Laparoscopic hernioplasty is assessed as a difficult operation. Operative technique determines the frequency of complications, the time of recovery and the rate of recurrences. A proper technique is absolutely necessary to achieve results that are superior to open hernia surgery.The key points in our technique are 1) use of nondisposable instruments; 2) use of blunt trocars, consisting of expanding and non-incisive cone-shaped tips; 3) spacious and curved opening to the peritoneum, high above all possible hernia openings; 4) meticulous dissection of the entire pelvic floor; 5) complete reduction of the hernial sac; 6) wide parietalization of the peritoneal sac, at least down to the mid of psoas muscle; 7) implantation of a large mesh, at least 10 cm × 15 cm; 8) fixation of the mesh by clip to Cooper's ligament, to the rectus muscle and lateral to the epigastric vessels, high above the ileopubic tract; 9) the use of glue allows fixation also to the latero-caudial region; and 10) closure of the peritoneum by running suture.With this technique in 12,678 hernia repairs, the following results could be achieved: operating time - 40 min; morbidity - 2.9%; recurrence rate - 0.7%; disability of work - 14 days. In all types of hernias , similar results could be achieved.Laparoscopic hernia repair can be performed successfully in clinical practice even by surgeons in training. Precondition for the success is a strictly standardized operative technique and a well-structured educational program. Among all inguinal hernia repair techniques that utilize a preperitoneal placement of mesh, the advantage of laparoscopic hernioplasty (TAPP) is based on the fact that any type of groin hernia can be treated safely and effectively in a standardized way. DiagnostThe degree of difficulty of TAPP is not only determined by pathologic-anatomic substrate of hernia  but also by physical attributes of the patient .To perform a first TAPP, the ideal patient is older than 60 years, has a flabby abdominal wall, has a poor muscular tone, has a wide pelvis, is slightly obese, has a small direct hernia and has had no previous abdominal surgery.The patient lies supine and flat on the operating table with both arms placed by the side. After obtaining the pneumoperitoneum, the patient needs to be placed in a Trendelenburg position and turned at an angle of 10–20° towards the surgeon, so that the surgeon can approach the inguinal region without the hindrance of the intestinal loops.To place the optical trocar, an incision of 1 cm needs to be made longitudinally superior of the umbilicus down to the umbilical base. The opposite wound edges are grasped using strong Backhaus clamps to lift up the abdominal wall. Thus, Veress needle can be positioned to induce a pneumoperitoneum. Semm's safety tests are always performed to ensure correct intraperitoneal position of the needle. During insufflation, the intra-abdominal pressure and the gas flow need to be observed. To ensure correct position of the tip of the Veress-needle in the abdominal cavity, the pressure should be low (about 0 mm/Hg), whereas the flow is required to be adequately high (about 2 L/min). Then insufflation can be continued until a maximal pressure of 12 mm/Hg is reached. The optical trocar is then placed. Again, the abdominal wall should be held tense by using Backhaus clamps. The optical trocar is screwed into the abdominal cavity softly, and the optic can be inserted. Usually we use a 30° angle optic .It is customary to perform a diagnostic laparoscopy to inspect the upper abdomen, including the liver. To expose the inguinal area, the patient needs to be positioned as mentioned above. The surgeon should stand on the opposite side of the hernia. The camera operator is required to sit on the hernia side. The video tower is placed at the feet of the patient, whereas the scrub nurse stays on the left side.In case of bilateral hernia, all the trocars are placed at the umbilical and midclavicular levels . In case of a unilateral hernia, one trocar can be positioned above the umbilicus at the hernia side, whereas the contralateral trocar may be placed below the umbilicus to avoid collision with the optical trocar.In order to avoid any injury to intra-abdominal organs, trocars should always be inserted under vision. Without exception, blunt and reusable trocars with expanding and non-incisive cone-shaped tips are used . Consequently, injuries of epigastric vessels causing bleeding complications as well as major tissue trauma, followed by late postoperative hernia formation, can be avoided completely.The dissection of the right inguinal area begins with a curved and a spacious opening of the peritoneum, starting in the region of the anterior superior iliac spine, going to the myopectinal orifice and ending at the medial umbilical ligament. In case of a prominent fatty ligament which obscures the access to the inguinal region, it should not be cut , but the incision of the peritoneum should be enlarged towards the cranium in a ‘J’ shape.The dissection of the inguinal region is done in accordance with a strict concept. Before dissecting the myopectinal orifice with the hernial sac, a preparation of the lateral and medial compartments is required, particularly in an obese patient. It is advantageous to identify important landmarks – such as the rectus muscle and symphysis, as well as testicular vessels laterally. Consequently, risk of injury to the spermatic cord, iliac vessels, nerves and urinary bladder can be eliminated. Dissection of the hernial sac should not be performed before demonstrating both the compartments clearly. An early identification of the epigastric vessels is recommended. In addition, it is advisable to free the epigastric vessels of fat so as to uncover the inner inguinal ring exactly. In case of a lipoma at the entry into the inguinal canal, dissection is required to identify to the hernial sac.By following a so-called ‘cobweb-like nonvascular zone,’ the space of Retzius  as well as the Bogros’ space  can be dissected in a blunt manner. The left hand is used to pull firmly on the leaf-like opened peritoneum, while the right hand performs either a blunt or a sharp dissection with a Metzenbaum scissors, which is connected to unipolar diathermy. As a matter of principle, accurate hemostasis is required to identify landmarks and obtain excellent exposure.Dissecting a direct hernia is a simple process: immediately after dissecting the medial compartment a preperitoneal lipomatous tissue is observed at the direct hernial orifice. By placing the peritoneum as well as the lipomatous tissue on tension, the transversalis fascia  becomes visible and appears to be a white circular structure. Stepwise, the lipomatous tissue gets separated from the transverse fascia without penetrating it. Furthermore, a thorough hemostasis with the use of monopolar diathermy as well as a meticulous dissection of the hernial sac play an important role in reducing postoperative formation of serohematoma. It has been observed that as the dissection progresses medial, Corona mortis is observed to occur in 20% of patients. Again, careful attention is required to avoid bleeding.The femoral hernial orifice is located in an angle formed by the Cooper's ligament (iliopubic tract inserting into the pubic os) and the iliac vein. Thus, the femoral hernial orifice can be exposed. Due to the proximity to the femoral vein, the dissection needs to be performed very carefully.Dissection of the indirect hernial sac is much more difficult as compared to the direct hernia, especially when the sac is long and contains scar formation near the cremaster encircling the spermatic cord. Proceeding systematically, at first the testicular vessels, located caudal and lateral, should be dissected. Afterwards, the hernial sac is separated off the adhesions to the above-mentioned structures by starting from caudal lateral and then going to cranial medial. Under careful hemostasis, dissection is achieved partly bluntly and partly sharply. Especially in large hernias, the double-instrument-rope-ladder method should be used, which means that the scissors in the right hand are replaced by a second forceps. Now, the hernial sac can be dissected step by step off the inguinal canal by adopting the rope-ladder principle. To release and separate the hernial sac off the spermatic cord, a fine and superficial coagulation of the adhesions normally suffices.Quite often, strong adhesions can be found at the entrance of the inguinal canal between the hernial sac and cremaster muscle, as well as the medial edge of the epigastric vessels. Again, superficial coagulation suffices to bluntly peel off the hernial sac. A stepwise progress under permanent view of the vessels of the spermatic cord permits the surgeon to reach the tip of the hernial sac. The following procedure is simple and only the freeing up of the vas deferens is left. Once again, the procedure is similar to the one used for the testicular vessels. This time, the dissection goes from cranial lateral to caudal medial. The usage of scissors combined with monopolar diathermy allows even firm adhesions to be dissected free. (Caveat: Dissect a safe distance away from the vas deferens!)The final step of dissecting the groin includes parietalization, at which peritoneum is dissected off the spermatic cord and the spermatic fascia beyond the middle region of the psoas muscle. In doing so, even the flimsiest of the connections between the peritoneum and the retroperitoneal space and spermatic fascia and spermatic cord respectively should be disconnected. The purpose of parietalization is to prevent the mesh  from being lifted up by the remaining connective tissue during peritoneal closure; this may especially occur laterally. Thus, a later recurrence of the hernia from caudal and lateral caused by shifting of the fatty tissue is prevented. One should be able to lift the peritoneum without causing movement of the mesh. Now the preparation of the groin is completed.During the next step, by using a forceps, the 10 cm × 15 cm mesh is pushed through the 12 mm trocar and placed in an umbrella-like manner in the dissected area. The myopectinal orifice should be covered adequately without allowing any folds in the mesh. By using two clips , the mesh should be fixed to the symphysis and Cooper's ligament. Two clips are placed on the rectus muscle medial to the epigastric vessels and two clips at the transverse fascia located lateral to the epigastric vessels. Thereby, the distance between clips and ileopubic tract should be at least 