Gaussian Network Model Research Articles

Dynamics of binding interactions of TDP-43 and RNA: An equally weighted multiscale elastic network model study.

Transactive response DNA binding protein 43 (TDP-43), an alternative-splicing regulator, can specifically bind long UG-rich RNAs, associated with a range of neurodegenerative diseases. Upon binding RNA, TDP-43 undergoes a large conformational change with two RNA recognition motifs (RRMs) connected by a long linker rearranged, strengthening the binding affinity of TDP-43 with RNA. We extend the equally weighted multiscale elastic network model (ewmENM), including its Gaussian network model (ewmGNM) and Anisotropic network model (ewmANM), with the multiscale effect of interactions considered, to the characterization of the dynamics of binding interactions of TDP-43 and RNA. The results reveal upon RNA binding a loss of flexibility occurs to TDP-43's loop3 segments rich in positively charged residues and C-terminal of high flexibility, suggesting their anchoring RNA, induced fit and conformational adjustment roles in recognizing RNA. Additionally, based on movement coupling analyses, it is found that RNA binding strengthens the interactions among intra-RRM β-sheets and between RRMs partially through the linker's mediating role, which stabilizes RNA binding interface, facilitating RNA binding efficiency. In addition, utilizing our proposed thermodynamic cycle method combined with ewmGNM, we identify the key residues for RNA binding whose perturbations induce a large change in binding free energy. We identify not only the residues important for specific binding, but also the ones critical for the conformational rearrangement between RRMs. Furthermore, molecular dynamics simulations are also performed to validate and further interpret the ENM-based results. The study demonstrates a useful avenue to utilize ewmENM to investigate the protein-RNA interaction dynamics characteristics.

Time- and ensemble-average statistical mechanics of the Gaussian network model

We present analytical results for a set of time- and ensemble-averaged physical observables in the non-Hookean Gaussian network model (GNM)—a generalization of the Rouse model to elastic networks with links that display a certain degree of extensional and rotational stiffness. We focus on a set of coarse-grained observables that may be of interest in the analysis of GNM in the context of internal motions in proteins and mechanical frames in contact with a heat bath. A C++ computer code is made available that implements all analytical results.

Normal Mode Analysis of KRas4B Reveals Partner Specific Dynamics.

Ras GTPase interacts with its regulators and downstream effectors for its critical function in cellular signaling. Targeting the disrupted mechanisms in Ras-related human cancers requires understanding the distinct dynamics of these protein-protein interactions. We performed normal mode analysis (NMA) of KRas4B in wild-type or mutant monomeric and neurofibromin-1 (NF1), Son of Sevenless 1 (SOS1) or Raf-1 bound dimeric conformational states to reveal partner-specific dynamics of the protein. Gaussian network model (GNM) analysis showed that the known KRas4B lobes further partition into subdomains upon binding to its partners. Furthermore, KRas4B interactions with different partners suppress the flexibility in not only their binding sites but also distant residues in the allosteric lobe in a partner-specific way. The conformational changes can be driven by intrinsic residue fluctuations of the open state KRas4B-GDP, as we illustrated with anisotropic network model (ANM) analysis. The allosteric paths connecting the nucleotide binding residues to the allosteric site at α3-L7 portray differences in the inactive and active states. These findings help in understanding the partner-specific KRas4B dynamics, which could be utilized for therapeutic targeting.

Global Dynamics Renders Protein Sites with High Functional Response.

Deep mutational scanning enables examination of the effects of many mutations at each amino acid position in a query protein, readily disclosing positions that are particularly sensitive. Mutations in these positions alter protein function the most. Here, on the premise that dynamics underlie function, we explore to what extent the measured sensitivity to mutations could be linked to-perhaps be explained by-the structural dynamics of the protein. We employ a minimalist perturbation-response approach based on the Gaussian Network Model (GNM) on a data set of seven proteins with deep mutational scanning data. The analysis shows that the mutation-sensitive positions are often of capacity to modulate the global dynamics and to intermediate allosteric interactions in the structure. With that, upon strain perturbation, these positions decrease residue fluctuations the most, affecting function via entropy changes. This is particularly relevant for positions that are distant from binding sites or other functional regions of the protein and are sensitive to mutations, nevertheless. Our results indicate that mutations in these positions allosterically manipulate protein function.

