The application of atlantoaxial screw and rod fixation in revision operations for postoperative re-dislocation in children.

INTRODUCTION: We evaluate the feasibility, safety, and efficacy of atlantoaxial screw and rod fixation for revision operations in the treatment of re-dislocation after atlantoaxial operations in children. METHODS: Eight consecutive children with atlantoaxial instability required a revision operation due to atlantoaxial re-dislocation caused by the failure of the initial posterior wire fixation. The children were 5-11 years of age with an average age of 8.5 years. The posterior atlantoaxial screw and rod fixation and fusion operation was then performed. Autograft bones harvested from rib (in 3 patients), local bone (2 patients), and the iliac crest bone (3 patients) were used. RESULTS: There were no complications such as vertebral artery or spinal cord injury during the operations or loosening or fracture of the fixations after the operations. Stability and reduction of the atlantoaxial segments were achieved in all patients postoperatively. Follow-up time was 24-55 months, with an average of 35 months. All patients achieved solid osseous fusion demonstrated on plain radiographs or CT scanning. Atlantoaxial screw and rod fixation is feasible in children and may be considered for use during the initial operation in the treatment of atlantoaxial dislocation in children to minimize the need for a revision operation. CONCLUSION: If a revision operation is required, atlantoaxial screw-rod fixation is a safe and effective method. Because the anatomical structure is complicated in revision operation patients, CAD-RP technology could guide the the procedures of exposure and screw placement.

Treatment of basilar invagination with atlantoaxial dislocation: atlantoaxial joint distraction and fixation with transoral atlantoaxial reduction plate (TARP) without odontoidectomy.

PURPOSE: Although direct transoral decompression and one-stage posterior instrumentation can obtain satisfactory cord decompression for the treatment of basilar invagination with atlantoaxial dislocation, surgical injuries run high as combinative anterior-posterior approaches were necessary. Furthermore, the complications will rise notably when involvement of dens and/or clivus in the decompression necessitates relatively complicated surgical techniques. First initiated in 2005, transoral atlantoaxial reduction plate (TARP) works as an internal fixation for the treatment of basilar invagination with irreducible atlantoaxial dislocation. Therefore, this article aimed to describe several operative experiences about this approach, which has delivered successful decompression, fixation and fusion. METHODS: 21 consecutive patients with basilar invagination underwent the TARP operation. The pre- and postoperative medulla-cervical angles were measured and compared. The JOA scores of spinal cord function were calculated pre- and post-operatively. 20 cases (20/21) were followed up to average 12.5 months. RESULTS: Symptoms of all the 20 cases were relieved in different degrees. The postoperative imaging showed the odontoid processes obtained ideal reduction and the internal fixators were all in good position. The medulla-cervical angle was correctd from an average (± standard deviation) 128.7° + 11.9° (n = 20) before surgery to 156.5° + 8.1° (n = 20) after surgery (P < 0.01). The average preoperative and postoperative Japaneses Orthopedic Association scores were 11.25 (n = 20) and 15.9 (n = 20), respectively, indicating 76 % improvement. Screw-loosening was observed in one patient due to severe osteoporosis. After a revised operation with a TARP in another size, the neurological symptoms showed no obvious improvements. Then the treatment was terminated. CONCLUSIONS: The TARP operation and intra-operative traction could reduce the odontoid process superiorly migrating into the foramen magnum, directly ease the ventral compression of spinal cord, and fix the reduced atlantoaxial joints through a single transoral approach without the need of a posterior operation. In this stury, 21 patients were evaluated and 20 did well with TARP operation. The preliminary clinical result was satisfactory.

Privacy-preserving data aggregation in two-tiered wireless sensor networks with mobile nodes.

Privacy-preserving data aggregation in wireless sensor networks (WSNs) with mobile nodes is a challenging problem, as an accurate aggregation result should be derived in a privacy-preserving manner, under the condition that nodes are mobile and have no pre-specified keys for cryptographic operations. In this paper, we focus on the SUM aggregation function and propose two privacy-preserving data aggregation protocols for two-tiered sensor networks with mobile nodes: Privacy-preserving Data Aggregation against non-colluded Aggregator and Sink (PDAAS) and Privacy-preserving Data Aggregation against Colluded Aggregator and Sink (PDACAS). Both protocols guarantee that the sink can derive the SUM of all raw sensor data but each sensor's raw data is kept confidential. In PDAAS, two keyed values are used, one shared with the sink and the other shared with the aggregator. PDAAS can protect the privacy of sensed data against external eavesdroppers, compromised sensor nodes, the aggregator or the sink, but fails if the aggregator and the sink collude. In PDACAS, multiple keyed values are used in data perturbation, which are not shared with the aggregator or the sink. PDACAS can protect the privacy of sensor nodes even the aggregator and the sink collude, at the cost of a little more overhead than PDAAS. Thorough analysis and experiments are conducted, which confirm the efficacy and efficiency of both schemes.

