and archeological data strongly support “Out of Africa” hypothesis for the origin and evolutionary history of modern humans In contrast to this approach, I use the framework developed in this paper to analyze some of data sets used in the studies mentioned above. I apply the framework to DNA sequences from four non-coding loci  in low recombination regions on chromosomes 22, 17, X, and Y to identify and differentiate recent homogenization events associated with the “Out of Africa” hypothesis. The data sets are published in  yr B.P. . Thus, tTo explore another possibility, I also consider human effective population size In this case, the likelihood functions of the data sets would not change dramatically as For this set of parameter values, I use Test III to differentiate the recent homogenization events at the four loci. The results of the tests are in Usually, after few weeks of HIV infection, plasma viraemia in infected patient declines rapidly as a result of a primary immune response, which coincides with HIV seroconversion For consistency of the data sets with the infinite-sites mutation model and with no intra-locus recombination, the following conditions are checked: (a) Each polymorphic site is a result of a single mutation event, that is only two nucleotide states are possible at each polymorphic site. (b) All pairs of sites in sample of DNA sequences pass the four-gamete test I consider the following values for the parameters in the model: population size These estimates are contrasted with the estimates provided by Shankarappa et. al The observed disagreements are robust with respect to The analytical method developed in this paper is a trade-off between computational efficiency and complexity of the underlying evolutionary model. Using multi-locus DNA sequence data, the method allows identification and differentiation of the signatures of recent severe bottleneck and hitchhiking effects in a computationally efficient way. However, the method uses the number of polymorphic sites instead of full polymorphism data in samples of DNA sequences, and it is constrained by the assumptions of the constant size Wright-Fisher reproduction model and the infinite-sites model. In contrast, coalescent based simulation methods can be implemented at the cost of computational feasibility to include full polymorphism data To illustrate the behavior of the likelihood function for small and large  of  see  for a saComputational efficiency of the method gives an advantage to explore various values for the parameters in the model for assessing the impact of parameter values on the inference. The application of the method to the human data shows that when the effective human population size As the analysis of the human DNA sequences data shows the method developed in this paper does not have enough power to give an estimate for the effective human population size. Although the method suggest that very large values of Text S1(PDF)Click here for additional data file.


When studying the genetic structure of human populations, the role of cultural factors may be difficult to ascertain due to a lack of formal models. Linguistic diversity is a typical example of such a situation. Patrilocality, on the other hand, can be integrated into a biological framework, allowing the formulation of explicit working hypotheses. The present study is based on the assumption that patrilocal traditions make the hypervariable region I of the mtDNA a valuable tool for the exploration of migratory dynamics, offering the opportunity to explore the relationships between genetic and linguistic diversity. We studied 85 Niger-Congo-speaking patrilocal populations that cover regions from Senegal to Central African Republic. A total of 4175 individuals were included in the study.By combining a multivariate analysis aimed at investigating the population genetic structure, with a Bayesian approach used to test models and extent of migration, we were able to detect a stepping-stone migration model as the best descriptor of gene flow across the region, with the main discontinuities corresponding to forested areas.Our analyses highlight an aspect of the influence of habitat variation on human genetic diversity that has yet to be understood. Rather than depending simply on geographic linear distances, patterns of female genetic variation vary substantially between savannah and rainforest environments. Our findings may be explained by the effects of recent gene flow constrained by environmental factors, which superimposes on a background shaped by pre-agricultural peopling. Understanding how human populations interact and admix is one of the primary aims of human evolutionary genetics. To date, three main factors have been studied in detail which could be possible determinants of gene flow within and among human groups: geography, language and social structure.Geographical factors have been shown to play an important role in shaping genetic structure, at both inter and intra-continental levels e.g. -7). Alon. Alon7])The relationship between linguistic and genetic diversity has been investigated in numerous studies aimed at understanding how cultural factors may shape gene pools e.g. -10). The. The10])Finally, following the seminal study by Seielstad et al. , there hEven though the vast literature accumulated over twenty years e.g. ,9) has p has p9])In this context, given their high cultural and linguistic diversity and their complex history, African populations probably represent one of the most interesting case studies. Recent studies on large-scale datasets regarding autosomal markers (both STRs and SNPs) support the role of both geography and language in explaining the distribution of genetic variation in Africa ,25. Amonex novo and 80 collected from the literature) of individuals settled in an area spanning from Central to Western Africa. The populations under study inhabit both the savannah and the rainforest regions, and all speak languages belonging to the Niger-Congo phylum [In this work, we investigated the genetic structure and the patterns of gene flow in a broad dataset . Thereao phylum -41. By cIntra-population diversity parameters are shown in Table Pairwise genetic distances were calculated among all populations and the matrix represented in a MDS plot, shown in Figure From a linguistic point of view . Cluster 6 was the less geographically homogeneous, including two populations from Nigeria (Yoruba and Idoma) and the three nomadic groups from north Cameroon  along with Western Africans. On the other hand, the ellipses of dispersion indicated that clusters 3 and 7, even though they account for the highest number of populations, had lower internal variances. This is probably due to the fact that they include the geographical areas with the densest sampling coverage, which results in a higher number of genetically more closely related populations.Most clusters were found to group populations that are geographically close together, with few exceptions  and stronger than in the latter (R2 = 0.73 vs R2 = 0.53) which was non-significant .In addition, the Mantel test showed a low but statistically significant correlation between geographic and genetic distances for the whole sample . When dividing the populations according to their habitat, geographic and genetic distances were highly correlated within the savannah region , while the rainforest area seemed characterized by a weaker but still significant correlation between the parameters . This trend was confirmed when plotting the linear regression for the genetic and geographic distances of the clusters in directions West to East , while the others ranged from a mean value of −14.052 to −21.832 , a linear stepping-stone (B) and an intermediate model  as well as including 5 out of the 7 populations with non-significant Fs values  .As an important evolutionary consideration, we should take into account the possibility that differences in Fu's statistical values between savannah and rainforest could be also explained by the role of selection. However, although the worldwide distribution of mtDNA lineages has been proposed to be driven by selective processes related to temperature changes, the geographic region here analysed appears to be quite homogeneous for this putative temperature effect . In futua priori definition of population units, based on the sampling location and the languages spoken by the individuals. We are aware that such a definition may lead to an approximation in the estimate of the spatial distribution of allele frequencies, since each population is considered as a sampling point. In the present case, we believe that, despite the vast geographical area covered by our dataset, the homogeneous nature of sampling helps overcoming this limitation and is allowing a reliable representation of the distribution of maternal lineages.Another caveat of the present study may be the The complexity of the migratory patterns observed here is further emphasized by a discontinuity detected between clusters 7 and 2, which overlaps with a broad area of the rainforest region  where the sampling coverage is fairly homogeneous. Cultural factors do not seem to offer an explanation for this separation. In fact, the populations composing the two clusters speak languages that are closely related, within the Narrow Bantu family and show no major differences in their subsistence economy. On the other hand, environmental factors could have played a role if one considers that the rainforest habitat may decrease the intensity of gene flow among populations after their initial settlement in deforested areas, making migration more difficult. Another discontinuity in the pattern (between clusters 1 and 6) overlapped with a gap in the sampling coverage of the dataset under study, corresponding to the area of Guinea, the Ivory Cost and Liberia, where tropical rainforest vegetation