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Bongard J, Levin M. There's Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-Scale Machines. Biomimetics (Basel) 2023; 8:110. [PMID: 36975340 PMCID: PMC10046700 DOI: 10.3390/biomimetics8010110] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2022] [Revised: 02/24/2023] [Accepted: 03/01/2023] [Indexed: 03/18/2023] Open
Abstract
The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic view. Such a view dissolves the contingent dichotomies driven by human cognitive biases (e.g., a tendency to oversimplify) and prior technological limitations in favor of a more continuous view, necessitated by the study of evolution, developmental biology, and intelligent machines. Form and function are tightly entwined in nature, and in some cases, in robotics as well. Thus, efforts to re-shape living systems for biomedical or bioengineering purposes require prediction and control of their function at multiple scales. This is challenging for many reasons, one of which is that living systems perform multiple functions in the same place at the same time. We refer to this as "polycomputing"-the ability of the same substrate to simultaneously compute different things, and make those computational results available to different observers. This ability is an important way in which living things are a kind of computer, but not the familiar, linear, deterministic kind; rather, living things are computers in the broad sense of their computational materials, as reported in the rapidly growing physical computing literature. We argue that an observer-centered framework for the computations performed by evolved and designed systems will improve the understanding of mesoscale events, as it has already done at quantum and relativistic scales. To develop our understanding of how life performs polycomputing, and how it can be convinced to alter one or more of those functions, we can first create technologies that polycompute and learn how to alter their functions. Here, we review examples of biological and technological polycomputing, and develop the idea that the overloading of different functions on the same hardware is an important design principle that helps to understand and build both evolved and designed systems. Learning to hack existing polycomputing substrates, as well as to evolve and design new ones, will have massive impacts on regenerative medicine, robotics, and computer engineering.
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Affiliation(s)
- Joshua Bongard
- Department of Computer Science, University of Vermont, Burlington, VT 05405, USA
| | - Michael Levin
- Allen Discovery Center at Tufts University, 200 Boston Ave., Suite 4600, Medford, MA 02155, USA
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Microtubules as a potential platform for energy transfer in biological systems: a target for implementing individualized, dynamic variability patterns to improve organ function. Mol Cell Biochem 2023; 478:375-392. [PMID: 35829870 DOI: 10.1007/s11010-022-04513-1] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Accepted: 06/24/2022] [Indexed: 02/07/2023]
Abstract
Variability characterizes the complexity of biological systems and is essential for their function. Microtubules (MTs) play a role in structural integrity, cell motility, material transport, and force generation during mitosis, and dynamic instability exemplifies the variability in the proper function of MTs. MTs are a platform for energy transfer in cells. The dynamic instability of MTs manifests itself by the coexistence of growth and shortening, or polymerization and depolymerization. It results from a balance between attractive and repulsive forces between tubulin dimers. The paper reviews the current data on MTs and their potential roles as energy-transfer cellular structures and presents how variability can improve the function of biological systems in an individualized manner. The paper presents the option for targeting MTs to trigger dynamic improvement in cell plasticity, regulate energy transfer, and possibly control quantum effects in biological systems. The described system quantifies MT-dependent variability patterns combined with additional personalized signatures to improve organ function in a subject-tailored manner. The platform can regulate the use of MT-targeting drugs to improve the response to chronic therapies. Ongoing trials test the effects of this platform on various disorders.
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Barvitenko N, Lawen A, Aslam M, Pantaleo A, Saldanha C, Skverchinskaya E, Regolini M, Tuszynski JA. Integration of intracellular signaling: Biological analogues of wires, processors and memories organized by a centrosome 3D reference system. Biosystems 2018; 173:191-206. [PMID: 30142359 DOI: 10.1016/j.biosystems.2018.08.007] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 08/03/2018] [Accepted: 08/20/2018] [Indexed: 02/07/2023]
Abstract
BACKGROUND Myriads of signaling pathways in a single cell function to achieve the highest spatio-temporal integration. Data are accumulating on the role of electromechanical soliton-like waves in signal transduction processes. Theoretical studies strongly suggest feasibility of both classical and quantum computing involving microtubules. AIM A theoretical study of the role of the complex composed of the plasma membrane and the microtubule-based cytoskeleton as a system that transmits, stores and processes information. METHODS Theoretical analysis presented here refers to (i) the Penrose-Hameroff theory of consciousness (Orchestrated Objective Reduction; Orch OR), (ii) the description of the centrosome as a reference system for construction of the 3D map of the cell proposed by Regolini, (iii) the Heimburg-Jackson model of the nerve pulse propagation along axons' lipid bilayer as soliton-like electro-mechanical waves. RESULTS AND CONCLUSION The ideas presented in this paper provide a qualitative model for the decision-making processes in a living cell undergoing a differentiation process. OUTLOOK This paper paves the way for the real-time live-cell observation of information processing by microtubule-based cytoskeleton and cell fate decision making.
