Narsis A. Kiani

Systems Medicine: from molecular features and models to the clinic in COPD

Background and hypothesisChronic Obstructive Pulmonary Disease (COPD) patients are characterized by heterogeneous clinical manifestations and patterns of disease progression. Two major factors that can be used to identify COPD subtypes are muscle dysfunction/wasting and co-morbidity patterns. We hypothesized that COPD heterogeneity is in part the result of complex interactions between several genes and pathways. We explored the possibility of using a Systems Medicine approach to identify such pathways, as well as to generate predictive computational models that may be used in clinic practice.Objective and methodOur overarching goal is to generate clinically applicable predictive models that characterize COPD heterogeneity through a Systems Medicine approach. To this end we have developed a general framework, consisting of three steps/objectives: (1) feature identification, (2) model generation and statistical validation, and (3) application and validation of the predictive models in the clinical scenario. We used muscle dysfunction and co-morbidity as test cases for this framework.ResultsIn the study of muscle wasting we identified relevant features (genes) by a network analysis and generated predictive models that integrate mechanistic and probabilistic models. This allowed us to characterize muscle wasting as a general de-regulation of pathway interactions. In the co-morbidity analysis we identified relevant features (genes/pathways) by the integration of gene-disease and disease-disease associations. We further present a detailed characterization of co-morbidities in COPD patients that was implemented into a predictive model. In both use cases we were able to achieve predictive modeling but we also identified several key challenges, the most pressing being the validation and implementation into actual clinical practice.ConclusionsThe results confirm the potential of the Systems Medicine approach to study complex diseases and generate clinically relevant predictive models. Our study also highlights important obstacles and bottlenecks for such approaches (e.g. data availability and normalization of frameworks among others) and suggests specific proposals to overcome them.

Methods of information theory and algorithmic complexity for network biology.

We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannons information entropy, compressibility and algorithmic complexity quantify different local and global aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdös-Rényi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data. We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs, characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labeled and unlabeled graphs and prove that the Kolmogorov complexity of a labeled graph is a good approximation of its unlabeled Kolmogorov complexity and thus a robust definition of graph complexity.

Low-algorithmic-complexity entropy-deceiving graphs

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measures range of applications and demonstrating the weaknesses of computable measures of complexity.

A Decomposition Method for Global Evaluation of Shannon Entropy and Local Estimations of Algorithmic Complexity

We investigate the properties of a Block Decomposition Method (BDM), which extends the power of a Coding Theorem Method (CTM) that approximates local estimations of algorithmic complexity based on Solomonoff–Levin’s theory of algorithmic probability providing a closer connection to algorithmic complexity than previous attempts based on statistical regularities such as popular lossless compression schemes. The strategy behind BDM is to find small computer programs that produce the components of a larger, decomposed object. The set of short computer programs can then be artfully arranged in sequence so as to produce the original object. We show that the method provides efficient estimations of algorithmic complexity but that it performs like Shannon entropy when it loses accuracy. We estimate errors and study the behaviour of BDM for different boundary conditions, all of which are compared and assessed in detail. The measure may be adapted for use with more multi-dimensional objects than strings, objects such as arrays and tensors. To test the measure we demonstrate the power of CTM on low algorithmic-randomness objects that are assigned maximal entropy (e.g., π) but whose numerical approximations are closer to the theoretical low algorithmic-randomness expectation. We also test the measure on larger objects including dual, isomorphic and cospectral graphs for which we know that algorithmic randomness is low. We also release implementations of the methods in most major programming languages—Wolfram Language (Mathematica), Matlab, R, Perl, Python, Pascal, C++, and Haskell—and an online algorithmic complexity calculator.

Quantifying loss of information in network-based dimensionality reduction techniques

To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been clear. Here we develop a framework, based on algorithmic information theory, to quantify the extent to which information is preserved when network motif analysis, graph spectra and spectral sparsification methods are applied to over twenty different biological and artificial networks. We find that the spectral sparsification is highly sensitive to high number of edge deletion, leading to significant inconsistencies, and that graph spectral methods are the most irregular, capturing algebraic information in a condensed fashion but largely losing most of the information content of the original networks. However, the approach shows that network motif analysis excels at preserving the relative algorithmic information content of a network, hence validating and generalizing the remarkable fact that despite their inherent combinatorial possibilities, local regularities preserve information to such an extent that essential properties are fully recoverable across different networks to determine their family group to which they belong to (eg genetic vs social network). Our algorithmic information methodology thus provides a rigorous framework enabling a fundamental assessment and comparison between different data dimensionality reduction methods thereby facilitating the identification and evaluation of the capabilities of old and new methods.

A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference.

