Managing models of signaling networks

Signaling pathways participate in complex information processing networks. These networks handle housekeeping functions of the cell as well as specialized functions such as synaptic plasticity. I report two developments in managing such networks: a compilation of mass-action kinetic models of signaling pathways, and shared motifs in the chemistry of interactions between signaling pathways. These motifs may prove useful in abstracting signaling networks, without compromising chemical reaction details. The combination of a library of signaling pathway models, and high-level rules to connect these pathways, may simplify development of complex signaling network models

Temporal computation by synaptic signaling pathways

Synaptic signaling comprises a complex molecular network. Such networks carry out diverse operations such as molecular logic, signal amplification, memory and other aspects of cellular decision-making ([Bray, 1995]). The synapse in particular encounters complex input patterns that have different temporal sequences. Different input patterns to the synapse are known to give rise to a range of synaptic responses, including facilitation, depression and various forms of short and long-term potentiation. In many cases the stimuli that generate these disparate responses are tens of seconds or more in length, much greater than the typical time-courses of calcium dynamics. In this paper I propose that the synaptic signaling network can perform temporal computation operations such as tuning for stimulus duration or interval. Using simulation methods I show that the simple time-courses of individual signaling pathways combine in the network to give rise to different temporally selective responses. Downstream pathways that exhibit temporal integration or amplitude thresholding select different input patterns and thus perform temporal computation

Models of cell signaling pathways

Cellular signaling circuits handle an enormous range of computations. Beyond the housekeeping, replicating and other functions of individual cells, signaling circuits must implement the immensely complex logic of development and function of multicellular organisms. Computer models are useful tools to understand this complexity. Recent studies have extended such models to include electrical, mechanical and spatial details of signaling, and to address the stochastic effects that arise when small numbers of molecules interact. Increasing numbers of models have been developed in close conjunction with experiments, and this interplay gives a deeper and more reliable insight into signaling function

Understanding complex signaling networks through models and metaphors

Signaling networks are complex both in terms of the chemical and biophysical events that underlie them, and in the sheer number of interactions. Computer models are powerful tools to deal with both aspects of complexity, but their utility goes beyond simply replicating signaling events in silicon. Their great advantage is as a tool to understanding. The completeness of the description demanded by computer models highlights gaps in knowledge. The quantitative description in models facilitates a mapping between different kinds of analysis methods for complex systems. Systems analysis methods can highlight stable states of signaling networks and describe the transitions between them. Modeling also reveals functional similarities between signaling network properties and other well-understood systems such as electronic devices and neural networks. These suggest various metaphors as a tool to understanding. Based on such descriptions, it is possible to regard signaling networks as systems that decode complex inputs in time, space and chemistry into combinatorial output patterns of signaling activity. This would provide a natural interface to the combinatorial input patterns required by genetic circuits. Thus, a combination of computer modeling methods to capture the complexity and details, and useful abstractions revealed by these models, is necessary to achieve both rigorous description as well as human understanding

Emergent properties of networks of biological signaling pathways

Many distinct signaling pathways allow the cell to receive, process, and respond to information. Often, components of different pathways interact, resulting in signaling networks. Biochemical signaling networks were constructed with experimentally obtained constants and analyzed by computational methods to understand their role in complex biological processes. These networks exhibit emergent properties such as integration of signals across multiple time scales, generation of distinct outputs depending on input strength and duration, and self-sustaining feedback loops. Feedback can result in bistable behavior with discrete steady-state activities, well-defined input thresholds for transition between states and prolonged signal output, and signal modulation in response to transient stimuli. These properties of signaling networks raise the possibility that information for "learned behavior" of biological systems may be stored within intracellular biochemical reactions that comprise signaling pathways

Adaptive stochastic-deterministic chemical kinetic simulations

Motivation: Biochemical signaling pathways and genetic circuits often involve very small numbers of key signaling molecules. Computationally expensive stochastic methods are necessary to simulate such chemical situations. Single-molecule chemical events often co-exist with much larger numbers of signaling molecules where mass-action kinetics is a reasonable approximation. Here, we describe an adaptive stochastic method that dynamically chooses between deterministic and stochastic calculations depending on molecular count and propensity of forward reactions. The method is fixed timestep and has first order accuracy. We compare the efficiency of this method with exact stochastic methods. Results: We have implemented an adaptive stochastic-deterministic approximate simulation method for chemical kinetics. With an error margin of 5%, the method solves typical biologically constrained reaction schemes more rapidly than exact stochastic methods for reaction volumes >1-10 μm3. We have developed a test suite of reaction cases to test the accuracy of mixed simulation methods