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Affiliation(s)
| | - Alfons Lawen
- Monash University, School of Biomedical Sciences, Department of Biochemistry and Molecular Biology, VIC, 3800, Australia
| | - Muhammad Aslam
- Medical Clininc I, Cardiology/Angiology, University Hospital, Justus-Liebig-University, Giessen, Germany
| | - Antonella Pantaleo
- Department of Biomedical Sciences, University of Sassari, Sassari, Italy
| | - Carlota Saldanha
- Instituto de Medicina Molecular, Instituto de Bioquimica, Faculdade de Medicina, Universidade de Lisboa, Lisbon, Portugal
| | | | - Marco Regolini
- Department of Bioengineering and Mathematical Modeling, AudioLogic, Milan, Italy
| | - Jack A Tuszynski
- Department of Oncology, University of Alberta, Edmonton, Alberta, Canada; Department of Physics, University of Alberta, Edmonton, Alberta, Canada; Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, IT-10128, Torino, Italy.
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Shirmovsky SE, Shulga DV. Elastic, dipole-dipole interaction and viscosity impact on vibrational properties of anisotropic hexagonal microtubule lattice. Biosystems 2018. [PMID: 29526816 DOI: 10.1016/j.biosystems.2018.03.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
The paper investigates microtubules lattice properties taking into consideration elastic, dipole-dipole interaction of tubulins and viscosity. A microtubule is modeled as a system of bound tubulins, forming a skewed hexagonal two-dimensional lattice. Wave frequencies and group velocities have been calculated. Calculations have been performed for various directions of wave front propagation: helix, along the protofilament, and anti-helix. Three different wave polarization directions have been considered. It has been shown that the direction of the wave polarization influences the frequency and wave group velocity values in the lattice considerably. The impact of dipole-dipole interaction greatly depends on the direction of the wave polarization; thus, it is only moderate for the longitudinally (LA) polarized waves while it is sufficient for the transversely (TA), and out-of-plane (ZA) polarized waves. Moreover dipole-dipole interaction may result in the waves which are able to cause the rupture of microtubules. With viscosity considered, lattice oscillations become harmonically damped only over a certain wavelength range when longitudinal polarization occurs. Out of this range as well as for the other polarization directions, lattice deviations from equilibrium are dampened exponentially. Taking viscosity into consideration also results in a noticeable decrease in frequency and increase in the group wave velocity when the waves are longitudinally polarized. Reverse wave domains which may be associated with a possible phenomenon of negative refraction have been determined for hexagonal microtubule lattice.
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Affiliation(s)
- S Eh Shirmovsky
- Theoretical and Nuclear Physics Chair, Far Eastern Federal University, 8 Sukhanov St., Vladivostok 690950, Russia.
| | - D V Shulga
- Theoretical and Nuclear Physics Chair, Far Eastern Federal University, 8 Sukhanov St., Vladivostok 690950, Russia.
