Geometric diffusions for the analysis of data from sensor networks

Harmonic analysis on manifolds and graphs has recently led to mathematical developments in the field of data analysis. The resulting new tools can be used to compress and analyze large and complex data sets, such as those derived from sensor networks or neuronal activity datasets, obtained in the laboratory or through computer modeling. The nature of the algorithms (based on diffusion maps and connectivity strengths on graphs) possesses a certain analogy with neural information processing, and has the potential to provide inspiration for modeling and understanding biological organization in perception and memory formation.     

Stochastical aspects of neuronal dynamics: Fokker-Planck approach

The Stochastical aspects of noise-perturbed neuronal dynamics are studied via the Fokker-Planck equation by considering the Langevin-type relaxational, nonlinear process associated with neuronal states. On the basis of a canonical, stochastically driven, dichotomous state modeling, the equilibrium conditions in the neuronal assembly are analyzed. The markovian structure of the random occurrence of action potentials due to the disturbances (noise) in the neuronal state is considered, and the corresponding solutions relevant to the colored noise spectrum of the disturbance effects are addressed. Stochastical instability (Lyapunov) considerations in solving discrete optimization problems via neural networks are discussed. The bounded estimate(s) of the Stochastical variates involved are presented, and the noise-induced perturbations on the saturated-state neuronal population are elucidated.     

Firing-rate models for neurons with a broad repertoire of spiking behaviors

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.     

Oscillations and Synchrony in Large-scale Cortical Network Models

Intrinsic neuronal and circuit properties control the responses of large ensembles of neurons by creating spatiotemporal patterns of activity that are used for sensory processing, memory formation, and other cognitive tasks. The modeling of such systems requires computationally efficient single-neuron models capable of displaying realistic response properties. We developed a set of reduced models based on difference equations (map-based models) to simulate the intrinsic dynamics of biological neurons. These phenomenological models were designed to capture the main response properties of specific types of neurons while ensuring realistic model behavior across a sufficient dynamic range of inputs. This approach allows for fast simulations and efficient parameter space analysis of networks containing hundreds of thousands of neurons of different types using a conventional workstation. Drawing on results obtained using large-scale networks of map-based neurons, we discuss spatiotemporal cortical network dynamics as a function of parameters that affect synaptic interactions and intrinsic states of the neurons.     

Thermodynamically feasible kinetic models of reaction networks

The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism, the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics, the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces, the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus, it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject to many detailed balance relations.     

A conceptual review on systems biology in health and diseases: from biological networks to modern therapeutics

Human physiology is an ensemble of various biological processes spanning from intracellular molecular interactions to the whole body phenotypic response. Systems biology endures to decipher these multi-scale biological networks and bridge the link between genotype to phenotype. The structure and dynamic properties of these networks are responsible for controlling and deciding the phenotypic state of a cell. Several cells and various tissues coordinate together to generate an organ level response which further regulates the ultimate physiological state. The overall network embeds a hierarchical regulatory structure, which when unusually perturbed can lead to undesirable physiological state termed as disease. Here, we treat a disease diagnosis problem analogous to a fault diagnosis problem in engineering systems. Accordingly we review the application of engineering methodologies to address human diseases from systems biological perspective. The review highlights potential networks and modeling approaches used for analyzing human diseases. The application of such analysis is illustrated in the case of cancer and diabetes. We put forth a concept of cell-to-human framework comprising of five modules (data mining, networking, modeling, experimental and validation) for addressing human physiology and diseases based on a paradigm of system level analysis. The review overtly emphasizes on the importance of multi-scale biological networks and subsequent modeling and analysis for drug target identification and designing efficient therapies.     

Exploring biological network structure using exponential random graph models

MOTIVATION: The functioning of biological networks depends in large part on their complex underlying structure. When studying their systemic nature many modeling approaches focus on identifying simple, but prominent, structural components, as such components are easier to understand, and, once identified, can be used as building blocks to succinctly describe the network. RESULTS: In recent social network studies, exponential random graph models have been used extensively to model global social network structure as a function of their 'local features'. Starting from those studies, we describe the exponential random graph models and demonstrate their utility in modeling the architecture of biological networks as a function of the prominence of local features. We argue that the flexibility, in terms of the number of available local feature choices, and scalability, in terms of the network sizes, make this approach ideal for statistical modeling of biological networks. We illustrate the modeling on both genetic and metabolic networks and provide a novel way of classifying biological networks based on the prevalence of their local features.     