2 cm. Placing clips below the iliopubic tract and 1–2 cm above is strictly avoided because doing so could lead to injuring large vessels (triangle of doom) or nerves (triangle of pain). To prevent shifting during surgery, fixation of the mesh could also be done by using sutures or fibrin glue . It is advisable to use a larger mesh (12 × 17 cm) for major - defects (measuring more than 5 cm).As soon as the mesh is placed in position, the peritoneal incision should be approximated using an absorbable, industrially manufactured suture, whose ends get fixed with absorbable clips . At the time of suturing the peritoneum, the intra-abdominal pressure is reduced to 6–8 mmHg, thereby allowing a tension-free peritoneal closure. An alternative is to close the peritoneum with a simple continuous suture with intracorporeal knotting.The procedure is terminated by removing all trocars under vision. In case bleeding is observed from the port sites, it is possible to control it by electrocoagulating the area with a grasper from the contralateral port. Finally, after deflating the abdominal cavity, the optical trocar needs to be removed. Therefore, an accurate closure of the fascia with a strong suture is required; because in contrast to the lateral working trocars, the fascial opening at the optical trocar is not covered by muscles.Between April 1993 and December 2005, we have performed a total of 12,678 hernia repairs using the TAPP technique. The patient population was completely unselected, and all types of hernias were included . The perWith strict application of our technique in 12,678 laparoscopic hernia repairs (TAPP), the following results have been achieved: operation time 40 min (12–276), morbidity 2.9%, reoperation rate 0.44%, recurrence rate 0.68%, period of disability 14 days (1–100). Tables Laparoscopic hernia repair by the TAPP technique is an excellent operation for treatment of inguinal hernia. In comparison to open surgery, morbidity and recurrence rate are favorably low. Precondition for excellent results is the strict application of a standardized technique. In experienced hands, all types of hernias, including large scrotal hernias and recurrent hernias after previous preperitoneal repair, can be operated with low morbidity and recurrence rates. The same is true for hernias in patients with a history of previous preperitoneal surgery, e.g., transabdominal prostate resections. Evidence-based data show that laparoscopic hernia repair is significantly better than the conventional operations, especially with respect to all pain-associated parameters.3 However


The fine tuning of two features of the bacterial regulatory machinery have been known to contribute to the diversity of gene expression within the same regulon: the sequence of Transcription Factor (TF) binding sites, and their location with respect to promoters. While variations of binding sequences modulate the strength of the interaction between the TF and its binding sites, the distance between binding sites and promoters alter the interaction between the TF and the RNA polymerase (RNAP).Kd) of several E. coli TFs in their interaction with variants of their binding sequences from the scores resulting from aligning them to Positional Weight Matrices. A correlation coefficient of 0.78 was obtained when pooling together sites for different TFs. The theoretically estimated Kd values were then used, together with the dissociation constants of the RNAP-promoter interaction to analyze activated and repressed promoters. The strength of repressor sites -- i.e., the strength of the interaction between TFs and their binding sites -- is slightly higher than that of activated sites. We explored how different factors such as the variation of binding sequences, the occurrence of more than one binding site, or different RNAP concentrations may influence the promoters' response to the variations of TF concentrations. We found that the occurrence of several regulatory sites bound by the same TF close to a promoter -- if they are bound by the TF in an independent manner -- changes the effect of TF concentrations on promoter occupancy, with respect to individual sites. We also found that the occupancy of a promoter will never be more than half if the RNAP concentration-to-Kp ratio is 1 and the promoter is subject to repression; or less than half if the promoter is subject to activation. If the ratio falls to 0.1, the upper limit of occupancy probability for repressed drops below 10%; a descent of the limits occurs also for activated promoters.In this paper we estimated the dissociation constants (The number of regulatory sites may thus act as a versatility-producing device, in addition to serving as a source of robustness of the transcription machinery. Furthermore, our results show that the effects of TF concentration fluctuations on promoter occupancy are constrained by RNAP concentrations. In the case of repressors, ω equals 0, which represent the mutual exclusion of the TF and the RNAP from their respective binding loci. In the case of activators, the cooperative binding of the TF and the RNAP is represented by a ω value of 20. See Methods for details.where  = Kp, and substituting ω by 20, we find that the probability of RNAP-promoter binding for activators may be calculated by:Every point in panel A of Figure Pol] = Kp), at the same TF concentrations, the dependency of the probability of promoter occupancy on regulatory site strength follows roughly a sigmoid curve. This may be obtained from the previous equation: if the TF concentration is kept at negligible values with respect to Kd, the promoter is half occupied. On the other hand, at high TF concentration values relative to Kd, activated promoters tend to be occupied almost permanently. These two boundaries of the equation determine the sigmoid shape of the probability (semi-log) graph, with its linear portion populated by regulatory sites with Kd values approximately within two orders of magnitude immediately above the TF concentration. Varying the TF concentration causes a shift of the probability distribution: as the former increases, the latter is displaced to the right, with more promoters close to saturation and fewer promoters in the half occupied state.The graph in panel A shows that if differences in promoters' strength are disregarded (with  by their values in this example, and calculating the probabilities of the lexA_dinF promoter occupancy considering a) only occupancy of site A by LexA, b) only occupancy of site B by LexA, and c) occupancy of either site by LexA. As expected, within the range of TF concentrations assayed the probability of promoter occupancy decays at a higher rate when both sites are considered than for each individual site. (Opposite results will be obtained for promoters under the control of more than one activator site). In sum, our results suggest that the location of multiple LexA binding sites in regulatory regions may be regarded not only as a source of robustness of the SOS system -- that increases its resistance to mutations affecting LexA binding sites -- but also as a device of gene expression fine tuning in response to changes of LexA concentration. This conclusion may be generalized to TFs that bind independently to several sites upstream a promoter: the occurrence of multiple binding sites of this nature may act, together with variations of TF binding sequences and promoter-site distances, as a modulator of the effects of TF binding upon promoter occupancy by the RNAP.Figure lexA_dinF promoter occupancy, as presented in Figure Kd of this theoretically mutated site B corresponds to a PWM score of approximately 7.02, very close to the weaker LexA site  in our starting data set. This limit is probably a mechanism that prevents any sequence within regulatory regions from significantly affecting the effect of strong TF sites on promoter occupancy. In other words, while weak sites may indeed ploy a role in affecting the regulatory output of strong sites located in their vicinity, only true TF binding sites may do this; and the stronger the strong site, the stronger the weak site must be in order to have a significant effect on polymerase-promoter interaction.However, there is a limit to the effect of a weak site on the probability of polymerase-promoter interaction. A mutation that rendered site B weaker by only one order of magnitude would almost override its effect on Kp of a promoter, and it is under the regulation of a repressor site, its occupancy will never be higher than 50% (or lower than 50% if its associated site is an activator), irrespective of the concentration of the TF that binds to the site. The variation of RNAP concentration changes these limits. For instance, if it falls to one-tenth of the Kp, the upper limit of occupancy probability for promoters associated with repressor sites drops below 10%; a descent of the limits occurs also in the case of activator sites . Briefly, we obtained microarray data for FNR-activated TUs in three experimental conditions from Constantinidou et al.  and usedTo analyze the results, we considered three levels of consistency between theoretically predicted ratios and experimental ones. First, the ratio of theoretical to experimental quotient is between 0.5 and 2 -- i.e.: the disagreement between theoretical and experimental ratios is no more than two-fold --; second, the ratio is between 0.25 and 4; third, the ratio is between 0.1 and 10. We found that 65% of the predicted ratios are consistent with experimental ones according to the first; the disagreement of 81% of them with experimental ratios is no more than four-fold; and 93% of them are of the same order of magnitude than experimental ratios. Several points may be raised to explain why we fail obtaining a perfect consistency between theoretical and experimental trends. First, it is important to bear in mind the limitations of the model we employed, limited to representing the first step of transcription initiation, a complex processed whose dynamical behavior is influenced by a number of other stages. Second, the computations rely on thermodynamic constants approximated from a correlation, which was obtained employing fragmented experimental data. Finally, the noisy nature of microarray data  is anothKd values and PWM scores of regulatory sites allowed us to approximate theoretical Kd values of E. coli known regulatory sequences and Kp values of their associated simple promoters. Using a formalism developed somewhere else /Kp) and Kd are set theoretically, here we estimated the values of Kp and