generally prevails. In the absence of these samples, any further inference on the validity of the observed discontinuity would be very speculative. However, their analysis could contribute to a more exhaustive testing of the influence of different environments on the intensity of migrations among human populations.Considering all the previous observations, we suggest that farming rainforest populations have probably undergone a local, more recent, and less intense demographic expansion than other food producer populations of the Niger-Congo phylum, which has been previously observed in Gabon through the analysis of Y chromosome lineages . EvidencIt is interesting to note the unexpected association observed in cluster 6 where populations of nomadic shepherds from Northern Cameroon  and Guinea Bissau and Senegal (clusters 6 and 5), which present a high linguistic diversity, seem to be characterized by a rather continuous gene flow and show smaller inter-population differences. This contradicts the expectations described above, based on linguistic data, of a recent demic expansion from the area of Nigeria-Cameroon towards Central Southern and Eastern Africa, and an earlier diffusion from Western to Central Africa .As a general conclusion, language does not seem to be the main predictor for the distribution of genetic variation among Niger-Congo-speaking populations. Despite the general belief that language is transmitted by migrating women, genetic analyses have repeatedly shown its preferential correlation with paternal rather than maternal genetic variation ,13,21.Unfortunately, we were unable to find a reliable approach for the definition of linguistic distances. Comprehensive classifications based on a quantitative measure of lexical similarities are only available for the Narrow Bantu languages, and not systematically for other Niger-Congo branches . Since in this dataset only 28/85 populations belong to the Narrow Bantu family, we decided to avoid this approach in order not to introduce interpretation biases due to inaccurate or questionable linguistic classification.Even though the genetic clusters here reported cannot be considered as random mating units, the picture presented in our study suggests that, in particular thanks to female-biased movements, gene flow occurs among human populations speaking very different languages.The analysis of paternal patterns of migration would be useful to shed light on the substructure and the random mating areas among patrilocal populations, while autosomal and X-chromosomal data could be productively investigated to explore whether sex-biased movements are detectable in the distribution of genome variation.In this paper, we present a genetic study on female patterns of migration in populations from Central and Western Africa which share a patrilocal tradition and belong to the same linguistic phylum. Our results show how macro habitats seem to play a major role in determining population genetic structure. Population samples from Guinea, the Ivory Coast and Liberia could allow us to test whether this working hypothesis applies to an even larger area of the continent. However, we highlight here how fundamental the knowledge of cultural factors is when planning a population genetic study. In fact, having reliable information about matrimonial behaviour, even the resolution provided by a relatively small region of mtDNA, proved useful in inferring complex patterns of migration and isolation.http://www.ethnologue.com/), while a tree representing structure within Niger-Congo and relations among languages spoken in the populations analysed is presented in Additional file Our dataset contains 4175 individuals from 85 Niger-Congo speaking populations from Western-Central sub-Saharan Africa  , with mi89 , withIntra-population diversity parameters, Fu's neutrality test, pairwise genetic distances, AMOVA and Mantel test statistics were calculated using Arlequin 3.5 software . The disGenetic structure was inferred through the Discriminant Analysis of Principal Components . To anak-means approach, which relies on classical ANOVA. This method maximizes the variance among groups and minimizes the variance within groups. The Bayesian Information Criterion (BIC) was used to detect the best number of groups comparing the decrease of the residual variance among different numbers of clusters, with the best number corresponding to the minimum BIC value [The first step of the structure analysis consisted in assigning populations or individuals to clusters through the IC value .k-means in order to investigate their separation which is summarized by the discriminant components [discriminant functions, thus maximize the ratio of the variance among groups and the variance within groups. Group positions, defined by the discriminant functions, are presented in a scatterplot. The residual of the probability of population assignment to true clusters versus randomly permuted clusters (a.score) was calculated to test the goodness-of-fit of the discriminant analysis [DAPC was performed on the clusters inferred with the mponents . This ananalysis ,69,70.A simple linear regression analysis was performed to evaluate the correlation between genetic and geographic distances among the clusters using the geographic coordinates of their centroids  and mean(long) of the populations in the cluster). This was then plotted for both East to West and West to East directions .Mega 5.05 software was used to calculate the alpha value of the gamma distribution for the mutation rate of the whole dataset and to obtain trees of Minimum Evolution for the sequences included in each cluster .Once the unbiased structure of the populations under study was determined, the migration pattern among the clusters identified was tested through a Bayesian approach, which is implemented in migrate-n software version 3.2.9 ,41. The In order to reduce the prohibitive computational time, migration estimates were carried out on a proportional sub-sampling of each cluster. A random sub-set accounting for 30% of each cluster, for a total of 1024 individuals, was pooled five times. Considering the high amount of samples included in cluster 3 and the fact that they belong to a very small geographical area, which is overrepresented in comparison to the rest of the region, the cluster 3 sampling was reduced to 15% in order to obtain a comparable sample size for all clusters. Each model was then run 3 times for each different sub-dataset for a total of 45 runs. Log Bayes Factors were calculated as follows for a total of 45 crossed comparisons among pairs of models:Log BayesFactor = 2ln (Prob(D|Model1)-Prob(D|Model2)ST values among each cluster and its subsets  Map of geographical positions of the 85 populations analysed in the present study: central (green), central-west (red), west (blue). b) Phylogenetic relationships among the languages spoken by the 85 populations analysed in the present study graphically reproduced according to ethnologue.com.Click here for filea) Curve of BIC decreasing in relation to number of clusters considered. The minimum BIC value corresponds to number of clusters = 7. b) Assignation of the populations to the clusters. The intensity of the colour is proportional to probability of assignation.Click here for fileSummary statistics for the 45 sub-datasets compared with the original sample belonging to each of the 7 clusters individuated. N is the number of individuals, K the number of haplotypes, k/N is ratio between the two previous values, S is the number of segregating sites and %S the percentual retain of variability in comparison with the original sample. HD is the haplotype diversity, MNPD the mean number of pairwise differences.Click here for fileMinimum Evolution tree topologies for the 7 DAPC clusters . The tree for cluster 3 was divided across 9 pages for a better graphical visualization.Click here for filePlot of the linear regression between genetic vs geographic distances based on the clusters' centroids. a) The linear distances are calculated starting from cluster 5 in direction West to East. b) The linear distances are calculated starting from cluster 2 in direction East to West.Click here for filePosterior distributions of the parameters estimated with migrate-n (θ and M) for one of the 15 runs.Click here for fileHaplotypes found in the populations typed in the present study.Click here for fileFrequencies of the main haplogroups in the populations analysed.Click here for file