Identification of Important Nodes in Directed Biological Networks: A Network Motif Approach

Identification of important nodes in complex networks has attracted an increasing attention over the last decade. Various measures have been proposed to characterize the importance of nodes in complex networks, such as the degree, betweenness and PageRank. Different measures consider different aspects of complex networks. Although there are numerous results reported on undirected complex networks, few results have been reported on directed biological networks. Based on network motifs and principal component analysis (PCA), this paper aims at introducing a new measure to characterize node importance in directed biological networks. Investigations on five real-world biological networks indicate that the proposed method can robustly identify actually important nodes in different networks, such as finding command interneurons, global regulators and non-hub but evolutionary conserved actually important nodes in biological networks. Receiver Operating Characteristic (ROC) curves for the five networks indicate remarkable prediction accuracy of the proposed measure. The proposed index provides an alternative complex network metric. Potential implications of the related investigations include identifying network control and regulation targets, biological networks modeling and analysis, as well as networked medicine.     

Computational approaches for modeling regulatory cellular networks

Cellular components interact with each other to form networks that process information and evoke biological responses. A deep understanding of the behavior of these networks requires the development and analysis of mathematical models. In this article, different types of mathematical representations for modeling signaling networks are described, and the advantages and disadvantages of each type are discussed. Two experimentally well-studied signaling networks are then used as examples to illustrate the insight that could be gained through modeling. Finally, the modeling approach is expanded to describe how signaling networks might regulate cellular machines and evoke phenotypic behaviors.     

A neuromime system for neural circuit analysis

A system of electronic analog neurons (neuromines) for modeling the activity in small neuronal networks is described. The system consists of sixteen analogs that simulate the integrative neuronal properties at the axon hillock and sixty-four analogs that serve to simulate synaptic interactions. The neuromime properties are based on a potential model incorporating the following properties: membrane potential, threshold, refractory period, adaption, post-inhibitory rebound, accommodation and pacemaker potential. Use of matrix switch boards provides for convenient interconnection of the neuromime elements, allowing the construction of even complex circuits.     

Coemergence of regularity and complexity during neural network development

With the growing recognition that rhythmic and oscillatory patterns are widespread in the brain and play important roles in all aspects of the function of our nervous system, there has been a resurgence of interest in neuronal synchronized bursting activity. Here, we were interested in understanding the development of synchronized bursts as information-bearing neuronal activity patterns. For that, we have monitored the morphological organization and spontaneous activity of neuronal networks cultured on multielectrode-arrays during their self-executed evolvement from a mixture of dissociated cells into an active network. Complex collective network electrical activity evolved from sporadic firing patterns of the single neurons. On the system (network) level, the activity was marked by bursting events with interneuronal synchronization and nonarbitrary temporal ordering. We quantified these individual-to-collective activity transitions using newly-developed system level quantitative measures of time series regularity and complexity. We found that individual neuronal activity before synchronization was characterized by high regularity and low complexity. During neuronal wiring, there was a transient period of reorganization marked by low regularity, which then leads to coemergence of elevated regularity and functional (nonstochastic) complexity. We further investigated the morphology-activity interplay by modeling artificial neuronal networks with different topological organizations and connectivity schemes. The simulations support our experimental results by showing increased levels of complexity of neuronal activity patterns when neurons are wired up and organized in clusters (similar to mature real networks), as well as network-level activity regulation once collective activity forms.     

Computer-aided design of biological circuits using TinkerCell

Synthetic biology is an engineering discipline that builds on modeling practices from systems biology and wet-lab techniques from genetic engineering. As synthetic biology advances, efficient procedures will be developed that will allow a synthetic biologist to design, analyze, and build biological networks. In this idealized pipeline, computer-aided design (CAD) is a necessary component. The role of a CAD application would be to allow efficient transition from a general design to a final product. TinkerCell is a design tool for serving this purpose in synthetic biology. In TinkerCell, users build biological networks using biological parts and modules. The network can be analyzed using one of several functions provided by TinkerCell or custom programs from third-party sources. Since best practices for modeling and constructing synthetic biology networks have not yet been established, TinkerCell is designed as a flexible and extensible application that can adjust itself to changes in the field.     

A biological approach to computational models of proteomic networks

Computational modeling is useful as a means to assemble and test what we know about proteins and networks. Models can help address key questions about the measurement, definition and function of proteomic networks. Here, we place these biological questions at the forefront in reviewing the computational strategies that are available to analyze proteomic networks. Recent examples illustrate how models can extract more information from proteomic data, test possible interactions between network proteins and link networks to cellular behavior. No single model can achieve all these goals, however, which is why it is critical to prioritize biological questions before specifying a particular modeling approach.     

