Learning feedback molecular network models using integer linear programming.

Analysis of intracellular molecular networks has many applications in understanding of the molecular bases of some complex diseases and finding effective therapeutic targets for drug development. To perform such analyses, the molecular networks need to be converted into computational models. In general, network models constructed using literature and pathway databases may not accurately predict experimental network data. This can be due to the incompleteness of literature on molecular pathways, the resources used to construct the networks, or some conflicting information in the resources. In this paper, we propose a network learning approach via an integer linear programming formulation that can systematically incorporate biological dynamics and regulatory mechanisms of molecular networks in the learning process. Moreover, we present a method to properly consider the feedback paths, while learning the network from data. Examples are also provided to show how one can apply the proposed learning approach to a network of interest. In particular, we apply the framework to the ERBB signaling network, to learn it from some experimental data. Overall, the proposed methods are useful for reducing the gap between the curated networks and experimental data, and result in calibrated networks that are more reliable for making biologically meaningful predictions.

Exploring extreme signaling failures in intracellular molecular networks.

Developing novel methods for the analysis of intracellular signaling networks is essential for understanding interconnected biological processes that underlie complex human disorders. A fundamental goal of this research is to quantify the vulnerability of a signaling network to the dysfunction of one or multiple molecules, when the dysfunction is defined as an incorrect response to the input signals. In this study, we propose an efficient algorithm to identify the extreme signaling failures that can induce the most detrimental impact on the physiological function of a molecular network. The algorithm finds the molecules, or groups of molecules, with the maximum vulnerability, i.e., the highest probability of causing the network failure, when they are dysfunctional. We propose another algorithm that efficiently accounts for signaling feedbacks. The algorithms are tested on experimentally verified ERBB and T-cell signaling networks. Surprisingly, results reveal that as the number of concurrently dysfunctional molecules increases, the maximum vulnerability values quickly reach to a plateau following an initial increase. This suggests the specificity of vulnerable molecule(s) involved, as a specific number of faulty molecules cause the most detrimental damage to the function of the network. Increasing the number of simultaneously faulty molecules does not further deteriorate the network function. Such a group of specific molecules whose dysfunction causes the extreme signaling failures can better elucidate the molecular mechanisms underlying the pathogenesis of complex trait disorders, and can offer new insights for the development of novel therapeutics.

Modeling and measurement of signaling outcomes affecting decision making in noisy intracellular networks using machine learning methods.

Characterization of decision-making in cells in response to received signals is of importance for understanding how cell fate is determined. The problem becomes multi-faceted and complex when we consider cellular heterogeneity and dynamics of biochemical processes. In this paper, we present a unified set of decision-theoretic, machine learning and statistical signal processing methods and metrics to model the precision of signaling decisions, in the presence of uncertainty, using single cell data. First, we introduce erroneous decisions that may result from signaling processes and identify false alarms and miss events associated with such decisions. Then, we present an optimal decision strategy which minimizes the total decision error probability. Additionally, we demonstrate how graphing receiver operating characteristic curves conveniently reveals the trade-off between false alarm and miss probabilities associated with different cell responses. Furthermore, we extend the introduced framework to incorporate the dynamics of biochemical processes and reactions in a cell, using multi-time point measurements and multi-dimensional outcome analysis and decision-making algorithms. The introduced multivariate signaling outcome modeling framework can be used to analyze several molecular species measured at the same or different time instants. We also show how the developed binary outcome analysis and decision-making approach can be extended to more than two possible outcomes. As an example and to show how the introduced methods can be used in practice, we apply them to single cell data of PTEN, an important intracellular regulatory molecule in a p53 system, in wild-type and abnormal cells. The unified signaling outcome modeling framework presented here can be applied to various organisms ranging from viruses, bacteria, yeast and lower metazoans to more complex organisms such as mammalian cells. Ultimately, this signaling outcome modeling approach can be utilized to better understand the transition from physiological to pathological conditions such as inflammation, various cancers and autoimmune diseases.

Computation capacities of a broad class of signaling networks are higher than their communication capacities.