Kd for each individual promoter and site, respectively from experimental data. Therefore, we only changed in each simulation the values of [Pol] and [TF]. The values of the RNAP concentration have been calculated within the nanomolar range in the E. coli cytoplasm . Therefore, we employed [Pol] values between 10-10 and 10-8 in all the simulations. The concentration of TFs was taken, most of the times, very close to the Kd of the site, in order to explore the behavior of promoter-site units within the responsive [TF] range. Alternatively, in some simulations, [TF] was varied across wider ranges, in order to explore the response of arrays of sites.Whereas in the work by Buchler ω, was given a qualitative two-level treatment: it took value 20 for activators and 0 for repressors. Although these two fixed values are set from empirical knowledge they do not invalidate our main findings, which are related to regulatory sites bound by the same TF. As the graph in Additional file ω parameter only displace the curve of RNAP-promoter interaction probability thus attaining saturation of the promoter at lower TF concentrations. Nevertheless, the shape of the curve remains unaltered, indicating that all simulations, if performed at lower TF concentrations will render identical results. In a future extension of this work, a mechanism of finer tuning should be put in place to better represent the variety of TF-RNAP interactions, in order to realistically expand this model to promoters regulated by more than one TF. All simulations were implemented by ad hoc PERL scripts; individual TUs' graphs were automatically built using GNUPLOT scripts.The other parameter in the equation, AGP and VEA participated in the conception of the study. AGP designed and implemented the study and drafted the manuscript. ATV and JCV supported the project and provided meaningful guidance. VEA, ATV and JCV helped revising the manuscript. All authors have read and approved the manuscript.E. coli simple promoters obtained as described in the Methods section.Kinetic graphs of all  This file can be opened with tar.Click here for fileKp on the sigmoid dependence of promoter occupancy probability on Kd for A) activator sites and B) repressor sites.Boundaries imposed by the reduction of RNAP concentration to one tenth of  This file can be open with PDF viewer.Click here for fileResults of confronting data produced by our model with microarray data from FNR-activated TUs in three experimental conditions. This file can be open with PDF viewer.Click here for filevs TF concentration calculated using four different ω values.Polymerase-promoter probability  This fail can be open with PDF viewer.Click here for file


Proteins interact through specific binding interfaces that contain many residues in domains. Protein interactions thus occur on three different levels of a concept hierarchy: whole-proteins, domains, and residues. Each level offers a distinct and complementary set of features for computationally predicting interactions, including functional genomic features of whole proteins, evolutionary features of domain families and physical-chemical features of individual residues. The predictions at each level could benefit from using the features at all three levels. However, it is not trivial as the features are provided at different granularity.To link up the predictions at the three levels, we propose a multi-level machine-learning framework that allows for explicit information flow between the levels. We demonstrate, using representative yeast interaction networks, that our algorithm is able to utilize complementary feature sets to make more accurate predictions at the three levels than when the three problems are approached independently. To facilitate application of our multi-level learning framework, we discuss three key aspects of multi-level learning and the corresponding design choices that we have made in the implementation of a concrete learning algorithm. 1) Architecture of information flow: we show the greater flexibility of bidirectional flow over independent levels and unidirectional flow; 2) Coupling mechanism of the different levels: We show how this can be accomplished via augmenting the training sets at each level, and discuss the prevention of error propagation between different levels by means of soft coupling; 3) Sparseness of data: We show that the multi-level framework compounds data sparsity issues, and discuss how this can be dealt with by building local models in information-rich parts of the data. Our proof-of-concept learning algorithm demonstrates the advantage of combining levels, and opens up opportunities for further research.. The programs are written in Java, and can be run on any platform with Java 1.4 or higher and Apache Ant 1.7.0 or higher installed. The software can be used without a license.The software and a readme file can be downloaded at  The functions of many proteins depend highly on their interactions with other proteins. Complete protein-protein interaction (PPI) networks provide insights into the working mechanisms of proteins at a global level. While high-throughput experiments such as yeast two-hybrid (Y2H) -4 and taThe construction of more reliable PPI networks has been assisted by computational techniques. These techniques usually employ a supervised -12 or unSince binding interfaces of proteins are enriched in conserved domains in permanent interactions , it is pAs will be described in the next section, some recent studies have started to perform interaction predictions at the domain and residue levels. The data features used by each level are quite distinct. While protein level features are mostly from functional genomic and proteomic data such as gene expression and sub-cellular localization of whole genes and proteins, domain level features are mainly evolutionary information such as phylogenetic-occurrence statistics of the domain families, and residue level features are largely structural or physical-chemical information derived from the primary sequences.In the literature of domain-level prediction, the term "domain" is usually used to mean a domain family, which could have multiple occurrences in different proteins. In this study we use the terms "domain family" and "domain instance" to refer to these two concepts respectively, in order to make a clear distinction between them. For example, PF07974 is a domain family from Pfam, where ADP1_YEAST.PF07974 is a domain instance in the protein ADP1_YEAST.Since the data features of the three levels describe very different aspects of the biological objects, potentially they could contribute to the prediction of different portions of the interaction networks. For example, some protein interactions could be difficult to detect using whole-protein level features since they lack fine-grained physical-chemical information. These can be supplemented by the residue level features such as charge complementarity.Likewise, for the protein interactions that occur within protein complexes, there could be a high correlation between the expressions of the corresponding genes. With proper gene expression datasets included in the protein features, there is a good chance of correctly predicting such protein interactions. Then if one such interaction involves a pair of proteins each with only one conserved domain, it is very likely that the domain instances actually interact.One may worry that if the predictions at a particular level are inaccurate, the errors would be propagated to the other levels and worsen their predictions. As we will discuss, this issue can be handled algorithmically by carefully deciding what information to propagate and how it is propagated. With a properly designed algorithm, combining the predictions and utilizing the data features of all three levels can improve the predictions at each level.In this work we propose a new multi-level machine-learning framework that combines the predictions at different levels. Since the framework is also potentially useful for other problems in computational biology that involve a hierarchy, such as biomedical text mining , we start with a high-level description of multi-level learning and discuss three key aspects of it. Then we suggest a practical algorithm for the problem of predicting interactions at the protein, domain and residue levels, which integrates the information of all three levels to improve the overall accuracy. We demonstrate the power of this algorithm by showing the improvements it brings to the prediction of yeast interactions relative to the predictions from independent levels  predicting which residues are in any interaction interfaces of a protein , and 2) From a theoretical perspective, our multi-level learning framework is loosely related to co-training  and the We now formally describe the learning problem we tackle in this study. The inputs of the problem consist of the following:• Objects: a set of proteins, each containing the instances of one or more conserved domains, each of which contains some residues. Each protein, domain instance and residue is described by a vector of feature values. Some additional features are available for pairs of objects, such as the likelihood for a pair of proteins to interact according to a high-throughput experiment.• Gold standard positive sets of known protein-protein, domain instance-domain instance and residue-residue interactions. As in other studies on protein interaction networks, we use the term "gold standard set" to mean a set of sufficiently reliable data useful for the prediction purpose, instead of a ground-truth set that is absolutely correct. The positive sets could be 1) contaminated with false positives, and 2) incomplete, with false negatives, and a pair of upper-level objects in the positive set may not have any corresponding lower-level object pairs known to be in the positive sets.