Both h and Pmean are higher in the DJ. The results of this study may indicate that elite biathletes are well adapted to eccentric work of the lower limbs, thus reaching greater values of power during the drop jump. These neuromuscular adaptive changes may allow for a more dynamic and efficient running technique.The main objective of the study was to determine to what degree higher muscular activity, achieved by increased load in the extension phase (eccentric muscle action) of the vertical jump, affects the efficiency of the vertical jump. Sixteen elite biathletes participated in this investigation. The biathletes performed tests that consisted of five, single “maximal” vertical jumps (counter movement jump – CMJ) and five, single vertical jumps, in which the task was to touch a bar placed over the jumping biathletes (specific task counter movement jump – SCMJ). Then, they performed five, single drop jumps from an elevation of 0.4m (DJ). Ground reaction forces were registered using the KISTLER 9182C force platform. MVJ software was used for signal processing  and enab Early research on human muscles by Two mechanisms are the basis of both, voluntary and involuntary motor processes involved in the stretch-shortening cycle.the neuromuscular model) is based on the so-called stretch reflex, which is also called the muscle spindle reflex or myotatic reflex, and on the Golgi tendon organ reflex  involves the use of the elastic energy of the muscle-tendon complex. Elastic energy arises from the returning of the muscle-tendon complex to its original shape after the resolution of the mechanical stress that caused the deformation. This mechanism is possible due to the construction of a muscle-tendon complex, which consists of the contractile and noncontractile elements. Contractile elements are contained within the sarcomere of a muscle and consist of actin and myosin. Non contractile elements consist of the series elastic component (SEC), also known as the muscle-tendon unit . This cycle includes the time it takes to switch from the eccentric loading phase of the movement to the concentric power production phase. During an eccentric contraction, the muscle elongates during tension. Elongation takes place because the opposing force is greater than the force being generated. A concentric contraction occurs when the muscle shortens during tension. Shortening appears because the force generated by the muscle is greater than the force opposing it. The rapid eccentric phase of muscle contraction stimulates the muscle spindle and the elastic properties of the muscle. A powerful and immediate concentric contraction is thus facilitated. The time between the eccentric phase and the concentric phase is the amortization phase. To recover part of the energy generated during the eccentric phase of movement, the amortization phase must be short  at a constant cadence of 70 RPM with a work load of 1.5 W/kg, followed by a 10-minute stretching program. The warm-up was followed by 3 counter movement jumps on a force plate. Afterwards, the subjects were instructed how to perform the jumps: “h) and kinetic parameters (mean power - Pmean and peak power -peakP during the take-off phase) of the subject’s jumping movements (on-line system).Then, tests were performed that consisted of five single “maximal” vertical jumps (counter movement jump – CMJ). A modified version of the test, without the use of arm swings, was adopted . The tasStatistical analysis were carried out using software Statistica v. 8.0 . Descriptive statistics  for all measured mechanical parameters were calculated. The normality distribution of data was checked with the Shapiro-Wilk test. Because data distribution was not normal, the Wilcoxon Matched Pairs Ranks test was used. Additionally, Spearman’s correlation tests were used to assess the relationships between the years of sport experience, and the measures of the plyometric jumps. The level of significance was set at p < 0.05.The height of a vertical jump is considered an athlete’s jumping potential. Based on the results of elite athletes from disciplines such as basketball and volleyball , the resIn similar conditions, elite athletes from 6 different individual sports and 6 different team sports obtained even lower results . The resCMJ= 0.402±0.05mh) were obtained compared to our results. In this case, however, the counter movement jump was performed allowing the arms swing.In studies conducted by h) were achieved when subjects performed the drop jump (Pmean) and peak power (peakP).Interestingly, in most of the examined cases, slightly higher values of jump heights (rop jump  and 3. Theight of the jump (h) between the CMJ and the DJ. In case of male biathletes the only statistically significant difference was observed in mean power (Pmean) between the CMJ and the DJ.The Wilcoxon Matched Pairs Ranks test was performed in order to verify these differences in CMJ, SCMJ and DJ, because data distribution was not normal. The results are presented in In addition, h) in the DJ and the CMJ is not dependent on sport experience . However, statistically significant correlations were found between sport experience and the difference between power output during the take-off phase in the DJ and the CMJ . In both cases (mean power and peak power) the effect of the drop jump was dependent on sport experience.Correlation analysis  shows thneural adaptations usually occur when athletes respond or react as a result of improved coordination between the CNS signal and proprioceptive feedback. neural adaptations occur via synchronous firing of the motor neurons or better facilitation of neural impulses to the spinal cord. Obviously, in our research we could not confirm both of these assumptions. It was only possible to indirectly determine whether the neural adaptations to increased stretching and amplified workload occurred as the result of plyometric training. However, further research should be carried out for this purpose. For example, research could be directed at determining the effects of plyometric training on muscle activation and performance of lower extremity during jumping exercises. Some researchers carrying out such studies have obtained contradictory results, thus further studies are fully justified , and peak power (peakP) were significantly higher in the DJ (h) of female gymnasts in the drop jump from different heights. The highest values were observed in a 0.40m height of the drop jump. Presumably, a 0.4m height of the drop jump is the closest to that which gymnasts experience in the landing phase, after performing a handspring or a round off. Komi  use the elastic and reactive properties of a muscle to generate maximal force production. The stretch-shortening exercises include various types of jumps, including drop (depth) jumps. Such activity requires muscles, in this case those of the lower limbs, to rapidly and forcefully contract while lengthening (eccentric) at the time of landing. Subsequent rapid and forceful contraction  is needed to perform a subsequent jump. Upon landing, the force of the body mass is amplified. The amount of amplification depends on the height of the initial drop. There is agreement about the benefits of basic stretch-shortening principles, but controversies exists in regards to the optimal training routine.In normal muscle function, the muscle is stretched before it contracts concentrically. The eccentric-concentric coupling, also referred to as the stretch-shortening cycle, employs the stimulation of the body’s proprioceptors to facilitate an increase muscle fiber recruitment over a minimal time period. Stretch-shortening exercises (- Jump heights in different forms of the vertical jump were not significant in elite biathletes. Most likely jumping ability is not the most important factor for success in this sport discipline.- Drop jumps proved to be a more effective way to increase power output and jumping performance than other vertical plyometric exercises such as the counter movement jump.- Higher values of jump height and mean power registered in the drop jumps, in comparison to the counter movement jump, indicate a better adaptation of the neuromuscular system of biathletes to increased stretching and a greater workload. The greatest workload was reached by drop jumps from an elevation of 0.4 m. On the basis of this research, it may be concluded that the stretch-shortening cycle is an effective manner for developing strength-speed abilities of biathletes.Based on the results obtained from in this study, the following conclusions were drawn:


The use of consumer digital cameras or webcams to characterize and monitor different features has become prevalent in various domains, especially in environmental applications. Despite some promising results, such digital camera systems generally suffer from signal aberrations due to the on-board image processing systems and thus offer limited quantitative data acquisition capability. The objective of this study was to test a series of radiometric corrections having the potential to reduce radiometric distortions linked to camera optics and environmental conditions, and to quantify the effects of these corrections on our ability to monitor crop variables. In 2007, we conducted a five-month experiment on sugarcane trial plots using original RGB and modified RGB (Red-Edge and NIR) cameras fitted onto a light aircraft. The camera settings were kept unchanged throughout the acquisition period and the images were recorded in JPEG and RAW formats. These images were corrected to eliminate the vignetting effect, and normalized between acquisition dates. Our results suggest that 1) the use of unprocessed image data did not improve the results of image analyses; 2) vignetting had a significant effect, especially for the modified camera, and 3) normalized vegetation indices calculated with vignetting-corrected images were sufficient to correct for scene illumination conditions. These results are discussed in the light of the experimental protocol and recommendations are made for the use of these versatile systems for quantitative remote sensing of terrestrial surfaces. The main advantage of digital photography lies in simplified image processing. The use of digital cameras or webcams has appeared across multiple different domains, including colorimetric applications -3 and enSeveral factors affect the signal, and the conversion between object luminance and digital image measurement is not straightforward . These fGamma correction: Digital cameras are based on CCD (charge-coupled device) or CMOS  detectors that are linear photoconductive devices. If twice the flux of photons is received on a given pixel, twice the output value will be generated. Despite the intrinsic linearity of these sensors, digital value output from standard digital images is not a linear measure of object brightness, since the image processing software embedded in digital cameras is designed to emulate the non-linear behavior of the human eye. Accordingly, most modern consumer cameras use some type of gamma adjustment to map the image to the available quantization range in order to improve esthetics .CFA interpolation (or demosaicing): Most of the digital cameras use a single sensor with a color filter array (CFA) that permits only one color