Cross-disciplinary mathematical modelling to benefit healthcare - could clinical pharmacology play an enabling role?

Clinical pharmacology is often the nexus in any cross-disciplinary team that is seeking solutions for human healthcare issues. The use and application of real-world data and artificial intelligence to better understand our ecosystem has influenced our view at the world and how we do things. This has resulted in remarkable advancements in the healthcare space and development of personalized medicines with great attributes from the application of models and simulations, contributing to a more efficient healthcare development process. A cross-disciplinary symposium was held in December 2023, whereby experts from different scientific disciplines engaged in a high-level discussion on the opportunities and challenges of mathematical models in different fields, possible future developments and decision making. A strong interlink amongst the disciplines represented was apparent, with clinical pharmacology identified as the one which integrates various scientific disciplines. Deliberate and strategic cross-disciplinary dialogues are required to break out of the silos and implement integration for efficiency and cost-effectiveness of novel interventions.

The effect of classical optimizers and Ansatz depth on QAOA performance in noisy devices.

The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) providing approximate solutions for combinatorial optimization problems. The QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a classical optimizer, to minimize some cost function, computed on the quantum device. This paper presents an investigation into the impact of realistic noise on the classical optimizer and the determination of optimal circuit depth for the Quantum Approximate Optimization Algorithm (QAOA) in the presence of noise. We find that, while there is no significant difference in the performance of classical optimizers in a state vector simulation, the Adam and AMSGrad optimizers perform best in the presence of shot noise. Under the conditions of real noise, the SPSA optimizer, along with ADAM and AMSGrad, emerge as the top performers. The study also reveals that the quality of solutions to some 5 qubit minimum vertex cover problems increases for up to around six layers in the QAOA circuit, after which it begins to decline. This analysis shows that increasing the number of layers in the QAOA in an attempt to increase accuracy may not work well in a noisy device.

Markovian noise modelling and parameter extraction framework for quantum devices.

In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been widely used as a test bed for quantum dynamics. This work provides a new hardware-agnostic framework for modelling the Markovian noise and dynamics of quantum systems in benchmark procedures used to evaluate device performance. As an accessible example, the application and performance of this framework is demonstrated on IBM Quantum computers. This framework serves to extract multiple calibration parameters simultaneously through a simplified process which is more reliable than previously studied calibration experiments and tomographic procedures. Additionally, this method allows for real-time calibration of several hardware parameters of a quantum computer within a comprehensive procedure, providing quantitative insight into the performance of each device to be accounted for in future quantum circuits. The framework proposed here has the additional benefit of highlighting the consistency among qubit pairs when extracting parameters, which leads to a less computationally expensive calibration process than evaluating the entire device at once.

Isotope effects on radical pair performance in cryptochrome: A new hypothesis for the evolution of animal migration: The quantum biology of migration.

Mechanisms occurring at the atomic level are now known to drive processes essential for life, as revealed by quantum effects on biochemical reactions. Some macroscopic characteristics of organisms may thus show an atomic imprint, which may be transferred across organisms and affect their evolution. This possibility is considered here for the first time, with the aim of elucidating the appearance of an animal innovation with an unclear evolutionary origin: migratory behaviour. This trait may be mediated by a radical pair (RP) mechanism in the retinal flavoprotein cryptochrome, providing essential magnetic orientation for migration. Isotopes may affect the performance of quantum processes through their nuclear spin. Here, we consider a simple model and then apply the standard open quantum system approach to the spin dynamics of cryptochrome RP. We changed the spin quantum number (I) and g-factor of hydrogen and nitrogen isotopes to investigate their effect on RP's yield and magnetic sensitivity. Strong differences arose between isotopes with I = 1 and I = 1/2 in their contribution to cryptochrome magnetic sensitivity, particularly regarding Earth's magnetic field strengths (25-65 µT). In most cases, isotopic substitution improved RP's magnetic sensitivity. Migratory behaviour may thus have been favoured in animals with certain isotopic compositions of cryptochrome.

Quantum tunnelling in the context of SARS-CoV-2 infection.