Due to structural and functional abnormalities or genetic variations and mutations, there may be dysfunctional molecules within an intracellular signaling network that do not allow the network to correctly regulate its output molecules, such as transcription factors. This disruption in signaling interrupts normal cellular functions and may eventually develop some pathological conditions. In this paper, computation capacity of signaling networks is introduced as a fundamental limit on signaling capability and performance of such networks. In simple terms, the computation capacity measures the maximum number of computable inputs, that is, the maximum number of input values for which the correct functional output values can be recovered from the erroneous network outputs, when the network contains some dysfunctional molecules. This contrasts with the conventional communication capacity that measures instead the maximum number of input values that can be correctly distinguished based on the erroneous network outputs. The computation capacity is higher than the communication capacity whenever the network response function is not a one-to-one function of the input signals, and, unlike the communication capacity, it takes into account the input-output functional relationships of the network. By explicitly incorporating the effect of signaling errors that result in the network dysfunction, the computation capacity provides more information about the network and its malfunction. Two examples of signaling networks are considered in the paper, one regulating caspase3 and another regulating NFκB, for which computation and communication capacities are investigated. Higher computation capacities are observed for both networks. One biological implication of this finding is that signaling networks may have more 'capacity' than that specified by the conventional communication capacity metric. The effect of feedback is studied as well. In summary, this paper reports findings on a new fundamental feature of the signaling capability of cell signaling networks.

Computation and measurement of cell decision making errors using single cell data.

In this study a new computational method is developed to quantify decision making errors in cells, caused by noise and signaling failures. Analysis of tumor necrosis factor (TNF) signaling pathway which regulates the transcription factor Nuclear Factor κB (NF-κB) using this method identifies two types of incorrect cell decisions called false alarm and miss. These two events represent, respectively, declaring a signal which is not present and missing a signal that does exist. Using single cell experimental data and the developed method, we compute false alarm and miss error probabilities in wild-type cells and provide a formulation which shows how these metrics depend on the signal transduction noise level. We also show that in the presence of abnormalities in a cell, decision making processes can be significantly affected, compared to a wild-type cell, and the method is able to model and measure such effects. In the TNF-NF-κB pathway, the method computes and reveals changes in false alarm and miss probabilities in A20-deficient cells, caused by cell's inability to inhibit TNF-induced NF-κB response. In biological terms, a higher false alarm metric in this abnormal TNF signaling system indicates perceiving more cytokine signals which in fact do not exist at the system input, whereas a higher miss metric indicates that it is highly likely to miss signals that actually exist. Overall, this study demonstrates the ability of the developed method for modeling cell decision making errors under normal and abnormal conditions, and in the presence of transduction noise uncertainty. Compared to the previously reported pathway capacity metric, our results suggest that the introduced decision error metrics characterize signaling failures more accurately. This is mainly because while capacity is a useful metric to study information transmission in signaling pathways, it does not capture the overlap between TNF-induced noisy response curves.

Advanced fault diagnosis methods in molecular networks.

Analysis of the failure of cell signaling networks is an important topic in systems biology and has applications in target discovery and drug development. In this paper, some advanced methods for fault diagnosis in signaling networks are developed and then applied to a caspase network and an SHP2 network. The goal is to understand how, and to what extent, the dysfunction of molecules in a network contributes to the failure of the entire network. Network dysfunction (failure) is defined as failure to produce the expected outputs in response to the input signals. Vulnerability level of a molecule is defined as the probability of the network failure, when the molecule is dysfunctional. In this study, a method to calculate the vulnerability level of single molecules for different combinations of input signals is developed. Furthermore, a more complex yet biologically meaningful method for calculating the multi-fault vulnerability levels is suggested, in which two or more molecules are simultaneously dysfunctional. Finally, a method is developed for fault diagnosis of networks based on a ternary logic model, which considers three activity levels for a molecule instead of the previously published binary logic model, and provides equations for the vulnerabilities of molecules in a ternary framework. Multi-fault analysis shows that the pairs of molecules with high vulnerability typically include a highly vulnerable molecule identified by the single fault analysis. The ternary fault analysis for the caspase network shows that predictions obtained using the more complex ternary model are about the same as the predictions of the simpler binary approach. This study suggests that by increasing the number of activity levels the complexity of the model grows; however, the predictive power of the ternary model does not appear to be increased proportionally.

Quantitative analysis of intracellular communication and signaling errors in signaling networks.

