Gibbs Energy and Gene Expression Combined as a New Technique for Selecting Drug Targets for Inhibiting Specific Protein-Protein Interactions.

One of the most important aspects of successful cancer therapy is the identification of a target protein for inhibition interaction. Conventionally, this consists of screening a panel of genes to assess which is mutated and then developing a small molecule to inhibit the interaction of two proteins or to simply inhibit a specific protein from all interactions. In previous work, we have proposed computational methods that analyze protein-protein networks using both topological approaches and thermodynamic quantification provided by Gibbs free energy. In order to make these approaches both easier to implement and free of arbitrary topological filtration criteria, in the present paper, we propose a modification of the topological-thermodynamic analysis, which focuses on the selection of the most thermodynamically stable proteins and their subnetwork interaction partners with the highest expression levels. We illustrate the implementation of the new approach with two specific cases, glioblastoma (glioma brain tumors) and chronic lymphatic leukoma (CLL), based on the publicly available patient-derived datasets. We also discuss how this can be used in clinical practice in connection with the availability of approved and investigational drugs.

Signal Propagation: The Framework for Learning and Inference in a Forward Pass.

We propose a new learning framework, signal propagation (sigprop), for propagating a learning signal and updating neural network parameters via a forward pass, as an alternative to backpropagation (BP). In sigprop, there is only the forward path for inference and learning. So, there are no structural or computational constraints necessary for learning to take place, beyond the inference model itself, such as feedback connectivity, weight transport, or a backward pass, which exist under BP-based approaches. That is, sigprop enables global supervised learning with only a forward path. This is ideal for parallel training of layers or modules. In biology, this explains how neurons without feedback connections can still receive a global learning signal. In hardware, this provides an approach for global supervised learning without backward connectivity. Sigprop by construction has compatibility with models of learning in the brain and in hardware than BP, including alternative approaches relaxing learning constraints. We also demonstrate that sigprop is more efficient in time and memory than they are. To further explain the behavior of sigprop, we provide evidence that sigprop provides useful learning signals in context to BP. To further support relevance to biological and hardware learning, we use sigprop to train continuous time neural networks with the Hebbian updates and train spiking neural networks (SNNs) with only the voltage or with biologically and hardware-compatible surrogate functions.

Personalized therapy design for systemic lupus erythematosus based on the analysis of protein-protein interaction networks.

We analyzed protein expression data for Lupus patients, which have been obtained from publicly available databases. A combination of systems biology and statistical thermodynamics approaches was used to extract topological properties of the associated protein-protein interaction networks for each of the 291 patients whose samples were used to provide the molecular data. We have concluded that among the many proteins that appear to play critical roles in this pathology, most of them are either ribosomal proteins, ubiquitination pathway proteins or heat shock proteins. We propose some of the proteins identified in this study to be considered for drug targeting.

Using the Gibbs Function as a Measure of Human Brain Development Trends from Fetal Stage to Advanced Age.

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain's protein-protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions.

Gibbs free energy of protein-protein interactions correlates with ATP production in cancer cells.

In this paper, we analyze several cancer cell types from two seemingly independent angles: (a) the over-expression of various proteins participating in protein-protein interaction networks and (b) a metabolic shift from oxidative phosphorylation to glycolysis. We use large data sets to obtain a thermodynamic measure of the protein-protein interaction network, namely the associated Gibbs free energy. We find a strong inverse correlation between the percentage of energy production via oxidative phosphorylation and the Gibbs free energy of the protein networks. The latter is a measure of functional dysregulation within the cell. Our findings corroborate earlier indications that signaling pathway upregulation in cancer cells is linked to the metabolic shift known as the Warburg effect; hence, these two seemingly independent characteristics of cancer phenotype may be interconnected.

Gibbs free energy as a measure of complexity correlates with time within C. elegans embryonic development.

We investigate free energy behavior in the nematode Caenorhabditis elegans during embryonic development. Our approach utilizes publicly available gene expression data, which gives us a picture of developmental changes in protein concentration and, resultantly, chemical potential and free energy. Our results indicate a clear global relationship between Gibbs free energy and time spent in development and provide thermodynamic indicators of the large-scale biological events of cell division and differentiation.

Personalized anticancer therapy selection using molecular landscape topology and thermodynamics.

Personalized anticancer therapy requires continuous consolidation of emerging bioinformatics data into meaningful and accurate information streams. The use of novel mathematical and physical approaches, namely topology and thermodynamics can enable merging differing data types for improved accuracy in selecting therapeutic targets. We describe a method that uses chemical thermodynamics and two topology measures to link RNA-seq data from individual patients with academically curated protein-protein interaction networks to select clinically relevant targets for treatment of low-grade glioma (LGG). We show that while these three histologically distinct tumor types (astrocytoma, oligoastrocytoma, and oligodendroglioma) may share potential therapeutic targets, the majority of patients would benefit from more individualized therapies. The method involves computing Gibbs free energy of the protein-protein interaction network and applying a topological filtration on the energy landscape to produce a subnetwork known as persistent homology. We then determine the most likely best target for therapeutic intervention using a topological measure of the network known as Betti number. We describe the algorithm and discuss its application to several patients.

Thermodynamic measures of cancer: Gibbs free energy and entropy of protein-protein interactions.

