Toward a classification of isodynamic feed-forward motifs

A preceding study analysed how the topology of network motifs affects the overall rate of the underlying biochemical processes. Surprisingly, it was shown that topologically non-isomorphic motifs can still be isodynamic in the sense that they exhibit the exact same performance rate. Because of the high prevalence of feed-forward functional modules in biological networks, one may hypothesize that evolution tends to favour motifs with faster dynamics. As a step towards ranking the efficiency of feed-forward network motifs, we use a linear flow model to prove theorems establishing that certain classes of motifs are isodynamic. In partitioning the class of all motifs on n nodes into equivalence classes based upon their dynamics, we establish a basis for comparing the efficiency/performance rates of different motifs. The potential biological importance of the theorems is briefly discussed and is the subject of an ongoing large-scale project.     

Feed-Forward versus Feedback Inhibition in a Basic Olfactory Circuit

Inhibitory interneurons play critical roles in shaping the firing patterns of principal neurons in many brain systems. Despite difference in the anatomy or functions of neuronal circuits containing inhibition, two basic motifs repeatedly emerge: feed-forward and feedback. In the locust, it was proposed that a subset of lateral horn interneurons (LHNs), provide feed-forward inhibition onto Kenyon cells (KCs) to maintain their sparse firing—a property critical for olfactory learning and memory. But recently it was established that a single inhibitory cell, the giant GABAergic neuron (GGN), is the main and perhaps sole source of inhibition in the mushroom body, and that inhibition from this cell is mediated by a feedback (FB) loop including KCs and the GGN. To clarify basic differences in the effects of feedback vs. feed-forward inhibition in circuit dynamics we here use a model of the locust olfactory system. We found both inhibitory motifs were able to maintain sparse KCs responses and provide optimal odor discrimination. However, we further found that only FB inhibition could create a phase response consistent with data recorded in vivo. These findings describe general rules for feed-forward versus feedback inhibition and suggest GGN is potentially capable of providing the primary source of inhibition to the KCs. A better understanding of how inhibitory motifs impact post-synaptic neuronal activity could be used to reveal unknown inhibitory structures within biological networks.     

Design and implementation of three incoherent feed-forward motif based biological concentration sensors

Synthetic biology is a useful tool to investigate the dynamics of small biological networks and to assess our capacity to predict their behavior from computational models. In this work we report the construction of three different synthetic networks in Escherichia coli based upon the incoherent feed-forward loop architecture. The steady state behavior of the networks was investigated experimentally and computationally under different mutational regimes in a population based assay. Our data shows that the three incoherent feed-forward networks, using three different macromolecular inhibitory elements, reproduce the behavior predicted from our computational model. We also demonstrate that specific biological motifs can be designed to generate similar behavior using different components. In addition we show how it is possible to tune the behavior of the networks in a predicable manner by applying suitable mutations to the inhibitory elements. Brian Aufderheide provided material support.     

Functional identification of biological neural networks using reservoir adaptation for point processes

The complexity of biological neural networks does not allow to directly relate their biophysical properties to the dynamics of their electrical activity. We present a reservoir computing approach for functionally identifying a biological neural network, i.e. for building an artificial system that is functionally equivalent to the reference biological network. Employing feed-forward and recurrent networks with fading memory, i.e. reservoirs, we propose a point process based learning algorithm to train the internal parameters of the reservoir and the connectivity between the reservoir and the memoryless readout neurons. Specifically, the model is an Echo State Network (ESN) with leaky integrator neurons, whose individual leakage time constants are also adapted. The proposed ESN algorithm learns a predictive model of stimulus-response relations in in vitro and simulated networks, i.e. it models their response dynamics. Receiver Operating Characteristic (ROC) curve analysis indicates that these ESNs can imitate the response signal of a reference biological network. Reservoir adaptation improved the performance of an ESN over readout-only training methods in many cases. This also held for adaptive feed-forward reservoirs, which had no recurrent dynamics. We demonstrate the predictive power of these ESNs on various tasks with cultured and simulated biological neural networks.     