BACKGROUND: Intracellular signaling networks transmit signals from the cell membrane to the nucleus, via biochemical interactions. The goal is to regulate some target molecules, to properly control the cell function. Regulation of the target molecules occurs through the communication of several intermediate molecules that convey specific signals originated from the cell membrane to the specific target outputs. RESULTS: In this study we propose to model intracellular signaling network as communication channels. We define the fundamental concepts of transmission error and signaling capacity for intracellular signaling networks, and devise proper methods for computing these parameters. The developed systematic methodology quantitatively shows how the signals that ligands provide upon binding can be lost in a pathological signaling network, due to the presence of some dysfunctional molecules. We show the lost signals result in message transmission error, i.e., incorrect regulation of target proteins at the network output. Furthermore, we show how dysfunctional molecules affect the signaling capacity of signaling networks and how the contributions of signaling molecules to the signaling capacity and signaling errors can be computed. The proposed approach can quantify the role of dysfunctional signaling molecules in the development of the pathology. We present experimental data on caspese3 and T cell signaling networks to demonstrate the biological relevance of the developed method and its predictions. CONCLUSIONS: This study demonstrates how signal transmission and distortion in pathological signaling networks can be modeled and studied using the proposed methodology. The new methodology determines how much the functionality of molecules in a network can affect the signal transmission and regulation of the end molecules such as transcription factors. This can lead to the identification of novel critical molecules in signal transduction networks. Dysfunction of these critical molecules is likely to be associated with some complex human disorders. Such critical molecules have the potential to serve as proper targets for drug discovery.

AKT/GSK3 signaling pathway and schizophrenia.

Schizophrenia is a prevalent complex trait disorder manifested by severe neurocognitive dysfunctions and lifelong disability. During the past few years several studies have provided direct evidence for the involvement of different signaling pathways in schizophrenia. In this review, we mainly focus on AKT/GSK3 signaling pathway in schizophrenia. The original study on the involvement of this pathway in schizophrenia was published by Emamian et al. in 2004. This study reported convergent evidence for a decrease in AKT1 protein levels and levels of phosphorylation of GSK-3ß in the peripheral lymphocytes and brains of individuals with schizophrenia; a significant association between schizophrenia and an AKT1 haplotype; and a greater sensitivity to the sensorimotor gating-disruptive effect of amphetamine, conferred by AKT1 deficiency. It also showed that haloperidol can induce a stepwise increase in regulatory phosphorylation of AKT1 in the brains of treated mice that could compensate for the impaired function of this signaling pathway in schizophrenia. Following this study, several independent studies were published that not only confirmed the association of this signaling pathway with schizophrenia across different populations, but also shed light on the mechanisms by which AKT/GSK3 pathway may contribute to the development of this complex disorder. In this review, following an introduction on the role of AKT in human diseases and its functions in neuronal and non-neuronal cells, a review on the results of studies published on AKT/GSK3 signaling pathway in schizophrenia after the original 2004 paper will be provided. A brief review on other signaling pathways involved in schizophrenia and the possible connections with AKT/GSK3 signaling pathway will be discussed. Moreover, some possible molecular mechanisms acting through this pathway will be discussed besides the mechanisms by which they may contribute to the pathogenesis of schizophrenia. Finally, different transcription factors related to schizophrenia will be reviewed to see how hypo-activity of AKT signaling pathway may impact such transcriptional mechanisms.

Fault diagnosis engineering in molecular signaling networks: an overview and applications in target discovery.

Fault diagnosis engineering is a key component of modern industrial facilities and complex systems, and has gone through considerable developments in the past few decades. In this paper, the principles and concepts of molecular fault diagnosis engineering are reviewed. In this area, molecular intracellular networks are considered as complex systems that may fail to function, due to the presence of some faulty molecules. Dysfunction of the system due to the presence of a single or multiple molecules can ultimately lead to the transition from the normal state to the disease state. It is the goal of molecular fault diagnosis engineering to identify the critical components of molecular networks, i.e., those whose dysfunction can interrupt the function of the entire network. The results of the fault analysis of several signaling networks are discussed, and possible connections of the findings with some complex human diseases are examined. Implications of molecular fault diagnosis engineering for target discovery and drug development are outlined as well.

Identification of critical molecules via fault diagnosis engineering.