to be measured at each pixel . To create the color image, the missing color values are estimated for each pixel by means of CFA interpolation. The color interpolation process, also known as demosaicing, is generally achieved using a proprietary algorithm.4 law. Other sources of vignetting are geometric in nature, including the light arriving at oblique angles to the optical axis and subsequently being partially obstructed by the field stop or lens rim [Vignetting: This distortion refers to the phenomenon of brightness attenuation away from the image center, and is an artifact that is prevalent in digital photography. Several mechanisms may be responsible for vignetting effects. Some arise from the optical properties of camera lenses, the most prominent of which is off-axis illumination falloff or the coslens rim . Althouglens rim .Radiometric normalization between images: The camera measures radiance, the energy reflected by the scene. This radiance depends on the incident radiation at the time the image was acquired, and on the optical properties of the scene . The quaWe observed that many factors play a role in image acquisition: built-in gamma correction and image interpolation, vignetting, camera settings, and quality and quantity of incoming radiation conditions. The printing industry and medical communities have investigated the properties of consumer digital cameras as colorimetric measurement device , 21, 22.To achieve this, in 2007 we conducted a five-month experiment in which we flew over sugarcane trial plots using original RGB and modified RGB (Red-Edge and NIR) cameras loaded onto an ultralight aircraft. Our hypothesis was that if accurate radiometric data could be derived from the images using simple post-processing, we could design a cost-effective imaging system that could lead to exciting possibilities for new approaches in precision farming.2.Our radiometric data acquisition system consisted of an ultralight aircraft equipped with modified digital cameras that acquired and measured the sunlight reflected in five different spectral bands. Between May and September 2007, seven airborne flight trials were conducted over a 7.3 ha experimental sugarcane field on Reunion Island, a French territory that lies in the Indian Ocean.2.1.We used three Canon® EOS 400D digital cameras (10.1 Megapixel CMOS sensor); each of which had a focal length of 35 mm. The spectral sensitivity of the three cameras was measured in the laboratory with a monochromatic source 1.2 nm wide -24. The The camera focus was set to infinite. The settings of the three cameras  were assembled and mounted on board an ultralight aircraft . The camSeven flights were undertaken over the La Mare site between May and September 2007: May 2, May 25, June 8, June 29, July 23, August 13, and September 5. The flights were performed between 11:00 am and 12:00 noon solar time, on clear days. The aircraft flew transects over the field at about 600 m altitude, producing images with a ground resolution of between 10 and 12 cm.During the same period, additional airborne acquisitions were taken from other agricultural regions of the island at different altitudes , leading to a total of about 500 photographic images per camera acquired under similar atmospheric conditions (clear days) and irradiance geometric parameters (around 12:00 solar hour).All the images were recorded in JPEG and RAW (termed CR2 for CANON cameras) formats.2.3.The sugarcane experimental field is located in La Mare, Sainte Marie , in the northern part of Reunion Island . The field was divided into three randomised blocks cultivated with three cultivars of sugarcane  under three different nitrogen inputs  and two water treatments (irrigated and rainfed) . For eacThe sugarcane field was in its seventh month of growth at the beginning of the experiment in May, and exhibited a closed canopy at that time. Plant measurements were performed monthly on the R570 and R575 cultivar plots, including Leaf Area Index (LAI) and leaf greenness . Values of LAI and SPAD were obtained using non-destructive measurements on the three central rows of each plot in order to avoid border effects, and were averaged for each plot . An inteThe CC index is linked to NDVI , 27. The3.-Decoding unprocessed digital photo;-Correcting the vignetting;-Normalizing the image series over time.The data processing steps aimed to recover comparable values of crop variables across both space and time. The sources of radiometric distortions in the measurements, derived both from the camera itself and from the acquisition conditions, were listed in the introduction. The radiometric correction process implemented in this study included the following stages:We then calculated the relationship between image spectral values and ground measurements.3.1.http://www.astrosurf.com/buil/iris/iris.htm). This software is based on a portable open source program, dcraw  which supports most RAW formats and is available on most operating systems. IRIS splits the CR2 files into four monospectral images, each corresponding to a spectral band . The resulting output images  are four times smaller than the originals. [dcraw program, demonstrated perfect linearity between the DN of decoded images and quantum sensor measurements.The CANON cameras produce their images by means of a Bayer matrix (or Bayer CFA) whereby each individual pixel is filtered and coded as red (R), green (G) or blue (B) . As expliginals.  who alsoFor the RGB camera, we kept the Red image, one of the two Green images, and the Blue image. Only the Red image extracted from the CFA was stored for the RDG and NIR cameras, as the Red band has the best signal to noise ratio . This prThe difference between the unprocessed images and JPEG images was studied by comparing their respective DN values. Because of the intrinsic nature of the JPEG and unprocessed formats, and the difference in image size , it was not possible to compare the images on a pixel-by-pixel basis. Consequently, we made the comparison on a set of training polygons representing a large range of radiometric values: dark road, bright flat roofs, dense vegetation, …etc. The polygons were selected in homogeneous areas to limit location uncertainty. The test was done on the three spectral bands  of an image acquired on June 29.3.2.The correction of the image vignetting was performed using three steps: preparation of the data set, calculation of the radiometric distortion by model fitting, and the correction itself. The calculations were made separately for each spectral band.To determine the vignetting effects in an image, the most straightforward approach involves capturing an image that spans a uniform scene region, such that brightness variations can be attributed solely to vignetting . HoweverMost methods for vignetting correction use a parametric model to simplify estimation and minimize the influence of image noise . EmpiricAssuming that illumination conditions could cause vignetting-like effects (for instance “hot spot” effects) this process was initially performed separately for each date. In our experiment, this approach did not improve correction results (results not shown), so we chose to average a larger number of images that covered all dates in our study (about 500 images) to derive the vignetting profile.3.3.Radiometric normalization consists of rendering images acquired under different irradiance conditions and with different cameras that are comparable in terms of DN. By normalization, we mean here that neither absolute calibration coefficient nor incident radiation measurement was available.The simplest and most common normalization method involves calculating normalized brightness for the RGB channels. This is performed for each image by dividing the brightness value for each of these channels by the total brightness of the image -7. This -th image as our reference for the normalization process. For each spectral band, we calculated a transfer function between the DN of the invariant targets on the reference image and the other dates.Six invariant targets were selected by photo-interpretation . Polygons were used to extract the DN in the five bands across all the images from the time series. Subsequently, we chose the June 29-In the absence of a global radiation measurement, we approximated the global radiation from the cosine of the sun's zenith angle (between 28.6° and 45.5° during the experiment). This method was possible only because the settings of the cameras did not change during our study.We tested two methods of radiometric normalization: normalization with invariant targets, and normalization using the cosine of the solar zenith angle:The invariant and cosine normalization methods were validated using four plastic panels ranging in color from white to dark grey . They were installed on the ground at each spectral acquisition date, close to the La Mare experimental field.3.4.To link the spectral and vegetation measurements, we first had to conduct some image postprocessing: geometric correction, extraction of values related to the experimental plots, calculation of spectral indices, and ground data interpolation.th).Referenced to a metric camera, the CANON camera lens distortion was measured as less than one pixel , and so no correction was applied. For each set of images  acquired simultaneously using the trigger, we first co-registered the different bands to each other. We then performed a geometric correction on each date using a reference image chosen from the data set :(1)NDVThe Green Normalized Difference Vegetation Index (GNDVI ):(2)GNDThe Normalized Difference of the Green and Red bands (VIgreen ):(3)VIgAs plant measurements were not taken on the same dates as the airborne acquisitions, a linear interpolation between two ground measurement dates was applied in order to estimate LAI and SPAD values on the required image acquisition dates . We