Signal propagation in nonlinear stochastic gene regulatory networks

The ability to build genetic circuits with a reproducible response to external stimuli depends on the experimental and theoretical methods used in the process. A theoretical formalism that describes the response of a nonlinear stochastic genetic network to the external stimuli (input signals), is proposed. Two applications are studied in detail: the design of a logic pulse and the interference of three signal generators in the E2F1 regulatory element. The gene interactions are presented using molecular diagrams that have a precise mathematical structure and retain the biological meaning of the processes.     

Engineering scalable biological systems

Synthetic biology is focused on engineering biological organisms to study natural systems and to provide new solutions for pressing medical, industrial and environmental problems. At the core of engineered organisms are synthetic biological circuits that execute the tasks of sensing inputs, processing logic and performing output functions. In the last decade, significant progress has been made in developing basic designs for a wide range of biological circuits in bacteria, yeast and mammalian systems. However, significant challenges in the construction, probing, modulation and debugging of synthetic biological systems must be addressed in order to achieve scalable higher-complexity biological circuits. Furthermore, concomitant efforts to evaluate the safety and biocontainment of engineered organisms and address public and regulatory concerns will be necessary to ensure that technological advances are translated into real-world solutions.     

Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.     

Implementation of a genetic logic circuit: bio-register

We introduce an idea of synthesizing a class of genetic registers based on the existing sequential biological circuits, which are composed of fundamental biological gates. In the renowned literature, biological gates and genetic oscillator have been unveiled and experimentally realized in recent years. These biological circuits have formed a basis for realizing a primitive biocomputer. In the traditional computer architecture, there is an intermediate load-store section, i.e. a register, which serves as a part of the digital processor. With which, the processor can load data from a larger memory into it and proceed to conduct necessary arithmetic or logic operations. Then, manipulated data are stored back to the memory by instruction via the register. We propose here a class of bio-registers for the biocomputer. Four types of register structures are presented. In silicon experiments illustrate results of the proposed design.     

Implementing re-configurable biological computation with distributed multicellular consortia

The use of synthetic biological circuits to deal with numerous biological challenges has been proposed in several studies, but its implementation is still remote. A major problem encountered is the complexity of the cellular engineering needed to achieve complex biological circuits and the lack of general-purpose biological systems. The generation of re-programmable circuits can increase circuit flexibility and the scalability of complex cell-based computing devices. Here we present a new architecture to produce reprogrammable biological circuits that allow the development of a variety of different functions with minimal cell engineering. We demonstrate the feasibility of creating several circuits using only a small set of engineered cells, which can be externally reprogrammed to implement simple logics in response to specific inputs. In this regard, depending on the computation needs, a device composed of a number of defined cells can generate a variety of circuits without the need of further cell engineering or rearrangements. In addition, the inclusion of a memory module in the circuits strongly improved the digital response of the devices. The reprogrammability of biological circuits is an intrinsic capacity that is not provided in electronics and it may be used as a tool to solve complex biological problems.     

A Formalized Design Process for Bacterial Consortia That Perform Logic Computing

The concept of microbial consortia is of great attractiveness in synthetic biology. Despite of all its benefits, however, there are still problems remaining for large-scaled multicellular gene circuits, for example, how to reliably design and distribute the circuits in microbial consortia with limited number of well-behaved genetic modules and wiring quorum-sensing molecules. To manage such problem, here we propose a formalized design process: (i) determine the basic logic units (AND, OR and NOT gates) based on mathematical and biological considerations; (ii) establish rules to search and distribute simplest logic design; (iii) assemble assigned basic logic units in each logic operating cell; and (iv) fine-tune the circuiting interface between logic operators. We in silico analyzed gene circuits with inputs ranging from two to four, comparing our method with the pre-existing ones. Results showed that this formalized design process is more feasible concerning numbers of cells required. Furthermore, as a proof of principle, an Escherichia coli consortium that performs XOR function, a typical complex computing operation, was designed. The construction and characterization of logic operators is independent of “wiring” and provides predictive information for fine-tuning. This formalized design process provides guidance for the design of microbial consortia that perform distributed biological computation.     