The SARS-CoV-2 pandemic has added new urgency to the study of viral mechanisms of infection. But while vaccines offer a measure of protection against this specific outbreak, a new era of pandemics has been predicted. In addition to this, COVID-19 has drawn attention to post-viral syndromes and the healthcare burden they entail. It seems integral that knowledge of viral mechanisms is increased through as wide a research field as possible. To this end we propose that quantum biology might offer essential new insights into the problem, especially with regards to the important first step of virus-host invasion. Research in quantum biology often centres around energy or charge transfer. While this is predominantly in the context of photosynthesis there has also been some suggestion that cellular receptors such as olfactory or neural receptors might employ vibration assisted electron tunnelling to augment the lock-and-key mechanism. Quantum tunnelling has also been observed in enzyme function. Enzymes are implicated in the invasion of host cells by the SARS-CoV-2 virus. Receptors such as olfactory receptors also appear to be disrupted by COVID-19. Building on these observations we investigate the evidence that quantum tunnelling might be important in the context of infection with SARS-CoV-2. We illustrate this with a simple model relating the vibronic mode of, for example, a viral spike protein to the likelihood of charge transfer in an idealised receptor. Our results show a distinct parameter regime in which the vibronic mode of the spike protein enhances electron transfer. With this in mind, novel therapeutics to prevent SARS-CoV-2 transmission could potentially be identified by their vibrational spectra.

Twisted Few-Mode Optical Fiber with Improved Height of Quasi-Step Refractive Index Profile.

This work presents designed and fabricated silica few-mode optical fiber (FMF) with induced twisting 10 and 66 revolutions per meter, core diameter 11 µm, typical "telecommunication" cladding diameter 125 µm, improved height of quasi-step refractive index profile and numerical aperture 0.22. Proposed FMF supports 4 guided modes over "C"-band. We discussed selection of specified optical fiber parameters to provide desired limited mode number over mentioned wavelength range. Some results of tests, performed with pilot samples of manufactured FMF, are represented, including experimentally measured spectral responses of laser-excited optical signals, that comprise researches and analysis of few-mode effects, occurring after fiber Bragg grating writing.

Implementation of an efficient SARS-CoV-2 specimen pooling strategy for high throughput diagnostic testing.

The rapid identification and isolation of infected individuals remains a key strategy for controlling the spread of SARS-CoV-2. Frequent testing of populations to detect infection early in asymptomatic or presymptomatic individuals can be a powerful tool for intercepting transmission, especially when the viral prevalence is low. However, RT-PCR testing-the gold standard of SARS-CoV-2 diagnosis-is expensive, making regular testing of every individual unfeasible. Sample pooling is one approach to lowering costs. By combining samples and testing them in groups the number of tests required is reduced, substantially lowering costs. Here we report on the implementation of pooling strategies using 3-d and 4-d hypercubes to test a professional sports team in South Africa. We have shown that infected samples can be reliably detected in groups of 27 and 81, with minimal loss of assay sensitivity for samples with individual Ct values of up to 32. We report on the automation of sample pooling, using a liquid-handling robot and an automated web interface to identify positive samples. We conclude that hypercube pooling allows for the reliable RT-PCR detection of SARS-CoV-2 infection, at significantly lower costs than lateral flow antigen (LFA) tests.

Detection of a SARS-CoV-2 variant of concern in South Africa.

Continued uncontrolled transmission of SARS-CoV-2 in many parts of the world is creating conditions for substantial evolutionary changes to the virus1,2. Here we describe a newly arisen lineage of SARS-CoV-2 (designated 501Y.V2; also known as B.1.351 or 20H) that is defined by eight mutations in the spike protein, including three substitutions (K417N, E484K and N501Y) at residues in its receptor-binding domain that may have functional importance3-5. This lineage was identified in South Africa after the first wave of the epidemic in a severely affected metropolitan area (Nelson Mandela Bay) that is located on the coast of the Eastern Cape province. This lineage spread rapidly, and became dominant in Eastern Cape, Western Cape and KwaZulu-Natal provinces within weeks. Although the full import of the mutations is yet to be determined, the genomic data-which show rapid expansion and displacement of other lineages in several regions-suggest that this lineage is associated with a selection advantage that most plausibly results from increased transmissibility or immune escape6-8.

A divide-and-conquer algorithm for quantum state preparation.

Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

Sixteen novel lineages of SARS-CoV-2 in South Africa.

