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3.  Digital clocks: simple Boolean models can quantitatively describe circadian systems 
The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day–night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we anticipate that the ability of logic models to provide a computationally efficient representation of system behaviour could greatly facilitate the reverse-engineering of large-scale biochemical networks.
doi:10.1098/rsif.2012.0080
PMCID: PMC3405750  PMID: 22499125
systems biology; circadian gene networks; Boolean logic; photoperiodism; Arabidopsis thaliana
4.  Role of the human supplementary eye field in the control of saccadic eye movements 
Neuropsychologia  2006;45(5):997-1008.
The precise function of the Supplementary Eye field (SEF) is poorly understood. Although electrophysiological and functional imaging studies are important for demonstrating when SEF neurones are active, lesion studies are critical to establish the functions for which the SEF is essential. Here we report a series of investigations performed on an extremely rare individual with a highly focal lesion of the medial frontal cortex. High resolution structural imaging demonstrated that his lesion was confined to the region of the left paracentral sulcus, the anatomical locus of the SEF. Behavioural testing revealed that the patient was significantly impaired when required to switch between anti- and pro-saccades, when there are conflicting rules governing stimulus-response mappings for saccades. Similarly, the results of an arbitrary stimulus-response associative learning task demonstrated that he was impaired when required to select the appropriate saccade from conflicting eye movement responses, but not for limb movements on an analogous manual task. When making memory-guided saccadic sequences, the patient demonstrated hypometria, like patients with Parkinson's disease, but had no significant difficulties in reproducing the order of saccades correctly. These findings are consistent with the hypothesis that the SEF plays a key role in implementing control when there is conflict between several, ongoing competing saccadic responses, but not when eye movements need to be made serially in sequence.
doi:10.1016/j.neuropsychologia.2006.09.007
PMCID: PMC2649282  PMID: 17069864
SUPPLEMENTARY MOTOR AREA; MEDIAL FRONTAL CORTEX; ASSOCIATIVE LEARNING; ANTI-SACCADES; MEMORY GUIDED SACCADES
5.  Volition and conflict in human medial frontal cortex 
Current biology : CB  2005;15(2):122-128.
Summary
Controversy surrounds the role of human medial frontal cortex in controlling actions[1-5]. Although damage to this area leads to severe difficulties in spontaneously initiating actions[6], the precise mechanisms underlying such ‘volitional’ deficits remain to be established. Previous studies have implicated the medial frontal cortex in conflict monitoring[7-10] and the control of voluntary action[11, 12], suggesting that these key processes are functionally related or share neural substrates. Here we combine a novel behavioural paradigm with functional imaging of the oculomotor system to reveal for the first time a functional subdivision of the pre-supplementary motor area (pre-SMA) into anatomically distinct areas responding exclusively to volition or to conflict. We also demonstrate that activity in the supplementary eye field (SEF) distinguishes between success and failure in changing voluntary action plans during conflict, suggesting a role for the SEF in implementing the resolution of conflicting actions. We propose a functional architecture of human medial frontal cortex that incorporates the generation of action plans and the resolution of conflict.
doi:10.1016/j.cub.2005.01.006
PMCID: PMC2648721  PMID: 15668167
6.  Role of the human supplementary eye field in the control of saccadic eye movements 
Neuropsychologia  2007;45(5-4):997-1008.
The precise function of the supplementary eye field (SEF) is poorly understood. Although electrophysiological and functional imaging studies are important for demonstrating when SEF neurones are active, lesion studies are critical to establish the functions for which the SEF is essential. Here we report a series of investigations performed on an extremely rare individual with a highly focal lesion of the medial frontal cortex. High-resolution structural imaging demonstrated that his lesion was confined to the region of the left paracentral sulcus, the anatomical locus of the SEF. Behavioural testing revealed that the patient was significantly impaired when required to switch between anti- and pro-saccades, when there were conflicting rules governing stimulus–response mappings for saccades. Similarly, the results of an arbitrary stimulus–response associative learning task demonstrated that he was impaired when required to select the appropriate saccade from conflicting eye movement responses, but not for limb movements on an analogous manual task. When making memory-guided saccadic sequences, the patient demonstrated hypometria, like patients with Parkinson's disease, but had no significant difficulties in reproducing the order of saccades correctly on a task that emphasized accuracy with a wide temporal segregation between responses. These findings are consistent with the hypothesis that the SEF plays a key role in implementing control when there is conflict between several, ongoing competing saccadic responses, but not when eye movements need to be made accurately in sequence.
doi:10.1016/j.neuropsychologia.2006.09.007
PMCID: PMC2649282  PMID: 17069864
Supplementary motor area; Medial frontal cortex; Associative learning; Anti-saccades; Memory-guided saccades

Results 1-6 (6)