• Gold standard negative sets of non-interactions at the three levels.We assume no crystal structures are available except for the proteins in the gold-standard positive sets, so that the input features cannot be derived from known structures. This is a reasonable assumption given the small number of known structures as compared to the availability of other data features.The objective is to use the gold standard sets and the data features to predict whether the object pairs outside the gold standard sets interact or not. Prediction accuracies are estimated by cross-validation using holdout testing examples in the gold standard sets not involved in the training process.In this study we focus on kernel methods  for learIn order to develop a method for predicting interactions at all three levels in a cohesive manner, we need to define the relationships between the levels, which is the topic of Section. We first describe two information flow architectures already considered in previous studies, and then propose a new architecture that maximally utilizes the available data. In Section we discuss various possible approaches to coupling the levels, i.e., ways to pass information between levels. In Section we discuss the data sparsity issue. In particular, we describe the idea of local modeling, which is also useful for network predictions in general. Finally, in Section we outline the actual concrete algorithm that we have developed and used in our experiments.A traditional machine-learning algorithm learns patterns from one single set of training examples and predicts the class labels of one single set of testing instances. When there are three sets of examples and instances instead, the most straightforward way to learn from all three levels is to handle them separately and make independent predictions Figure . We use A second architecture is to allow downward (from protein to domain to residue) or upward (from residue to domain to protein) flow of information, but not both Figure . This arA third architecture is to allow the learning algorithm of each level to access the information of any other levels, upper or lower Figure . By alloTo design a concrete learning algorithm, we need to specify what information is to be passed between different levels and how it is passed. Here we suggest several possibilities, and briefly discuss the pros and cons of each of them.One simple idea is to pass training data to other levels Figure , arrow 1The major limitation of passing only training data is that the usually much larger set of data instances not in the training sets (the "unlabeled data") would not benefit from multi-level learning. In contrast, if the predictions made at a level are also passed to the other levels, much more data instances could benefit  , which iTaking a closer look at the prediction problem at each individual level, one would realize that applying a traditional learning method is actually non-trivial since we are dealing with network data. In a traditional setting, each training instance has a class label and the job of a learning algorithm is to identify patterns in the feature values for predicting the class label of each unlabeled object. In our current situation, each data instance is a pair of biological objects (proteins/domain instances/residues), with two possible class labels: interacting and non-interacting. In order to construct a learner, one would need features for pairs of objects. A model can then be learned using a traditional machine learning method for all object pairs. We call this 'global modeling' since a single regression model is built for all the data instances. Global modeling has a number of major drawbacks:1. Features for object pairs: it is not easy to construct features for pairs of objects, since most available data features are for single objects. This is particularly a problem for kernel methods, which require a kernel matrix to encapsulate the similarity between each pair of data instances. For network data, this means a similarity value for each pair of object pairs. While methods have been proposed to construct such kernel matrices , the res2. Time complexity: working with pairs of objects squares the time requirement with respect to the number of objects in the dataset. While state-of-the-art implementations of kernel methods could easily handle thousands of proteins, it would still be challenging to deal with millions of protein pairs, let alone the even more daunting numbers of domain instance pairs and residue pairs.n objects at a level, there are O(n2) pairs and thus the kernel matrix contains O(n4) entries.3. Space complexity: the kernel matrix has a size quadratic in the number of data instances. With 4. Sub-clusters: the two classes of data instances may contain many sub-clusters that cannot be handled by one single global model. For instance, proteins involved in permanent complexes may use a very different interaction mechanism from transient interactions in signaling pathways.n proteins, then n models are built, one for each protein, for predicting whether this protein interacts with each of the n proteins. The advantages of local modeling are obvious: 1) data features are needed for individual objects only, 2) the time complexity is smaller than global modeling whenever the learning method has a super-linear time complexity, 3) much less memory space is needed for the kernel matrix, and 4) each object can have its very specific local model. For all these benefits, in our experiments we only considered local modeling.To avoid these problems, one alternative is local modeling . InsteadLocal modeling is most useful when the training data are abundant and evenly distributed across different objects, such that each object receives a reasonable amount of positive and negative examples to train its local model. However, when the training data are sparse and uneven, some objects may have insufficient  training examples. For instance, among the millions of yeast protein pairs, there are only a few thousand known interactions, so many proteins have very few of them.Our proposed solution uses concepts related to semi-supervised learning: use high confidence predictions to augment training sets. Suppose protein A has sufficient known positive and negative examples in the original training sets, and the local model learned from these examples predicts with high confidence protein B to be an interaction partner with A. Then when building the local model for B, A can be used as a positive training example. Predicted non-interactions can be added as negative examples in a similar way. This idea is consistent with the training set expansion method proposed above for inter-level communication. As a result, the information flow both between levels and within a level can be handled in a unified framework. The expanded training set of a level thus involves the input training data, highly confident predictions of the local models of the level, and highly confident predictions from other levels. Practically, training set expansion within the same level requires an ordered construction of the local models. Objects with many (input or derived) training examples should have their local models constructed first, as more accurate models are likely to be obtained from larger training sets. As these objects are added as training examples of their predicted interaction partners and non-partners, they would progressively accumulate training examples for their own local models.We now explain how we used the ideas described in the previous sections, namely bidirectional information flow, coupling by predictions passing, and local modeling with training set expansion, to develop out concrete learning algorithm for prediction of protein, domain instance and residue interactions. We first give a high-level overview of the algorithm, then explain the components in more detail.The main steps of the algorithm are:1. Setup a learning sequence of the levels.2. Use the model learned for the first level in the sequence to predict interactions at the level.3. Propagate the most confident predictions to the next level in the sequence as auxiliary training examples.4. Repeat the previous two steps for the second and third levels, and so on.We use training set expansion with support vector regression (SVR) to perform learning at each level. Each pair of objects in the positive and negative training sets is given a class label of 1 and 0, respectively. An SVR model is learned for the object (e.g. protein) with the largest number of training examples (denoted as A). The model predicts a real value for each object, indicating the likelihood that it interacts with A. The ones with the largest and smallest predicted values are treated as the most confident positive and negative predictions, and are used to expand the training set. For example, if B is an object with the largest predicted value, then A and B are predicted to interact, and A is added as an auxiliary positive training example of B. After training set expansion, the next object with the largest number of training examples is re-determined, its SVR is learned, and the most confident predictions are used to expand the training set in the same manner. The whole process then repeats until all models have been learned. Finally, each pair of objects A and B received two predicted values, one from the model learned for A and one from the model learned for B. The two values are weighted according to the training accuracies of the local models for A and B to produce the predicted value for the pair. Sorting the predicted values in descending order gives a list of predictions from the pair most likely to interact to the one least likely. The list is then used to evaluate the accuracy by the area under the receiver operator characteristic curve (AUC) . We haveOne way to setup the learning sequence is to use the above procedure to deduce the training accuracy of the three levels when treated independently, then order the three levels into a learning sequence according to their accuracies. For example, if the protein level gives the highest accuracy, followed by the domain level, and then the residue level, the sequence would be "PDRPDR...", where P, D and R stand for the protein, domain and residue levels, respectively. Having the level with the highest training accuracy earlier in the sequence ensures the reliability of the initial predictions of the whole multi-level learning process, which is important since all latter levels depend on them. Notice that after learning at the last level, we feedback the predictions to the first level to start a new iteration of learning.In our computational experiments we also tested the accuracy when only two levels are involved. In such situations, we simply bypassed the left-out level. For example, to test how much the domain and residue levels could help each other without the protein level, the learning sequence would be "DRDR...".The mechanism of propagating predictions from a level to another depends on the direction of information flow.X and Y be the two sets of lower-level objects, and p denotes the probability of interaction between two objects x ∈ X and y ∈ Y, then the chance that the two parent objects interact is 1 - ∏x∈X, y∈Y), i.e., the parent objects interact if and only if at least one pair of its children objects interact. In the second method, we simply take the maximum of the values. In the ideal case where all predicted values are either 0 or 1, both methods are exactly the same as taking the OR of the values. When the values are noisy, the former is more robust as it does not depend on a single value. Yet its value is dominantly affected by a large number of fuzzy predicted values with intermediate confidence, and is thus less sensitive. Since in our tests it does not provide superior performance, in the following we report results for the second method.For an upward propagation , each object pair in the next level receives a predicted likelihood of interaction from each pair of their child objects. For example, if predictions are propagated from the domain level to the protein level, each pair of domain instances provides a predicted value to their pair of parent proteins. We tried two methods to integrate these values. In the first method, we normalize the predicted values to the  range as a proxy of the probability of interaction, then use the noisy-OR function  to inferFor a downward propagation , we inherit the predicted value of the parent pair as the prior belief that the object pairs from the two parents will interact. For example, if we are propagating information from the protein level to the domain level, each pair of domain instances has a prior belief of interaction equal to the predicted likelihood that their parent proteins interact.In both cases, after computing the probability of interaction for each pair of objects in the next level based on the predicted values at the current level, we again add the most confident positive and negative predictions as auxiliary training examples for the next level, with the probabilities used as the confidence values of these examples. for some matrix manipulations.In the actual implementation, we used the Java package libsvm  for SVR,We tested the effectiveness of multi-level learning by predicting protein, domain instance and residue interactions of the yeast Saccharomyces cerevisiae.Data features were gathered from multiple sources Table , includiA gold standard positive set was constructed from the union of experimentally verified or structurally determined protein interactions from MIPS , DIP 6565 and iPWe included two types of features at the domain level: co-evolution and statistics related to parent proteins Table . These aThe gold standard positive set was taken from iPfam, where two domain instances are defined as interacting if they are close enough in 3D structure and some of their residues are predicted to form bonding according to their distances and chemistry. After intersecting with the proteins considered at the protein level, a total of 422 domain instance interactions were included, which involves 272 protein interactions and 317 domain instances from 223 proteins and 252 domain families. A negative set with the same number of domain instance pairs was then formed from random pairs of domain instances in the positive set. All known yeast Pfam domain instances of the proteins were involved in the learning, many of which do not have any known interactions in the gold standard positive set. Altogether 2389 domain instances from 1681 proteins and 1184 domain families were included.We used three data features derived from sequences Table . Charge In a previous study , the feaThe gold standard positive set was taken from iPfam, where the interacting residues are determined based on their proximity in known crystal structures of interacting proteins. Since there is a large number of residue pairs, we only sampled 2000 interactions, which involve 228 protein pairs, 327 domain instance pairs and 3053 residues from 195 proteins, 279 domain instances and 224 domain families. Only these 3053 residues were included in the data set. A negative set was created by randomly sampling from these residues 2000 residue pairs that do not have known interactions in iPfam.We used ten-fold cross validation to evaluate the performance of our algorithm. Since the objects in the three levels are correlated, an obvious performance gain would be obtained if in a certain fold the training set of a level contains some direct information about the testing set instances of another level. For example, if a residue interaction in the positive training set comes from a protein pair in the testing set, then the corresponding protein interaction can be directly inferred and thus the residue interaction would create a fake improvement for the predictions at the protein level. This problem was avoided by partitioning the object pairs in the three levels consistently. First, the known protein interactions in iPfam were divided into ten folds. Then, each domain instance interaction and each residue interaction was put into the fold in which the parent protein interaction was assigned. Finally, the remaining protein interactions and all the negative sets were randomly divided into ten folds.Each time, one of the folds was held out as the testing set and the other nine folds were used for training. We used the area under the ROC (Receiver Operator Characteristics) curve (AUC)  to evaluWe compared the prediction accuracies in three cases: independent levels, unidirectional flow of training information only, and bidirectional flow of both training information and predictions. For the latter two cases, we compared the performance when different combinations of the three levels were involved in training.For independent levels, we trained each level independently using its own training set, and then used the predictions as initial estimates to retrain for ten feedback iterations. This iterative procedure was to make sure that any accuracy improvements observed in the other architectures were at least in part due to the communications between the different levels, instead of merely the effect of semi-supervised learning at a single level. For unidirectional flow, we focused on downward flow of information. The levels were always arranged with upper levels coming before lower levels.Table We first notice that the results for independent levels are consistent with our expectations. Having many diverse data features, the protein level has a satisfactory accuracy. On the other hand, the accuracies of the domain and residue levels were relatively low due to their weak and noisy features. Note that we are predicting whether two arbitrary domain instances or two arbitrary residues interact, rather than only those in known interacting protein pairs. This setting is more realistic for organisms with no known protein interaction network, and the problem is significantly harder than when the protein interaction network is available.Downward flow of training information did help the prediction of domain instance interactions. However, the results of the residue level are quite unsatisfactory, with accuracies even lower than those with independent levels no matter assisted by the training examples of the protein level or domain level. In contrast, the results for bidirectional flow are encouraging. In all cases, the accuracies are higher than the other two architectures. For example, while using the domain level to help the residue level decreased the accuracy of the latter from 0.5675 to 0.5128 with unidirectional flow, the accuracy was increased to 0.6182 with bidirectional flow. As an illustration of the difference in performance of the three architectures, the various ROC curves of protein, domain and residue interaction predictions are shown in Figures The improvements for both the domain and residue levels are quite dramatic, with maximum AUC gains of more than 0.15. This clearly shows the benefits of passing not only training information, but also highly confident predictions. Consider a domain instance pair in the testing set of a certain fold. Since the corresponding parent protein pair must not be in the training set at the protein level of the fold, the passing of training information does not directly help predict the interaction status of the domain instance pair. On the other hand, if the interaction status of the protein pair is predicted correctly with high confidence, passing this information to the domain level can make a direct influence on the prediction of the domain instance interaction. For instance, if the protein pair is correctly predicted as not interacting, the domain instance pair would probably be correctly predicted as not interacting, too.In general, it is observed that levels with a higher raw accuracy with independent levels could offer a bigger improvement to the other levels. For example, the protein level increased the accuracy of the residue interaction predictions from 0.5675 to 0.6581, while the domain level could only increased it to 0.6182. However, it is also crucial to note that although the domain level has a low accuracy with independent levels, it could still make good improvements to the prediction of residue interactions. This observation supports our design of passing only highly confident predictions in avoiding the propagation of errors. The combination of all three levels has the potential to further improve accuracy. For both the protein and residue levels, the best results were obtained when all three levels were involved in training. In particular, while each of the protein and domain levels improved the residue level by a certain amount, the combination of them provided yet another significant amount of improvement.As a concrete example of information flow between the three levels, several of the interacting residue pairs between the hexokinase 1 (PF00349) and hexokinase 2 (PF03727) domains of the hexokinase isoenzyme 2 (HXK2) protein are correctly identified with high likelihood of interaction. For example, residue 46 in the hexokinase 1 domain and residue 278 in the hexokinase 2 domain are predicted to interact with a score of 0.89 out of 1.0. This might be partially due to the charge complementarity of the two residues in their PSI-BLAST profiles, with the most conserved residues being the positively-charged arginine and the negatively-charged aspartic acid at the two positions, respectively. The detecting of such residue interaction helps raise the likelihood of the corresponding domain interaction from a score of 0.27 to 0.72. In turn, this helps detect the self-interaction of the glucokinase (GLK1) protein, which also has the two domains. The interaction was verified in