The first severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in South Africa was identified on 5 March 2020, and by 26 March the country was in full lockdown (Oxford stringency index of 90)1. Despite the early response, by November 2020, over 785,000 people in South Africa were infected, which accounted for approximately 50% of all known African infections2. In this study, we analyzed 1,365 near whole genomes and report the identification of 16 new lineages of SARS-CoV-2 isolated between 6 March and 26 August 2020. Most of these lineages have unique mutations that have not been identified elsewhere. We also show that three lineages (B.1.1.54, B.1.1.56 and C.1) spread widely in South Africa during the first wave, comprising ~42% of all infections in the country at the time. The newly identified C lineage of SARS-CoV-2, C.1, which has 16 nucleotide mutations as compared with the original Wuhan sequence, including one amino acid change on the spike protein, D614G (ref. 3), was the most geographically widespread lineage in South Africa by the end of August 2020. An early South African-specific lineage, B.1.106, which was identified in April 2020 (ref. 4), became extinct after nosocomial outbreaks were controlled in KwaZulu-Natal Province. Our findings show that genomic surveillance can be implemented on a large scale in Africa to identify new lineages and inform measures to control the spread of SARS-CoV-2. Such genomic surveillance presented in this study has been shown to be crucial in the identification of the 501Y.V2 variant in South Africa in December 2020 (ref. 5).

Early transmission of SARS-CoV-2 in South Africa: An epidemiological and phylogenetic report.

OBJECTIVES: The Network for Genomic Surveillance in South Africa (NGS-SA) was formed to investigate the introduction and understand the early transmission dynamics of the SARS-CoV-2 epidemic in South-Africa. DESIGN: This paper presents the first results from this group, which is a molecular epidemiological study of the first 21 SARS-CoV-2 whole genomes sampled in the first port of entry - KwaZulu-Natal (KZN) - during the first month of the epidemic. By combining this with calculations of the effective reproduction number (R), it aimed to shed light on the patterns of infections in South Africa. RESULTS: Two of the largest provinces - Gauteng and KZN - had a slow growth rate for the number of detected cases, while the epidemic spread faster in the Western Cape and Eastern Cape. The estimates of transmission potential suggested a decrease towards R = 1 since the first cases and deaths, but a subsequent estimated R average of 1.39 between 6-18 May 2020. It was also demonstrated that early transmission in KZN was associated with multiple international introductions and dominated by lineages B1 and B. Evidence for locally acquired infections in a hospital in Durban within the first month of the epidemic was also provided. CONCLUSION: The COVID-19 pandemic in South Africa was very heterogeneous in its spatial dimension, with many distinct introductions of SARS-CoV2 in KZN and evidence of nosocomial transmission, which inflated early mortality in KZN. The epidemic at the local level was still developing and NGS-SA aimed to clarify the dynamics in South Africa and devise the most effective measures as the outbreak evolved.

Early transmission of SARS-CoV-2 in South Africa: An epidemiological and phylogenetic report.

Background: The emergence of a novel coronavirus, SARS-CoV-2, in December 2019, progressed to become a world pandemic in a few months and reached South Africa at the beginning of March. To investigate introduction and understand the early transmission dynamics of the virus, we formed the South African Network for Genomics Surveillance of COVID (SANGS_COVID), a network of ten government and university laboratories. Here, we present the first results of this effort, which is a molecular epidemiological study of the first twenty-one SARS-CoV-2 whole genomes sampled in the first port of entry, KwaZulu-Natal (KZN), during the first month of the epidemic. By combining this with calculations of the effective reproduction number (R), we aim to shed light on the patterns of infections that define the epidemic in South Africa. Methods: R was calculated using positive cases and deaths from reports provided by the four major provinces. Molecular epidemiology investigation involved sequencing viral genomes from patients in KZN using ARCTIC protocols and assembling whole genomes using meticulous alignment methods. Phylogenetic analysis was performed using maximum likelihood (ML) and Bayesian trees, lineage classification and molecular clock calculations. Findings: The epidemic in South Africa has been very heterogeneous. Two of the largest provinces, Gauteng, home of the two large metropolis Johannesburg and Pretoria, and KwaZulu-Natal, home of the third largest city in the country Durban, had a slow growth rate on the number of detected cases. Whereas, Western Cape, home of Cape Town, and the Eastern Cape provinces the epidemic is spreading fast. Our estimates of transmission potential for South Africa suggest a decreasing transmission potential towards R=1 since the first cases and deaths have been reported. However, between 06 May and 18 May 2020, we estimate that R was on average 1.39 (1.04 - 2.15, 95% CI). We also demonstrate that early transmission in KZN, and most probably in all main regions of SA, was associated with multiple international introductions and dominated by lineages B1 and B. The study also provides evidence for locally acquired infections in a hospital in Durban within the first month of the epidemic, which inflated early mortality in KZN. Interpretation: This first report of SANGS_COVID consortium focuses on understanding the epidemic heterogeneity and introduction of SARS-CoV-2 strains in the first month of the epidemic in South Africa. The early introduction of SARS-CoV-2 in KZN included caused a localized outbreak in a hospital, provides potential explanations for the initially high death rates in the province. The current high rate of transmission of COVID-19 in the Western Cape and Eastern Cape highlights the crucial need to strength local genomic surveillance in South Africa. Funding: UKZN Flagship Program entitled: Afrocentric Precision Approach to Control Health Epidemic, by a research Flagship grant from the South African Medical Research Council (MRC-RFA-UFSP-01-2013/UKZN HIVEPI, by the the Technology Innovation Agency and the the Department of Science and Innovation and by National Human Genome Re- search Institute of the National Institutes of Health under Award Number U24HG006941. H3ABioNet is an initiative of the Human Health and Heredity in Africa Consortium (H3Africa).