Protein dynamics analysis identifies candidate cancer driver genes and mutations in TCGA data.

Recently, it has been showed that cancer missense mutations selectively target the neighborhood of hinge residues, which are key sites in protein dynamics. Here, we show that this approach can be extended to find previously unknown candidate mutations and genes. To this aim, we developed a computational pipeline to detect significantly enriched three-dimensional (3D) clustering of missense mutations around hinge residues. The hinge residues were detected by applying a Gaussian network model. By systematically analyzing the PanCancer compendium of somatic mutations in nearly 10 000 tumors from the Cancer Genome Atlas, we identified candidate genes and mutations in addition to well known ones. For instance, we found significantly enriched 3D clustering of missense mutations in known cancer genes including CDK4, CDKN2A, TCL1A, and MAPK1. Beside these known genes, we also identified significantly enriched 3D clustering of missense mutations around hinge residues in PLA2G4A, which may lead to excessive phosphorylation of the extracellular signal-regulated kinases. Furthermore, we demonstrated that hinge-based features improves pathogenicity prediction for missense mutations. Our results show that the consideration of clustering around hinge residues can help us explain the functional role of the mutations in known cancer genes and identify candidate genes.

Study on functional sites in human multidrug resistance protein 1 (hMRP1).

Human multidrug resistance protein 1 (hMRP1) is an important member of the ATP-binding cassette (ABC) transporter superfamily. It can extrude a variety of anticancer drugs and physiological organic anions across the plasma membrane, which is activated by substrate binding, and is accompanied by large-scale cooperative movements between different domains. Currently, it remains unclear completely about how the specific interactions between hMRP1 and its substrate are and which critical residues are responsible for allosteric signal transduction. To the end, we first construct an inward-facing state of hMRP1 using homology modeling method, and then dock substrate proinflammatory agent leukotriene C4 (LTC4) to hMRP1 pocket. The result manifests LTC4 interacts with two parts of hMRP1 pocket, namely the positively charged pocket (P pocket) and hydrophobic pocket (H pocket), similar to its binding mode with bMRP1 (bovine MRP1). Additionally, we use the Gaussian network model (GNM)-based thermodynamic method proposed by us to identify the key residues whose perturbations markedly alter their binding free energy. Here the conventional GNM is improved with covalent/non-covalent interactions and secondary structure information considered (denoted as sscGNM). In the result, sscGNM improves the flexibility prediction, especially for the nucleotide binding domains with rich kinds of secondary structures. The 46 key residue clusters located in different subdomains are identified which are highly consistent with experimental observations. Furtherly, we explore the long-range cooperation within the transporter. This study is helpful for strengthening the understanding of the work mechanism in ABC exporters and can provide important information to scientists in drug design studies.

Enhancements of the Gaussian network model in describing nucleotide residue fluctuations for RNA

Gaussian network model (GNM) is an efficient method to investigate the structural dynamics of biomolecules. However, the application of GNM on RNAs is not as good as that on proteins, and there is still room to improve the model. In this study, two novel approaches, named the weighted GNM (wGNM) and the force-constant-decayed GNM (fcdGNM), were proposed to enhance the performance of ENM in investigating the structural dynamics of RNAs. In wGNM, the force constant for each spring is weighted by the number of interacting heavy atom pairs between two nucleotides. In fcdGNM, all the pairwise nucleotides were connected by springs and the force constant decayed exponentially with the separate distance of the nucleotide pairs. The performance of these two proposed models was evaluated by using a non-redundant RNA structure database composed of 51 RNA molecules. The calculation results show that both the proposed models outperform the conventional GNM in reproducing the experimental B-factors of RNA structures. Compared with the conventional GNM, the Pearson correlation coefficient between the predicted and experimental B-factors was improved by 9.85% and 6.76% for wGNM and fcdGNM, respectively. Our studies provide two candidate methods for better revealing the dynamical properties encoded in RNA structures.