a two-hybrid assay [The experimental results have demonstrated the great potential of linking up the prediction problems at the different levels. This initial success encourages deeper investigations of the idea along various directions. Algorithmically, other approaches to combining the different levels, including combined optimization and predictions as extra features, need to be studied. Currently the features at the domain and residue levels are weak, as reflected by their low accuracy when learned independently, and the small improvement they could cause to the protein level. It is interesting to study ways to improve the predictions at these two levels, and more directly extract the complementary information hidden in these levels that are useful for the protein level.The current study is limited by a highly disproportionate dataset, with much more training examples at the protein level than the domain level. Together with a much weaker feature set, the raw accuracy at the domain level is much lower than the protein level, and the former could only slightly improve the predictions of the latter in the multi-level learning framework. It is hoped that as more structures of protein complexes are solved, the disproportionality would be alleviated. In the meantime, it is interesting to study ways to derive other features that could better predict the domain interactions, and the mechanism by which the domain-level information improved the protein-level predictions.In this article we have pointed out some important issues of both multi-level learning and network prediction, including data sparseness and the existence of sub-clusters. While we have proposed methods to tackle them, a detailed analysis of how these issues affect prediction performance and what other algorithmic strategies for tackling them are yet to be studied.To predict the whole interaction network, it is needed to reduce the time and space requirements. One possible way is to intelligently select what data to exclude, such as residues that are predicted to be buried deep inside the core of a protein. Another idea is to group objects into interaction groups so that each cluster can be handled independently.More insights could be gained by studying some theoretical aspects of multi-level learning, such as the hierarchical structure of the prediction problems, and the issue of noisy and incomplete training sets. With multiple levels, performance evaluation is very tricky. As we discussed, careless definitions of training and testing sets could produce biases to the resulting performance. It is instrumental to study the optimal way of evaluation.Biologically, there are many interesting follow-up questions to be studied. The intricate interactions between the different levels are not yet clear, and could form a larger study of how the predictions change after receiving information from the other levels. One could compare different kinds of data features at the three levels and identify the ones with the greatest complementary effects. Another direction is to choose different kinds of residue samples  and inspect the relative improvements they provide to the protein and domain levels, to determine the residues that are more significant in a protein interaction.In this article we have introduced the approach of integrating protein interaction prediction at the protein, domain and residue levels. We have described the potential benefits of this multi-level learning framework due to the availability of distinct and complementary data features at each level. We have defined three information flow architectures for learning from the different levels, and proposed various ways to couple the levels in terms of what and how information is passed between them. We have focused on the training set expansion method, which is a meta-algorithm that passes predictions of a level as augmented training examples of other levels. To avoid the propagation of errors, we have discussed soft coupling, which associates confidence values to predictions and passes only highly confident predictions other levels. The confidence values are used as the inputs of support vector regression. For learning the interaction network at each level, we have compared global and local modeling, which has also highlighted the issue of data sparsity. We have performed computational experiments using yeast data, and shown that the bidirectional flow of supervised and semi-supervised information between the different levels improved the predictions over independent levels and mere downward flow of training information. The evaluation procedure involved special experimental procedures including training-set balancing and consistent cross validation. Finally, we have suggested a number of follow-up research topics.All authors conceived the project and design. KY and PK prepared the data. KY implemented the algorithms, performed the computational experiments, and analyzed the results. KY and MG wrote the paper. All authors read and approved the document.The multi-level learning program. Compiled Java code of the multi-level learning program.Click here for file


How gene duplication has influenced the evolution of gene networks is one of the core problems in evolution. Current duplication-divergence theories generally suggested that genes on the periphery of the networks were preferentially retained after gene duplication. However, previous studies were mostly based on gene networks in invertebrate species, and they had the inherent shortcoming of not being able to provide information on how the duplication-divergence process proceeded along the time axis during major speciation events.In this study, we constructed a model system consisting of human G protein-coupled receptors (GPCRs) and their downstream genes in the GPCR pathways. These two groups of genes offered a natural partition of genes in the peripheral and the backbone layers of the network. Analysis of the age distributions of the duplication events in human GPCRs and "downstream genes" gene families indicated that they both experienced an explosive expansion at the time of early vertebrate emergence. However, we found only GPCR families saw a continued expansion after early vertebrates, mostly prominently in several small subfamilies of GPCRs involved in immune responses and sensory responses.In general, in the human GPCR model system, we found that the position of a gene in the gene networks has significant influences on the likelihood of fixation of its duplicates. However, for a super gene family, the influence was not uniform among subfamilies. For super families, such as GPCRs, whose gene basis of expression diversity was well established at early vertebrates, continued expansions were mostly prominent in particular small subfamilies mainly involved in lineage-specific functions. Gene duplications at genomic and local levels are believed to have played important roles in the evolution of vertebrates -4. WavesHowever, these studies did not provide information as to how the duplication-divergence process  proceedeIn view of these problems, in this study, we used human G-protein coupled receptors (GPCRs) and their downstream genes in the pathways ("downstream genes") as the model system to examine the impact of gene duplication on the evolution of genes in different layers of the network. It has been shown that the gene regulatory network roughly maps to the cellular organization, with the genes on the periphery of the cell maps to the peripheral layer of the gene network . In thisvs. the "downstream genes" provided a more detailed view of the duplication-divergence process along the time axis in the context of major speciation events in vertebrates. Furthermore, GPCRs were partitioned according to the GRAFS system [In this study, we estimated the ages of the duplication events in human GPCRs and the "downstream genes" gene families. Comparison of the age distributions of GPCRs S system  into subs, Gαi/o, Gαq/11, and Gα12/13, which define the corresponding GPCR-related signaling pathways: Gs, Gi/o, Gq/11, G12/13 and Gβγ pathways. We included the major genes in these pathways from the summary [βγ pathway was not specifically shown as all its downstream genes were covered in the Gi/opathway already. Vertebrate and invertebrate homologues of the human "downstream genes" were identified and added to the families in order to reconstruct the phylogenetic trees and estimate of the ages of the duplication events (see Methods).Our model system of human GPCRs and the "downstream genes" was based on the classical GPCR signal pathways, which has been summarized in . Typical summary  as the "We studied the human non-olfactory GPCRs in this study which were classified based on the GRAFS classification system . The olfWe estimated the ages of the duplication events of human GPCRs and "downstream genes" using the "nearest neighbor clock" approach we introduced in a previous work . BrieflyFor the "downstream genes", the process was essentially the same. The ages were estimated using the "nearest neighbor clock" approach as well for each family and were summarized in Additional file We first compared the age distributions of GPCRs and the "downstream genes" in general. We focused on the divergence events happened after 1000 Myrs , as we were mainly interested in the evolution of vertebrates. Single homologues in fly were identified in most of the families, suggesting most of the gene families emerged early in evolution and stayed in single copy in the genomes up at least to the fly. As was shown in Figure We further examined the age distribution of duplication events of different subclasses of GPCRs to see if they contributed equally to the age distribution of GPCRs. Shown in Figure Tetraodon nigroviridis more than 230 Myrs ago. We examined if the same was true for GPCRs in general. Based on the report [In a recent report , GPCRs we report , GPCRs te report . This maIn general, our results have shown that more duplication events were found for the GPCRs than the "downstream genes", particularly in more recent evolutionary stages when the duplication events were mostly local. This was consistent with the current theory of gene duplication and gene network. However, we have found several aspects that have not been covered in the current theory. First, at the time of emergence of early vertebrate, both GPCRs and the "downstream genes" families experienced explosive expansion. The asymmetric duplication-divergence process may be a good model for gene duplication at normal times, but