then4.4.1.The images acquired from the ultra-light aircraft (ULA) were generally neat, with good contrast in the visible and NIR bands . The quaThe RGB image time series over the La Mare experimental site is shown in 4.2.We compared the unprocessed (RAW) and JPEG images on a polygon basis. The relationships between the digital numbers from the unprocessed and JPEG versions of one image are shown in As shown previously in rd and 4th degree. A second decrease between the 5th and 6th degree was observed for the NIR band; the 6th degree polynomial resulted in a good fit at the centre and corners of the image . This vignetting distribution function expresses the vignetting factor for a given position in the image as a polynomial function of position . Different degrees of polynomial were tested for each band and the resulting Root Mean Square Errors (RMSE) are as shown in he image . These rOnce the optimal polynomial function had been found, we produced a vignetting filter image for each spectral band . AnalysiThe results obtained with the RGB camera indicate that today's commercial digital cameras are far from perfect, but are still of relatively good optical quality provided the borders of the photo are ignored. This is because vignetting effects are reduced during the manufacturing process. However, when the cameras are modified and equipped with an external pass-band filter, as in the case of the RDG and NIR cameras, the vignetting effects are substantial .To isolate vignetting effects, we tested the correction on images taken under identical irradiance conditions , but with changing object positions within the image . The effect of the vignetting corrections on the DN of three targets  with different spectral properties is shown in The vignetting effect was visible in all spectral bands and for the three targets, with progressively decreasing DN away from the image centre. The vignetting correction was generally appropriate, yielding a slight over-correction in the NIR. This over-correction does not seem to be linked to the nature of the target. The relative dispersion of the points in all spectral bands can be explained by different flight altitudes, which partly resulted in variable atmospheric noise in the signal. For the sugarcane target, the variability of points in the visible bands (Green and Blue not shown) can be explained by the effects of wind on the canopy . Given these external effects, we consider the vignetting correction to be successful.We applied the cosine and invariant normalization methods on a time series of images acquired at 600 m altitude. The effects of these radiometric normalizations on the artificial targets' DNs are shown in When examining the invariant targets in the Red and NIR bands , we obseOverall, the cosine and invariant methods gave similar results. The advantage of the invariant method is to take into account atmospheric variations. The atmosphere is not a first order driving factor in this case as the atmospheric conditions on the acquisition dates were similar (clear days); the first order driving factor is the solar zenith angle.4.3.-NDVI_jpg, calculated from the Red and NIR bands extracted from the JPEG images. The JPEG images are downloaded directly from the camera, and the spectral bands are split using image processing software.-NDVI_raw, calculated from the spectral bands extracted from the decoded unprocessed images.-NDVI_raw+dev, calculated from spectral bands extracted from the decoded unprocessed images, and corrected from the vignetting effect.-NDVI_ raw+dev+norm, calculated from spectral bands extracted from the decoded unprocessed images, corrected from the vignetting effect, and normalized over time using the invariant method.To assess the impact of the radiometric correction on vegetation monitoring, we tested the quality of regressions obtained between NDVI and chlorophyll content (CC). As observed in other studies , the relThe absence of an effect from decoding unprocessed images can be explained by two factors. First, the DN values of the vegetation were low in the visible image (strong radiation was absorbed by the vegetation) and in the NIR (resulting from under-exposure of the camera). With DNs of below 200 , the vegIn conclusion, the vignetting correction is the only correction that significantly improves the quality of the vegetation indices when a visible (red or green) and a Near Infrared band are used. When two visible bands are incorporated into a vegetation index (VIgreen for example), the vignetting correction is less pronounced. This is because the NIR and visible bands were derived from different cameras with different vignetting functions , while tWe were surprised to note that the normalization of the spectral bands prior to the calculation of the vegetation index reduced the quality of the relationship. Normalization is a difficult operation with various sources of errors . When individual bands (Red or NIR) are related to vegetation parameters, the relationships are improved by the normalization step (data not shown). In the case of vegetation indices, the radiometric errors of the individual bands are summed, resulting in a very variable result.5.In this paper, we tested a simple method of radiometric correction of a series of images acquired over time with three digital consumer cameras onboard a light aircraft. Two out of the three cameras were modified in order to measure radiation in bands other than the default RGB. The quality of the radiometric correction was evaluated against a ground data set of biophysical variables that were independently acquired from sugarcane trials on Reunion Island. The sources of radiometric distortions were both camera-related (image format and vignetting) and environment-dependent (incident radiation).The modification of digital cameras to allow acquisition in the near infrared band is not new. In 2002,  infra-reThere are two reasons to use unprocessed images instead of JPEG or TIFF images: JPEG compression is lost and the DNs are not linear with the brightness of the scene. In our case, results show that the image format (JPEG versus unprocessed) has no effect on the correlation between a spectral band (or a vegetation index) and actual surface parameters. This is linked to our range of values for vegetation surface that lies in the linear region of the tone mapping algorithm; this is particularly true for the Near Infrared images that were under-exposed . We did In respect of image vignetting, the effect was low on the vegetation indices that were calculated with visible bands only, but was high on the vegetation indices calculated with visible and infrared bands like the NDVI. To characterize and subsequently correct the vignetting effects, we developed an original method that is based only on the acquisition data set. Our method has the advantage that it remains usable even when the camera type is unknown or unavailable. However, our method does require a large series of different images with different acquisition and illumination scene conditions. Our results showed that: 1) vignetting is still present in modern RGB digital cameras, and it can be modelled with a second-degree polynomial function, 2) modification of the camera increases the vignetting observed on the images as quantified by , and 3) Ultimately, the radiometric normalization between images still remains a problematic operation. Radiometric normalization using scene invariant targets and linear regression calculations for each spectral band has the advantage that it takes into account variations in incident radiation in each band  to take into account the spectral variations in radiation due to atmospheric conditions, and 2) to correct for any directional effects .6.The use of consumer digital cameras or webcams is increasingly prevalent in environmental applications. The acquisitions are generally performed with automatic settings and the images are saved in JPEG or TIFF formats. Under these conditions, image analysis can be qualitatively satisfying, but the accuracy of the image radiometry is generally too low to permit quantitative estimation of surface parameters.We showed in this paper that, with a simple procedure, it is possible to increase the radiometric measurement capacity of images acquired by an ultralight aircraft. Putting together several known solutions for radiometric corrections , we showed that a comprehensive image processing workflow was possible for realtime crop monitoring using commercial digital cameras.The use of modified cameras permits image acquisition in spectral bands that are not currently used in traditional photography, such as NIR, but that are important for accurate surface characterization. Using free software, we read the images in unprocessed camera output format to obtain spectral images that exhibited values close to the true radiance. These spectral images were corrected from the camera vignetting effect using an original method, and were normalized across acquisition dates. The results showed that the Normalized Vegetation Indices calculated from vignetting-corrected images are acceptable indicators for crop monitoring purposes.In conclusion, for quantitative remote sensing of terrestrial surfaces, the use of commercial digital cameras will increase in the future, thanks to the versatility and multispectral capacities of the available acquisition systems. Their versatility is increased thanks to the flexibility and cost of various lightweight acquisition systems  that can transport this type of camera. Modifications to camera filters permit narrow-band acquisitions in the visible and in the near-infrared domains; these measurements could be used for example to calculate hyperspectral indices like the PRI . However, in cases where bands are too narrow, more investigation is yet required to avoid motion blur due to the speed and vibrations of the aircraft.