Oncogenic mutations on Rac1 affect global intrinsic dynamics underlying GTP and PAK1 binding

Rac1 is a small member of the Rho GTPase family. One of the most important downstream effectors of Rac1 is a serine/threonine kinase, p21-activated kinase 1 (PAK1). Mutational activation of PAK1 by Rac1 has oncogenic signaling effects. Here, although we focus on Rac1-PAK1 interaction by atomic-force-microscopy-based single-molecule force spectroscopy experiments, we explore the effect of active mutations on the intrinsic dynamics and binding interactions of Rac1 by Gaussian network model analysis and molecular dynamics simulations. We observe that Rac1 oncogenic mutations are at the hinges of three global modes of motion, suggesting the mechanical changes as potential markers of oncogenicity. Indeed, the dissociation of wild-type Rac1-PAK1 complex shows two distinct unbinding dynamic states that are reduced to one with constitutively active Q61L and oncogenic Y72C mutant Rac1, as revealed by single-molecule force spectroscopy experiments. Q61L and Y72C mutations change the mechanics of the Rac1-PAK1 complex by increasing the elasticity of the protein and slowing down the transition to the unbound state. On the other hand, Rac1’s intrinsic dynamics reveal more flexible GTP and PAK1-binding residues on switches I and II with Q61L, Y72C, oncogenic P29S and Q61R, and negative T17N mutations. The cooperativity in the fluctuations of GTP-binding sites around the p-loop and switch I decreases in all mutants, mostly in Q61L, whereas some PAK1-binding residues display enhanced coupling with GTP-binding sites in Q61L and Y72C and within each other in P29S. The predicted binding free energies of the modeled Rac1-PAK1 complexes show that the change in the dynamic behavior likely means a more favorable PAK1 interaction. Overall, these findings suggest that the active mutations affect intrinsic functional dynamic events and alter the mechanics underlying the binding of Rac1 to GTP and upstream and downstream partners including PAK1.

Equally Weighted Multiscale Elastic Network Model and Its Comparison with Traditional and Parameter-Free Models.

Dynamical properties of proteins play an essential role in their function exertion. The elastic network model (ENM) is an effective and efficient tool in characterizing the intrinsic dynamical properties encoded in biomacromolecule structures. The Gaussian network model (GNM) and anisotropic network model (ANM) are the two often-used ENM models. Here, we introduce an equally weighted multiscale ENM (equally weighted mENM) based on the original mENM (denoted as mENM), in which fitting weights of Kirchhoff/Hessian matrixes in mENM are removed since they neglect the details of pairwise interactions. Then, we perform its comparison with the mENM, traditional ENM, and parameter-free ENM (pfENM) in reproducing dynamical properties for the six representative proteins whose molecular dynamics (MD) trajectories are available in http://mmb.pcb.ub.es/MoDEL/. In the results, for B-factor prediction, mENM performs best, while the equally weighted mENM performs also well, better than the traditional ENM and pfENM models. As to the dynamical cross-correlation map calculation, mENM performs worst, while the results produced from the equally weighted mENM and pfENM models are close to those from MD trajectories with the latter a little better than the former. Furthermore, encouragingly, the equally weighted mANM displays the best performance in capturing the functional motional modes, followed by pfANM and traditional ANM models, while the mANM fails in all the cases. This work is helpful for strengthening the understanding of the elastic network model and provides a valuable guide for researchers to utilize the model to explore protein dynamics.

Synchronous and Asynchronous Response in Dynamically Perturbed Proteins.

We present a dynamic perturbation-response model of proteins based on the Gaussian Network Model, where a residue is perturbed periodically, and the dynamic response of other residues is determined. The model shows that periodic perturbation causes a synchronous response in phase with the perturbation and an asynchronous response that is out of phase. The asynchronous component results from the viscous effects of the solvent and other dispersive factors in the system. The model is based on the solution of the Langevin equation in the presence of solvent, noise, and perturbation. We introduce several novel ideas: The concept of storage and loss compliance of the protein and their dependence on structure and frequency; the amount of work lost and the residues that contribute significantly to the lost work; new dynamic correlations that result from perturbation; causality, that is, the response of j when i is perturbed is not equal to the response of i when j is perturbed. As examples, we study two systems, namely, bovine rhodopsin and the class of nanobodies. The general results obtained are (i) synchronous and asynchronous correlations depend strongly on the frequency of perturbation, their magnitude decreases with increasing frequency, (ii) time-delayed mean-squared fluctuations of residues have only synchronous components. Asynchronicity is present only in cross correlations, that is, correlations between different residues, (iii) perturbation of loop residues leads to a large dissipation of work, (iv) correlations satisfy the hypothesis of pre-existing pathways according to which information transfer by perturbation rides on already existing equilibrium correlations in the system, (v) dynamic perturbation can introduce a selective response in the system, where the perturbation of each residue excites different sets of responding residues, and (vi) it is possible to identify nondissipative residues whose perturbation does not lead to dissipation in the protein. Despite its simplicity, the model explains several features of allosteric manipulation.