The biphasic behavior of incoherent feed-forward loops in biomolecular regulatory networks

An incoherent feed-forward loop (FFL) is one of the most-frequently observed motifs in biomolecular regulatory networks. It has been thought that the incoherent FFL is designed simply to induce a transient response shaped by a 'fast activation and delayed inhibition'. We find that the dynamics of various incoherent FFLs can be further classified into two types: time-dependent biphasic responses and dose-dependent biphasic responses. Why do the structurally identical incoherent FFLs play such different dynamical roles? Through computational studies, we show that the dynamics of the two types of incoherent FFLs are mutually exclusive. Following from further computational results and experimental observations, we hypothesize that incoherent FFLs have been optimally designed to achieve distinct biological function arising from different cellular contexts. Additional Supporting Information may be found in the online version of the article.     

Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.     

Some generalized conjugacy theorems and the concepts of fitness and survival in logistic growth models

Current research into the dynamics of iterative ecological and biological models has lead to a number of theorems concerning the existence of various types of iterative dynamical behavior. In particular, much study has been done on the dynamical behavior of the “simplest dynamical system”f _b(x)=bx(1−x), which is just the canonical discrete form of logistic growth equations found in ecology, sociobiology, and population biology. In this paper, we make use of some of the techniques and concepts of topological dynamics to construct a number of generalized conjugacy theorems. These theorems are then used to demonstrate that the mappingf _b has a number of conjugacy classes in which the dynamics of the iterates is equivalent to within a change of variables. The concepts of fitness and survival in logistic equations are then shown to be independent, if we follow certain intuitive definitions for these concepts. This conclusion follows from a comparison of the conjugacy classes of the functionf _b and the extinction sets off _b.     

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.     

Unraveling the design principle for motif organization in signaling networks

Cellular signaling networks display complex architecture. Defining the design principle of this architecture is crucial for our understanding of various biological processes. Using a mathematical model for three-node feed-forward loops, we identify that the organization of motifs in specific manner within the network serves as an important regulator of signal processing. Further, incorporating a systemic stochastic perturbation to the model we could propose a possible design principle, for higher-order organization of motifs into larger networks in order to achieve specific biological output. The design principle was then verified in a large, complex human cancer signaling network. Further analysis permitted us to classify signaling nodes of the network into robust and vulnerable nodes as a result of higher order motif organization. We show that distribution of these nodes within the network at strategic locations then provides for the range of features displayed by the signaling network.     

Signal transduction network motifs and biological memory

Memory is a ubiquitous phenomenon in biological systems, yet the mechanisms responsible for memory, and how to manipulate it at the subcellular level, remain poorly understood. Subjected to transient stimuli, biological systems can exhibit short early responses and/or prolonged (or permanent) late responses. Experimental evidence suggests that early responses (short-term memory) involve post-translational modification of existing proteins and/or their intracellular relocalization, whereas late responses (long-term memory) depend on new protein synthesis. Although this provides an intuitive explanation at the basic molecular level, it does little to clarify the important dynamics that actually maintain memory at the systems level. In this study, we use mathematical modeling to study dynamical mechanisms of biological memory. We first examined the response of four fundamental motifs (positive/negative feedforward and feedback) to external stimuli. Because motifs do not exist in isolation within the cell, we then combined these motifs to form signaling modules to understand how they confer biological memory. These motifs, and different combinations thereof, displayed distinct behavior in response to external stimuli. The principles described in this study have important implications for experimental approaches to identify the mechanisms for biological memory and for the development of therapeutic strategies to modulate signaling network responses in the setting of human disease.     