Feature augmentation based on information fusion rectification for few-shot image classification.

In the issue of few-shot image classification, due to lack of sufficient data, directly training the model will lead to overfitting. In order to alleviate this problem, more and more methods focus on non-parametric data augmentation, which uses the information of known data to construct non-parametric normal distribution to expand samples in the support set. However, there are some differences between base class data and new ones, and the distribution of different samples belonging to same class is also different. The sample features generated by the current methods may have some deviations. A new few-shot image classification algorithm is proposed on the basis of information fusion rectification (IFR), which adequately uses the relationship between the data (including the relationship between base class data and new ones, and the relationship between support set and query set in the new class data), to rectify the distribution of support set in the new class data. In the proposed algorithm, feature of support set is expanded through sampling from the rectified normal distribution, so as to augment the data. Compared with other image augmentation algorithms, the experimental results on three few-shot datasets show that the accuracy of the proposed IFR algorithm is improved by 1.84-4.66% on 5-way 1-shot task and 0.99-1.43% on 5-way 5-shot task.

Deep convolution stack for waveform in underwater acoustic target recognition.

In underwater acoustic target recognition, deep learning methods have been proved to be effective on recognizing original signal waveform. Previous methods often utilize large convolutional kernels to extract features at the beginning of neural networks. It leads to a lack of depth and structural imbalance of networks. The power of nonlinear transformation brought by deep network has not been fully utilized. Deep convolution stack is a kind of network frame with flexible and balanced structure and it has not been explored well in underwater acoustic target recognition, even though such frame has been proven to be effective in other deep learning fields. In this paper, a multiscale residual unit (MSRU) is proposed to construct deep convolution stack network. Based on MSRU, a multiscale residual deep neural network (MSRDN) is presented to classify underwater acoustic target. Dataset acquired in a real-world scenario is used to verify the proposed unit and model. By adding MSRU into Generative Adversarial Networks, the validity of MSRU is proved. Finally, MSRDN achieves the best recognition accuracy of 83.15%, improved by 6.99% from the structure related networks which take the original signal waveform as input and 4.48% from the networks which take the time-frequency representation as input.

A quasi-physical algorithm for the structure optimization in an off-lattice protein model.

In this paper, we study an off-lattice protein AB model with two species of monomers, hydrophobic and hydrophilic, and present a heuristic quasi-physical algorithm. First, by elaborately simulating the movement of the smooth solids in the physical world, we find low-energy conformations for a given monomer chain. A subsequent off-trap strategy is then proposed to trigger a jump for a stuck situation in order to get out of the local minima. The algorithm has been tested in the three-dimensional AB model for all sequences with lengths of 13-55 monomers. In several cases, we renew the putative ground state energy values. The numerical results show that the proposed methods are very promising for finding the ground states of proteins.

The anatomical study of transoral atlantoaxial reduction plate internal fixation.