An increasing number of biological machines have been revealed to have more than two macroscopic states. Quantifying the underlying multiple-basin functional landscape is essential for understanding their functions. However, the present models seem to be insufficient to describe such multiple-state systems. To meet this challenge, we have developed a coarse grained triple-basin structure-based model with implicit ligand. Based on our model, the constructed functional landscape is sufficiently sampled by the brute-force molecular dynamics simulation. We explored maltose-binding protein (MBP) which undergoes large-scale domain motion between open, apo-closed  and holo-closed (fully closed) states responding to ligand binding. We revealed an underlying mechanism whereby major induced fit and minor population shift pathways co-exist by quantitative flux analysis. We found that the hinge regions play an important role in the functional dynamics as well as that increases in its flexibility promote population shifts. This finding provides a theoretical explanation of the mechanistic discrepancies in PBP protein family. We also found a functional “backtracking” behavior that favors conformational change. We further explored the underlying folding landscape in response to ligand binding. Consistent with earlier experimental findings, the presence of ligand increases the cooperativity and stability of MBP. This work provides the first study to explore the folding dynamics and functional dynamics under the same theoretical framework using our triple-basin functional model. A central goal of biology is to understand the function of the organism and its constituent parts at each of its scales of complexity. Function at the molecular level is often realized by changes in conformation. Unfortunately, experimental explorations of global motions critical for functional conformational changes are still challenging. In the present work, we developed a coarse grained triple-well structure-based model to explore the underlying functional landscape of maltose-binding protein (MBP). By quantitative flux analysis, we uncover the underlying mechanism by which the major induced fit and minor population shift pathways co-exist. Though we have previously lent credence to the assertion that dynamical equilibrium between open and minor closed conformations exist for all the free PBPs, the generality of this rule is still a matter of open debate. We found that the hinge flexibility is favorable to population shift mechanism. This finding provides a theoretical explanation of the mechanism discrepancies in PBP protein family. We also simulated the folding dynamics using this functional multi-basin model which successfully reproduced earlier protein melting experiment. This represents an exciting opportunity to characterize the interplay between folding and function, which is a long-standing question in the community. The theoretical approach employed in this study is general and can be applied to other systems. Biomolecular function is executed through conformational dynamics at physiological conditions, ranging from small fluctuations in atomic positions to large movements of parts of or even entire molecules Though local conformational changes can be detected using experimental probes such as NMR, there are still a number of challenges for exploring large conformational changes in experiment. On the other hand, computational exploration of large conformational changes is made difficult by the fact that the time scale of the conformational changes are often on the order of sub-seconds to minutes, while the molecular dynamics simulations for moderately sized proteins are on the order of microseconds, thus presenting a challenge for modeling conformational changes. Advancing the modeling in this would not only provide us the local information and connect the modeling directly to experiments, but would also predict and give guidance for the ongoing and future experimental explorations of global conformational changes.In recent years, theoretical models have been developed to explore functional dynamics near the bottom of the energy landscape through integrating native structural information from two reference states. These models have been used to investigate the conformational transitions of typical allosteric proteins such as adenylate kinase (ADK) We explored maltose binding protein (MBP) which has three observed states. MBP is a member of the large family of periplasmic binding proteins (PBPs) MBP is found in the periplasmic space of gram-negative bacteria and serves as a receptor for osmotic shock and chemotaxis in response to the maltose and other maltodextrins from the environment So far, there are relatively few computational studies on the conformational dynamics of MBP In this work, we explored the multi-state dynamics from a global perspective by building a coarse-grained functional landscape based on available structural information , which wBased on our model, we approximated various perturbations including ligand concentration and hinge flexibility. We revealed the dependence of shape of the functional landscape and the robustness of the underlying mechanism of conformational transition in MBP. We established a link between the underlying energy landscape and thermodynamic stability, kinetic paths/speed, and structure function correlation.Text S1 for more details. In addition, molecular dynamics simulations were used to probe the sensitivity of the model on energetic parameters. Several thousands of basin transitions indicated sufficient sampling.In this work we integrated structural information of three states of MBP to explore the conformational transition mechanisms. The key to construct a triple-basin model is to define a mixed contact map which integrates heterogeneous sources of structural information together. In our model, the mixed contact map contains the core contacts which are shared with all the native states as well as the state-specific contacts. The strengths of the core contacts and the state-specific contacts are rescaled by their energetic contributions which are denoted as Recently, a statistical survey for a set of allosteric proteins Text S1 for details), we calibrated our triple-well model so that the relative population of open and apo-closed states is comparable to experimental measurements in the absence of ligand binding . Here, Text S1). , and the protein changes its conformation into fully closed state (H basin) passing through A basin. The induced fit mechanism indicates the direct transitions from O basin to H basin without the need of passing through the minor populated state A. Therefore, the mechanism can be simply described by two possible kinetic routes: (i) the “induced fit route” (IF route), where predominantly the open form of MBP changes into H basin directly, that is, The conformational energy landscape of MBP shows that the landscape has three major basins with one basin biased towards the open and the other two toward the apo-closed and holo-closed conformations of the protein. This indicates that the experimentally determined structures are perfectly integrated into our model. The entire conformational dynamics of the system is characterized by the inter-basin transitions, which depends on the barriers between and relative energies of basins In Text S1). A typical kinetic PS route in MBP is shown in Figure S6 in Text S1. A thermodynamically invisible path may actually exist. Under certain conditions related to reactant concentrations and rate constants, the flux through a given pathway can quantitatively reflect a reaction proceeding along the respective path By analysing the kinetic trajectories, we found the evidence that PS routes exist which are hidden in thermodynamic free energy profiles . As pointed out by Zhou We next considered the kinetic response of MBP to changes in ligand concentration. The relationships of the fractional flux and transition rate constant with The relationships between kinetic behaviors and ligand concentration were studied using  model . To alleIn particular, we analyze the detailed kinetic trajectories generated by the specific model with Moreover, for the timescale of the transitions between the open state and the apo-closed state, the experiments suggest an upper limit of Clearly, the rate of AText S1). In the following, we will investigate the influence of hinge flexibility on the thermodynamics and kinetics of the system.It is widely accepted that enzyme activity is closely related to the fast, local fluctuations reflecting the flexibility of mostly the hinge regions. These hinges were computationally identified from differences in both pseudo-angles and pseudo-dihedral angles between native states . From the correlations between fractional flux of IF routes and hinge flexibility, we can see that the increase of hinge rigidity in both models facilitates the conformational transition of MBP along the induced fit pathway. The PS routes are more favored for high hinge flexibility as the transition between the open and the apo-closed conformations is not only accompanied by domain rotation, but also by significant domain twist, both of which depend on hinge flexibility.Furthermore, we investigate the effects of hinge flexibility on kinetics  between linker1 and NTD at the bottom of the ligand bind cleft, which are not broken in TS. It indicates that the domain twist does not occur in Text S1.Characterization of the transition state properties, especially the inhomogeneous distribution of contacts between residues, will help us to understand the microscopic structural mechanism of conformational change through locating the sites or seeds for the nucleation. The Text S1.We