Systems in nature capable of collective behaviour are nonlinear, operating across several scales. Yet our ability to account for their collective dynamics differs in physics, chemistry and biology. Here, we briefly review the similarities and differences between mathematical modelling of adaptive living systems versus physico-chemical systems. We find that physics-based chemistry modelling and computational neuroscience have a shared interest in developing techniques for model reductions aiming at the identification of a reduced subsystem or slow manifold, capturing the effective dynamics. By contrast, as relations and kinetics between biological molecules are less characterized, current quantitative analysis under the umbrella of bioinformatics focuses on signal extraction, correlation, regression and machine-learning analysis. We argue that model reduction analysis and the ensuing identification of manifolds bridges physics and biology. Furthermore, modelling living systems presents deep challenges as how to reconcile rich molecular data with inherent modelling uncertainties (formalism, variables selection and model parameters). We anticipate a new generative data-driven modelling paradigm constrained by identified governing principles extracted from low-dimensional manifold analysis. The rise of a new generation of models will ultimately connect biology to quantitative mechanistic descriptions, thereby setting the stage for investigating the character of the model language and principles driving living systems. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’.

Signaling networks in MS: A systems-based approach to developing new pharmacological therapies

The pathogenesis of multiple sclerosis (MS) involves alterations to multiple pathways and processes, which represent a significant challenge for developing more-effective therapies. Systems biology approaches that study pathway dysregulation should offer benefits by integrating molecular networks and dynamic models with current biological knowledge for understanding disease heterogeneity and response to therapy. In MS, abnormalities have been identified in several cytokine-signaling pathways, as well as those of other immune receptors. Among the downstream molecules implicated are Jak/Stat, NF-Kb, ERK1/3, p38 or Jun/Fos. Together, these data suggest that MS is likely to be associated with abnormalities in apoptosis/cell death, microglia activation, blood-brain barrier functioning, immune responses, cytokine production, and/or oxidative stress, although which pathways contribute to the cascade of damage and can be modulated remains an open question. While current MS drugs target some of these pathways, others remain untouched. Here, we propose a pragmatic systems analysis approach that involves the large-scale extraction of processes and pathways relevant to MS. These data serve as a scaffold on which computational modeling can be performed to identify disease subgroups based on the contribution of different processes. Such an analysis, targeting these relevant MS-signaling pathways, offers the opportunity to accelerate the development of novel individual or combination therapies.

Evaluating Network Inference Methods in Terms of Their Ability to Preserve the Topology and Complexity of Genetic Networks

Network inference is a rapidly advancing field, with new methods being proposed on a regular basis. Understanding the advantages and limitations of different network inference methods is key to their effective application in different circumstances. The common structural properties shared by diverse networks naturally pose a challenge when it comes to devising accurate inference methods, but surprisingly, there is a paucity of comparison and evaluation methods. Historically, every new methodology has only been tested against gold standard (true values) purpose-designed synthetic and real-world (validated) biological networks. In this paper we aim to assess the impact of taking into consideration aspects of topological and information content in the evaluation of the final accuracy of an inference procedure. Specifically, we will compare the best inference methods, in both graph-theoretic and information-theoretic terms, for preserving topological properties and the original information content of synthetic and biological networks. New methods for performance comparison are introduced by borrowing ideas from gene set enrichment analysis and by applying concepts from algorithmic complexity. Experimental results show that no individual algorithm outperforms all others in all cases, and that the challenging and non-trivial nature of network inference is evident in the struggle of some of the algorithms to turn in a performance that is superior to random guesswork. Therefore special care should be taken to suit the method to the purpose at hand. Finally, we show that evaluations from data generated using different underlying topologies have different signatures that can be used to better choose a network reconstruction method.

Algorithmic complexity of motifs clusters superfamilies of networks

Representing biological systems as networks has proved to be very powerful. For example, local graph analysis of substructures such as subgraph over representation (or motifs) has elucidated different sub-types of networks. Here we report that using numerical approximations of Kolmogorov complexity, by means of algorithmic probability, clusters different classes of networks. For this, we numerically estimate the algorithmic probability of the sub-matrices from the adjacency matrix of the original network (hence including motifs). We conclude that algorithmic information theory is a powerful tool supplementing other network analysis techniques.

An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems.

We introduce a new conceptual framework and a model-based interventional calculus to steer, manipulate, and reconstruct the dynamics and generating mechanisms of non-linear dynamical systems from partial and disordered observations based on the contributions of each of the systems, by exploiting first principles from the theory of computability and algorithmic information. This calculus entails finding and applying controlled interventions to an evolving object to estimate how its algorithmic information content is affected in terms of positive or negative shifts towards and away from randomness in connection to causation. The approach is an alternative to statistical approaches for inferring causal relationships and formulating theoretical expectations from perturbation analysis. We find that the algorithmic information landscape of a system runs parallel to its dynamic attractor landscape, affording an avenue for moving systems on one plane so they can be controlled on the other plane. Based on these methods, we advance tools for reprogramming a system that do not require full knowledge or access to the system’s actual kinetic equations or to probability distributions. This new approach yields a suite of universal parameter-free algorithms of wide applicability, ranging from the discovery of causality, dimension reduction, feature selection, model generation, a maximal algorithmic-randomness principle and a system’s (re)programmability index. We apply these methods to static (e.coli Transcription Factor network) and to evolving genetic regulatory networks (differentiating naïve from Th17 cells, and the CellNet database). We highlight their ability to pinpoint key elements (genes) related to cell function and cell development, conforming to biological knowledge from experimentally validated data and the literature, and demonstrate how the method can reshape a system’s dynamics in a controlled manner through algorithmic causal mechanisms.