Computational aspects of feedback in neural circuits

It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We demonstrate these computational implications of feedback both theoretically, and through computer simulations of detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike trains over longer periods of time, and to process new information contained in such spike trains in diverse ways according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with feedback provide a new model for working memory that is consistent with a large set of biological constraints. Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks.     

Enzyme logic gates for the digital analysis of physiological level upon injury

A biocomputing system composed of a combination of AND/IDENTITY logic gates based on the concerted operation of three enzymes: lactate oxidase, horseradish peroxidase and glucose dehydrogenase was designed to process biochemical information related to pathophysiological conditions originating from various injuries. Three biochemical markers: lactate, norepinephrine and glucose were applied as input signals to activate the enzyme logic system. Physiologically normal concentrations of the markers were selected as logic 0 values of the input signals, while their abnormally increased concentrations, indicative of various injury conditions were defined as logic 1 input. Biochemical processing of different patterns of the biomarkers resulted in the formation of norepi-quinone and NADH defined as the output signals. Optical and electrochemical means were used to follow the formation of the output signals for eight different combinations of three input signals. The enzymatically processed biochemical information presented in the form of a logic truth table allowed distinguishing the difference between normal physiological conditions, pathophysiological conditions corresponding to traumatic brain injury and hemorrhagic shock, and abnormal situations (not corresponding to injury). The developed system represents a biocomputing logic system applied for the analysis of biomedical conditions related to various injuries. We anticipate that such biochemical logic gates will facilitate decision-making in connection to an integrated therapeutic feedback-loop system and hence will revolutionize the monitoring and treatment of injured civilians and soldiers.     

Feedback regulation of EGFR signalling: decision making by early and delayed loops

Human-made information relay systems invariably incorporate central regulatory components, which are mirrored in biological systems by dense feedback and feedforward loops. This type of system control is exemplified by positive and negative feedback loops (for example, receptor endocytosis and dephosphorylation) that enable growth factors and receptor Tyr kinases of the epidermal growth factor receptor (EGFR)/ERBB family to regulate cellular function. Recent studies show that the collection of feedback regulatory loops can perform computational tasks - such as decoding ligand specificity, transforming graded input signals into a digital output and regulating response kinetics. Aberrant signal processing and feedback regulation can lead to defects associated with pathologies such as cancer.     

Design and construction of a double inversion recombination switch for heritable sequential genetic memory

Background

Inversion recombination elements present unique opportunities for computing and information encoding in biological systems. They provide distinct binary states that are encoded into the DNA sequence itself, allowing us to overcome limitations posed by other biological memory or logic gate systems. Further, it is in theory possible to create complex sequential logics by careful positioning of recombinase recognition sites in the sequence.

Methodology/Principal Findings

In this work, we describe the design and synthesis of an inversion switch using the fim and hin inversion recombination systems to create a heritable sequential memory switch. We have integrated the two inversion systems in an overlapping manner, creating a switch that can have multiple states. The switch is capable of transitioning from state to state in a manner analogous to a finite state machine, while encoding the state information into DNA. This switch does not require protein expression to maintain its state, and “remembers” its state even upon cell death. We were able to demonstrate transition into three out of the five possible states showing the feasibility of such a switch.

Conclusions/Significance

We demonstrate that a heritable memory system that encodes its state into DNA is possible, and that inversion recombination system could be a starting point for more complex memory circuits. Although the circuit did not fully behave as expected, we showed that a multi-state, temporal memory is achievable.     

Using plasma membrane nanoclusters to build better signaling circuits

Cellular signaling pathways do not simply transmit data; they integrate and process signals to operate as switches, oscillators, logic gates, memory modules and many other types of control system. These complex processing capabilities enable cells to respond appropriately to the myriad of external cues that direct growth and development. The idea that crosstalk and feedback loops are used as control systems in biological signaling networks is well established. Signaling networks are also subject to exquisite spatial regulation, yet how spatial control modulates signal outputs is less well understood. Here, we explore the spatial organization of two different signal transduction circuits: receptor tyrosine kinase activation of the mitogen-activated protein kinase module; and glycosylphosphatidylinositol-anchored receptor activation of phospholipase C. With regards to these pathways, recent results have refocused attention on the crucial role of lipid rafts and plasma membrane nanodomains in signal transmission. We identify common design principals that highlight how the spatial organization of signal transduction circuits can be used as a fundamental control mechanism to modulate system outputs in vivo.     