Signaling logic of activity-triggered dendritic protein synthesis: an mTOR gate but not a feedback switch

Changes in synaptic efficacy are believed to form the cellular basis for memory. Protein synthesis in dendrites is needed to consolidate long-term synaptic changes. Many signals converge to regulate dendritic protein synthesis, including synaptic and cellular activity, and growth factors. The coordination of these multiple inputs is especially intriguing because the synthetic and control pathways themselves are among the synthesized proteins. We have modeled this system to study its molecular logic and to understand how runaway feedback is avoided. We show that growth factors such as brain-derived neurotrophic factor (BDNF) gate activity-triggered protein synthesis via mammalian target of rapamycin (mTOR). We also show that bistability is unlikely to arise from the major protein synthesis pathways in our model, even though these include several positive feedback loops. We propose that these gating and stability properties may serve to suppress runaway activation of the pathway, while preserving the key role of responsiveness to multiple sources of input

PyMOOSE: Interoperable Scripting in Python for MOOSE

Python is emerging as a common scripting language for simulators. This opens up many possibilities for interoperability in the form of analysis, interfaces, and communications between simulators. We report the integration of Python scripting with the Multi-scale Object Oriented Simulation Environment (MOOSE). MOOSE is a general-purpose simulation system for compartmental neuronal models and for models of signaling pathways based on chemical kinetics. We show how the Python-scripting version of MOOSE, PyMOOSE, combines the power of a compiled simulator with the versatility and ease of use of Python. We illustrate this by using Python numerical libraries to analyze MOOSE output online, and by developing a GUI in Python/Qt for a MOOSE simulation. Finally, we build and run a composite neuronal/signaling model that uses both the NEURON and MOOSE numerical engines, and Python as a bridge between the two. Thus PyMOOSE has a high degree of interoperability with analysis routines, with graphical toolkits, and with other simulators

How To Record a Million Synaptic Weights in a Hippocampal Slice

A key step toward understanding the function of a brain circuit is to find its wiring diagram. New methods for optical stimulation and optical recording of neurons make it possible to map circuit connectivity on a very large scale. However, single synapses produce small responses that are difficult to measure on a large scale. Here I analyze how single synaptic responses may be detectable using relatively coarse readouts such as optical recording of somatic calcium. I model a network consisting of 10,000 input axons and 100 CA1 pyramidal neurons, each represented using 19 compartments with voltage-gated channels and calcium dynamics. As single synaptic inputs cannot produce a measurable somatic calcium response, I stimulate many inputs as a baseline to elicit somatic action potentials leading to a strong calcium signal. I compare statistics of responses with or without a single axonal input riding on this baseline. Through simulations I show that a single additional input shifts the distribution of the number of output action potentials. Stochastic resonance due to probabilistic synaptic release makes this shift easier to detect. With ∼80 stimulus repetitions this approach can resolve up to 35% of individual activated synapses even in the presence of 20% recording noise. While the technique is applicable using conventional electrical stimulation and extracellular recording, optical methods promise much greater scaling, since the number of synapses scales as the product of the number of inputs and outputs. I extrapolate from current high-speed optical stimulation and recording methods, and show that this approach may scale up to the order of a million synapses in a single two-hour slice-recording experiment

Representation of odor habituation and timing in the Hippocampus

We performed simultaneous single-neuron recordings from the hippocampus and the olfactory bulb of anesthetized, freely breathing rats. Odor response properties of neurons in the olfactory bulb and hippocampus were characterized as firing rate changes or respiration-coupled changes. A panel of five odors was used. The rats had not been exposed to the odors on the panel before the experiment. The olfactory bulb and hippocampal neurons responded to repeated odor presentations in two ways: first, by changes in firing rate, and second, by respiratory tuning changes. Approximately 60% of bulbar neurons, 48% of hippocampal CA1 neurons, and 12% of hippocampal CA3 neurons showed statistically significant responses. None of the odor-responsive neurons in either the bulb or hippocampus responded to all of the odors on the panel. Repeated 10 sec odor stimuli presented at the intervals of 20, 30, 60, 110, and 160 sec were used to analyze the effect of the interval on odor response properties of the recorded neurons. Bulbar neurons were relatively nonselective for odor interval. Hippocampal neurons showed unexpected selectivity for the interval between repeated odor presentations. CA1 and CA3 neurons responded to only one to three of the intervals in the range. On the basis of these findings, we postulate that the hippocampus has the ability to keep track of the time elapsed between consecutive odor stimuli. This may act as a neuronal substrate for habituation and for complex tasks such as odor-guided navigation