calculate the functional It shows that certain residues in NTD  and in CTD  play a key role in stabilizing the holo-closed state (Text S1), there are not only high The Interestingly, we found that Text S1. The results of local cracking calculation are summarized in Figure S10 in Text S1. Our model indicates that the local unfolding points contain V106, L117, P119, E149, E168 and N328 in Text S1) for E168 which is located at the balancing loop may be caused by the high flexibility of balancing loop that are not in contact with NTD. In addition, N328 in It is well known that large structural arrangement of protein can be realized by changes of several dihedral angles at the hinge regions. In some cases the high strain energy may accumulate in various localized regions. It can be relaxed by local unfolding or cracking if the energy exceeds a threshold In MBP, the hydrophibic residues have been found to be important to the domain closure Text S1. It indicates that the specific heat curves shift to higher temperatures with increasing ligand concentration, suggesting an increase of protein stability. In addition, the folding cooperativity increases as well, which is illustrated by the narrowing of the specific heat profile.We further explored the relationship between unfolding characteristics of MBP and ligand concentration through simulation. The thermodynamics of unfolding in MBP has been previously explored by a combination of differential scanning and titration calorimetry and fluorescence spectroscopy under different solvent conditions Structurally, MBP contains two globular domains. Between the two domains, it forms a deep groove whose base locates the ligand-binding site. The X-ray structure of MBP in complex with maltotriose Conformational transitions are central to a multitude of physiological processes, such as enzyme catalysis, and also essential for nonenzymatic binding events. Due to the limit of current experimental techniques, the molecular details for the microscopic structural mechanism of conformational change are often lacking. Therefore we developed a theoretical model for describing the structure-function relationship, and extended the double-well model It is worthwhile noting that the microscopic mixed double-well models with two reference conformations may construct additional basins in the free energy landscape, such as in Lu and Wang's microscopic double-well model Constant temperature molecular dynamics simulations were performed to obtain the free energy landscape and kinetics for conformational changes. It clearly reveals an induced fit pathway on the free energy surface. In addition, a minor population shift pathway is found through the analysis of kinetic trajectories. By introducing the flux analysis as suggested by Hammes et al. The thermodynamic and kinetic manifestations of function transitions are closely related due to the correlation between transition rates and free energy barriers of basin hopping. Rigorously speaking, the population shift route  that corresponds to distinct but related topological states. This work demonstrates that a multiple native basin biased landscape which follows the principle of minimal frustration is sufficient to fold and function with complex topologies. From this perspective, we extend the application of the funneled energy landscape that explains how most proteins fold efficiently and robustly to their structures in functional transitions. Furthermore, we expect that our model can be extended to address more complex allosteric systems.Depending on how pairwise interactions between residues are treated, current multiple-basin structure-based models can be broadly divided into two categories: microscopic and macroscopic. In macroscopic models, techniques borrowed from the Marcus theory of electron transfer To account for the side-chain dynamics, especially for active site, we developed a mixed coarse-grained model in which part of amino acids are represented by two beads. The coarse-graining process is similar to SMOG tool Text S1. Changing the dielectric constant or the salt concentration did not significantly affect the functional dynamics of MBP. Finally, we employed a salt concentration 0.10 M and a dielectric constant 80. All the analysis in manuscript was based on this values except where specified. Of course, the DH model is valid for low salt concentration and mainly for dilute solution. See Text S1 for the detailed descriptions of these terms and the accompanying parameters of the force field.For the last term Simulations were performed with Gromacs 4.0.5 Text S1.Q  has been suggested to be useful when studying the folding landscape. Unfortunately, for functional dynamics which occurs at the bottom of the energy funnel, the traditional folding Q is unable to monitor the process due to the fact that most of the contacts shared by the native states are not needed to be broken. Fortunately, the reaction coordinates from protein folding can be borrowed to describe the functional landscape with minor modification. That is, to measure the formation of state-specific contacts instead of all native contacts. We can denote this quantity as the state-specific Q fraction or functional Q. The state-specific Q fraction can distinguish the conformational transitions between the native basins. This reaction coordinate has also been successfully used in other allosteric studies Text S1Supporting information of multi-state functional dynamics of MBP.(PDF)Click here for additional data file.


Remarkably, it is found that most  which accommodate specific sets of coregulated genes can be in close spatial proximity despite their possibly large sequence separation. The findings pose the question of whether gene coregulation and gene colocalization are related in general. Here, we tackle this problem using a knowledge-based coarse-grained model of human chromosome 19. Specifically, we carry out steered molecular dynamics simulations to promote the colocalization of hundreds of gene pairs that are known to be significantly coregulated. We show that most (in vivo.Recent high-throughput experiments have shown that chromosome regions ( Towards this goal, some of us have recently carried out a comprehensive bioinformatic survey of data gathered in more than 20,000 gene expression profiles measured for several cell lines in different human tissues lociFurthermore, for various model organisms, specific sets of genes that are systematically coexpressed were shown to be in spatial contact too While not all sets of coexpressed or coregulated genes are expected to be nearby in space These considerations motivated the present numerical study where a knowledge-based coarse-grained model of eukaryotic chromosome 19 is used to ascertain whether the large number of coregulated gene pairs on a given chromosome can be actually colocalized in space. The analysis therefore complements recent efforts through which the organization of model chromatin fibers was investigated by bringing distant regions into contact by using attractive interactions, which either mimicked the effect of transcription factories in vivo . This chromosome, which is typically located at the nucleus center Notably, for initial chromosome conformations with low entanglement, it is found that most  pairs of coregulated genes? Secondly, in case there exists a strong association between gene coexpression and colocalization, is it at all feasible to use gene coexpression data as distance restraints to pin down viable chromosome conformations?To make progress on these standing issues we developed and used a knowledge based numerical approach to investigate the gene coregulation–colocalization relationship in human Chr19 using a coarse-grained chromosome model.Chr19 which is To this purpose we started by considering Notably, the selected pairs of genes are typically far apart along the chromosome contour. The median genomic separation of the midpoints of the coregulated genes is as large as To clarify whether, and to what extent, the coregulated gene pairs can be simultaneously colocalized we used a coarse-grained model for chromatin filaments that has been previously shown to be capable of accounting for the fractal-like organization observed for eukaryotic chromosomes To mimic inter-chromosome interactions in the dense nuclear environment, we considered a system where six copies of Chr19 are placed in a cubic simulation box (with periodic boundary conditions) of side equal to This mitotic arrangement was further evolved for a much longer simulation time, roughly corresponding to After setting up the mitotic and interphase systems, we next applied a steered molecular dynamics protocol to each of them see  to promoThe compliance of the two systems to the steering protocol is illustrated in It is striking to observe that for both system it is possible to simultaneously colocalize a very high fraction of the target pairs, namely 80% of them (averaged over the six chromosome copies). The conformations reached at the end of the steering protocol are shown in the right panels of Considering the relatively-high density of the simulated system of chromosomes and that most of the coregulated pairs lie at large genomic distances, the results point to an unexpectedly high degree of plasticity of the mitotic and interphase conformations, which is presumably ascribable to their fractal-like metric properties which keeps at a minimum the entanglement of the chromatin fiber a priori that the chromosomal configurations corresponding to different tissues or experimental conditions would be so heterogeneous that it would be impossible to satisfy the cumulated set of colocalization constraints. By contrast, the results of a posteriori, that the set of