more factors were likely to be in play at that evolutionary stage when massive genomic duplications and explosive increase in tissues complexity happened. Second, the expansion of gene families in the peripheral layer of the gene network may also be asymmetric. Certain small branches of the big family may get disproportional expansion in particular species at particular evolutionary stages, as exemplified by the type 2 taste receptors in human.Duplicated genes often have divergent expression patterns in tissues. We further examined the expression profiles of human GPCRs and the "downstream genes" with respect to their duplication ages. The expression profiles were based on the EST count information from UniGene . For eacShown in Figure Shown in Figure In general, these results of tissue distribution indicated that a substantial enrichment of both GPCRs and the "downstream genes" expressed in brain and nerve tissues happened during the 800-400 Myrs interval. However, similar surge were not observed during the 400-0 Myrs interval. Instead, an enrichment of the GPCRs that expressed in the immune-related tissues of blood and spleen were observed, and this again was contributed mostly by several small GPCRs subfamilies.Current theories of gene duplication and gene networks suggest that genes on the periphery of the network are preferentially retained after gene duplication, in comparison to the genes form the backbones of the network. This is actually necessary for the gene network to remain scale-free after rounds of gene duplication. However, the data supporting these theories were mostly based on the genetic network or the PPI network in yeast and worm. Similar data on gene networks in more advanced species, including vertebrates, were not yet complete and reliable enough. Our model system of GPCRs and the "downstream genes", took the advantage of the knowledge that the gene network roughly maps to the cellular organization , offeredvs. non-peptide ligands in human vs. in fish [There may also be a species-dependence influencing the preference of fixation of duplicated genes within GPCRs. This was reflected in the difference in the preference of retention of GPCRs of peptide ligands  in fish . In fishIn this study, we have kept the model system simple by including only the downstream genes in the classical GPCR pathways. Many other genes that were indirectly influenced by GPCRs were not included in the study, which are mostly kinases and transcription factors in the signaling pathways. However, one of our previous studies  on the hIn general, using the human GPCR model system, our results confirmed that the position of a gene in the gene networks has great influences on the likelihood of expansion of its gene family in evolution. However, we also found that the influence was asymmetric among subfamilies of GPCRs. We found that the gene basis of expression diversity of most GPCR pathways, which cover a substantial portion of the gene network, have been established at the time of early vertebrate emergence. Continued expansions in human GPCR families were to a large extent contributed by several small subfamilies involved in immune responses and sensory responses in human. Exactly which subfamilies may see extra expansion may be contingent on environmental factors for different species at different evolutionary stages, as was exemplified by our comparison of the differences in retention preference of GPCRs binding peptide or non-peptide ligands between humans and fishes.In the future, we shall further investigate the association between gene family expansions and GPCR-related networks -27. For The GPCR gene families analyzed in this study were classified based on the GRAFS classification system , which cThe "downstream genes" families were constructed similarly. Families were constructed for each entry in Figure In bifurcate trees, each new human homologue is created by a duplication event. As a result, for a gene family with n human genes, there will be n-1 duplication events. We used the "nearest-neighbor clock" approach  to date We used the EST counts in UniGene  as the eThe authors declare that they have no competing interests.XG, ZS, YZ and YH conceived the study. XG coordinated the project and the manuscript preparation. YH, YZ and ZS carried out the data analysis and drafted the manuscript. XG and ZS coordinated the project and the manuscript preparation. All authors read and approved the final manuscript.Duplication age distribution of GPCR genes.Click here for fileDuplication age distribution of "downstream genes".Click here for file


Experimental studies of gene expression have identified some of the individual molecular components and elementary reactions that comprise and control cellular behavior. Given our current understanding of gene expression, and the goals of biotechnology research, both scientists and engineers would benefit from detailed simulators that can explicitly compute genome-wide expression levels as a function of individual molecular events, including the activities and interactions of molecules on DNA at single base pair resolution. However, for practical reasons including computational tractability, available simulators have not been able to represent genome-scale models of gene expression at this level of detail., which enables the precise representation of individual molecules and events in gene expression for genome-scale systems. We use a single molecule computational engine to track individual molecules interacting with and along nucleic acid polymers at single base resolution. Tabasco uses logical rules to automatically update and delimit the set of species and reactions that comprise a system during simulation, thereby avoiding the need for a priori specification of all possible combinations of molecules and reaction events. We confirm that single molecule, base-pair resolved simulation using TABASCO (Tabasco) can accurately compute gene expression dynamics and, moving beyond previous simulators, provide for the direct representation of intermolecular events such as polymerase collisions and promoter occlusion. We demonstrate the computational capacity of Tabasco by simulating the entirety of gene expression during bacteriophage T7 infection; for reference, the 39,937 base pair T7 genome encodes 56 genes that are transcribed by two types of RNA polymerases active across 22 promoters.Here we develop a simulator, TABASCO Tabasco enables genome-scale simulation of transcription and translation at individual molecule and single base-pair resolution. By directly representing the position and activity of individual molecules on DNA, Tabasco can directly test the effects of detailed molecular processes on system-wide gene expression. Tabasco would also be useful for studying the complex regulatory mechanisms controlling eukaryotic gene expression. The computational engine underlying Tabasco could also be adapted to represent other types of processive systems in which individual reaction events are organized across a single spatial dimension . Mechanistic models of the individual biochemical events that comprise gene expression are quite detailed and are continuously improving. For example, experiments studying the kinetics of promoter initiation and single molecule studies of processive protein movements along DNA have revealed intricate regulatory processes that control gene expression -4. As thThere are several mathematical approaches for computing the dynamics of systems of biochemical reactions. For example, the chemical species that define a system can be modeled as continuous variables that change over time. In this "continuous" approach, reactions between chemical species are modeled as a set of coupled ordinary differential equations (ODEs) ,8. The sendo16 expression during S. purpuratu development is controlled by a 2,300 base-pair (bp) sequence . In addition, Tabasco should be a good base to further study interactions on DNA that lead to transcription and translation. For example, Tabasco provides a platform to explicitly simulate hypotheses how many transcription factors can interact to direct eukaryotic gene expression, such as in control of endo16 expression [Executables, source code, documentation, and usage notes for Tabasco are freely available, and should facilitate future extensions on the current design (Availability and Requirements). We have already found Tabasco to be useful in constraining models of T7 gene expression by comparing simulator output to new experimental measurements of absolute copies of mRNA abundance during infection; these results will be presented in a forthcoming paper [Keller S, Endy D, Kosuri S, pression . FinallyTabasco implements a modified version of the Gibson Next Reaction Method (NRM) . Gibson'The NRM uses a dependency graph to determine which reactions are affected by any particular reaction's execution. In the NRM, the dependency graph is constructed only once at the start of simulation and remains unchanged afterwards. However, since Tabasco creates reactions and complexes at the single-molecule level dynamically during simulation, a static dependency graph and indexed priority queue will not work. In order to solve this problem, Tabasco contains two specialized classes per DNA molecule within the overall indexed priority queue that are used to track a set of dynamically generated reactions. Each class contains a dynamic priority queue that stores the dynamically generated transcriptional and translational reactions and their tentative reaction times, as well the dependencies of any particular reaction . The minimum tentative reaction time for all the dynamic reactions is set as the tentative reaction time of that dynamic priority queue with respect to the overall priority queue. Since, as in the NRM, Tabasco uses absolute times for determining the next reaction, the particular choice of the data structures containing the reactions does not affect the simulation results. The reason to separate the dynamic queues from the main indexed priority queue is to allow the size of the dynamic queues to change over time. As long as all dependencies are accurately updated upon reaction execution in the dynamic priority queues, the results are equivalent to the NRM. The structure of these dynamic priority queues will now be discussed in more detail.A special class tracks the transcriptional processes for each DNA molecule. This class contains a dynamic priority queue that keeps track of all reactions related to that DNA molecule, such as transcriptional elongation