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Pezzulo G, Levin M. Top-down models in biology: explanation and control of complex living systems above the molecular level. J R Soc Interface 2017; 13:rsif.2016.0555. [PMID: 27807271 DOI: 10.1098/rsif.2016.0555] [Citation(s) in RCA: 108] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2016] [Accepted: 10/11/2016] [Indexed: 12/23/2022] Open
Abstract
It is widely assumed in developmental biology and bioengineering that optimal understanding and control of complex living systems follows from models of molecular events. The success of reductionism has overshadowed attempts at top-down models and control policies in biological systems. However, other fields, including physics, engineering and neuroscience, have successfully used the explanations and models at higher levels of organization, including least-action principles in physics and control-theoretic models in computational neuroscience. Exploiting the dynamic regulation of pattern formation in embryogenesis and regeneration requires new approaches to understand how cells cooperate towards large-scale anatomical goal states. Here, we argue that top-down models of pattern homeostasis serve as proof of principle for extending the current paradigm beyond emergence and molecule-level rules. We define top-down control in a biological context, discuss the examples of how cognitive neuroscience and physics exploit these strategies, and illustrate areas in which they may offer significant advantages as complements to the mainstream paradigm. By targeting system controls at multiple levels of organization and demystifying goal-directed (cybernetic) processes, top-down strategies represent a roadmap for using the deep insights of other fields for transformative advances in regenerative medicine and systems bioengineering.
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Affiliation(s)
- Giovanni Pezzulo
- Institute of Cognitive Sciences and Technologies, National Research Council, Rome, Italy
| | - Michael Levin
- Biology Department, Allen Discovery Center at Tufts, Tufts University, Medford, MA 02155, USA
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Tonello L, Cocchi M, Gabrielli F, Tuszynski JA. Stream of consciousness: Quantum and biochemical assumptions regarding psychopathology. Med Hypotheses 2017; 101:78-84. [PMID: 28351500 DOI: 10.1016/j.mehy.2017.02.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2016] [Revised: 02/09/2017] [Accepted: 02/26/2017] [Indexed: 10/20/2022]
Abstract
The accepted paradigms of mainstream neuropsychiatry appear to be incompletely adequate and in various cases offer equivocal analyses. However, a growing number of new approaches are being proposed that suggest the emergence of paradigm shifts in this area. In particular, quantum theories of mind, brain and consciousness seem to offer a profound change to the current approaches. Unfortunately these quantum paradigms harbor at least two serious problems. First, they are simply models, theories, and assumptions, with no convincing experiments supporting their claims. Second, they deviate from contemporary mainstream views of psychiatric illness and do so in revolutionary ways. We suggest a possible way to integrate experimental neuroscience with quantum models in order to address outstanding issues in psychopathology. A key role is played by the phenomenon called the "stream of consciousness", which can be linked to the so-called "Gamma Synchrony" (GS), which is clearly demonstrated by EEG data. In our novel proposal, a unipolar depressed patient could be seen as a subject with an altered stream of consciousness. In particular, some clues suggest that depression is linked to an "increased power" stream of consciousness. It is additionally suggested that such an approach to depression might be extended to psychopathology in general with potential benefits to diagnostics and therapeutics in neuropsychiatry.
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Affiliation(s)
- Lucio Tonello
- "Paolo Sotgiu" Research Institute, LUdeS Foundation HEI, Kalkara, Malta.
| | - Massimo Cocchi
- "Paolo Sotgiu" Research Institute, LUdeS Foundation HEI, Kalkara, Malta; University of Bologna, Italy
| | - Fabio Gabrielli
- "Paolo Sotgiu" Research Institute, LUdeS Foundation HEI, Kalkara, Malta
| | - Jack A Tuszynski
- Department of Physics, University of Alberta, Edmonton, AB, Canada.
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Craddock TJA, Priel A, Tuszynski JA. Keeping time: could quantum beating in microtubules be the basis for the neural synchrony related to consciousness? J Integr Neurosci 2015; 13:293-311. [PMID: 25012713 DOI: 10.1142/s0219635214400019] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
This paper discusses the possibility of quantum coherent oscillations playing a role in neuronal signaling. Consciousness correlates strongly with coherent neural oscillations, however the mechanisms by which neurons synchronize are not fully elucidated. Recent experimental evidence of quantum beats in light-harvesting complexes of plants (LHCII) and bacteria provided a stimulus for seeking similar effects in important structures found in animal cells, especially in neurons. We argue that microtubules (MTs), which play critical roles in all eukaryotic cells, possess structural and functional characteristics that are consistent with quantum coherent excitations in the aromatic groups of their tryptophan residues. Furthermore we outline the consequences of these findings on neuronal processes including the emergence of consciousness.