Allosteric and transport modulation of human concentrative nucleoside transporter 3 at the atomic scale.

Nucleosides are important precursors of nucleotide synthesis in cells, and nucleoside transporters play an important role in many physiological processes by mediating transmembrane transport and absorption. During nucleoside transport, such proteins undergo a significant conformational transition between the outward- and inward-facing states, which leads to alternating access of the substrate-binding site to either side of the membrane. In this work, a variety of molecular simulation methods have been applied to comparatively investigate the motion modes of human concentrative nucleoside transporter 3 (hCNT3) in three states, as well as global and local cavity conformational changes; and finally, a possible elevator-like transport mechanism consistent with experimental data was proposed. The results of the Gaussian network model (GNM) and anisotropic network model (ANM) show that hCNT3 as a whole tends to contract inwards and shift towards a membrane inside, exhibiting an allosteric process that is more energetically favorable than the rigid conversion. To reveal the complete allosteric process of hCNT3 in detail, a series of intermediate conformations were obtained by an adaptive anisotropic network model (aANM). One of the simulated intermediate states is similar to that of a crystal structure, which indicates that the allosteric process is reliable; the state with lower energy is slightly inclined to the inward-facing structure rather than the expected intermediate crystal structure. The final HOLE analysis showed that except for the outward-facing state, the transport channels were gradually enlarged, which was conductive to the directional transport of nucleosides. Our work provides a theoretical basis for the multistep elevator-like transportation mechanism of nucleosides, which helps to further understand the dynamic recognition between nucleoside substrates and hCNT3 as well as the design of nucleoside anticancer drugs.

Local and Global Motions Underlying Antibiotic Binding in Bacterial Ribosome.

The bacterial ribosome is one of the most important targets in the treatment of infectious diseases. As antibiotic resistance in bacteria poses a growing threat, a significant amount of effort is concentrated on exploring new drug-binding sites where testable predictions are of significance. Here, we study the dynamics of a ribosomal complex and 67 small and large subunits of the ribosomal crystal structures (64 antibiotic-bound, 3 antibiotic-free) from Deinococcus radiodurans, Escherichia coli, Haloarcula marismortui, and Thermus thermophilus by the Gaussian network model. Interestingly, a network of nucleotides coupled in high-frequency fluctuations reveals known antibiotic-binding sites. These sites are seen to locate at the interface of dynamic domains that have an intrinsic dynamic capacity to interfere with functional globular motions. The nucleotides and the residues fluctuating in the fast and slow modes of motion thus have promise for plausible antibiotic-binding and allosteric sites that can alter antibiotic binding and resistance. Overall, the present analysis brings a new dynamic perspective to the long-discussed link between small-molecule binding and large conformational changes of the supramolecule.

Folding nucleus and unfolding dynamics of protein 2GB1* *Project supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA17010504) and the National Natural Science Foundation of China (Grant No. 11947302).

The folding of many small proteins is kinetically a two-state process with one major free-energy barrier to overcome, which can be roughly regarded as the inverse process of unfolding. In this work, we first use a Gaussian network model to predict the folding nucleus corresponding to the major free-energy barrier of protein 2GB1, and find that the folding nucleus is located in the β-sheet domain. High-temperature molecular dynamics simulations are then used to investigate the unfolding process of 2GB1. We draw free-energy surface from unfolding simulations, taking RMSD and contact number as reaction coordinates, which confirms that the folding of 2GB1 is kinetically a two-state process. The comparison of the contact maps before and after the free energy barrier indicates that the transition from native to non-native structure of the protein is kinetically caused by the destruction of the β-sheet domain, which manifests that the folding nucleus is indeed located in the β-sheet domain. Moreover, the constrained MD simulation further confirms that the destruction of the secondary structures does not alter the topology of the protein retained by the folding nucleus. These results provide vital information for upcoming researchers to further understand protein folding in similar systems.