processes. All reactions that are stored in this dynamic priority queue have tentative reaction times , and the minimum tentative reaction time is used to set when this class should be called to execute within the indexed priority queue. In order to determine what the effects of a particular binding or elongation reaction are, the class contains two arrays where each element represents one DNA base. Each element of the first array contains pointers to transcriptional elements encoded at that location such as promoters and terminators. The second array contains pointers to all DNA-protein complexes that reside on the DNA such as elongating RNA polymerase. Only one transcriptional control element or DNA complex can occupy any particular position at any time.The framework we use here to simulate protein-DNA binding is shown in Figure Once an elongation complex is formed, each elongation reaction causes the complex to move one base pair, and the elongation reaction is updated with a new time for the next elongation step. When an elongation reaction executes, the algorithm also checks whether another complex's footprint prevents the current polymerase from moving forward by checking the array containing all complex positions on the DNA. If there is another polymerase blocking the current polymerase's path, the polymerases will behave according to the polymerase interaction model chosen at the start of simulation. For example, the upstream polymerase can terminate, or signal the downstream polymerase to terminate the next time the polymerase is set to elongate, or simply hold its position until the next opportunity to elongate. The elongation reaction also does a check for transcriptional elements on the DNA such as promoters and transcriptional terminators. Upon arriving at a transcriptional terminator, a polymerase will either continue transcribing or terminate depending on a stochastic decision that will also be discussed below. If a transcribing polymerase occludes an open promoter, then the promoter will be decremented and unavailable for binding.The "stochastic decisions" described above for transcriptional termination and abortive initiation on the promoter are used as methods to simplify parameterization in the models, so as to be consistent with how experimental data for such events is typically reported. In the case of termination, a uniform random number is chosen, and if that number is less than the termination efficiency, the polymerase will terminate transcription and fall off the DNA. Analogously, in the case of abortive initiation, if the uniform random number is less than the abortive initiation percentage, then the next reaction will be an abortive initiation step rather than formation of an elongation complex. These decisions take no simulator time, but cause changes in the downstream actions the complexes may take. This simplification is not done for computational efficiency, but more for model simplicity. Tabasco could be modified, with little computational load, to replace the stochastic decisions into competing rates of different reactions. However, these rates are not well understood, and thus we chose to incorporate the measurable models of termination efficiencies and abortive initiation frequencies into the simulator.The transcribing RNA polymerase complexes also produce mRNA, which are tracked by a separate class. Since there are many more copies of RNA than DNA during simulation, and because we were uncertain as to the importance of protein-protein interactions on the mRNA, we chose to treat the majority of translation at the species level. However, if, for example, an RNA polymerase prematurely terminates before reaching the translation stop site, the mRNA and the ribosomes translating it will not produce function proteins. Thus, so long as the coding sequence is still being transcribed, we must treat all translation events at the single-molecule level as well. However, as soon as the entire coding sequence of an open reading frame is transcribed, Tabasco transitions to tracking species of mRNA molecules.We used two classes to model the formation of RBSs and their respective start sites, the Nascent RBSs and Mature RBSs, in order to differentiate when mRNA should be tracked at the single-molecule level or the species-level, respectively. At the start of simulation, one more array of genome length is created that contains the positions of translation start and stop sites on the DNA. As RNA polymerase elongates (as described above), if the polymerase transcribes past a translational start site, a Nascent RBS is made. This Nascent RBS is available for binding by free ribosomes, and a reaction is automatically created and placed into the dynamic priority queue for translation processes. Once the polymerase arrives at the corresponding translation termination site, the Nascent RBS is converted to a Mature RBS, which is tracked at the species-level in the overall Indexed Priority Queue.Translation, both at the single-molecule level and species level, occurs in three steps. First, ribosomes can bind either Nascent or Mature RBSs; there is an initial reaction to form the (Nascent or Mature) Initiation Complex. Second, these initiation complexes are converted to (Nascent or Mature) Elongation Complexes and an RBS at a rate that depends on the speed of the ribosome and the length the ribosome must travel to clear the ribosome binding site. This reaction is treated as a single step, however the distribution of times is chosen from a gamma distribution, in order to better represent a series of individual elongation steps. Third, the Elongation Complex then forms a finished protein and a free ribosome at a rate proportional to the remaining length of the open reading frame. This reaction also is computed via a gamma distribution.At the single molecule level, two additional mechanisms allow for the state of the transcribing RNA polymerase to affect translations. First, if the transcribing RNA polymerase terminates before reaching a corresponding translation stop site, all bound ribosomes are immediately released, the Nascent RBS is removed, and no protein product is formed. Also, for any particular Nascent RNA, the maximal number of Nascent Elongation Complexes that can be formed is capped at the length of the currently transcribed portion of the open reading frame divided by the footprint of the ribosome.Finally, to note, all transitions between single-molecule tracking and species-level tracking occur when a reaction, such as RNA polymerase termination or Initiation Complex conversion into an Elongation Complex. Thus, the transition from single-molecule tracking back to the species level tracking should also not affect the validity of using the NRM.We developed multiple models to represent DNA entry into a cell or compartment (such a step can be useful in starting a simulation of infection or transformation). First, DNA can enter the cell via a zero-order constant reaction rate. Second, RNA polymerases have themselves been implicated as molecular motors that can drive DNA entry ,43. Thus® 1.4. The input file to the simulator is an XML file that describes and parameterizes the relevant genetic elements, initial conditions, and any other reactions that occur. The visualization is created by producing images that are then merged using Quicktime® to create a movie. The source code, executables, along with documentation and instructions for use are available within Additional Files Tabasco is written in JavaAll constants used are provided for completeness. Please see the Supplementary Materials for input files and exact constants used.The distribution of expected times for a reaction to occur in a stochastic simulator depends on the underlying model Figure . ElementWe simulated two models of a promoter driving expression of a coding domain. The first model, termed single-molecule simulation, used the described Tabasco simulator to account for each reaction step during transcription and translation. The model uses the schemes shown in Figures The simulations for the polymerase interactions and bacteriophage T7 development used parameters that can be found in the input files in the Supplementary Materials. Table S1 details the meaning of each of the parameters in the input files. The parameters used were based on empirical measurements where possible. However, in general, the exact values of the constants are ancillary to this section, which is to show that Tabasco is able to simulate processes such as polymerase interactions and entire genetic systems such as T7. The parameter derivations are detailed are detailed elsewhere .Project name: TABASCO;;Project home page: Operating system(s): Platform independent;Programming language: Java;Other requirements: J2SE 1.4.2 or higherLicense: Public domain;Any restrictions to use by non-academics: n/a.SK and DE developed the idea of Tabasco. SK did all work on Tabasco design, code development, modeling and simulation, and drafted the manuscript. SK and JRK developed the Tabasco visualization software. SK and DE edited the manuscript. All authors read and approved the final manuscript.E. coli RNA polymerases are shown as blue and yellow lines moving directly along and above the genomes; directly below the genomes are promoters (dark blue) and terminators (dark red). In addition, the extent of each genomes entry is shown as a solid white line that extends above and below the genome representation (while genome entry is occurring). Protein levels (solid bars) and mRNA levels (white lines) of T7 genes and other host RNA polymerase and ribosome levels are plotted as numbers of molecules per cell on a log-scale below the genome depictions. Each frame is a snapshot of the simulation taken at 5-second intervals; time is displayed in seconds directly below the genome representations.Visualization of T7 genome simulation using Tabasco. We developed a general visualization tool for depicting graphically and dynamically depicting output from Tabasco. Here, we show output from a Tabasco simulation of three T7 phage simultaneously infecting a single cell over the course of 25 minutes. Each of the three white lines at the top represents a distinct copy of the 39,937 bp T7 genome. The T7 and Click here for fileInput files for simulations described in the text of the paper.Click here for fileTABASCO website.Click here for fileParameter definitions within the input file. The table describes the parameter definitions that are used in the input files that are contained in the supplementary materials.Click here for file