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Affiliation(s)
- Travis J A Craddock
- Center for Psychological Studies, Graduate School of Computer and Information Sciences, College of Osteophatic Medicine and the Institute for Neuro-Immune Medicine, Nova Southeastern University, Fort Lauderdale, Florida 33314-7796, USA
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Hameroff SR, Craddock TJA, Tuszynski JA. Quantum effects in the understanding of consciousness. J Integr Neurosci 2015; 13:229-52. [PMID: 25012711 DOI: 10.1142/s0219635214400093] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
This paper presents a historical perspective on the development and application of quantum physics methodology beyond physics, especially in biology and in the area of consciousness studies. Quantum physics provides a conceptual framework for the structural aspects of biological systems and processes via quantum chemistry. In recent years individual biological phenomena such as photosynthesis and bird navigation have been experimentally and theoretically analyzed using quantum methods building conceptual foundations for quantum biology. Since consciousness is attributed to human (and possibly animal) mind, quantum underpinnings of cognitive processes are a logical extension. Several proposals, especially the Orch OR hypothesis, have been put forth in an effort to introduce a scientific basis to the theory of consciousness. At the center of these approaches are microtubules as the substrate on which conscious processes in terms of quantum coherence and entanglement can be built. Additionally, Quantum Metabolism, quantum processes in ion channels and quantum effects in sensory stimulation are discussed in this connection. We discuss the challenges and merits related to quantum consciousness approaches as well as their potential extensions.
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Affiliation(s)
- Stuart R Hameroff
- Center for Consciousness Studies, The University of Arizona, Tucson, Arizona 85721, USA
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Clark KB. Basis for a neuronal version of Grover's quantum algorithm. Front Mol Neurosci 2014; 7:29. [PMID: 24860419 PMCID: PMC4029008 DOI: 10.3389/fnmol.2014.00029] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2014] [Accepted: 03/31/2014] [Indexed: 11/25/2022] Open
Abstract
Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca2+ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release and the search (or signaling) velocity of Ca2+ wave propagation. As chemical processes, such as the duration of Ca2+ mobilization, become rate-limiting over interstore distances, Ca2+ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca2+ diffusion coefficient, D1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca2+ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.
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Affiliation(s)
- Kevin B Clark
- Research and Development Service, Veterans Affairs Greater Los Angeles Healthcare System Los Angeles, CA, USA ; Complex Biological Systems Alliance North Andover, MA, USA
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Tang R, Dai J. Biophoton signal transmission and processing in the brain. JOURNAL OF PHOTOCHEMISTRY AND PHOTOBIOLOGY B-BIOLOGY 2013; 139:71-5. [PMID: 24461927 DOI: 10.1016/j.jphotobiol.2013.12.008] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2013] [Revised: 12/13/2013] [Accepted: 12/13/2013] [Indexed: 11/19/2022]
Abstract
The transmission and processing of neural information in the nervous system plays a key role in neural functions. It is well accepted that neural communication is mediated by bioelectricity and chemical molecules via the processes called bioelectrical and chemical transmission, respectively. Indeed, the traditional theories seem to give valuable explanations for the basic functions of the nervous system, but difficult to construct general accepted concepts or principles to provide reasonable explanations of higher brain functions and mental activities, such as perception, learning and memory, emotion and consciousness. Therefore, many unanswered questions and debates over the neural encoding and mechanisms of neuronal networks remain. Cell to cell communication by biophotons, also called ultra-weak photon emissions, has been demonstrated in several plants, bacteria and certain animal cells. Recently, both experimental evidence and theoretical speculation have suggested that biophotons may play a potential role in neural signal transmission and processing, contributing to the understanding of the high functions of nervous system. In this paper, we review the relevant experimental findings and discuss the possible underlying mechanisms of biophoton signal transmission and processing in the nervous system.
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Affiliation(s)
- Rendong Tang
- Wuhan Institute for Neuroscience and Neuroengineering, South-Central University for Nationalities, Wuhan 430074, China
| | - Jiapei Dai
- Wuhan Institute for Neuroscience and Neuroengineering, South-Central University for Nationalities, Wuhan 430074, China.