OBJECTIVE: To study relevant anatomical features of the structures involved in transoral atlanto-axial reduction plate (TARP) internal fixation through transoral approach for treating irreducible atlanto-axial dislocation and providing anatomical basis for the clinical application of TARP. METHODS: Ten fresh craniocervical specimens were microsurgically dissected layer by layer through transoral approach. The stratification of the posterior pharyngeal wall, the course of the vertebral artery, anatomical relationships of the adjacent structures of the atlas and axis, and the closely relevant anatomical parameters for TARP internal fixation were measured. RESULTS: The posterior pharyngeal wall consisted of two layers and two interspaces: the mucosa, prevertebral fascia, retropharyngeal space, and prevertebral space. The range from the anterior edge of the foramen magnum to C(3) could be exposed by this approach. The thickness of the posterior pharyngeal wall was (3.6+/-0.3) mm (ranging 2.9-4.3 mm) at the anterior tubercle of C1, (6.1+/-0.4) mm (ranging 5.2-7.1 mm) at the lateral mass of C(1) and (5.5+/-0.4) mm (ranging 4.3-6.5 mm) at the central part of C(2), respectively. The distance from the incisor tooth to the anterior tubercle of C(1), C(1) screw entry point, and C(2)screw entry point was (82.5+/-7.8) mm (ranging 71.4-96.2 mm), (90.1+/-3.8) mm (ranging 82.2-96.3 mm), and (89.0+/-4.1) mm (ranging 81.3-95.3 mm), respectively. The distance between the vertebral artery at the atlas and the midline was (25.2+/- 2.3) mm (ranging 20.4-29.7 mm) and that between the vertebral artery at the axis and the midline was (18.4+/- 2.6) mm (ranging 13.1-23.0 mm). The allowed width of the atlas and axis for exposure was (39.4+/-2.2) mm (ranging 36.2-42.7 mm) and (39.0+/-2.1) mm (ranging 35.8-42.3 mm), respectively. The distance (a) between the two atlas screw insertion points (center of anterior aspect of C(1) lateral mass) was (31.4+/-3.3) mm (ranging 25.4-36.6 mm). The vertical distance (b) between the line connecting the two C(1) screw entry points and that connecting the two C(2) screw entry points (at the central part of the vertebrae, namely 3-4 mm lateral to the midline of C(2) vertebrae) was (21.3+/-2.7) mm (ranging 19.4-24.3 mm), with an a/b ratio of 1.3-1.5. The screws of TARP had a lateral tilt of 12.2 degrees+/-0.4 degrees(ranging 10.2 degrees-14.6 degrees) at C(1) and a medial tilt of 7.3 degrees+/-0.3 degrees (ranging 5.1 degrees-9.4 degrees) at C(2) relative to the coronal plane. CONCLUSIONS: An atlanto-axial surgery through transoral approach is safe and feasible. This approach is suitable for an anterior TARP internal fixation, and the design of the internal fixation system should be based on the above anatomical data.

Transoral atlantoaxial reduction plate fixation for irreducible atlantoaxial dislocation.

OBJECTIVE: To design a clinically applicable transoralpharyngeal atlantoaxial reduction plate (TARP), introduce the operation procedure, and evaluate its preliminary clinical effects. METHODS: A novel TARP system, including butterfly titanium alloy plate, self-locking screws, atlantoaxial reductor and other operational instruments was developed. This system was applied clinically on five patients with irreducible atlantoaxial dislocation of congenital or traumatic origin. During operation, the reduction was completed by the combined action of the plate and the atlantoaxial reductor after transoral joint release and cord decompression. Bone graft granules were implanted between the bilateral atlantoaxial joints and TARP was used to immobilize subsequently the atlas and axis. RESULTS: Clinical application demonstrated that TARP could induce instant reduction and that the method was operationally feasible and its postoperational effect was satisfactory. CONCLUSIONS: The design of TARP is novel. The operational procedure is simple and easy to use. Furthermore, instant reduction can be completed during the operation and the fixation is relatively stable. TARP is an ideal alternative for irreducible atlantoaxial dislocation and may have excellent prospects for further clinical applications.

[Anatomic evaluation the entry point of C2 pedicle screw].

OBJECTIVE: To study the relevant position of C(2) pedicle to C(2) inferior articular process, set up a technique of C(2) pedicle screw placement with the inferior articular process of axis as an anatomic landmark. METHODS: Fifty C(2) bone specimens were used to measure the distance from the sagittal midline to the medial border, the midpoint and the lateral border of C(2) inferior articular process or C(2) pedicle; the width and the height of the C(2) pedicle were also evaluated. The anatomic relation between the measurements data of C(2) pedicle and that of C(2) inferior articular process were analyzed, and the technique of C(2) pedicle screw fixation was established. RESULTS: The medial border of C(2) inferior articular process was averaged (3.67 +/- 0.41) mm lateral to that of C(2) pedicle, and the midpoint C(2) inferior articular process was averaged (1.15 +/- 0.44) mm lateral to the lateral border of C(2) pedicle, respectively. Using the C(2) inferior articular process as landmark, two techniques was established for C(2) pedicle screw placement. The entry point of method A was located in 2 mm medial and superior to the central point of C(2) inferior articular process; the entry point of method B was at the crossing point of the medial border C(2) inferior articular process with the superior quarter of C(2) inferior articular process. CONCLUSIONS: There is a steady anatomic relation between C(2) pedicle and C(2) inferior articular process, the C(2) inferior articular process could be as a convenient key anatomic landmark to determine the location of C(2) pedicle and the position of C(2) pedicle screw entry point.

[Anatomic identification of the location of the pedicle of atlas with the lateral mass of C2 to C4 as the landmark].