Origin of orientation-dependent R1 (=1/T1 ) relaxation in white matter.

PURPOSE: In a recent MRI study, it was shown that the longitudinal relaxation rate, R1 , in white matter (WM) is influenced by the relative orientation of nerve fibers with respect to the main magnetic field (B0 ). Even though the exact nature of this R1 orientation dependency is still unclear, it can be assumed that the origin of the phenomenon can be attributed to the anisotropic and unique molecular environment within the myelin sheath surrounding the axons. The current work investigates the contribution of dipolar induced R1 relaxation of the myelin associated hydrogen nuclei theoretically and compares the results with the experimentally observed R1 orientation dependency. METHODS: Atomistic molecular dynamics simulations were employed and the R1 relaxation rate of hydrogen nuclei of a myelin-alike molecular environment was calculated for various orientations of the trajectory sets relative to the B0 -field. Based on the calculated relaxation rates, the observable R1 relaxation was simulated for various fiber orientations and fitted to the experimental data using a suitable signal weighting-scheme. RESULTS: The results obtained show that the R1 relaxation rate of both solid myelin (SM) and myelin water (MW) depends on the fiber orientation relative to the main B0 -field. Moreover, employing a realistic signal weighing scheme and tissue characteristics, the theoretically investigated R1 orientation dependency matches the experimental data well. CONCLUSION: The good agreement between theoretical and experimental findings indicates that the R1 orientation dependency in WM mainly originates from anisotropic dipole-dipole interactions between hydrogen nuclei located within the myelin sheath.

Dynamical and thermodynamical approaches to open quantum systems.

The non-Markovian dynamics of open quantum systems is studied from two different points of view. The first one coincides with the traditional tracing out of the environmental degrees of freedom, presented in classical textbooks on open quantum systems. The second one is an approximation of the exact density operator with the knowledge of only several dynamical variables in the spirit of non-equilibrium thermodynamics. The approximation is based on the principle of maximal entropy. We discuss the information and the Renyi entropies, which lead to different approximations. The time-convolutionless master equation governs the dynamics of both traditional and approximated reduced density operator with a particular projection operator. Considering the example of two interacting qubits in a thermal environment, we compare the traditional and thermodynamical approaches.

Formation of dialysis-free Kombucha-based bacterial nanocellulose embedded in a polypyrrole/PVA composite for bulk conductivity measurements.