Weighted-persistent-homology-based machine learning for RNA flexibility analysis.

With the great significance of biomolecular flexibility in biomolecular dynamics and functional analysis, various experimental and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibility. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models have been proposed for flexibility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model has been proposed. By using the features from persistent homology, this model achieves a remarkable high Pearson correlation coefficient (PCC) in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH) to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a PCC of up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent improvement in performance by at least 10% is achieved in our current model.

A study on allosteric communication in U1A-snRNA binding interactions: network analysis combined with molecular dynamics data

The allosteric regulation during the binding interactions between small nuclear RNAs (snRNAs) and the associated protein factors is critical to the function of spliceosomes in alternative RNA splicing. Although network models combined with molecular dynamics simulations have shown to be powerful tools for the analysis of protein allostery, the atomic-level simulations are, however, too expensive and with limited accuracy for the large-size systems. In this work, we use a residual network model combined with a coarse-grained Gaussian network model (GNM) to investigate the binding interactions between the snRNA and the human U1A protein which is a major component of the spliceosomal U1 small nuclear ribonucleoprotein particle, and to identify the residues that play an important role in the allosteric communication in U1A during this process. We also utilize the Girvan-Newman method to detect the structural organization in U1A-snRNA recognition and interactions. Our results reveal that: (Ι) not only the residues at the binding sites that are traditionally considered to play a major role in U1A-snRNA association, but those residues that are far away from the RNA binding interface participate in the U1A's allosteric signal transmission induced by the RNA binding; (Π) the structure of U1A protein is well organized with different communities acting different roles for its RNA binding and allosteric regulation. The study demonstrates that the combination of the residual network and elastic network models is an effective and efficient method which can be readily extended to the investigation of the allosteric communication for other macromolecular interaction systems.

Exploring the dynamics of RNA molecules with multiscale Gaussian network model

RNA molecules play important roles in biological processes, their functions are intimately related to structural dynamics. Elastic network model (ENM) has achieved great success in predicting the large-amplitude collective behavior of proteins. However, for loosely-packed RNA structures, ENM models can not reproduce their dynamics as accurate as the densely-packed ones. In this work, the multiscale Gaussian network model (mGNM) is extended to predict dynamic properties of RNAs. All tests are performed on a non-redundant RNA structure database we constructed. In results, for B-factor reproduction, encouragingly mGNM achieves a significant improvement with the average value of Pearson correlation coefficient (PCC) between theoretical and experimental B-factors being 0.732, much higher than 0.494 and 0.321 obtained by conventional GNM and parameter-free GNM (pfGNM) models, respectively. Furtherly, mGNM attains a larger improvement in B-factor prediction for loosely-packed parts. Additionally, based on the analysis of functional movements, mGNM can properly make domain decompositions for tRNAAsp and xrRNA. This work can strengthen the understanding of the intrinsic dynamics of RNAs, and mGNM is expected to have a bright prospect in dynamic analyses for loosely folded biomolecules, especially RNAs.

A Drift-Compensating Novel Deep Belief Classification Network to Improve Gas Recognition of Electronic Noses

Electronic nose (E-nose) systems have a good effect on the identification of distinct odours. However, the properties of chemical gas sensors indicate that ageing, poisoning, fluctuation of environmental conditions (moisture, temperature, etc.) and a lack of fabrication repeatability, etc. have a large impact on the sensitivity and accuracy of sensors, which leads to sensor data drift. Although previous studies have indicated the feasibility and validity of deep learning in drift compensation of gas sensor data, the actual performances of these deep learning models are less impressive compared with some existing methods. Thus, we intend to further explore a novel deep learning model for drift compensation for E-noses. In this paper, we investigate the drift compensation effect of E-nose data based on a deep belief network (DBN) and constructed a Gaussian deep belief classification network (GDBCN) model by cascading a Gaussian-Bernoulli restricted Boltzmann machines based DBN with a softmax classifier layer to compensate for sensor drift at the decision level. The merits of our method are as follows: 1) it is a unified classification model for drift auto-compensation at the decision level rather than a feature extractor; 2) it couples unsupervised and supervised techniques by modelling the intrinsic distribution of the data from different domains in an unsupervised manner and fine-tunes the model parameters by leveraging the label information of the source domain; 3) the supervised fine-tuning process for the coupled GDBCN model fits well with the nature of the supervised task and guarantees that the parameters of the DBN will be useful for classification; 4) the GDBCN model is a classification model and thus automatically compensates for drift without manually setting specific model rules for domain alignment before classification. Experimental results on real sensor datasets demonstrate the effectiveness and superiority compared with several existing control methods.