OBJECTIVE: To study the relevant position of the pedicle of C1 to the lateral mass of C(2-4), set up an identification technique for the entry point decision of C1 pedicle screw by using the lateral mass of C(2-4) as anatomic landmarks. METHODS: Twenty cadaver specimens were used to measure the distance from the sagittal midline of spine to the medial border, the midpoint and the lateral border of C1 pedicle or the lateral mass of C2, C3 or C4. The anatomic relation between the measurements data of C1 pedicle and that of the lateral masses of the cervical vertebrae were analyzed, and the technique of C1 pedicle screw fixation was established. RESULTS: The average medial border of the lateral mass of C2, C3 and C4 was 0.37 mm, 0.27 mm and 0.24 mm lateral to that of C1 pedicle, the average midpoint of the lateral mass of C2, C3 and C4 was 1.18 mm, 1.41 mm and 1.74 mm lateral to that of C1 pedicle, and the average lateral border of the lateral mass of C2, C3 and C4 was 1.96 mm, 2.54 mm and 3.24 mm lateral to that of C1 pedicle, respectively. CONCLUSION: There is a steady anatomic location relation between C1 pedicle and the lateral mass of C2, C3 or C4. As well as the lateral mass of C2, the lateral mass of C3 or that of C4 could be convenient anatomic landmarks to determine the location of C1 pedicle and the position of C1 pedicle screw entry point.

[Results of 1310 knees of meniscal treatment evaluated by arthroscopy].

OBJECTIVE: To evaluate results of 1310 knees of meniscal treatments by arthroscopy and to present good method of meniscal treatment. METHODS: Their age, traumatic mechanism and effects under arthroscopy were analysed in a series of 254 patients with meniscal injuries, there were 880 males and 374 females, the average of the patients was 25.5 years. The meniscal repair in 68 knee, partial meniscectomy in 756 knee, total meniscectomy in 480 knee and conservative treatment in 6 cases. RESULTS: The patients were followed up 1 to 12 years with the average of 4 years and 3 months. The mean Lysholm score was 86.3 points in arthroscopic meniscal repair, 84.0 points in partial meniscectomy and 76.1 points in total meniscectomy. The mean Lysholm 98.7 points in all children patients with conservative treatment. They showed significant difference (P < 0.01) in the results of three treatments. CONCLUSIONS: Meniscal injuries should not cut off as it, should be repaired in 5 mm from meniscus to synovium and or partial meniscectomy. The general adoption is not the surgical operation on meniscal injuries of the child.

[Mosaicplasty osteochondral grafting to repair cartilaginous defects under arthroscopy].

OBJECTIVE: To study mosaicplasty a as method of autogenous osteochondral transplantation in the treatment of cartilaginous defects. METHODS: The technique involves obtaining small cylindrical grafts from the non-weight bearing periphery of the femur at the patellar femoral joint, and transporting them to the prepared recipient site by arthroscopy. RESULTS: Fifteen patients with defects cartilaginous received mosaicptasty osteochondral grafting. Follow up for 12 to 21 months (mean 15 months) showed good results. CONCLUSION: The treatment is indicated for patients with focal cartilaginous defects under the age of 45.

[The reason and prevention of upper cervical reoperations].

OBJECTIVE: To discuss the reasons for the operation performed on 13 patients with upper cervical disease and to explore the management and prevention of upper cervical disease. METHODS: Thirteen patients with upper cervical disease were retrospectively reviewed. The reason for of reoperations on these patients were analyzed. The measures to reduce upper cervical operational complication and bad prognosis were discussed to avoid reoperations. RESULTS: The reasons for reoperations included 9 cases with unstable or re-dislocated atlantoaxial joint, 10 cases with residual spinal cord compression, 1 case with malposition of odontoid screw, 1 case with adjacent cervical spine regression, 1 case with occipital-cervical fusion failure, 1 case with spinal cord injury during operation, 1 case with bone-plant slipped into canales spinalis, and 1 case with demand to take out internal fixation for aggravated symptom. CONCLUSIONS: The common reasons for upper cervical reoperations were due to instability or redislocation of atlantoaxial joint and residual of spinal cord compression. Some measures such as reducing operate miss, using firm internal fixation and decompressing were advisable to decrease the incidence of reoperations.

[Design and preliminary clinical application of transoralpharyngeal atlantoaxial reduction plate].