pairwise colocalization constraints are largely mutually compatible because most of them can be simultaneously satisfied.A second noteworthy feature of the results of The findings are therefore not only consistent with the coregulation–colocalization hypothesis but, based on such hypothesis, also suggest that the conformations adopted by a chromosome in various conditions can share a common underlying pattern of colocalized genes.et al.To further characterize the overall organization of the steered conformations shown in et al.In both cases, the starting point of the analysis was the construction of the chromosome contact map with a A clustering analysis of the contact maps was next used to subdivide Chr19 into up to ten spatial macrodomains, each spanning an uninterrupted chromosome stretch, and with the proviso that one domain should cover the centromere. For both maps the consensus domain boundaries were well-captured by the subdivision into eight spatial domains, see The good consistency of the domains found using HiC-based and steered-MD contacts maps is visually conveyed by the matching colored regions in the schematic chromosome partitioning of Besides the previous considerations, the results of To address these issues we re-applied the steering protocol starting from 3 different initial conditions, which correspond to specifically designed variants of the model chromosomes. Specifically, the three systems are:random-walk-like chromosome arrangement as shown and described in A randomized gene pairings, see A mitotic-like spatial arrangement but with randomized gene positions, see A mitotic-like spatial arrangement but with As for the native network of target gene pairs, we report on the properties measured at the end of the steering protocol after averaging them over the six chromosome copies in the simulation cell.We stress that the three variants are prepared so to preserve the native overall density, number of coregulated genes and also the number of coregulated pairs to which a selected gene takes part to. They nevertheless present major differences which allow for probing the impact of different system properties on gene “colocalizability”.In particular, the random-walk-like arrangement has a much higher degree of intra- and inter-chain entanglement than all other arrangements, as illustrated by the much wider distribution of gene pairwise distances in the initial configuration, see The results of the steering protocol applied to the three system variants are shown in ive case .These findings provide valuable clues for interpreting the high degree of “colocalizability” of coregulated genes observed in In particular, the very low asymptotic value of the percentage of successfully colocalized gene pairs for the random-walk-like system clarifies that the low intra- and inter-chromosome entanglement of both the mitotic and decondensed configurations is crucial for bringing into contact the coregulated gene pairs.Furthermore, the comparison of the randomly-paired and randomly-repositioned gene cases shows that the connectivity properties of the native coregulatory network appear even more important than the detailed positioning of the coregulated genes along the chromosomes. In fact, the randomly-repositioned genes – which retain the same clustering coefficient of the native coregulatory graph – have the same high degree of colocalizability of the native system. By converse, the low clustering coefficient of the randomly-paired gene case – corresponding to a significant disruption of the original network – reflects in an appreciably lower value of percentage of successfully colocalized gene pairs. It is also worth noticing that, in all cases, a significant fraction of gene pairs brought in contact are at large genomic distances  when the system was initially prepared in a random-walk like arrangement, or if the genes to be colocalized were randomly paired or displaced along the chromosome. Likewise, the macrodomain organization of these alternative systems was found to be much less similar to the HiC-data based one.The present findings allow to draw several conclusions. First, the data in The much poorer compliance of alternative systems  to the steering protocol provides valuable insight into the native chromosomal properties that allow for gene colocalization.The first and most important property is the low degree of entanglement that mitotic or interphase chromosomes are known to have compared to equilibrated polymer solutions of equivalent density To further validate this conclusion we considered an additional target network for the steered-MD simulations. This network was obtained by a partial randomization of the native gene pairings and its average clustering coefficient was In perspective, because the computational strategy employed here is formulated in a general and transferable way, it would be most interesting to apply it to other eukaryotic chromosomes for which extensive co-regulatory data is available. This could clarify the more general validity of the gene coregulation-colocalization relationship as well as the broader implications of using it  of chromosome 19. Next, to perform a robust comparison between the differently normalized gene expression profiles we coarse-grained all expression levels to one of three discrete states only: low, medium and high, as done in Ref. To single out the pairs of probe sets with statistically-significant coexpression we proceeded according to the procedure described below and summarized graphically in First, to account for the expected dependence of gene coregulation on genomic distance, we subdivided the probe set pairs in The comparison with the reference, null distribution is used to define the Mutual Information threshold above which at most one false-positive entry is expected to occur. All probe set pairs exceeding this stringent MI threshold were retained see .The number of selected pairs for each bin ranged from Besides the “native case”, in which the gene pairs to colocalize are obtained from coregulatory network of Chr19, we considered another non-native set of target gene pairs. As described hereafter, these alternative sets were generated by randomizing the native gene pairing network while preserving various overall network properties.Randomized pairings. The 1,487 native pairings between the considered set of Randomized positions. The set of The feasibility to colocalize in space the A system of densely packed chromosomes was modelled at a resolution of The potential energy of each chain is written as,Finally, the excluded volume interaction between distinct beads, including consecutive ones, corresponds to a purely repulsive Lennard-Jones potential:The LAMMPS molecular dynamics software package mitotic, interphase and random arrangements, whereas the randomized cases systems were evolved from the mitotic one.The “native case” system was evolved from three different starting conditions shown in The colocalization of the http://www.affymetrix.com)) covered by the two genes. The stiffness of the harmonic constraint was controlled by the time-dependent parameter a priori, was implemented using the PLUMED plugin for LAMMPS Specifically, for each pair of selected genes, percentage of coregulated pairs that are colocalized and the clustering coefficient of the coregulated pair graph. The two parameters are defined hereafter.To monitor the progress of the steered molecular dynamics simulations and to characterize the salient properties of the resulting configurations we computed two order parameters, namely the percentage of coregulated pairs that are colocalized, The In the above expression, the sum runs over the coregulated pairs of genes, clustering coefficient, The The clustering coefficient of the individual The overall spatial organization of Chr19 was encoded in a binary contact matrix, A clustering analysis of the contact maps was next used to subdivide Chr19 into up to ten spatial macrodomains. Each domain spans an uninterrupted stretch of the chromosome and one domain always matches the centromere region. Following the K-medoids clustering strategy For a given number of domains, the consistency of the steered-MD and HiC-based subdivisions was measured by establishing a one-to-one correspondence of each domain in the two cases and next measuring the percentage of elements, Figure S1Chr19 spatial macrodomains. The filled circles mark the boundaries of the Chr19 spatial macrodomains obtained from the clustering analysis of the steered-MD contact maps (top) and inferred from HiC data (bottom). The number of imposed macrodomains is shown on the (TIF)Click here for additional data file.Figure S2Comparison of macrodomain subdivisions. (A). Schematic representation of the Chr19 partitioning in (TIF)Click here for additional data file.Figure S3Genomic distance distribution for the target gene pairings established at the end of the steering protocol. The plots on the left provide the genomic distance distributions of target gene pairings that are actually satisfied at the end of the steering protocols for the native and randomized cases. The analogous distribution for non-satisfied pairings is shown on the right. Dashed lines correspond to the median values. The results are cumulated over all (TIF)Click here for additional data file.Figure S4Gene colocalizability and gene network cliquishness. The time evolution of the fraction of satisfied gene pairings for three different steered-MD simulations. The target gene pairing networks for the simulations are: the native network and two variants of it obtained by partial and full randomizations of gene pairings. The curves for the native and fully-randomized cases are the same as in (TIF)Click here for additional data file.