Systems biology envisions that the application of complex system engineering approaches to cell signaling molecular networks can lead to novel understandings of complex human disorders. In this paper we show that by developing biologically-driven vulnerability assessment methods, the vulnerability of complex signaling networks to the dysfunction of each molecule can be determined. We have analyzed signaling networks that regulate mitosis and the activity of the transcription factor CREB. Our results indicate that biologically-relevant critical components of intracellular molecular networks can be identified using the proposed systems biology/fault diagnosis engineering technique. The application of this approach can improve our physiological understanding of the functionality of biological systems, can be used as a tool to identify novel genes associated with complex human disorders, and ultimately, has the potential to find the most prominent targets for drug discovery.

Complex human disorders and molecular system engineering: historical perspective and potential impacts.

The challenging nature of complex human disorders has taught us that we can not untangle a disorder unless we understand how the "engine" of molecular systems works. After learning the basic physiology of different organs in the human body, a "molecular revolution" occurred, which has now generated a huge amount of information regarding the function of individual molecules in human cells. The difficult task, however, is to understand how thousands of molecules communicate and work together to deliver a specific function, and more importantly, what goes wrong when the system fails and causes different diseases. The emerging field of systems biology is now opening the door for engineers, to join molecular biologists and enter the era of molecular biomedical engineering.

NMDA receptor phosphorylation at a site affected in schizophrenia controls synaptic and behavioral plasticity.

Phosphorylation of the NR1 subunit of NMDA receptors (NMDARs) at serine (S) 897 is markedly reduced in schizophrenia patients. However, the role of NR1 S897 phosphorylation in normal synaptic function and adaptive behaviors are unknown. To address these questions, we generated mice in which the NR1 S897 is replaced with alanine (A). This knock-in mutation causes severe impairment in NMDAR synaptic incorporation and NMDAR-mediated synaptic transmission. Furthermore, the phosphomutant animals have reduced AMPA receptor (AMPAR)-mediated synaptic transmission, decreased AMPAR GluR1 subunit in the synapse, and impaired long-term potentiation. Finally, the mutant mice exhibit behavioral deficits in social interaction and sensorimotor gating. Our results suggest that an impairment in NR1 phosphorylation leads to glutamatergic hypofunction that can contribute to behavioral deficits associated with psychiatric disorders.

Fault diagnosis engineering of digital circuits can identify vulnerable molecules in complex cellular pathways.

The application of complex system engineering approaches to cell signaling networks should lead to novel understandings and, subsequently, new treatments for complex disorders. In the area of circuit fault diagnosis engineering, there are various methods to identify the defective or vulnerable components of complex digital electronic circuits. In biological systems, however, knowledge is limited regarding the vulnerability of interconnected signaling pathways to the dysfunction of each specific molecule. By developing proper biologically driven digital vulnerability assessment methods, the vulnerability of complex signaling networks to the possible dysfunction of each molecule can be determined. To show the utility of this approach, we analyzed three well-characterized signaling networks--a cellular network that regulates the activity of caspase3, a network that regulates the activity of p53, and a central nervous system network that regulates the activity of the transcription factor CREB (adenosine 3',5'-monophosphate response element-binding protein). We found important differences among the vulnerability values of different molecules. Most of the identified highly vulnerable molecules are functionally related and known key regulators of these networks. Experimental data confirmed the ability of digital vulnerability assessment to correctly predict key regulators in the CREB network. Because this approach may provide insight into key molecules that contribute to human diseases, it may aid in the identification of critical targets for drug development.

Decreased phosphorylation of NMDA receptor type 1 at serine 897 in brains of patients with Schizophrenia.

NMDA receptor hypofunction in schizophrenia has been inferred by a large number of clinical and preclinical observations; however, whether and how NMDA receptors are exactly involved in the pathogenesis of schizophrenia are still unknown and subject to interpretation. Here we show, in two independent samples of brains from patients with schizophrenia, a significant decrease in the phosphorylation level at serine 897 (S897) of the NMDA receptor type 1 (NR1) subunit. Our finding, together with a previous report that antipsychotics increase phosphorylation of NR1 at S897 in vivo, strongly suggests that insufficient phosphorylation at S897 may contribute to the neuronal pathology underlying schizophrenia.

Convergent evidence for impaired AKT1-GSK3beta signaling in schizophrenia.