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11
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Craddock TJA, Tuszynski JA, Chopra D, Casey N, Goldstein LE, Hameroff SR, Tanzi RE. The zinc dyshomeostasis hypothesis of Alzheimer's disease. PLoS One 2012; 7:e33552. [PMID: 22457776 PMCID: PMC3311647 DOI: 10.1371/journal.pone.0033552] [Citation(s) in RCA: 110] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2011] [Accepted: 02/13/2012] [Indexed: 11/20/2022] Open
Abstract
Alzheimer's disease (AD) is the most common form of dementia in the elderly. Hallmark AD neuropathology includes extracellular amyloid plaques composed largely of the amyloid-β protein (Aβ), intracellular neurofibrillary tangles (NFTs) composed of hyper-phosphorylated microtubule-associated protein tau (MAP-tau), and microtubule destabilization. Early-onset autosomal dominant AD genes are associated with excessive Aβ accumulation, however cognitive impairment best correlates with NFTs and disrupted microtubules. The mechanisms linking Aβ and NFT pathologies in AD are unknown. Here, we propose that sequestration of zinc by Aβ-amyloid deposits (Aβ oligomers and plaques) not only drives Aβ aggregation, but also disrupts zinc homeostasis in zinc-enriched brain regions important for memory and vulnerable to AD pathology, resulting in intra-neuronal zinc levels, which are either too low, or excessively high. To evaluate this hypothesis, we 1) used molecular modeling of zinc binding to the microtubule component protein tubulin, identifying specific, high-affinity zinc binding sites that influence side-to-side tubulin interaction, the sensitive link in microtubule polymerization and stability. We also 2) performed kinetic modeling showing zinc distribution in extra-neuronal Aβ deposits can reduce intra-neuronal zinc binding to microtubules, destabilizing microtubules. Finally, we 3) used metallomic imaging mass spectrometry (MIMS) to show anatomically-localized and age-dependent zinc dyshomeostasis in specific brain regions of Tg2576 transgenic, mice, a model for AD. We found excess zinc in brain regions associated with memory processing and NFT pathology. Overall, we present a theoretical framework and support for a new theory of AD linking extra-neuronal Aβ amyloid to intra-neuronal NFTs and cognitive dysfunction. The connection, we propose, is based on β-amyloid-induced alterations in zinc ion concentration inside neurons affecting stability of polymerized microtubules, their binding to MAP-tau, and molecular dynamics involved in cognition. Further, our theory supports novel AD therapeutic strategies targeting intra-neuronal zinc homeostasis and microtubule dynamics to prevent neurodegeneration and cognitive decline.
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Saha AA, Craddock TJ, Tuszynski JA. An investigation of the plausibility of stochastic resonance in tubulin dimers. Biosystems 2012; 107:81-7. [DOI: 10.1016/j.biosystems.2011.09.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2011] [Revised: 09/09/2011] [Accepted: 09/26/2011] [Indexed: 01/23/2023]
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Kubli-Garfias C, Salazar-Salinas K, Perez-Angel EC, Seminario JM. Light activation of the isomerization and deprotonation of the protonated Schiff base retinal. J Mol Model 2011; 17:2539-47. [PMID: 21207087 DOI: 10.1007/s00894-010-0927-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2010] [Accepted: 11/29/2010] [Indexed: 11/29/2022]
Abstract
We perform an ab initio analysis of the photoisomerization of the protonated Schiff base of retinal (PSB-retinal) from 11-cis to 11-trans rotating the C10-C11=C12-C13 dihedral angle from 0° (cis) to -180° (trans). We find that the retinal molecule shows the lowest rotational barrier (0.22 eV) when its charge state is zero as compared to the barrier for the protonated molecule which is ∼0.89 eV. We conclude that rotation most likely takes place in the excited state of the deprotonated retinal. The addition of a proton creates a much larger barrier implying a switching behavior of retinal that might be useful for several applications in molecular electronics. All conformations of the retinal compound absorb in the green region with small shifts following the dihedral angle rotation; however, the Schiff base of retinal (SB-retinal) at trans-conformation absorbs in the violet region. The rotation of the dihedral angle around the C11=C12 π-bond affects the absorption energy of the retinal and the binding energy of the SB-retinal with the proton at the N-Schiff; the binding energy is slightly lower at the trans-SB-retinal than at other conformations of the retinal.
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Affiliation(s)
- Carlos Kubli-Garfias
- Department of Chemical Engineering, Texas A&M University, College Station, TX, USA
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