OBJECTIVE: To design transoralpharyngeal atlantoaxial reduction plate (TARP), evaluate its biomechanical performance and observe its preliminary clinical effect. METHODS: A brand-new TARP system was designed, including butterfly titanium alloy plate, self-locking screws, atlantoaxial reductor and other operation instruments. Twelve fresh occipital bone-C(3) specimen were designed for biomechanical test including range of motion (ROM) (n = 6) and screw pull-out strength (n = 12). Preliminary clinical application of TARP was reported. RESULTS: The reduction mechanism of the TARP system was designed cleverly. TARP had equal effect with Magerl + Brooks and it was more stable than the other three clinically widely used atlantoaxial fixators: Magerl, Brooks and anterior transarticular screw fixation through C(2) vertebral body. TARP's C(1) and C(2) screws were strong enough for atlantoaxial arthrodesis and their antipull-out performance was excellent. Clinical application on irreducible atlantoaxial dislocation proved that TARP had the function of instant reduction, the operation was feasible and the operation effect was significant. CONCLUSION: TARP's design is novel and it has excellent biomechanical performance. The operation procedure is simple and reasonable. Furthermore, instant reduction could be completed during the operation and the fixation is strong. Above all, TARP is creative and will have excellent prospect.

Wang-Landau sampling in face-centered-cubic hydrophobic-hydrophilic lattice model proteins.

Finding the global minimum-energy structure is one of the main problems of protein structure prediction. The face-centered-cubic (fcc) hydrophobic-hydrophilic (HP) lattice model can reach high approximation ratios of real protein structures, so the fcc lattice model is a good choice to predict the protein structures. The lacking of an effective global optimization method is the key obstacle in solving this problem. The Wang-Landau sampling method is especially useful for complex systems with a rough energy landscape and has been successfully applied to solving many optimization problems. We apply the improved Wang-Landau (IWL) sampling method, which incorporates the generation of an initial conformation based on the greedy strategy and the neighborhood strategy based on pull moves into the Wang-Landau sampling method to predict the protein structures on the fcc HP lattice model. Unlike conventional Monte Carlo simulations that generate a probability distribution at a given temperature, the Wang-Landau sampling method can estimate the density of states accurately via a random walk, which produces a flat histogram in energy space. We test 12 general benchmark instances on both two-dimensional and three-dimensional (3D) fcc HP lattice models. The lowest energies by the IWL sampling method are as good as or better than those of other methods in the literature for all instances. We then test five sets of larger-scale instances, denoted by the S, R, F90, F180, and CASP target instances on the 3D fcc HP lattice model. The numerical results show that our algorithm performs better than the other five methods in the literature on both the lowest energies and the average lowest energies in all runs. The IWL sampling method turns out to be a powerful tool to study the structure prediction of the fcc HP lattice model proteins.

Heuristic-based tabu search algorithm for folding two-dimensional AB off-lattice model proteins.

The protein structure prediction problem is a classical NP hard problem in bioinformatics. The lack of an effective global optimization method is the key obstacle in solving this problem. As one of the global optimization algorithms, tabu search (TS) algorithm has been successfully applied in many optimization problems. We define the new neighborhood conformation, tabu object and acceptance criteria of current conformation based on the original TS algorithm and put forward an improved TS algorithm. By integrating the heuristic initialization mechanism, the heuristic conformation updating mechanism, and the gradient method into the improved TS algorithm, a heuristic-based tabu search (HTS) algorithm is presented for predicting the two-dimensional (2D) protein folding structure in AB off-lattice model which consists of hydrophobic (A) and hydrophilic (B) monomers. The tabu search minimization leads to the basins of local minima, near which a local search mechanism is then proposed to further search for lower-energy conformations. To test the performance of the proposed algorithm, experiments are performed on four Fibonacci sequences and two real protein sequences. The experimental results show that the proposed algorithm has found the lowest-energy conformations so far for three shorter Fibonacci sequences and renewed the results for the longest one, as well as two real protein sequences, demonstrating that the HTS algorithm is quite promising in finding the ground states for AB off-lattice model proteins.

Energy-landscape paving for prediction of face-centered-cubic hydrophobic-hydrophilic lattice model proteins.