Bistable responses in bacterial genetic networks: designs and dynamical consequences

A key property of living cells is their ability to react to stimuli with specific biochemical responses. These responses can be understood through the dynamics of underlying biochemical and genetic networks. Evolutionary design principles have been well studied in networks that display graded responses, with a continuous relationship between input signal and system output. Alternatively, biochemical networks can exhibit bistable responses so that over a range of signals the network possesses two stable steady states. In this review, we discuss several conceptual examples illustrating network designs that can result in a bistable response of the biochemical network. Next, we examine manifestations of these designs in bacterial master-regulatory genetic circuits. In particular, we discuss mechanisms and dynamic consequences of bistability in three circuits: two-component systems, sigma-factor networks, and a multistep phosphorelay. Analyzing these examples allows us to expand our knowledge of evolutionary design principles networks with bistable responses.     

Attenuation of noise in ultrasensitive signaling cascades

Ultrasensitive cascades often implement thresholding operations in cell signaling and gene regulatory networks, converting graded input signals into discrete all-or-none outputs. However, the biochemical and genetic reactions involved in such cascades are subject to random fluctuations, leading to noise in output signal levels. Here we prove that cascades operating near saturation have output signal fluctuations that are bounded in magnitude, even as the number of noisy cascade stages becomes large. We show that these fluctuation-bounded cascades can be used to attenuate the noise in an input signal, and we find the optimal cascade length required to achieve the best possible noise reduction. Cascades with ultrasensitive transfer functions naturally operate near saturation, and can be made to simultaneously implement thresholding and noise reduction. They are therefore ideally suited to mediate signal transfer in both natural and artificial biological networks.     

Methods for and results from the study of design principles in molecular systems

Most aspects of molecular biology can be understood in terms of biological design principles. These principles can be loosely defined as qualitative and quantitative features that emerge in evolution and recur more frequently than one would expect by chance alone in biological systems that perform a given type of process or function. Furthermore, such recurrence can be rationalized in terms of the functional advantage that the design provides to the system when compared with possible alternatives. This paper focuses on those design features that can be related to improved functional effectiveness of molecular and regulatory networks. We begin by reviewing assumptions and methods that underlie the study of such principles in molecular networks. We follow by discussing many of the design principles that have been found in genetic, metabolic, and signal transduction circuits. We concentrate mainly on results in the context of Biochemical Systems Theory, although we also briefly discuss other work. We conclude by discussing the importance of these principles for both, understanding the natural evolution of complex networks at the molecular level and for creating artificial biological systems with specific features.     

Dynamical compensation in physiological circuits

Biological systems can maintain constant steady‐state output despite variation in biochemical parameters, a property known as exact adaptation. Exact adaptation is achieved using integral feedback, an engineering strategy that ensures that the output of a system robustly tracks its desired value. However, it is unclear how physiological circuits also keep their output dynamics precise—including the amplitude and response time to a changing input. Such robustness is crucial for endocrine and neuronal homeostatic circuits because they need to provide a precise dynamic response in the face of wide variation in the physiological parameters of their target tissues; how such circuits compensate their dynamics for unavoidable natural fluctuations in parameters is unknown. Here, we present a design principle that provides the desired robustness, which we call dynamical compensation (DC). We present a class of circuits that show DC by means of a nonlinear feedback loop in which the regulated variable controls the functional mass of the controlling endocrine or neuronal tissue. This mechanism applies to the control of blood glucose by insulin and explains several experimental observations on insulin resistance. We provide evidence that this mechanism may also explain compensation and organ size control in other physiological circuits.