Revealing Design Principles of Biological Networks through Optimization and Dynamical System Approaches

Biological networks, such as vascular networks and neural circuits, are ubiquitous in nature. An understanding of these networks can help us understand their response to damages, which could lead to novel treatments. They can also inspire the design of man-made networks, as evolution has millions of years to figure out optimal designs. The advancement in imaging techniques has created high-dimensional data streams, which is difficult to analyze by conventional approaches. On the other hand, quantitative tools are naturally suited for processing large data sets, and they become more and more important in improving our knowledge on biological networks. Among existing tools ranging from network science to stochastic analysis, here we focus on optimization and dynamical system approach. Optimization links biological functions to corresponding network structures, which can give predictions to be compared with the data. The dynamical system approach is suited for analyzing time series data and complex interaction between the vertices, which is often exploited in biological systems for intricate signalings and regulations.This thesis is devoted to the study of biological networks with optimization and dynamical system, focused on two specific biological systems: microvascular network and bipolar disorder. For microvascular networks, we first study a specific example of embryonic zebrafish trunk network, and reveal the significance of flow uniformity in this network. Then we derive analytical structures of networks with optimal transport efficiency, which is widely regarded as the organizing principle of vascular networks, especially for large vessels such as aorta. To compare the morphologies of transport efficient and uniform flow networks, we develop algorithm that is capable of finding optimal networks with general target functions and constraints, and show that the principle of uniform flow creates more realistic microvascular networks under many different topologies. Finally, we propose an vessel adaptation mechanism based on stress sensing dynamic to explain how microvascular networks stay resilient to noise, and how they grow into uniform flow networks. For bipolar disorder, we mathematically analyze a dynamical model based on the interaction of mood and expectation. We show that bipolar disorder can be viewed as a bifurcation in the direction from normal to cyclic personality. We also consider the case where positive and negative events are sensed differently, and describe the bifurcation in this case. Finally we apply commonly used medicine on the model, and recover clinically observed phenomena on bipolar disorder patients

Clustered nuclei maintain autonomy and nucleocytoplasmic ratio control in a syncytium

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Molecular Biology of the Cell 27 (2016): 2000-2007, doi:10.1091/mbc.E16-02-0129.Nuclei in syncytia found in fungi, muscles, and tumors can behave independently despite cytoplasmic translation and the homogenizing potential of diffusion. We use a dynactin mutant strain of the multinucleate fungus Ashbya gossypii with highly clustered nuclei to assess the relative contributions of nucleus and cytoplasm to nuclear autonomy. Remarkably, clustered nuclei maintain cell cycle and transcriptional autonomy; therefore some sources of nuclear independence function even with minimal cytosol insulating nuclei. In both nuclear clusters and among evenly spaced nuclei, a nucleus’ transcriptional activity dictates local cytoplasmic contents, as assessed by the localization of several cyclin mRNAs. Thus nuclear activity is a central determinant of the local cytoplasm in syncytia. Of note, we found that the number of nuclei per unit cytoplasm was identical in the mutant to that in wild-type cells, despite clustered nuclei. This work demonstrates that nuclei maintain autonomy at a submicrometer scale and simultaneously maintain a normal nucleocytoplasmic ratio across a syncytium up to the centimeter scale.his work was supported by National Institutes of Health R01-GM081506 (A.S.G., S.E.R., and P.O.), the National Science Foundation GK-12 Program and the Neukom Institute at Dartmouth College (S.E.R.), the Alfred P. Sloan Foundation and National Science Foundation DMS-1351860 (M.R. and S.-S.C.), a National Institutes of Health Ruth L. Kirschstein National Research Service Award (T32-GM008185; S.-S.C.), and the Intramural Research Programs of the National Institutes of Health National Institute of Biomedical Imaging and Bioengineering Whitman Investigator and Grass Foundation Programs at the Marine Biological Laboratory at Woods Hole (A.K. and H.S.

Revealing Design Principles of Biological Networks through Optimization and Dynamical System Approaches

Biological networks, such as vascular networks and neural circuits, are ubiquitous in nature. An understanding of these networks can help us understand their response to damages, which could lead to novel treatments. They can also inspire the design of man-made networks, as evolution has millions of years to figure out optimal designs. The advancement in imaging techniques has created high-dimensional data streams, which is difficult to analyze by conventional approaches. On the other hand, quantitative tools are naturally suited for processing large data sets, and they become more and more important in improving our knowledge on biological networks. Among existing tools ranging from network science to stochastic analysis, here we focus on optimization and dynamical system approach. Optimization links biological functions to corresponding network structures, which can give predictions to be compared with the data. The dynamical system approach is suited for analyzing time series data and complex interaction between the vertices, which is often exploited in biological systems for intricate signalings and regulations.This thesis is devoted to the study of biological networks with optimization and dynamical system, focused on two specific biological systems: microvascular network and bipolar disorder. For microvascular networks, we first study a specific example of embryonic zebrafish trunk network, and reveal the significance of flow uniformity in this network. Then we derive analytical structures of networks with optimal transport efficiency, which is widely regarded as the organizing principle of vascular networks, especially for large vessels such as aorta. To compare the morphologies of transport efficient and uniform flow networks, we develop algorithm that is capable of finding optimal networks with general target functions and constraints, and show that the principle of uniform flow creates more realistic microvascular networks under many different topologies. Finally, we propose an vessel adaptation mechanism based on stress sensing dynamic to explain how microvascular networks stay resilient to noise, and how they grow into uniform flow networks. For bipolar disorder, we mathematically analyze a dynamical model based on the interaction of mood and expectation. We show that bipolar disorder can be viewed as a bifurcation in the direction from normal to cyclic personality. We also consider the case where positive and negative events are sensed differently, and describe the bifurcation in this case. Finally we apply commonly used medicine on the model, and recover clinically observed phenomena on bipolar disorder patients