Protein structure prediction (PSP) is a classical NP-hard problem in computational biology. The energy-landscape paving (ELP) method is a class of heuristic global optimization algorithm, and has been successfully applied to solving many optimization problems with complex energy landscapes in the continuous space. By putting forward a new update mechanism of the histogram function in ELP and incorporating the generation of initial conformation based on the greedy strategy and the neighborhood search strategy based on pull moves into ELP, an improved energy-landscape paving (ELP+) method is put forward. Twelve general benchmark instances are first tested on both two-dimensional and three-dimensional (3D) face-centered-cubic (fcc) hydrophobic-hydrophilic (HP) lattice models. The lowest energies by ELP+ are as good as or better than those of other methods in the literature for all instances. Then, five sets of larger-scale instances, denoted by S, R, F90, F180, and CASP target instances on the 3D FCC HP lattice model are tested. The proposed algorithm finds lower energies than those by the five other methods in literature. Not unexpectedly, this is particularly pronounced for the longer sequences considered. Computational results show that ELP+ is an effective method for PSP on the fcc HP lattice model.

New clinical classification system for atlantoaxial dislocation.

The purpose of this study was to define a new clinical classification of atlantoaxial dislocation based on its clinical manifestations, namely reducible atlantoaxial dislocation (RAAD), irreducible atlantoaxial dislocation (IAAD), and fixed atlantoaxial dislocation (FAAD). A total of 107 patients with atlantoaxial dislocation were respectively treated based on this clinical classification, including 66 patients with RAAD, 39 patients with IAAD, and 2 patients with FAAD. Six of the 66 patients with RAAD with rotatory atlantoaxial dislocation were treated with traction and a cervical collar, 9 with fresh type II dens fracture were treated with cannulated screw fixation, and 51 were treated with posterior atlantoaxial or occipitocervical arthrodesis. Thirty-eight patients with IAAD received a transoral atlantoaxial reduction plate system, and 1 with a giant cell tumor was treated with lesion resection and vertebral reconstruction by a shaped titanium mesh system followed by posterior occipitocervical screw-rod fixation. The 2 patients with FAAD underwent anterior decompression and received a transoral atlantoaxial reduction plate system. Follow-up data were obtained for a minimum of 6 months. All patients' neurological symptoms improved postoperatively. Bony union was accomplished by 3-month follow-up. Donor-site infection was found in 1 patient, with no occurrence of other complications. This article proposes a new classification of atlantoaxial dislocation indicating the severity and difficulty in reduction of the atlantoaxial joint. The classification system assists with decision making regarding therapeutic options. Transoral atlantoaxial reduction plate fixation and posterior atlantoaxial screw-rod fixation are commonly performed for atlantoaxial dislocation.

Heuristic energy landscape paving for protein folding problem in the three-dimensional HP lattice model.

The protein folding problem, i.e., the prediction of the tertiary structures of protein molecules from their amino acid sequences is one of the most important problems in computational biology and biochemistry. However, the extremely difficult optimization problem arising from energy function is a key challenge in protein folding simulation. The energy landscape paving (ELP) method has already been applied very successfully to off-lattice protein models and other optimization problems with complex energy landscape in continuous space. By improving the ELP method, and subsequently incorporating the neighborhood strategy with the pull-move set into the improved ELP method, a heuristic ELP algorithm is proposed to find low-energy conformations of 3D HP lattice model proteins in the discrete space. The algorithm is tested on three sets of 3D HP benchmark instances consisting 31 sequences. For eleven sequences with 27 monomers, the proposed method explores the conformation surfaces more efficiently than other methods, and finds new lower energies in several cases. For ten 48-monomer sequences, we find the lowest energies so far. With the achieved results, the algorithm converges rapidly and efficiently. For all ten 64-monomer sequences, the algorithm finds lower energies within comparable computation times than previous methods. Numeric results show that the heuristic ELP method is a competitive tool for protein folding simulation in 3D lattice model. To the best of our knowledge, this is the first application of ELP to the 3D discrete space.

Protein-folding simulations of the hydrophobic-hydrophilic model by combining pull moves with energy landscape paving.

The energy landscape paving (ELP) method is a class of heuristic global optimization algorithms based on Monte Carlo sampling. By incorporating the generation of an initial conformation based on a greedy strategy, the conformation update mechanism based on pull moves, and some heuristic off-trap strategies into an improved ELP method, we propose an alternative version of the ELP method, called the ELP-pull move method. We test the ELP-pull move method on both two-dimensional (2D) and 3D hydrophobic-hydrophilic protein-folding models. For ten 2D benchmark sequences of length ranging from 20 to 100, the proposed algorithm finds the lowest energies so far. Within the achieved results, the algorithm converges more rapidly and efficiently than previous methods. For all ten 3D sequences with a length of 64, the ELP-pull move method finds lower energies within comparable computational times. The numerical results demonstrate that our algorithm is a powerful method to study the lattice protein-folding model.