Dynamical comparison between Drosha and Dicer reveals functional motion similarities and dissimilarities

Drosha and Dicer are RNase III family members of classes II and III, respectively, which play a major role in the maturation of micro-RNAs. The two proteins share similar domain arrangement and overall fold despite no apparent sequence homology. The overall structural and catalytic reaction similarity of both proteins, on the one hand, and differences in the substrate and its binding mechanisms, on the other, suggest that both proteins also share dynamic similarities and dissimilarities. Since dynamics is essential for protein function, a comparison at their dynamics level is fundamental for a complete understanding of the overall relations between these proteins. In this study, we present a dynamical comparison between human Drosha and Giardia Dicer. Gaussian Network Model and Anisotropic Network Model modes of motion of the proteins are calculated. Dynamical comparison is performed using global and local dynamic programming algorithms for aligning modes of motion. These algorithms were recently developed based on the commonly used Needleman-Wunsch and Smith-Waterman algorithms for global and local sequence alignment. The slowest mode of Drosha is different from that of Dicer due to its more bended posture and allow the motion of the double-stranded RNA-binding domain toward and away from its substrate. Among the five slowest modes dynamics similarity exists only for the second slow mode of motion of Drosha and Dicer. In addition, high local dynamics similarity is observed at the catalytic domains, in the vicinity of the catalytic residues. The results suggest that the proteins exert a similar catalytic mechanism using similar motions, especially at the catalytic sites.

Weighted-Persistent-Homology-based Machine Learning for RNA Flexibility Analysis

With the great significance of biomolecular flexibility in biomolecular dynamics and function analysis, various experimental methods and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibilities. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models, have been proposed for flexility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model is proposed. By using the features from persistent homology, this model achieves remarkable high accuracy in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH), which is not to consider the topology of a whole RNA structure, but to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a Pearson correlation coefficient up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent increase of accuracy by at least 10% is achieved in our current model.

Sparse inverse covariance matrix estimation via the -norm with Tikhonov regularization**The research is supported by the Special Project on High-performance Computing under the National Key R&D Program (Grant No. 2016YFB0200602), by the Natural Science Foundation of China under Grant Nos. 11701189 and 11771464.

Sparse inverse covariance matrix estimation is a fundamental problem in a Gaussian network model and has attracted much attention in the last decade. A widely used approach for estimating the sparse inverse covariance matrix is the regularized negative log-likelihood minimization, where the regularization term promotes the sparsity of the inverse covariance matrix. Although the -norm is the most popular sparsity promoting function due to its convexity, it may not result in sufficiently satisfied estimations. The -norm is the most natural function to measure sparsity and the -norm regularized negative log-likelihood minimization has been demonstrated to produce favorable results. However, when the sample covariance matrix is singular, the -norm problem has no optimal solution. In this paper, we propose to estimate the sparse inverse covariance matrix via simultaneously using the -norm and the Tikhonov regularization. The resulting minimization problem is guaranteed to have optimal solutions. To overcome the numerical difficulty caused by the -norm, we utilize the penalty decomposition approach. We prove the asymptotic approximation and exact approximation to local (resp., global) minimizers of the original problem by those of the penalty decomposition problem. Then, local minimizers of the penalty decomposition problem are characterized as fixed-points of a system of fixed-point equations with the help of proximity operators. Based on these theoretical results, we design for solving the proposed minimization problem a penalty decomposition fixed-point proximity algorithm and provide the convergence analysis of the algorithm. Numerical results indicate that the proposed algorithm outperforms the compared state-of-the-art algorithms in terms of accuracy.