AKT-GSK3beta signaling is a target of lithium and as such has been implicated in the pathogenesis of mood disorders. Here, we provide evidence that this signaling pathway also has a role in schizophrenia. Specifically, we present convergent evidence for a decrease in AKT1 protein levels and levels of phosphorylation of GSK3beta at Ser9 in the peripheral lymphocytes and brains of individuals with schizophrenia; a significant association between schizophrenia and an AKT1 haplotype associated with lower AKT1 protein levels; and a greater sensitivity to the sensorimotor gating-disruptive effect of amphetamine, conferred by AKT1 deficiency. Our findings support the proposal that alterations in AKT1-GSK3beta signaling contribute to schizophrenia pathogenesis and identify AKT1 as a potential schizophrenia susceptibility gene. Consistent with this proposal, we also show that haloperidol induces a stepwise increase in regulatory phosphorylation of AKT1 in the brains of treated mice that could compensate for an impaired function of this signaling pathway in schizophrenia.

Serine 776 of ataxin-1 is critical for polyglutamine-induced disease in SCA1 transgenic mice.

Polyglutamine-induced neurodegeneration in transgenic mice carrying the spinocerebellar ataxia type 1 (SCA1) gene is modulated by subcellular distribution of ataxin-1 and by components of the protein folding/degradation machinery. Since phosphorylation is a prominent mechanism by which these processes are regulated, we examined phosphorylation of ataxin-1 and found that serine 776 (S776) was phosphorylated. Residue 776 appeared to affect cellular deposition of ataxin-1[82Q] in that ataxin-1[82Q]-A776 failed to form nuclear inclusions in tissue culture cells. The importance of S776 for polyglutamine-induced pathogenesis was examined by generating ataxin-1[82Q]-A776 transgenic mice. These mice expressed ataxin-1[82Q]-A776 within Purkinje cell nuclei, yet the ability of ataxin-1[82Q]-A776 to induce disease was substantially reduced. These studies demonstrate that polyglutamine tract expansion and localization of ataxin-1 to the nucleus of Purkinje cells are not sufficient to induce disease. We suggest that S776 of ataxin-1 also has a critical role in SCA1 pathogenesis.

Prenatal viral infection leads to pyramidal cell atrophy and macrocephaly in adulthood: implications for genesis of autism and schizophrenia.

We investigated the role of maternal exposure to human influenza virus (H1N1) in C57BL/6 mice on Day 9 of pregnancy on pyramidal and nonpyramidal cell density, pyramidal nuclear area, and overall brain size in Day 0 neonates and 14-week-old progeny and compared them to sham-infected cohorts. Pyramidal cell density increased significantly (p < 0.0038) by 170% in Day 0 infected mice vs. controls. Nonpyramidal cell density decreased by 33% in Day 0 infected progeny vs. controls albeit, nonsignificantly. Pyramidal cell nuclear size decreased significantly (p < 0.0465) by 29% in exposed newborn mice vs. controls. Fourteen-week-old exposed mice continued to show significant increases in both pyramidal and nonpyramidal cell density values vs. controls respectively (p < 0.0085 E1 (exposed group 1), p < 0.0279 E2 (exposed group 2) pyramidal cell density; p < 0.0092 E1, p < 0.0252 E2, nonpyramidal cell density). By the same token, pyramidal cell nuclear size exhibited 37-43% reductions when compared to control values; these were statistically significant vs. controls (p < 0.04 E1, p < 0.0259 E2). Brain and ventricular area measurements in adult exposed mice also showed significant increases and decreases respectively vs. controls. Ventricular brain ratios exhibited 38-50% decreases in exposed mice vs. controls. While the rate of pyramidal cell proliferation per unit area decreased from birth to adulthood in both control and exposed groups, nonpyramidal cell growth rate increased only in the exposed adult mice. These data show for the first time that prenatal exposure of pregnant mice on Day 9 of pregnancy to a sublethal intranasal administration of influenza virus has both short-term and long-lasting deleterious effects on developing brain structure in the progeny as evident by altered pyramidal and nonpyramidal cell density values; atrophy of pyramidal cells despite normal cell proliferation rate and final enlargement of brain. Moreover, abnormal corticogenesis is associated with development of abnormal behavior in the exposed adult mice.