Thermodynamics is an important driving factor for chemical processes and for life. Earlier work has shown that each cancer has its own molecular signaling network that supports its life cycle and that different cancers have different thermodynamic entropies characterizing their signaling networks. The respective thermodynamic entropies correlate with 5-year survival for each cancer. We now show that by overlaying mRNA transcription data from a specific tumor type onto a human protein-protein interaction network, we can derive the Gibbs free energy for the specific cancer. The Gibbs free energy correlates with 5-year survival (Pearson correlation of -0.7181, p value of 0.0294). Using an expression relating entropy and Gibbs free energy to enthalpy, we derive an empirical relation for cancer network enthalpy. Combining this with previously published results, we now show a complete set of extensive thermodynamic properties and cancer type with 5-year survival.

Design principles for cancer therapy guided by changes in complexity of protein-protein interaction networks.

BACKGROUND: The ever-increasing expanse of online bioinformatics data is enabling new ways to, not only explore the visualization of these data, but also to apply novel mathematical methods to extract meaningful information for clinically relevant analysis of pathways and treatment decisions. One of the methods used for computing topological characteristics of a space at different spatial resolutions is persistent homology. This concept can also be applied to network theory, and more specifically to protein-protein interaction networks, where the number of rings in an individual cancer network represents a measure of complexity. RESULTS: We observed a linear correlation of R = -0.55 between persistent homology and 5-year survival of patients with a variety of cancers. This relationship was used to predict the proteins within a protein-protein interaction network with the most impact on cancer progression. By re-computing the persistent homology after computationally removing an individual node (protein) from the protein-protein interaction network, we were able to evaluate whether such an inhibition would lead to improvement in patient survival. The power of this approach lied in its ability to identify the effects of inhibition of multiple proteins and in the ability to expose whether the effect of a single inhibition may be amplified by inhibition of other proteins. More importantly, we illustrate specific examples of persistent homology calculations, which correctly predict the survival benefit observed effects in clinical trials using inhibitors of the identified molecular target. CONCLUSIONS: We propose that computational approaches such as persistent homology may be used in the future for selection of molecular therapies in clinic. The technique uses a mathematical algorithm to evaluate the node (protein) whose inhibition has the highest potential to reduce network complexity. The greater the drop in persistent homology, the greater reduction in network complexity, and thus a larger potential for survival benefit. We hope that the use of advanced mathematics in medicine will provide timely information about the best drug combination for patients, and avoid the expense associated with an unsuccessful clinical trial, where drug(s) did not show a survival benefit.

Algebraic and topological indices of molecular pathway networks in human cancers.

Protein-protein interaction networks associated with diseases have gained prominence as an area of research. We investigate algebraic and topological indices for protein-protein interaction networks of 11 human cancers derived from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. We find a strong correlation between relative automorphism group sizes and topological network complexities on the one hand and five year survival probabilities on the other hand. Moreover, we identify several protein families (e.g. PIK, ITG, AKT families) that are repeated motifs in many of the cancer pathways. Interestingly, these sources of symmetry are often central rather than peripheral. Our results can aide in identification of promising targets for anti-cancer drugs. Beyond that, we provide a unifying framework to study protein-protein interaction networks of families of related diseases (e.g. neurodegenerative diseases, viral diseases, substance abuse disorders).

Theoretical Biology and Medical Modelling: ensuring continued growth and future leadership.

Theoretical biology encompasses a broad range of biological disciplines ranging from mathematical biology and biomathematics to philosophy of biology. Adopting a broad definition of "biology", Theoretical Biology and Medical Modelling, an open access journal, considers original research studies that focus on theoretical ideas and models associated with developments in biology and medicine.

An integrated multidisciplinary model describing initiation of cancer and the Warburg hypothesis.

BACKGROUND: In this paper we propose a chemical physics mechanism for the initiation of the glycolytic switch commonly known as the Warburg hypothesis, whereby glycolytic activity terminating in lactate continues even in well-oxygenated cells. We show that this may result in cancer via mitotic failure, recasting the current conception of the Warburg effect as a metabolic dysregulation consequent to cancer, to a biophysical defect that may contribute to cancer initiation. MODEL: Our model is based on analogs of thermodynamic concepts that tie non-equilibrium fluid dynamics ultimately to metabolic imbalance, disrupted microtubule dynamics, and finally, genomic instability, from which cancers can arise. Specifically, we discuss how an analog of non-equilibrium Rayleigh-Benard convection can result in glycolytic oscillations and cause a cell to become locked into a higher-entropy state characteristic of cancer. CONCLUSIONS: A quantitative model is presented that attributes the well-known Warburg effect to a biophysical mechanism driven by a convective disturbance in the cell. Contrary to current understanding, this effect may precipitate cancer development, rather than follow from it, providing new insights into carcinogenesis, cancer treatment, and prevention.

Interactomes, manufacturomes and relational biology: analogies between systems biology and manufacturing systems.

BACKGROUND: We review and extend the work of Rosen and Casti who discuss category theory with regards to systems biology and manufacturing systems, respectively. RESULTS: We describe anticipatory systems, or long-range feed-forward chemical reaction chains, and compare them to open-loop manufacturing processes. We then close the loop by discussing metabolism-repair systems and describe the rationality of the self-referential equation f = f (f). This relationship is derived from some boundary conditions that, in molecular systems biology, can be stated as the cardinality of the following molecular sets must be about equal: metabolome, genome, proteome. We show that this conjecture is not likely correct so the problem of self-referential mappings for describing the boundary between living and nonliving systems remains an open question. We calculate a lower and upper bound for the number of edges in the molecular interaction network (the interactome) for two cellular organisms and for two manufacturomes for CMOS integrated circuit manufacturing. CONCLUSIONS: We show that the relevant mapping relations may not be Abelian, and that these problems cannot yet be resolved because the interactomes and manufacturomes are incomplete.

Review and application of group theory to molecular systems biology.

In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.