The preparation of dialysis-free bacterial nanocrystalline cellulose (BNCC) combined with a suitable polymer to form a robust conducting material remains a challenge. In this work, we developed a polypyrrole@BNCC/PVA nanocomposite that avoids the time-consuming dialysis step and which exhibits bulk electrical conductivity. The nanocellulose (NC) was derived from bacterial cellulose (BC) that was grown from a symbiotic colony of bacteria and yeast (SCOBY) starting from Kombucha tea, and then subjected to sulfuric acid hydrolysis that led to isolable bacterial nanocrystalline cellulose (BNCC) product and subsequently utilized as a stabilizer and support. Pyrrole monomer was reacted with FeCl3·6H2O as a polymerization initiator to form polypyrrole (PPy) and combined with BNCC it produced PPy@BNCC nanocomposite. We found PPy to BNCC in a 1 : 1 ratio provided the best suspension of the components and formed a well dispersed homogeneous network. The PPy@BNCC nanocomposite was then suspended in polyvinyl alcohol (PVA), that facilitated the construction of a continuous PPy@BNCC/PVA conductive network in the matrix. We designed an in-house electrical measurement apparatus and developed a method that recorded bulk resistance. The results obtained from the measurements of the electrical properties of the PPy@BNCC/PVA composite prepared dialysis-free were then compared with (i) a dialyzed sample of similar composition, and (ii) a traditional four-point probe measurement. The PPy@BNCC/PVA dialysis-free sample showed a higher conductivity compared to the dialyzed composite at 4.27 × 10-1 and 3.41 × 10-1 S m-1, respectively, and both values closely matched the traditional four-point probe measurement.

Dipolar induced spin-lattice relaxation in the myelin sheath: A molecular dynamics study.

Interactions between hydrogen protons of water molecules and macromolecules within the myelin sheath surrounding the axons are a major factor influencing the magnetic resonance (MR) contrast in white matter (WM) regions. In past decades, several studies have investigated the underlying effects and reported a wide range of R1 rates for the myelin associated compartments at different field strengths. However, it was also shown that the experimental quantification of the compartment-specific R1 rates is associated with large uncertainties. The current study therefore investigates the longitudinal relaxation rates within the myelin sheath using a molecular dynamic (MD) simulation. For this purpose, a realistic molecular model of the myelin sheath was employed to determine the dipole-dipole induced R1 relaxation rate of the hydrogen protons at clinically relevant field strengths. The results obtained clearly reflect the spatial heterogeneity of R1 with a increased relaxivity of myelin water due to a reduced molecular mobility near the membrane surface. Moreover, the calculated R1 rates for both myelin water and macromolecules are in excellent agreement with experimental findings from the literature at different field strengths.

Circuit-Based Quantum Random Access Memory for Classical Data.

A prerequisite for many quantum information processing tasks to truly surpass classical approaches is an efficient procedure to encode classical data in quantum superposition states. In this work, we present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way. For registering or updating classical data consisting of M entries, each represented by n bits, the method requires O(n) qubits and O(Mn) steps. With post-selection at an additional cost, our method can also store continuous data as probability amplitudes. As an example, we present a procedure to convert classical training data for a quantum supervised learning algorithm to a quantum state. Further improvements can be achieved by reducing the number of state preparation queries with the introduction of quantum forking.

Fibre-orientation dependent R1(=1/T1) relaxation in the brain: The role of susceptibility induced spin-lattice relaxation in the myelin water compartment.

We have recently observed a dependence of the longitudinal relaxation rate, R1, on the orientation of nerve fibres with respect to the main magnetic field. A similar dependence of R2∗ is long established and can be well explained by spin-dephasing in an inhomogeneous magnetic field induced by the susceptibility shift between myelin and water protons. The current study investigates if the same effect can also explain the R1 dependence, neglecting a possible directional dependence of magnetisation transfer between solid myelin and myelin water. A molecular model of the myelin lipid bilayer was employed to simulate the susceptibility induced fields on a microscopic scale for the different nerve fibre orientations. The resulting simulated magnetic fields were used to calculate an orientation dependent relaxation offset, ΔR1, based on both first-order perturbation theory and a simulation of the spin transition probabilities. Even though both methods yielded consistent orientation dependent relaxation offsets with a distribution that resembles the experimental data, the determined ΔR1 values are too low to explain the reported R1 angular dependency. Therefore, unlike R2∗, susceptibility induced spin flips can be excluded as a dominant source for the observed R1 angular dependence.

The future of quantum biology.

Biological systems are dynamical, constantly exchanging energy and matter with the environment in order to maintain the non-equilibrium state synonymous with living. Developments in observational techniques have allowed us to study biological dynamics on increasingly small scales. Such studies have revealed evidence of quantum mechanical effects, which cannot be accounted for by classical physics, in a range of biological processes. Quantum biology is the study of such processes, and here we provide an outline of the current state of the field, as well as insights into future directions.

An open quantum system approach to the radical pair mechanism.

The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.