Molecular mechanism of signal perception and integration by the innate immune sensor retinoic acid-inducible gene-I (RIG-I)

RIG-I is a major innate immune sensor for viral infection, triggering an interferon (IFN)-mediated antiviral response upon cytosolic detection of viral RNA. Double-strandedness and 5'-terminal triphosphates were identified as motifs required to elicit optimal immunological signaling. However, very little is known about the response dynamics of the RIG-I pathway, which is crucial for the ability of the cell to react to diverse classes of viral RNA while maintaining self-tolerance. In the present study, we addressed the molecular mechanism of RIG-I signal detection and its translation into pathway activation. By employing highly quantitative methods, we could establish the length of the double-stranded RNA (dsRNA) to be the most critical determinant of response strength. Size exclusion chromatography and direct visualization in scanning force microscopy suggested that this was due to cooperative oligomerization of RIG-I along dsRNA. The initiation efficiency of this oligomerization process critically depended on the presence of high affinity motifs, like a 5'-triphosphate. It is noteworthy that for dsRNA longer than 200 bp, internal initiation could effectively compensate for a lack of terminal triphosphates. In summary, our data demonstrate a very flexible response behavior of the RIG-I pathway, in which sensing and integration of at least two distinct signals, initiation efficiency and double strand length, allow the host cell to mount an antiviral response that is tightly adjusted to the type of the detected signal, such as viral genomes, replication intermediates, or small by-products.     

Memorizing environmental signals through feedback and feedforward loops

Cells in diverse organisms can store the information of previous environmental conditions for long periods of time. This form of cellular memory adjusts the cell's responses to future challenges, providing fitness advantages in fluctuating environments. Many biological functions, including cellular memory, are mediated by specific recurring patterns of interactions among proteins and genes, known as ‘network motifs.’ In this review, we focus on three well-characterized network motifs — negative feedback loops, positive feedback loops, and feedforward loops, which underlie different types of cellular memories. We describe the latest studies identifying these motifs in various molecular processes and discuss how the topologies and dynamics of these motifs can enable memory encoding and storage.     

Information processing in social insect networks

Investigating local-scale interactions within a network makes it possible to test hypotheses about the mechanisms of global network connectivity and to ask whether there are general rules underlying network function across systems. Here we use motif analysis to determine whether the interactions within social insect colonies resemble the patterns exhibited by other animal associations or if they exhibit characteristics of biological regulatory systems. Colonies exhibit a predominance of feed-forward interaction motifs, in contrast to the densely interconnected clique patterns that characterize human interaction and animal social networks. The regulatory motif signature supports the hypothesis that social insect colonies are shaped by selection for network patterns that integrate colony functionality at the group rather than individual level, and demonstrates the utility of this approach for analysis of selection effects on complex systems across biological levels of organization.     

Biochemical and motile properties of Myo1b splice isoforms

Myo1b is a widely expressed myosin-I isoform that concentrates on endosomal and ruffling membranes and is thought to play roles in membrane trafficking and dynamics. Myo1b is alternatively spliced within the regulatory domain of the molecule, yielding isoforms with six (myo1b(a)), five (myo1b(b)), or four (myo1b(c)) non-identical IQ motifs. The calmodulin binding properties of the myo1b IQ motifs have not been investigated, and the mechanical and cell biological consequences of alternative splicing are not known. Therefore, we expressed the alternatively spliced myo1b isoforms truncated after the final IQ motif and included a sequence at their C termini that is a substrate for bacterial biotin ligase. Site-specific biotinylation allows us to specifically attach the myosin to motility surfaces via a biotin-streptavidin linkage. We measured the ATPase and motile properties of the recombinant myo1b splice isoforms, and we correlated these properties with calmodulin binding. We confirmed that calcium-dependent changes in the ATPase activity are due to calcium binding to the calmodulin closest to the motor. We found that calmodulin binds tightly to some of the IQ motifs (Kd < 0.2 microM) and very weakly to the others (Kd > 5 microM), suggesting that a subset of the IQ motifs are not calmodulin bound under physiological conditions. Finally, we found the in vitro motility rate to be dependent on the myo1b isoform and the calmodulin concentration and that the myo1b regulatory domain acts as a rigid lever arm upon calmodulin binding to the high affinity and low affinity IQ motifs.     

Single molecule conformational analysis of DNA G-quadruplexes

Single molecule fluorescence resonance energy transfer (FRET) can be employed to study conformational heterogeneity and real-time dynamics of biological macromolecules. Here we present single molecule studies on human genomic DNA G-quadruplex sequences that occur in the telomeres and in the promoter of a proto-oncogene. The findings are discussed with respect to the proposed biological function(s) of such motifs in living cells.