A Dynamical Bifurcation Model of Bipolar Disorder Based on Learned Expectation and Asymmetry in Mood Sensitivity.

Bipolar disorder is a common psychiatric dysfunction characterized by recurring episodes of mania and depression. Despite its prevalence, the causes and mechanisms of bipolar disorder remain largely unknown. Recently, theories focusing on the interaction between emotion and behavior, including those based on dysregulation of the so-called behavioral approach system (BAS), have gained popularity. Mathematical models built on this principle predict bistability in mood and do not invoke intrinsic biological rhythms that may arise from interactions between mood and expectation. Here we develop and analyze a model with clinically meaningful and modifiable parameters that incorporates the interaction between mood and expectation. Our nonlinear model exhibits a transition to limit cycle behavior when a mood-sensitivity parameter exceeds a threshold value, signaling a transition to a bipolar state. The model also predicts that asymmetry in response to positive and negative events can induce unipolar depression/mania, consistent with clinical observations. We analyze the model with asymmetric mood sensitivities and show that large unidirectional mood sensitivity can lead to bipolar disorder. Finally, we show how observed effects of lithium- and antidepressant-induced mania can be explained within the framework of our proposed model

Correction: A Biologically-Inspired Symmetric Bidirectional Switch.

[This corrects the article DOI: 10.1371/journal.pone.0169856.]

A Biologically-Inspired Symmetric Bidirectional Switch.

Stimuli-sensitive hydrogels have been intensively studied because of their potential applications in drug delivery, cell culture, and actuator design. Although hydrogels with directed unidirectional response, i.e. capable of bending actuated by different chemical components reaction in response to several stimuli including water and electric fields, these hydrogels are capable of being actuated in one direction only by the stimulus. By contrast the challenge of building a device that is capable of responding to the same cue (in this case a temperature gradient) to bend in either direction remains unmet. Here, inspired by the structure of pine cone scales, we design a temperature-sensitive hydrogel with bending directed an imposed fishing line. The layers with same PNIPAAm always shrinks in response to the heat. Even the layers made with different chemical property, bends away from a warm surface, whether the warm surface is applied at its upper or lower boundary. To design the bending hydrogel we exploited the coupled responses of the hydrogel; a fishing line intercalating structure and change its construction. In addition to revealing a new capability of stimulus sensitive hydrogels, our study gives insight into the structural features of pine cone bending

Motion of various layered structures (a-b).

<p>The pine cone inspired model (Fp) lifts up its body after heating. <b>(a)</b> The structural change of Fp is observed in the top view and white dash lines represents the initial size of the structure. <b>(b)</b> The lifting height is clearly shown in the side view. <b>(c)</b> Heterogeneous (C1-C3-C1) triple layers (Fu) becomes crinkly in response to heating. <b>(d)</b> One side is slightly lifted. <b>(e-f)</b> After heating, the topless structure (Fd) rolls up. Thus, the structure is capable of bending in both directions. <b>(h-i)</b> Temporal variations of the curvature in the x-direction and y-directions during heating. <b>(h)</b> The Fp structure bends the most in the x-direction compared to other structures. <b>(i)</b> The Fd structure bends the most in the y-direction. However its asymmetric structure would not allow it to bend according to the direction of the temperature gradient, which Fp and Fu structures are capable of.</p

Morphological characteristics of pine cone scales.

<p><b>(a)</b> Pine cone scales fully open on sunny dry days. <b>(b)</b> When pine cone gets wet, pine cone folds its scales <b>(c)</b> Hemisected pine cone shows layered structure. In dry condition, scales are fully opened. Pine cone scale consists of fibers (F) and sclerids (S). ‘B’ signifies bract scale. <b>(d)</b> Pine cone fold its scale after wetting. <b>(e)</b> Cross sectional image of scale is captured using X-ray microscopy. The large pores are surrounded by small pores like layer structure. Fibers penetrate into the scale structure. ‘S’ and ‘F’ signify sclerids and fibers, respectively. Anatomic 3D structure of sclerid <b>(f)</b> and fiber <b>(g)</b> are investigated 3-dimensionally using multi-photon microscopy. The sclerid has dense structure like rock, while the fibers are tangled up.</p