Problem of identity of functional states of neuronal systems

A compartmental conception of modeling the neuron networks is presented. Stationary and other regimes under standard electrical stimulation of neuron networks are described. Neuron networks may be reducible and irreducible. The mathematical model of the stationary state is a model of a normal neuron network under hyperventilation. The role of output stimuli in identifying the hierarchical structure of neuron networks and the stability of special regimes and such structure is discussed. A biological interpretation of the results of modeling is presented.     

Discrete modeling for integration and analysis of large-scale signaling networks

Most biological processes are orchestrated by large-scale molecular networks which are described in large-scale model repositories and whose dynamics are extremely complex. An observed phenotype is a state of this system that results from control mechanisms whose identification is key to its understanding. The Biological Pathway Exchange (BioPAX) format is widely used to standardize the biological information relative to regulatory processes. However, few modeling approaches developed so far enable for computing the events that control a phenotype in large-scale networks.Here we developed an integrated approach to build large-scale dynamic networks from BioPAX knowledge databases in order to analyse trajectories and to identify sets of biological entities that control a phenotype. The Cadbiom approach relies on the guarded transitions formalism, a discrete modeling approach which models a system dynamics by taking into account competition and cooperation events in chains of reactions. The method can be applied to every BioPAX (large-scale) model thanks to a specific package which automatically generates Cadbiom models from BioPAX files.The Cadbiom framework was applied to the BioPAX version of two resources (PID, KEGG) of the Pathway Commons database and to the Atlas of Cancer Signalling Network (ACSN). As a case-study, it was used to characterize sets of biological entities implicated in the epithelial-mesenchymal transition. Our results highlight the similarities between the PID and ACSN resources in terms of biological content, and underline the heterogeneity of usage of the BioPAX semantics limiting the fusion of models that require curation. Causality analyses demonstrate the smart complementarity of the databases in terms of combinatorics of controllers that explain a phenotype. From a biological perspective, our results show the specificity of controllers for epithelial and mesenchymal phenotypes that are consistent with the literature and identify a novel signature for intermediate states.     

TinkerCell: modular CAD tool for synthetic biology

Background

Synthetic biology brings together concepts and techniques from engineering and biology. In this field, computer-aided design (CAD) is necessary in order to bridge the gap between computational modeling and biological data. Using a CAD application, it would be possible to construct models using available biological "parts" and directly generate the DNA sequence that represents the model, thus increasing the efficiency of design and construction of synthetic networks.

Results

An application named TinkerCell has been developed in order to serve as a CAD tool for synthetic biology. TinkerCell is a visual modeling tool that supports a hierarchy of biological parts. Each part in this hierarchy consists of a set of attributes that define the part, such as sequence or rate constants. Models that are constructed using these parts can be analyzed using various third-party C and Python programs that are hosted by TinkerCell via an extensive C and Python application programming interface (API). TinkerCell supports the notion of a module, which are networks with interfaces. Such modules can be connected to each other, forming larger modular networks. TinkerCell is a free and open-source project under the Berkeley Software Distribution license. Downloads, documentation, and tutorials are available at http://www.tinkercell.com.

Conclusion

An ideal CAD application for engineering biological systems would provide features such as: building and simulating networks, analyzing robustness of networks, and searching databases for components that meet the design criteria. At the current state of synthetic biology, there are no established methods for measuring robustness or identifying components that fit a design. The same is true for databases of biological parts. TinkerCell's flexible modeling framework allows it to cope with changes in the field. Such changes may involve the way parts are characterized or the way synthetic networks are modeled and analyzed computationally. TinkerCell can readily accept third-party algorithms, allowing it to serve as a platform for testing different methods relevant to synthetic biology.     

Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes

A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the “inputs” and “outputs”, respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The “scaling-up” issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models.     

计算系统生物学:理论、方法及在药物研发中的应用

计算系统生物学是一个多学科交叉的新兴领域,旨在通过整合海量数据建立其生物系统相互作用的复杂网络。数据的整合和模型的建立需要发展合适的数学方法和软件工具,这也是计算系统生物学的主要任务。生物系统模型有助于从整体上理解生物体的内在功能和特性。同时,生物网络模型在药物研发中的应用也越来越受到制药企业以及新药研发机构的重视,如用于特异性药物作用靶点的预测和药物毒性评估等。该文简要介绍计算系统生物学的常见网络和计算模型,以及建立模型所用的研究方法,并阐述其在建模和分析中的作用及面临的问题和挑战。